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1
Probing Polaritons in the Mid- to Far-Infrared
T. G. Folland1), L. Nordin2), D. Wasserman2), and J. D. Caldwell1),*
1Department of Mechanical Engineering, Vanderbilt University, TN, 37212, USA
2Department of Electrical and Computer Engineering, University of Texas at Austin, Austin, TX, 78758, USA
*josh.caldwell@vanderbilt.edu
ABSTRACT
The long free-space wavelengths associated with the mid- to far-infrared spectral range impose significant
limitations on the form-factor of associated optic and electro-optic components. Specifically, current commercial
optical sources, waveguides, optical components (lenses, waveplates) and detector elements are larger than the
corresponding diffraction limit, resulting in reduced image resolution and bulky optical systems, with deleterious
effects for a number of imaging and sensing applications of interest to commercial, medical and defense related
arenas. The field of nanophotonics, where the ultimate objective is to confine and manipulate light at deeply sub-
wavelength, nanometer length-scales, offers significant opportunities to overcome these limitations. The
demonstration of nanoscale optics in the infrared can be achieved by leveraging polaritons, quasiparticles comprised
of oscillating charges within a material coupled to electromagnetic excitations. However, the predominant
polaritonic materials and the characterization techniques and methods implemented for measuring these
quasiparticles in the mid- to far-IR require a different approach with respect to similar efforts in the ultraviolet,
visible and near-IR. The purpose of this tutorial is to offer an overview of the basic materials, tools and techniques
for exciting, manipulating, and probing polaritons in the mid- to far-infrared wavelength range, providing a general
guide to sub-wavelength, and nano-scale optics for those entering this exciting and burgeoning research field.
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I. INTRODUCTION
Polaritons are quasiparticles that consist of light coupled to coherently oscillating charges in a material. A broad
range of different types of polaritons exist,1 with arguably the most well-studied being surface plasmon polaritons
(SPPs). These quasiparticles are surface waves where the oscillating charge that couples to the electromagnetic
waves are free carriers within a conductive material, resulting in the formation of an evanescent wave that
propagates along the interface between the conductor and the dielectric environment (e.g. metal film in air).2 The
frequency range across which SPPs can be supported by a given metal/dielectric interface is determined by the
plasma frequency of the carriers (electrons or holes) in the conductor – essentially how rapidly electrons/holes
can respond to an incident electromagnetic field – and the permittivity of the dielectric material. In noble metals
(e.g. Ag, Au), is in the ultraviolet or visible range due to the high free-carrier concentrations of metals, and thus,
SPPs are predominantly observed in the shorter wavelength visible and near-infrared (NIR) spectral ranges. The
main advantage of SPPs over traditional dielectric materials is found in their ability to dramatically compress the
free-space wavelength at a given frequency. This allows for the confinement of optical frequency electromagnetic
fields to spatial volumes well below the diffraction limit, which in turn provides a method for realizing significant
reductions in the size and form-factor of optical components.3 In addition SPPs offer mechanisms for strengthening
light-matter interactions for enhanced chemical sensing,4,5,6 modifying the radiative recombination rates of emitters7
or enhanced radiative heat transfer rates.8 However, one major limitation of noble-metal SPPs in the visible is the
high material absorption inside the metal when the electromagnetic field becomes confined.9 This has prevented
visible SPP modes from being used to replace traditional diffraction-limited dielectric waveguides and/or cavities
with polariton-supporting optical structures, as existing technologies are often superior. However, optical loss can
also be an advantage,10,11 as absorption results in power dissipation and an associated local temperature increase,
which has provided significant advantages in strongly localized (subwavelength) heat sources.12-14 As a result,
many of the most promising potential applications for plasmonic structures at these wavelengths, such as heat-
assisted magnetic recording (HAMR),15 photothermal cancer therapy,16 and nanoparticle assisted solar vapor
generation,17 all leverage the ability of plasmonic nanoparticles to absorb light and thus heat their local environment.
In effect, such structures act as transducers, efficiently converting optical to thermal energy, with the heat provided
only to the local region within the evanescent fields of the nanoparticles.
The limitations of SPPs in replacing diffraction-limited optical components in the visible motivates the study of
polaritonic phenomena in different spectral windows, where technologies are less developed and robust, and thus
the requirements for improving component properties are somewhat more relaxed. The mid- (MIR) to far-infrared
(FIR) provides a natural choice for the study of polaritons for numerous reasons. First, a broader range of materials
support SPPs in the IR, including doped commercial semiconductors (including III-V’s and Si), 2D materials,
3
intermetallics, and semiconducting oxides. In addition to SPP modes, this spectral range also offers the ability to
realize surface phonon polaritons (SPhPs), which form at the surface of polar dielectrics.18,19 These alternative
polaritons arise from the interaction of light with polar optic phonons and inherently exhibit longer scattering
lifetimes than SPPs, resulting in lower optical losses.19,20 The confinement of IR light to dimensions below the
diffraction limit with SPPs and/or SPhPs has significant implications for IR devices, as the long free-space
wavelengths reduce the strength of interactions with matter and the achievable optical component sizes in traditional
approaches. Furthermore, unlike noble metals, the number of charge carriers in semiconductors can be controlled,
hence providing the opportunity to dictate the SPP frequency using dopants21,22 or carrier excitation,23-25 making
them tunable spectrally, and offering schemes towards optical modulation.26 Infrared polaritons are therefore highly
versatile, with the potential to significantly advance the current state-of-the-art in IR optics, including IR
modulators, light sources, polarizers and detectors. One of the major challenges in realizing IR-polariton-based
devices is finding the appropriate materials, tools and experimental designs for these investigations. In contrast to
visible wavelengths, where glass-based objectives, optics and spectrometers are ubiquitous, compact and highly
efficient, the techniques for studying IR optical properties, and specifically IR polaritons, are generally less widely
used and understood.
This tutorial is designed to introduce the general concepts associated with IR polaritonics, specifically addressing
the basic underlying physical mechanisms of the origin of the predominant polariton types, how they can be
stimulated, the measurement approaches required for such investigations, and how these efforts are modified when
transitioning from the MIR to FIR. Unlike earlier reviews,1,19 which focus on the physics and applications of infrared
polaritons, here we instead focus on the experimental techniques used to measure polariton systems. As there are a
number of challenges associated with solid state IR spectroscopy, which are not readily discussed in well-known
textbooks,27 or summarized in the literature, such a tutorial is a distinct need. Therefore, our approach will be to
discuss the primary types of IR experiments, including Fourier transform infrared (FTIR) spectroscopy, MIR laser-
based spectroscopy, MIR scattering-type scanning near-field optical microscopy (s-SNOM) and additional
complexities that arise when extending these measurements into the FIR. We aim to provide a comprehensive
tutorial, for the effective design of polaritonic experiments in the infrared. To highlight these techniques, we follow
these details with specific examples of how various IR polaritons have been studied to illustrate the concepts we
discuss. It is our hope that this tutorial will provide a complete introduction to better prepare scientists and engineers
to the expanding fields of IR nanophotonics and metamaterials and aid in shortening the learning curve for those
applying these concepts for realizing advanced IR technologies.
II. INFRARED POLARITONS
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Polaritons are quasiparticles that form when light strongly couples to coherently oscillating charges in a material.
They can exist both within the bulk of a material (volume polaritons) or alternatively on the surface of the material
(surface polaritons). Volume polaritons occur when the dielectric function of the polaritonic medium is positive and
the charges oscillate coherently with the incident electromagnetic wave (examples including phonon polaritons,
plasmon polaritons and intersubband polaritons28). However, as introduced above, for this tutorial we are focused
on the class of surface polaritons, which are supported at the interface between a metallic-like material (negative
real part of the dielectric permittivity) and a dielectric (positive real permittivity). It is this class of polaritons that
enables the confinement of light to length-scales below the diffraction limit due to the formation of an evanescent
wave at the interface between the two materials. Overcoming the diffraction limit has significant implications for
IR optics, providing a path towards enhancing the interaction of IR light featuring long free-space wavelengths to
deeply sub-wavelength scale structures, devices and materials.29 Negative permittivity is a direct consequence of
the coherently oscillating charges in a material, which induce a surface screening field, causing a high reflection of
the incident optical field, and hence prevents propagation into the bulk. In the IR, negative permittivity is commonly
realized in materials with excess free charge carriers and/or polar optic phonons. We highlight that other processes,
such as strong intersubband absorption and exciton formation, can also produce negative permittivity, however
these are outside the scope of this tutorial, and are discussed elsewhere.1,30
We will now address how IR SPPs and SPhPs form, their characteristic properties and the mechanisms by which
they can be excited. For SPPs, the negative permittivity is a result of free charge carriers, which produces a local
screening field that occurs when electrons with density are stimulated to move coherently within an incident
electric field2. Mathematically, this can be well-defined by the Drude formalism, which takes the functional form:
1
(1)
where is the the plasma frequency, and is defined by / ( is the carrier concentration,
is the electron mass, is the electronic charge), is the high frequency dielectric constant, and γ represents the
free carrier damping. The sets the upper frequency limit where the free carriers in that material can coherently
respond to the incident radiation and effectively screen it out. At the high carrier concentrations of metals (~1023
cm-3), will occur within the visible or UV, and thus these materials form the basis of visible plasmonics.2 To
support SPPs in the IR we can instead use heavily doped semiconductors. A major advantage of SPPs in doped
semiconductors is found in the ability to dictate and potentially modulate the carrier density through intentional
doping31,32,33, electrostatic gating 34-36 or optical pumping24,25,37. This means that the dielectric function can be
potentially tuned over a broad range of frequencies throughout the IR during the growth process or dynamically
modified using external stimuli.
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Surface phonon polaritons, while similar in many ways to the previously described SPPs, offer a significant suite
of novel properties that are desired for a range of potential IR applications. All crystalline materials support phonons
(coherent vibrations of the atomic lattice), of which certain classes interact with light. Here we are interested in
optic phonons, as these oscillate at frequencies commensurate with light in the mid- to far-IR. Optic phonons exist
as transverse (transverse optic; TO) or longitudinal (longitudinal optic; LO) displacement waves. The frequencies
of these phonons (,) are determined by the crystal lattice structure, the constituent atomic masses, bond
strength and transverse effective charge.19,38 For non-polar bonds (e.g. Si or Ge) the TO and LO phonons are
degenerate in energy at the Γ point (center of the Brillouin zone), however, the difference in electronegativities
across a diatomic bond (e.g. SiC) results in a net dipole moment, causing a spectral splitting of the LO phonon to
higher energies with respect to the TO.38 The corresponding net dipole moment of the TO phonon in turn makes it
IR active, allowing this net charge to induce a surface screening field. Thus, analogous to free carriers in a metal or
highly doped semiconductor, the coherently oscillating ionic lattice induces a high reflectivity within a defined
spectral range. This spectral window is referred to as the ‘Reststrahlen band’, and is spectrally located between TO
and LO phonon energies.38,39 Correspondingly, this will result in the real part of the permittivity becoming negative,
mathematically expressed using the well-known “TOLO” formalism:
1
. (2)
Similar to electrons, each phonon mode has a characteristic scattering time τ, and an corresponding damping
constantΓ, for full details see Ref 40. This region of negative permittivity is where SPhPs can be supported. Two
important distinctions between the free carrier plasma and polar phonons is the increased scattering lifetime of the
phonon oscillations and the significantly larger spectral dispersion of the permittivity for polar crystals. In the case
of the former, the scattering lifetime of phonons is generally on the order of picoseconds19 (vs tens to hundreds of
femtoseconds for the scattering of free carriers41), significantly reducing losses associated with SPhPs. Indeed,
recently phonon lifetimes within MoO3 were reported upwards of 20 ps.42 This increased phonon lifetime has been
demonstrated to have an equivalent increase in the lifetime of resulting polaritons.11,43-45 However, the large spectral
dispersion within the Reststrahlen band of polar materials results in a very slow group velocity, and thus extremely
slow light propagation.19,42,46
The surface polariton is a direct solution of Maxwell’s equations,2 and is characterized by the evanescent decay of
the electromagnetic fields from the surface of the polaritonic medium both into that medium and the adjacent
dielectric, along with propagation of the fields along the interface with the wavevector ( 2/), where
represents the compressed wavelength of the surface polariton. The relationship between and the dielectric
function at the two boundaries is provided by the phonon polariton dispersion expression:
(3)
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where and are the relative permittivity of the polaritonic and dielectric materials, respectively, and
represents the free-space wavevector of the incident light (2/
). This function is plotted in Fig. 1a for a
polar crystal, highlighting the dispersion of the bulk volume phonon polaritons at frequencies above and below the
Reststrahlen band (gray curves), with the SPhP dispersion found within this band (black curve). Here we have
assumed a lossless (γ=0) polar dielectric material and vacuum as the dielectric environment. Note that as the real
part of the permittivity of the polar material approaches , asymptotically approaches
infinitely large values. As is inversely proportional to , this implies becomes infinitely small, and thus, at
this point the light can be confined to essentially arbitrarily small sizes in a loss-less medium. While the form plotted
in Fig. 1a assumes a TOLO dielectric function, a similar dispersion curve is observed for any polaritonic material.
While the relation in Eq. (3) describes the properties of a surface polariton propagating on an infinitely thick
polaritonic medium, polaritons can also be supported in extremely thin films (<λ/100). In such systems, polaritons
can form on both interfaces of the film, but due to the reduced thickness, the two modes may couple resulting in a
nearly dispersionless, highly absorbing mode at a fixed frequency near ωp or ωLO, where the permittivity crosses
zero.47-51 This so-called ‘epsilon near zero (ENZ) polariton’52 exhibits a reduced linewidth with respect to the surface
polariton modes, and provides an extremely efficient light absorber, which is discussed at greater length in
Refs. 47,50,53-55.
Figure 1: Surface Polariton dispersion and coupling, adapted from 29. a) The dispersion relationship for electromagnetic waves
in a polar semiconductor, highlighting the region between ωTO and ωLO which supports surface phonon polaritons. b)-e) Due
to the momentum mismatch between free space light and polaritons, methods to probe them require this mismatch to be
overcome. This can be realized by coupling light to the polaritonic medium through a high index prism in either the b)
Kretschmann or c) Otto configurations, by d) imparting higher momentum through grating coupling or e) through
nanostructuring of the polaritonic medium, resulting in sub-diffractional resonant cavities.
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The challenge associated with both studying and using surface polaritons is that they propagate much slower than
free-space electromagnetic radiation. Thus, due to the requirement to conserve both energy and momentum, it is
impossible to directly excite surface polaritons with regular plane waves (which lie on the light line, red line in Fig.
1a). This ‘momentum mismatch’ between plane waves and polaritons can be overcome by slowing down the
incident light using a range of techniques. One of the easiest methods incorporates prism coupling (shown in Fig.
1b and c).56,57 Prism coupling exploits the evanescent wave that results at the boundary of a high refractive index
prism, either in contact with (Fig. 1b) or close to the polaritonic medium (Fig. 1c), with these two approaches
referred to as the Kretschmann and Otto configurations, respectively. This allows coupling into polaritons with
, where is the incident angle (blue line for light line in ZnSe in Fig. 1a). A second route
is through exploiting diffraction gratings, where additional momenta is provided by the periodicity of the grating
(Fig. 1d):
sin
(4)
Where is the grating period, and is an integer. This is essentially a form of Bragg scattering - light interacts
with the grating, coupling into diffractive modes, which results in a slowing of the light propagation. In all of these
approaches by changing the angle of incidence , the momentum at a given incident frequency can be tuned to
match the momentum offset between free-space light and the polariton mode (See Fig. 1a). The final method of
exciting surface polaritons is by coupling free-space light to sub-wavelength particles (Fig. 1e), where the additional
momentum is provided by Mie scattering from the small particle size.18 This is visualized for spherical particles in
Fig. 1e, but is generally observed in a range of resonant nanoparticle geometries fabricated via top-down58-60 or
bottom-up approaches.61 Note that in this case we are generally exciting localized polaritons, as opposed to the
propagating modes excited via prism or grating coupling. The result is the formation of a resonant antenna that can
be deeply subdiffractional in scale, with the resonant frequency determined by the shape and size of the structure.
Therefore, by plotting the resonant frequency as a function of nanoparticle size and/or shape, the surface polariton
dispersion can again be extracted, analogous to Fig. 1a. Nanoparticle scattering is also the methodology behind the
stimulation of polaritons within the near-field optical microscopy techniques, which will be covered later in this
tutorial. While the above description describes any polaritonic system (including those in both visible and infrared),
the IR poses a unique set of challenges when compared to the near-IR or visible including the longer free-space
wavelengths, associated window materials, detectors and sources.
The remainder of this tutorial article will introduce the appropriate measurement techniques, beginning with FTIR
spectroscopy, the predominant method for collecting spectra within the MIR to FIR. We will then highlight methods
for measuring spectra from smaller regions of interest including FTIR microscope operation and nano-FTIR and
scanning optical probe techniques. We follow this by discussing the additional challenges associated with such
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measurements in the FIR. Building upon this introduction, we then provide a few key examples where some of
these techniques have been implemented previously in the literature.
III. MEASUREMENT TECHNIQUES
In this section of the tutorial we aim to describe the variety of experimental techniques which can be employed to
excite, measure, characterize and investigate polaritonic materials in the MIR to FIR. We begin by discussing the
workhorse of IR spectroscopy, the FTIR, which can be used to characterize the IR optical properties of bulk
materials over large areas and broad spectral bands. However, traditional FTIR spectroscopy is not always suitable
for probing ultra-thin films, small areas or singular features. Moreover, without coupling mechanisms capable of
momentum matching incident light from the broadband source of the FTIR, direct measurement of polaritonic
modes is not possible. For this reason, we extend our discussion of FTIR spectroscopy to cover the attenuated total
reflectance (ATR) technique, which is capable of probing weakly absorbing thin films and modes with momenta
larger than that of free-space light. We also discuss FTIR microscopy for spectroscopic probing of small (but still
diffraction-limited) areas, and modulation spectroscopy, for the investigation of weak spectroscopic signals. While
FTIR provides a powerful technique for broadband spectral studies, the incoherent nature of the broadband source
makes the study of small features and incident-angle-dependent response difficult. For this reason, we cover thermal
emission FTIR spectroscopy, a technique particularly well-suited to the MIR to FIR that does not rely on the internal
light source of the FTIR. Building on this, we then move to a discussion of laser-based techniques for probing IR
polaritons. The ever-growing options for IR coherent light generation are explored, and the advantages of coherent
and highly collimated sources, with the potential for high-speed modulation, are examined. Ultimately, the deeply
subwavelength nature of IR polaritons requires characterization techniques capable of achieving sub-diffraction-
limited spatial resolution, which leads to an extended description of nano-probe techniques for investigating IR
polaritons. Leveraging our previous discussion of laser-based techniques, we describe how the use of near-field
probes offer unprecedented spatial resolution for investigation of ultra-subwavelength IR polaritonic modes, and
how such near-field probes can be combined with FTIR spectroscopy to offer high spatial and spectral resolution
characterization across a broad range of IR frequencies. Finally, we conclude with a discussion of the limited
characterization techniques available at FIR wavelengths, and the prospects for improved optical and optoelectronic
components that could potentially open this optical frontier to the kind of advanced spectroscopic analysis just now
becoming available for the study of MIR polaritonics.
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Technique Field of
View
Smallest
Sample
Spectral
Bandwidth (µm)
Spectral
Resolution
Films Gratings Particles
FTIR – Reflection/
Transmission
2cm 3mm 1-1000 <1GHz N Y Y
FTIR – ATR 2cm 3mm 1-1000 <1GHz Y N N
FTIR – Thermal Emission 1cm 1mm 1-1000 <1GHz N Y Y
FTIR-Microscopy 200um 5-100um 1-100 <1GHz N Y Y
Laser Spectroscopy – Gas 1cm 10um 3.3,9.5-11 <1MHz N Y Y
Laser Spectroscopy – FEL 1cm 40 3-1000 125GHz62 N Y Y
Laser Spectroscopy - QCL 1cm 10 3-12 <1MHz N Y Y
Laser Spectroscopy - DFG 1cm 50 3-20 1 THz? N Y Y
s-SNOM (laser) 20um 50nm 3-12 <1MHz Y Y Y
s-SNOM (nano-FTIR) 20um 50nm 3-20 2 GHz Y Y Y
Table 1. Summary of different techniques discussed, their key spatial and spectral properties, as well as capability
to measure polaritons in different types of samples. Field of view is the maximum sample size that can typically be
examined in a single measurement. Smallest sample is the minimum size sample that can be measured in these
systems. Spectral bandwidth is the range of frequencies over which this technique is valid, for FTIR microscopy,
standard operation with MCT detectors limits this technique to ~20 µm, however, as noted in the parentheses, using
other detectors such as a cooled bolometer, this can be extended out to ~100 µm wavelengths, where diffraction
limit and field of view preclude measurements at longer wavelengths. Spectral resolution indicates the maximum
frequency selectivity. Films, gratings and particles indicate whether the technique is capable of measuring polaritons
in different types of samples.
Fourier Transform Infrared (FTIR) Spectroscopy of Polaritons in the Mid-IR
All methods of exciting surface polaritons result in resonant reflection (R), transmission (T), absorption (A) and/or
scattering (S) of electromagnetic waves incident on the polaritonic medium, (where R+T+A+S=100%). For full
characterization of the polariton modes, the frequency and linewidth must be measured, requiring appropriate IR
spectroscopic techniques. The primary tool for such measurements in the IR is the FTIR spectrometer. However,
FTIR is based upon different operational principles, components and techniques than the dispersive spectrometers
typically used in the UV-visible-NIR spectral ranges. This section will outline the operation and specific techniques
relevant for measuring polaritons via FTIR spectroscopy.
In brief, a FTIR spectrometer consists of a broadband IR source (typically a SiC glowbar), a Michelson
interferometer, a sample compartment, and an IR detector (see Fig. 2a). The optical power transmitted through the
sample compartment is measured by the detector as a function of the position of a moving mirror, forming an
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interferogram, which is the Fourier transform (FT) of the IR spectrum. A discrete FT is then performed on the
interferogram, extracting the spectrally dependent IR signal passing through the spectrometer. This approach to
optical spectroscopy has several advantages over dispersive spectroscopic techniques. First, the measurement is
inherently broadband, appropriate for measurements from >1000 µm to approximately 1 µm (depending on the
performance of the source, beam splitter and detector). Second, as all frequencies are collected simultaneously,
there is no trade-off between spectral resolution and signal strength, generally resulting in high signal-to-noise.
Finally, the spectral resolution is determined by the interferometer path length, which can be extremely large, with
commercial models available with sub-GHz frequency resolution. There are also several complications associated
with FTIR spectroscopy. Some of the most significant challenges arise from the process of converting an
interferogram into a spectrum. Signal processing techniques are applied in the process of creating the spectrum
(notably phase correction, apodization and zero filling63), which can influence the interpretation of the results if
applied incorrectly. Furthermore, detector nonlinearities induce significant spectral distortion into the FT process,
and as such, any experiment must be carefully designed to achieve reliable results.
It is also worth discussing the specific components used within an FTIR spectrometer, as these influence the system
performance. Conventionally, an FTIR uses an incandescent bulb as a light source, using a filament designed to
operate at a temperature providing the most light at a given IR frequency. For example, whilst a traditional tungsten-
filament incandescent bulb is appropriate for NIR applications, a lower temperature silicon carbide glow bar is more
Figure 2: FTIR schematic and transmission properties of common infrared windows and substrates. (a) Schematic of an FTIR
spectrometer configured for transmission and reflection, ATR and thermal emission measurements. (b) Common classes of IR
transmission windows with the frequencies where polaritons can be supported for series of key polaritonic media. Filled bars
indicate the Reststrahlen band of different materials and dashed lines indicate the maximum achievable plasma frequency for
a conductor. Data for this plot is taken from the literature.33,45,59,64
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conventionally used in the MIR. The next component is the interferometer and associated optics. Almost all optics
in the system are reflective, using gold- or aluminum-coated mirrors to enable broadband operation. However, the
beam-splitter is required to be made of IR transparent materials, typically KBr (transparent from 25 µm into the
visible, Fig. 2b). Short-wavelength measurements often use CaF2 beam-splitters, while longer wavelength
measurements (FIR to THz) usually employ biaxially-oriented polyethylene terephthalate (BoPET) beam-splitters,
that will be discussed later in this tutorial. Detection is typically achieved with one of two standard detector types
– pyroelectric deuterated L-alanine-doped triglycene sulphate (DLaTGS) and cryogenically cooled photovoltaic or
photoconductive mercury cadmium telluride (MCT) detectors. The former requires no external cooling, is extremely
broadband (covering the full IR spectrum) and has a linear response function, but is not very sensitive and has
extremely slow response times (<1 kHz). MCT detectors can be extremely sensitive (approaching the photovoltaic
limit65), and are quite fast (tens of MHz, typically), but are slightly less broadband (conventionally ~20 to 1.3 µm,
with a peak responsivity dependent on MCT alloy used), and generally exhibits nonlinearities in the output, limiting
the dynamic range available for FTIR measurements. Finally, we also need to address the ambient atmosphere
inside the FTIR. Atmospheric water and CO2 have large absorption bands in the IR, which can interfere with FTIR
spectra. To prevent these gas-phase molecules from inducing artefacts, it is important to purge the FTIR
spectrometer with either CO2-free nitrogen or air, or to hold the FTIR under a modest vacuum.
Reflection and Transmission
Reflection and transmission spectroscopy are the two most common and straightforward types of FTIR
measurements. In both techniques a reference spectrum is collected, which consists of reflection from a metallic
mirror (near-perfect reflection at IR wavelengths), or an open path for transmission and then the sample spectrum
is collected and the two are divided. Transmission experiments are extremely easy to do within an FTIR – a sample
is simply mounted in the sample compartment and the transmitted light intensity as a function of frequency can be
directly collected. In addition, using various commercially available tools, a sample can be rotated with respect to
the incident beam path, enabling angle-dependent transmission measurements. Due to the straight beam-path
through the sample compartment, reflection spectra require an array of mirrors that allow the light to be incident on
a sample at a fixed position, with the angle modified by controlling the mirror arrays in concert (see Fig. 3a for a
schematic of such a tool). By performing correlated reflection and transmission experiments, it is possible to
determine the extinction spectrum (e.g. total absorbed and scattered light), by using 1, where
assuming negligible scattering (true for spectra of sub-diffraction nanostructures and metamaterials). However, in
the IR both techniques have four major challenges. First – all common optical glasses are opaque in the IR. This
means that substrates such as high resistivity silicon, germanium, or chalcogenide glasses, materials that are highly
reflective or translucent in the visible, provide more appropriate IR windows. An extensive list of available IR
window materials in reference to the operational range of several key polaritonic materials are provided in Fig. 2b
12
as a guide. Second, the long wavelength of IR light makes these experiments extremely sensitive to etalon effects
arising in high-index samples and substrates that can significantly distort the spectral response. Third – conventional
reflection and transmission measurements within the standard sample compartments can only be performed on
samples relatively large in size, typically >1 cm2, but with defined apertures can be made on regions of interest in
the mm-range. Finally, an FTIR typically uses focusing mirrors that introduce some angular spread to the incident
beam – this spread can artificially broaden the measured linewidth of resonances, including polaritonic modes due
to their high sensitivity to incident angle. An example where such bench-based reflection or transmission
measurements can be used for polaritonic experiments is the measurement of large-area arrays of polaritonic
resonators, gratings or dispersed nanoparticles. In all, reflection and transmission are routine experiments for
measuring relatively large (>mm scale) samples of different polaritonic media.
Attenuated total Reflectance (ATR)
In many cases, pure reflection and/or transmission spectroscopy are not sufficient to collect the IR response of a
material or film of interest. For instance, in thin films, such as polymers or thin dielectrics, the long-wavelengths
associated with the IR significantly suppress the IR absorption cross-section. Within polaritonic media, the large
momentum mismatch between free-space light and the surface polaritons (see Fig. 1a) also causes additional
challenges, which in many cases may be overcome by implementing the ATR technique. In these experiments, light
is directed to a sample surface through a prism of a high refractive index (Fig. 1b and c). Due to total internal
reflection, when the incident light reaches the bottom prism surface, an evanescent wave is launched that propagates
in the dielectric medium on the opposite side of that interface. For instance, in the Otto configuration experiment
illustrated in Fig. 1c, this evanescent field propagates in the air-gap between the prism and the polaritonic material.
This field provides the additional momentum to overcome the momentum mismatch, thereby enabling direct
measurements of polaritonic absorption via prism coupling (Fig. 1 a-c). The ready availability of IR transparent,
high-index materials (including ZnSe, Si and Ge, see Fig. 2b) makes this approach extremely appealing for
measuring IR polaritons. It should be noted that as the polaritons excited in ATR experiments have in-plane
momentum and out-of-plane evanescent fields, they are only launched by p-polarized light, so comparisons of the
angle dependence of p- and s-polarized ATR spectra allow for easy identification of polaritonic modes from other
absorptive modes within the material (e.g. IR active phonons or vibrational bands).
13
Figure 3: Optics for infrared reflection/transmission and ATR for variable-angle measurements in the bench and for
microscope-based methods. a) Due to the linear beam path in the FTIR sample compartment, in order to perform reflection
measurements, the light must be coupled into a multiple, coordinated mirror apparatus. A schematic for such a commercially
available system (Pike Technologies) is provided here, highlighting how the four mirrors work in concert to focus the light to
the sample position, albeit with a relatively broad incident angle spread. Note, that to change the incident angle, one simply
needs to rotate these mirrors in concert so that the focal spot spatial position is maintained. Typically angles between ~30° and
80° are possible. (b) Microscope measurements effectively redirect the incident broadband beam from the bench sample
compartment, making the microscope the defacto sample compartment. The optical path of a typical IR microscope, configured
for viewing of the sample with a visible camera before IR reflection measurements is provided. c) For performing FTIR
measurements in the microscope over a broad spectral range, Cassegrain-type objectives are required. A schematic of a typical
Cassegrain objective, which has a weighted mean incident angle of approximately ~25 degrees, and a total angular spread of
~10°. d) Such objectives can be modified to accommodate a prism for the purpose of performing small area ATR measurements.
A schematic of such an “ATR Objective” is provided. In d) an aperture is used to reduce the incident angular spread, which
can also be applied in the context of c).6,56
The direct measurement of polaritons via ATR methods can be achieved in one of two configurations. Through-
film coupling termed the Kretschmann-Raether or Kretschmann configuration, relies on bonding or pressing a
polaritonic film onto the surface of the prism (Fig. 1b). In this approach, the evanescent field induced at the
prism/polaritonic-medium interface can launch a polariton, provided the skin-depth of the evanescent field extends
to the opposite side of the polaritonic material. This can provide a very simple approach to measuring the polaritonic
dispersion, aided by changing the incident angle and/or the index of refraction of the prism, both of which directly
change the momentum of the incident light. However, while bonding a polaritonic film onto a prism is effective,
films can be difficult to remove making the experiment difficult to repeat, and in many cases, destructive. In
14
addition, pressing a sample onto a prism requires a dielectric substrate on which the polaritonic medium is grown
or deposited. However, for polariton excitation to be possible, the substrate must have a lower index than the prism
(otherwise the optical mode is ‘pulled’ into the substrate).56 Furthermore, excellent optical contact needs to be
achieved between the substrate and the polaritonic film, which can be problematic with stiff materials. Thus, a
commonly used alternative involves coupling to the polaritonic mode through an air gap (Otto configuration, Fig.
1c), which is a much more versatile approach, as a clean interface between sample and prism is no longer required,
and the substrate has a less significant effect. However, the position between prism and sample needs to be precisely
controlled at a length-scale below the compressed polariton wavelength. This has been achieved using piezo stages
and interferometers to accurately calibrate the prism-sample distance.49,66 In the case of Otto experiments, the
momentum can again may be modified through changing the incident angle and/or prism material, but additionally
by changing the size of the air gap, the evanescent extent of the mode can be probed. An optimal overlap between
the evanescent field from the reflection at the prism surface and that of the polaritonic medium occurs, with this
condition deemed the ‘critical coupling’ point.2
Thermal Emission and Emissivity Measurements
Beyond reflection and transmission, the strong absorptive nature of polaritonic resonances provides an alternative
method for probing their response. This can be realized through measuring thermal emission from a sample. For
room and elevated temperatures, from 300-1400 K, the peak blackbody emission from a surface inherently occurs
within the MIR. While a perfect blackbody emits in accordance with Planck’s Law of Blackbody radiation, with a
peak emission occurring at the Wien wavelength, for any real surface, this thermal emission is modified by the
spectral dependence of the emissivity of the surface. Kirchhoff’s law of thermal emission tells us that the
absorptivity is equivalent to the emissivity at the same temperature1, where
is the surface reflectivity and scattering is assumed to be negligible. Within polaritonic nanostructures, specific
resonant modes will result in narrowband absorptive antenna resonances, which as stated above provides
narrowband resonances in the emissivity spectrum. Therefore, when heated to elevated temperatures, these
resonances will produce strong narrow-band thermal emission, with the irradiated power dictated by the emissivity
and the temperature-dependent thermal energy available.14 In addition, by controlling the periodicity of the
polaritonic structures, the spatial coherence (directivity) of the thermal emission can be controlled,12 while through
implementing anisotropic nanostructures the emitted light can be polarized into the far-field.13,14 Thus, one
particularly intriguing opportunity for IR polaritonic materials is the design and demonstration of spectrally or
spatially selective thermal emitters. Moreover, measuring thermal emission from polaritonic nanostructures can
also provide direct observation of the resonances and therefore provides an extremely useful platform for
characterizing polaritonic nanostructures14 and in some cases thin films.50,53,67-70
15
It is relatively easy to measure thermal emission spectra from a sample in a FTIR spectrometer by using the sample
as a light source, provided the interferometer is configured appropriately. However, the collected spectrum is not a
calibrated measurement of the sample emission or emissivity.71 The spectrum that is measured, ,, contains
the sample emission at a given temperature , designated as ,, and a blackbody thermal background from
the FTIR optics . Furthermore, this sample emission and thermal background are multiplied by the spectral
responsivity of the FTIR, . The measured spectrum can then be expressed as , ,.
The simplest way of correctly calibrating an FTIR is therefore to compare the measured spectrum of a blackbody
at two different temperatures ,, with the spectra for an ideal blackbody , used for calibration. Using
these two measurements, we can write;72
,,
,, (5)
,
,
(6)
This calibration procedure can be used to estimate the emissivity of a sample relative to the reference. By taking
the ratio of the calibrated spectra to that of an ideal blackbody, one can extract the emissivity spectrum of the sample
at the measured temperature.73 Note that finding a material that serves as an accurate blackbody reference is
extremely challenging, as materials typically exhibit temperature-variable emissivity. At temperatures below
600 K, a layer of soot deposited using a candle acts as a reasonable approximation, however self-absorption of the
thermal emission can occur within thick films and thus care must be taken in the optimizing the preparation
conditions.27 More recently, arrays of carbon nanotubes have also been deployed as more robust blackbody
references.71 Back-reflections into the interferometer from the detector can also play a significant role in calibrating
these measurements at low temperatures. For weak thermal emitters (where the emitter temperature is less than the
temperature of the detector or the FTIR optics, the situation becomes even more complicated, as the relative phase
difference of the emission from the source, beam-splitter, and detector must be taken into account.73 Although a
discussion of these effects is beyond the scope of this tutorial, early FTIR work offers insight for best practices in
this regard.27,73
FTIR Microscope Measurements
The techniques mentioned above all use bench-based measurements within the sample compartment of a FTIR
spectrometer (Fig. 2a), thereby implying low magnification and thus, relatively large samples. However, it is also
possible to do micron-scale sampling using a specially designed FTIR microscope. This is particularly important
for polaritonic antennas fabricated using top-down approaches, as nanoparticle arrays are typically small, on the
order of tens of µm on a side. In such approaches, the IR beam is passed through the interferometer and then out to
the microscope, which contains specialized IR objectives, and then typically into a microscope-mounted liquid-
nitrogen cooled MCT detector. In this way, the microscope acts as the ‘sample compartment’, offering higher
16
magnification and therefore the ability to measure small regions of interest (Fig. 3b). However, the objectives used
for IR microscopy require special discussion. While refractive objectives using IR transparent materials such as
ZnSe or Ge are available, these components have restricted spectral bandwidths due to the anti-reflection coatings
and inherent spectral dispersion of the materials. More conventionally, reflective objectives, with a Cassegrain
design consisting of two opposing mirrors are employed (Fig. 3c). These objectives are capable of measuring
samples in both reflection and transmission geometries. In the case of the latter, a condenser must be paired with
the objective that provides the ability to compensate for the index of refraction of the substrate so that the focal
point can be positioned at the sample of interest. Specialized objectives are also available that can perform ATR
measurements using a prism with a front face only 100 µm across (Fig. 3d), while others are available for grazing-
incidence measurements where the light can be directed to a micron-scale region of interest at angles on the order
of 70° with respect to the surface normal. These are especially well-suited for thin film absorption measurements
or performing polaritonic dispersion measurements on small-area flakes or regions of interest.56 In general, the FTIR
objectives offer moderate magnification factors (15x and 36x are standard), and a Cassegrain objective does not
excite or collect at normal incidence light (see Fig. 3c). This has important implications for the excitation (and
measurement) of propagating polaritons in experimental systems, as the wide range of angles for the incident light
will generally blur any spectral features associated with the momentum-matching requirements for coupling to
propagating modes. For localized polaritonic antenna resonances, this ensures that both in- and out-of-plane
excitation will occur simultaneously for all standard collection conditions.
Infrared microscope objectives do not focus the IR light to a diffraction-limited spot, but instead focus into a spot
size on the order of hundreds of µm. To measure samples smaller than this beam-spot, apertures are used to define
the region of interest. While in principle this area can be as small as 5 µm, in practice this significantly reduces the
optical throughput of the system, and the diffraction limit begins to prevent the propagation of long-wavelength IR
light, and correspondingly the spatial resolution of any measurement. Thus, while this technique can be used to
effectively map out IR spectra across different spatial positions on a non-uniform sample, an alternative route is to
use a focal plane array (FPA) attached to the IR microscope in place of the aforementioned detector. An FPA is a
detector array, allowing the collection of a hyperspectral image across the full microscope field of view. As a result,
this is an extremely effective way of collecting IR spectra over a large area simultaneously, though IR FPAs are
orders of magnitude more expensive than their short wavelength counterparts and are not commercially available
at wavelengths much past the long-wave IR (~800 cm-1 as low frequency cutoff for FTIR microscope mounted
systems).
Modulation spectroscopy
17
Beyond the collection of optical spectra, FTIR also offers opportunities for performing time-dependent and lock-in
amplifier integrated measurements. In conventional FTIR spectroscopy the mirror is continuously scanned, and the
detector signal is continuously monitored. However, in another mode of FTIR called ‘step-scan’, the mirror is
stopped at a series of different positions, and a time-dependent response can be collected, assuming the optical
phenomena is repeated for every mirror position. For each time point, the interferogram can be collected and a FT
can be performed to extract a spectrum. By using a fast analogue-to-digital converter, spectra can be collected with
as fast as 2.5 ns temporal resolution. This approach can be implemented for performing pump-probe measurements
(though typically not with the time-resolution required to observe the characteristic timescales of polaritons or the
associated fundamental charge oscillations). The same step-scan approach can be used to collect a lock-in amplifier
integrated spectrum for extracting the differential IR response of materials under optical or other external stimulus.
Instead of measuring a time-dependent signal at each interferogram point, the lock-in amplifier integrated signal
can be collected at each interferogram point. This technique allows the measurement of modulated spectroscopies,
such as photo- or electro-reflectance, or modulated emission from IR materials.
Laser-Based Spectroscopic Methods for Probing Polaritons
FTIR-based characterization of IR polaritonic materials and structures offers valuable broadband spectral
information about the polaritonic modes they support. However, such measurements typically employ incoherent
light sources, which are difficult to focus and collimate. Collimated beams from internal FTIR sources can be used
to spectrally interrogate large-area, periodic structures, but are of little utility for investigation of individual
polaritonic structures or for visualization of polariton propagation across the surface of a sample. This is because
polariton propagation lengths are often significantly smaller than the spatial extent of the probe beam. More
localized investigations of polaritonic surfaces are achievable with incoherent FTIR sources, typically using all-
reflective large numerical aperture (NA) objective lenses in an IR microscope, as discussed above. However, such
an approach is poorly suited for characterization of propagating polaritonic modes, as coupling to free-space light
into these modes is strongly angle-dependent, and the large NA of the IR objective lens ensures a broad range of
incident angles for the probe beam, washing out any angle-dependent spectral features.
Most of the challenges outlined above are alleviated through the use of a coherent probe beam, which allows for
significant reduction in the incident spot-size and angular resolution, although this is achieved at the expense of
spectral bandwidth. Historically, the coherent sources available in the IR were limited to a number of gas lasers,
specifically the HeNe (3.39 μm) and CO2 (9.5-11 μm) lasers,74 with the latter utilized to demonstrate critical
coupling to SPhPs at ~10.8μm.75 Alternatively, free-electron lasers and IR synchrotron radiation offer broadly
tunable, coherent sources for excitation and characterization of IR polaritonic modes, though the cost and size are
unsuitable for future polariton-based optical systems and optoelectronic devices.76,77 The advent of the quantum
18
cascade laser (QCL)78 and its counterpart the interband cascade laser (ICL),79 have provided compact, frequency
tunable, high power, commercially available coherent sources across a wide range of IR frequencies. The narrow
linewidth and collimated nature of the IR light from a QCL allows for angle-resolved coupling to propagating IR
surface modes on metallic films. Such coupling has been demonstrated in the Kretschmann geometry (using a
Ti/Au-coated CaF2 prism) for measuring CO absorption,80 or alternatively for probing the coupling to, and
propagation of, IR surface modes on extraordinary optical transmission (EOT) gratings81 or corrugated beam-
steering or beam-shaping structures.82 Though the emission from QCLs and ICLS is generally narrow band,
spectroscopic characterization is possible using broadband gain media, fabricated into arrays of addressable
narrowband emitters, or alternatively, using external cavity tuning.83
In parallel with the development of cascade lasers, significant improvements in fiber-based IR light sources over
the past decades have resulted in viable alternatives for IR applications. These light sources often leverage
fluoride-, telluride- or chalcogenide-based fibers, either doped with rare-earth ions to form an optically-pumped IR
gain medium,84 or alternatively, leveraging non-linear optical effects in highly nonlinear step-index or micro-
structured IR-fibers. Such sources can achieve ultra-fast supercontinuum pulses using either ultra-fast mid-IR
pumps,85 or alternatively, concatenated fibers designed to generate a supercontinuum in successive long-wavelength
bands.86 IR fiber lasers not only offer reasonably compact sources for probing the optical properties of IR materials
and structures, but also the opportunity to probe IR polaritons on time scales commensurate with ultrafast carrier
and lattice excitation dynamics. Such sources have led to a wealth of time-resolved experiments, most frequently
combined with the spatially resolved experimental techniques discussed in the next section.
Not only have the new generation of mid-IR sources allowed for more effective probing of IR polaritonic modes,
but recent work has demonstrated the potential utility of polaritons for the design and demonstration of new types
of sources operating in this spectral range. Patterned metallic structures, fabricated directly onto the facet of a QCL,
have been used to demonstrate highly directional, polarization-controlled collimated beams.87 In this work, light at
the laser facet is coupled via a subwavelength slit to propagating surface modes (polaritons) on the metal-coated
laser facet. Structures patterned onto the laser facet then scatter the surface modes with a carefully designed phase
relationship, resulting in directional light emission, with control over the emitted beam shape and polarization
state.87,88 Such devices offer unique control of the IR light by direct integration of polariton-supporting structures
onto the laser output. Alternatively, IR polaritonic structures have been directly integrated into IR gain materials, a
prime example being the so-called plasmonic waveguides used as the mode-confinement mechanism for some early
QCLs.89 Though such waveguiding structures were largely discarded due to the lower loss afforded by all-dielectric
waveguides, recent work has explored the potential of SPhP waveguides for far-IR QCL devices. In these emitters,
thin slabs of polar materials are used to support SPhP modes for QCL designs with low-energy intersubband
transitions, offering a route towards phonon-polariton enabled sources for far-IR wavelengths.90 Such emitters mark
19
the first compact sources with the potential for characterization applications at far-IR frequencies (a wavelength
range currently devoid of coherent sources), though they are as of yet limited to narrow wavelength bands around
the LO phonon energies of III-V materials that are lattice-matched to QCL architectures.
The coherent sources discussed above offer narrowband, high-power, and in some cases, ultra-fast IR sources for
characterization of IR polaritonic materials and structures. The coherent nature of the light emission offers the
opportunity for high power, collimated probes, as well as high-speed modulation for lock-in measurements. In
general, coherent sources offer reduced spot sizes for spatially-resolved probing of IR materials and devices, though
these spot-sizes will always be diffraction-limited in any set-up using standard optical components. In the
subsequent section we discuss the significant advances in sub-diffraction-limit characterization of IR materials and
devices that can be achieved by leveraging coherent sources and a new generation of IR imaging technology.
Nano-probe-based Methods for Spatial and Spectral Characterization of Infrared Polaritons
Both FTIR and laser-based spectroscopies are inherently constrained by the diffraction limit of IR light – which is
almost always above a micron across the IR portion of the electromagnetic spectrum. Infrared characterization took
a significant leap forward in the late 1990’s with the advent of scattering-type scanning near-field optical
microscopy (s-SNOM).91,92 This development allowed for coherent IR light sources to be coupled into an atomic-
force microscope (AFM), thereby combining the ability to experimentally probe light-matter interactions well
below the diffraction limit, while also collecting topographical information about a sample (schematic provided in
Fig. 4). In regards to IR nanophotonics these capabilities of s-SNOM were transformational. For the first time there
existed an experimental probe that could quantify the frequency-dependent optical behavior of a material or
structure with spatial resolution on the order of the length-scale of the polaritonic effects.
20
Figure 4: Schematics of scattering-type scanning near-field optical microscope (s-SNOM). (a) CW laser sources (b) ultra-
broadband synchrotron light source (c) table top ultrafast broadband IR laser source (d) table top THz broadband sources
utilizing photoconductive antennas (PCA) (e) AFM-based near-field platform with optics and sample stages. (f) Interferometric
detection. Light is directed to the AFM tip via parabolic mirrors. The scattered light is then directed from the sample to an
additional parabolic mirror, which is collected using an appropriate detector. Figure modified from Ref. 91.
The methodology for the s-SNOM technique is based upon the scattering of incident light by a metallized AFM tip,
providing a strong scattering element for incident, continuous-wave IR light (Fig. 4a). The implementation of an
AFM is critical for multiple reasons. First, the scattering induces strongly p-polarized (along z-axis) evanescent
fields with high wavevectors that are induced within nanometer-scale proximity of a sample surface. In the case of
polaritons, this is essential as the high- provides the means to overcome the momentum mismatch between free-
space light and the polaritonic modes.92 The implementation of tapping-mode AFM for these measurements also
enables the optical signal to be extracted at multiple harmonics of the AFM-tip oscillation frequency using a lock-
in amplifier to more efficiently filter the incident fields from those corresponding to the local near-field response
(Fig. 4b). In practice, each higher harmonic improves this filtering, but also comes with weaker signal strength.
Typically for polaritonic measurements the 2nd to 4th harmonics are plotted. Finally, the AFM configuration and
21
Figure 5: a) Schematic of an IR light being scattered off of an AFM tip, launching radial polaritonic waves. When the polariton
waves reach the edge of a flake, they are reflected, interfering with the launched wave forming the interference patterns with a
periodicity of /, this is shown here for hexagonal boron nitride that is isotopically enriched with 98.7% 10B (top),
99.2 11B (bottom) and in its naturally abundant form (center). c) By extracting linescans and performing a fast Fourier transform,
the spatial frequency at that incident frequency can be extracted. d) By plotting the spatial frequency at multiple incident
frequencies, the polaritonic dispersions can be extracted. Note that here, due to the hyperbolic nature of hBN that the
isotopically enriched flakes (left and right) exhibit higher order modes shown as high (shorter ) polaritons at the
same incident frequency. a) is reprinted with permission from S. Dai, et al. Nano Letters 17(9), 5285-5290 (2017). Copyright
2017 American Chemical Society.93 Figures for b)-d) are reprinted with permission from A. Giles, et al. Nature Materials 17,
134-139 (2018).45
heterodyne detection scheme (Fig. 4c) allows for simultaneous mapping of the optical amplitude and phase, along
with the topographic information of the sample. This spatial mapping therefore enables imaging of polariton
propagation,34,36,45,46,94 identifying material-specific optical modifications,20,95 demonstration of hyper- and
superlensing concepts and designs96 and the electromagnetic field distributions of localized surface polariton
antennas.14,97
Perhaps one of the most powerful features of s-SNOM methods for characterizing polaritons is in the ability to
directly image the wavelength of a propagating mode.34,36,45,94 Initially realized with metallic elements fabricated
on the top of SiC to focus SPhPs launched by the s-SNOM tip,98 it has since evolved into a method for extracting
the polariton dispersion relationship. 34,36,45,94,99 Demonstrated by the Koppens and Hillenbrand34 groups
simultaneously with the Basov group36 for SPPs in graphene, this method requires the implementation of a sharp
22
edge that can serve to reflect the tip-launched wave, and in many cases directly launch the polaritonic waves,
resulting in an interference pattern. This has been demonstrated quite elegantly within nanoscale thickness slabs of
hexagonal boron nitride (hBN).94 This is shown in Fig. 5a-d for hBN. Initially, the scattering of the incident light
from the tip couples to higher momentum polaritons, launching a radially propagating mode (Fig. 5a). This mode
continues to propagate radially, until reaching a sharp boundary (e.g. flake edges in Fig. 5b) the wave is then
reflected, establishing an interference pattern between the forward- and backward-scattered waves. A cross-
sectional view the hyperbolic rays within the hBN at the edge of a flake is provided in the inset of Fig. 5a.
Additionally, direct launching of the polariton can also be induced due to scattering off of the flake edge or
boundary, resulting in two different interference patterns with periodicities of /2 and for tip- and edge-
launched polaritons, respectively (again see inset of Fig. 5a).93 By extracting a series of linescans normal to the
flake edge (Fig. 5c) and performing a Fourier transform, () of the polaritonic mode can be extracted. By
performing this as a function of incident frequency, the polariton dispersion can be experimentally determined (Fig.
5d). This has several specific implications with regards to this tutorial. This implies that measuring the polariton
dispersion provides an avenue to determine many material-specific properties of interest for IR nanophotonics, for
instance the optical conductivity (dielectric function for bulk semiconductors), Fermi energy and scattering rate for
free-carriers, or phonon scattering and energies for polar materials with spatial precision that can even surpass the
radius of curvature of the s-SNOM tip. Thus, this method can also be utilized for probing subsurface features100 or
for characterization of defects in semiconducting materials and devices.101
Within nanostructured polaritonic antennas, s-SNOM can provide a means to directly map the localized
electromagnetic field profiles. Such spatial maps can be directly compared to calculated field profiles using
commercial solvers to validate theory.14,97 However, the use of a metallized AFM tip can cause modifications to the
fields due to the large dipolar field associated with this additional antenna and its non-trivial interaction with the
polaritonic dipole(s). Thus, to avoid such effects, one may implement a dielectric (typically Si) tip that can be used
to extract the topographic and optical fields, without serving as a significant source of polariton launching. This
was demonstrated for mapping the localized modes of SiC SPhP bowtie antennas, providing local near-field
distributions nominally free from the impact of the tip-induced artifacts.14 However, to be able to map the resonant
modes, one must first know the spectral position of the antenna resonances, typically extracted by far-field FTIR
measurements of periodic arrays of the antennas of interest. However, there does exist a spectral shift between the
far- and near-field resonant conditions due to the presence of the s-SNOM tip,97 and thus the far-field measurements
only provide a rough estimate of the spectral position. Therefore, ideally one should measure the near-field spectra
in the presence of this tip, which can be achieved through the implementation of a broad-band light source for nano-
FTIR,102 providing direct measurements of the local spectral response.
23
In contrast to s-SNOM, nano-FTIR utilizes a broadband coherent light source [e.g. a synchroton or difference-
frequency-generation-based broadband laser (Fig. 5d)] with an interferometer similar to an FTIR system, but
coupled through the s-SNOM apparatus (Fig. 5c). In the case of slabs of polaritonic media, nano-FTIR can provide
a means for directly extracting the polaritonic dispersion at low- within a single measurement, as in Ref. 42,94. In
the context of localized antenna resonances, nano-FTIR can provide direct measurement of the resonance spectra.97
When compared with the corresponding far-field reflection and/or transmission spectra, nano-FTIR offers the
ability to quantify the degree of linewidth broadening that results from inhomogeneities within the nanostructure
geometry among the periodic lattice in addition to measuring the IR spectra within the local dielectric environment
of the s-SNOM tip.97 More recently, time-dependent methods have been developed enabling the imaging of the
group and phase propagation of polaritons. For hBN, nano-FTIR was used to demonstrate the positive (negative)
group (phase) velocity of the hyperbolic polaritons within the upper Reststrahlen band, along with direct
measurement of the HPhP lifetimes42,46 within both the lower and upper bands. Building on this, ultrafast pump-
probe lasers have since been integrated (Fig. 5e),103,104 allowing measurements of polaritonic near-fields under
strongly non-equilibrium conditions such as in the presence of high free-carrier densities.
While s-SNOM has provided significant advancements in our understanding of IR nanophotonic materials and
devices, it is still limited by the availability of coherent continuous-wave laser sources at frequencies below the
long-wave IR (roughly 11 µm for s-SNOM, 15.4 µm for nano-FTIR). This limited spectral coverage extends out to
the THz (Fig. 5f), where s-SNOM measurements again become possible.105 The lack of coherent continuous-wave
laser sources can be overcome by integrating the s-SNOM with a synchrotron (Fig. 5d) as demonstrated by the
Raschke group,106 however, this is not an accessible option for research groups that are not associated with such
facilities. A complementary method that can integrate pulsed lasers and implements a mechanical read-out of local
thermal expansion due to resonant excitation of a material or structure is the photothermal induced resonance (PTIR)
technique,107,108 which has the same operating principle as the photo-induced force microscopy (PIFM) method.109
In these techniques, a pulsed laser illuminates a metallized AFM tip as in s-SNOM, however, the tip is typically
operated in contact mode and the optical signal is read-out via nanoscale thermal expansion of the film or
nanostructure being probed.107,109 This mechanical read-out implies that these techniques measure the local
absorption of light due to polaritonic resonances. As well as the ability to probe the local fields associated with
strongly scattering optical modes that can be measured in s-SNOM, it is also sensitive to dark or weakly scattering
modes,107 as recently demonstrated by the Caldwell and Centrone groups. Furthermore, the ability to implement
pulsed-laser sources within this methodology also extends the spectral range for these measurements into lower
frequency regimes, however, this is still currently limited from extending into the far-IR due to the lack of
appropriate laser sources. However, the PTIR/PIFM methods are still in the nascent stage in terms of their use for
24
polaritonic characterization and thus offer significant promise as complementary characterization tools for
polaritonic materials and devices in the years to come.
Complexities for Probing Polaritons within the Far-IR (FIR)
As it is for the MIR, the FTIR is also the spectroscopic workhorse for FIR measurements. However, FTIR
spectroscopy in the longest wavelength portion of the IR, though similar in general experimental set-up to its MIR
counterpart, comes with a number of additional challenges. For broadband spectroscopic applications, the bench-
top available light source is often the same SiC globar. The utility of this source is largely limited by the high
operational temperature of the bar, which by Wien’s law, puts the bulk of the IR thermal radiation at much higher
frequencies, which produces limited additional FIR power with further increases in globar temperature. Moreover,
the sub-unity emissivity of SiC at such long wavelengths also contributes to the weak spectral power density as one
moves further from the blackbody emission peak. Alternatively, mercury vapor lamps can be used as FIR sources,
offering marginal improvement in spectral power density within this range, resulting from near-unity emissivity
across the majority of the 20-60 µm spectral range. However, mercury vapor lamps typically require water-cooling,
and thus have a sizeable footprint. High power, coherent emission has been realized with free electron lasers
(FEL),49,66,76,110 synchrotrons,106 and molecular lasers, but all of the above are costly and poorly suited for compact,
bench-top applications.
The dearth of FIR sources are far from the only obstacle facing spectroscopic analysis at such long wavelengths.
FIR beam splitters are similarly sub-optimal compared to their MIR counterparts. The beam splitter of choice for
the FIR is typically made of a single thin BoPET film, or alternatively, multiple thin films of BoPET. Unfortunately,
the response function of thin film BoPET is far from uniform or broadband, due to absorption in the BoPET (~100
cm-1 across the FIR)111 and variations in the film thickness across the beam splitter. Stacking multiple thin films
increases the bandwidth of the beam splitter at the expense of increasing absorption and the introduction of
additional absorption features. Furthermore, BoPET is microphonic, so laboratory vibrations can reduce the
sensitivity of the interferometer. Another potential FIR beamsplitter material is CsI, which has a well-behaved
response function over the FIR. However, the highly hygroscopic nature of CsI makes it unsuitable for applications
requiring extended exposure to atmosphere, and only operates down to 150 cm-1. It is also worth noting that BoPET
and CsI windows are used as viewports for evacuated FTIRs and for FIR detectors. Often the CsI is coated in a thin
layer of polyethylene to prevent environmental damage.
The two primary detector classes used in the FIR are the pyroelectrics (LiTaO3, DTGS, and the improved DLaTGS)
and bolometers (Si and superconducting). As previously mentioned, pyroelectric detectors can detect light across
the entire FIR spectrum with a flat and linear response across a broad range of FIR frequencies, both important for
FIR spectroscopic applications. However, they have significantly lower sensitivity (specific detectivity, or
25
D*= of ~108 Jones) compared to bolometers (D*~1012 Jones) and have severely limited response times,
usually on the order of 1 to 10 Hz, making them susceptible to 1/f noise. Furthermore, pyroelectrics are often
piezoelectric, so vibrations from the lab can further reduce the sensitivity of these devices. Bolometers offer a
significant increase in sensitivity, ~3-4 orders of magnitude, and modulation speeds into the kHz, but require either
liquid helium, or expensive cryo-free systems to cool the detector element to liquid helium temperatures (4.2 K)
using closed-cycle compressors.
As a rule, the speed of detectors in the FIR is severely limited compared to those operating in the MIR. This makes
time-resolved measurements essentially impossible. Even step-scan measurements, which are based on the
modulation of the signal on the FIR detector, can be incredibly time-consuming, as step-delay and lock-in amplifier
signal integration times will have to be comparable (but at least ~3x longer) than the detector response times. One
approach to overcome the slow detector response is to use detector window materials that are only transparent in
the spectral range of interest. Alternatively, additional filters can be placed in the optical path to pass only light in
this small spectral range of interest. This filtering allows one to take larger steps in mirror position in step-scan
mode and therefore attain shorter total scan times. Zero transmission outside the filter passband is required as the
larger mirror steps can be conceptualized as folding the entirety of the optical spectrum into the wavelength range
of interest. Any signal outside of the filter passband is therefore folded into the wavelength range of interest,
resulting in artefacts that cannot be easily separated from the ‘real’ spectra.
The emission from the experimental optical components becomes even more important in the FIR, especially when
measuring emission from samples colder than your detector and beam splitter. Given a weak sample emission, if
one were to subtract the self-emission of the FTIR in spectral space, they would likely find spectral regions with
negative emission. One method of overcoming emission from the interferometer is to cool the entire system to
cryogenic temperatures. Obviously, evacuating and cooling all the optical components in an interferometer
introduces a plethora of additional problems. An easier method to overcome self-emission of the FTIR is to leverage
the phase difference between the detector and the beam-splitter emission relative to the sample. All one has to do
is subtract the self-emission of the FTIR in interferogram space rather than spectral space and then compute the
discrete FT, with a high phase resolution, of the subtracted interferogram.73
IV. EXAMPLES AND APPLICATIONS
While the bulk of the tutorial is designed to provide the necessary background in both experimental tools and
methods for probing investigating nanophotonic materials and devices, this description would be incomplete
without providing key examples of how these tools and methods have been previously implemented. We have
distributed these examples to specifically highlight experiments investigating localized IR polaritons, thermal
emission, nanoprobe measurements and FIR spectroscopy. While a complete description of the extensive work in
26
this field is better suited for review articles previously provided and well beyond the scope of this work, within this
section we provide some specific examples with the goal of providing the reader with the necessary context as to
how such tools and methods can be employed for probing nanophotonic materials and devices, with the desired
goal of shortening the learning curve for those entering the field.
1. Semiconductor Nanoresonators for Surface Sensing
As discussed in Section II, nanoresonators offer one of the simplest routes to coupling far-field radiation into a
surface polariton mode, manifesting as resonant absorption, transmission or reflection in the spectral response. As
localized resonators concentrate the electromagnetic fields close to the surface of the sample, this allows them to
be used for sensitive surface sensors. In this case, the change in the local dielectric environment caused by the
presence of an absorbing molecule or film on the surface of the resonator causes a frequency and amplitude shift in
resonant modes. This shift is detected using either FTIR or laser-based spectroscopy techniques. Localized polariton
nano-resonators in the IR can be realized using both SPP and SPhP modes in semiconductors – in this case we
examine structures formed with doped InAs112,113 or SiC14,114-116. InAs has a low electron effective mass and can be
doped over a large range of carrier concentrations, maximizing spectral tunability for associated SPP modes, while
these modes may also be spectrally tuned or modulated using continuous-wave visible excitation due to free carrier
injection as was recently demonstrated for InP.23 SiC can be grown on a wafer scale with long phonon lifetimes and
hence low material losses, featuring a Reststrahlen band in the long-wave IR.20,114,117 This makes both of these
materials ideal for localized surface polariton resonators.
27
Figure 6: a) Absorption and transmission spectra collected using an FTIR microscope from nanostructures fabricated from
highly doped InAs (Inset shows SEM image of sample at 45 degrees incidence). The simulated electromagnetic loss profiles
field profiles in b)-d) were calculated for the frequencies denoted in a). Figures reproduced with permission from Ref. 21 e)
Experimental and simulated long-wave IR spectra from periodic arrays of SiC nanopillars (inset: SEM image of representative
array), using an FTIR microscope. Two distinct resonances with significantly different electromagnetic field distributions were
observed, designated as the f) transverse dipole (TD) and g) monopole (M) resonances. Figure is reprinted with permission
from J.D. Caldwell, et al. Nano Letters 13(8), 3690-3697 (2013). Copyright 2013 American Chemical Society.59
In Ref. 21 films of InAs with various carrier concentrations were grown by MBE and subsequently patterned into
nanoresonators (inset Fig. 6a). The films were characterized by a combination of electrical transport measurements
and FTIR microscopy (Fig. 6a), which allowed accurate determination of the opto-electronic properties for each
sample. It was found that the plasma frequency could be tuned significantly by doping, from approximately 5-15
µm in free-space wavelength. This is critical for achieving resonances over a broad range of frequencies, however,
it should be noted that the mobility drops significantly as the doping density is increased. Resonators formed from
these films supported a localized SPP mode, which can be verified through careful comparison with numerical
simulations (Fig. 6b-d). Subsequent work112 demonstrated that by careful design of both the plasma frequency and
the resonator size, the polariton resonances can be tuned. Furthermore, the localized SPP modes were used to detect
the presence of a PMMA membrane, demonstrating the ability to create localized infrared surface sensors.112 It is
worth noting that similar results can be achieved by utilizing a grating geometry32, where almost perfect absorption
28
can be achieved, though the periodic nature of such sensors precludes the development of subwavelength
localization of the probe field in all three dimensions.
An alternative approach to obtain narrow-band polaritonic resonances is through the fabrication of such structures
using polar crystals capable of supporting SPhPs. Such resonators were fabricated into a SiC substrate using electron
beam lithography and reactive ion etching and characterized using FTIR microscopy.114 Extremely sharp resonances
were observed, with quality factors in excess of 100 and confinement factors of up to 200x smaller than the free
space wavelength reported, which occurs due to the inherently low losses of this material (See Fig. 6e). Subsequent
work on similar nanostructures in SiC were shown to have record quality factors in excess of 300,115 while work
within hBN nanostructures exhibited values as high as 286.60 Each of the different resonances is associated with a
different electromagnetic mode - which can be characterized by comparison against numerical simulations (Fig. 6f
and g). These resonances can be individually tuned to some degree by changing size or aspect ratio of the
particles,14,115,116,118 which can also be used to produce a dependence of the excited resonance on light
polarization.13,14,116,118 While the narrow spectral window in which these resonances can be measured notably limits
some applications, these extremely sharp resonances have continued to motivate the study of SPhP resonators. For
example, SPhPs in SiC have been exploited for surface sensing, with detection possible down to a few atomic
layers,5 while hBN resonators have been demonstrated for femtomolar sensitivity using the surface enhanced IR
absorption (SEIRA) effect.119
2. Investigating Narrow-band and Spatially Coherent Thermal Light Sources
The strong absorption of polaritonic modes, and the ability to engineer absorption by control of material properties
or nanostructure geometry offers an opportunity to engineer absorptive resonances and thus realize selective thermal
emission from the same surfaces when heated.12-14 Though thermal emitters are extremely inefficient light sources
(the incandescent light bulb being the most obvious example), at MIR wavelengths they provide reasonable power
densities across a broad range of wavelengths, and are thus ubiquitous in IR spectroscopy. However, as Kirchoff’s
law states, the emissivity of a reciprocal medium is equal to the absorption, thus, through polaritonic resonator
design, one can achieve narrow-band thermal emitters, rather than the broadband response typically observed with
incandescent light sources.
29
Figure 7: a) AFM topographical plot of a SiC grating used to demonstrate spatially coherent thermal emission in the long-
wave IR. The period was 0.55, with =11.36 µm. The ridges were etched to /. b) Polar plot of the thermal emission
spatial coherence at =11.04 (red), 11.36 (blue) and 11.86 µm. Experimental data extracted by specular reflectivity and
applying Kirchoff’s law are provided as the data points, while theoretical simulations are presented as the solid lines. Plots
reproduced from Ref.
12
.
Spectral and angular control of polarized thermal emission was demonstrated in 2002 by Greffet et al. using a SiC
surface that was patterned and etched into a periodic grating structure (Fig. 7a).
12
At wavelengths in the SiC
Reststrahlen band, the negative permittivity of the material enabled propagating SPhPs to be supported at the SiC/air
interface. Coupling from free space to the SPhP modes was achieved via the momentum matching provided by the
etched grating, with the coupling wavelength dependent upon the grating period at a specific angle. Conversely,
thermally excited SPhP modes are able to out-couple via the same mechanism. This resulted in a spatially coherent
light source with each of the SPhP frequencies emitted at a specific angle into free-space, dictated by the grating
pitch (Fig. 7b). Strong, narrow and spatially coherent emission peaks were observed by the authors, via angular-
and polarization-dependent FTIR emission and reflection spectroscopy, with the results matching well with the
simulated response. While random thermal motion should generally result in incoherent thermal emission, the
thermal excitation of a SPhP converts thermal energy into a delocalized collective and coherent oscillation, whose
spatial coherence is sufficient to allow for far-field interference of photons out-coupled from the periodic grating
structure. The demonstration of this coherent thermal emission came at an opportune time, with the fields of
metamaterials, metasurfaces, plasmonics and phononics providing numerous examples of structures and materials
with designable optical properties. In particular, due to the top-down nature of standard microelectronic fabrication
processes, engineering the optical properties of surfaces or few-layer patterned thin films allowed for rather
straightforward engineering of emissivity across the broad range of IR wavelengths.
50,120
Thermal emission from
patterned metallic films, via out-coupling of surface waves on the metal/air interface have been demonstrated from
periodic gratings,
12,67,121
bullseye structures,
122
and organ pipe resonators.
123
As discussed in Section II, the propagating polariton requires momentum matching to couple to free space. This
requirement allows for the highly directional nature of emission from periodically patterned surfaces, as well as the
30
ability to structure the far-field interference of scattered surface waves to form beaming or focusing structures.122,124
The spatial dependence of thermal emission will vary significantly as a function of emission wavelength, such that
the spatially integrated thermal emission from such a surface will be broadband in nature. Leveraging localized
polaritons, however, allows for spectrally distinct, but largely angle-independent, coupling to free space light. The
localized polariton analog of the patterned grating is the antenna, demonstrated initially in Ref. 13, which shows
spectrally distinct emission peaks from a single SiC whisker antenna. These resonant peaks correspond to various
antenna modes, even when thermal emission is collected by a high numerical aperture objective. Arrays of antenna
structures, or metal-insulator-metal resonators, allow for control of surface emissivity over large areas,14,70,125 with
the thermal emission spectra controlled across the MIR and even into the FIR via choice of materials and resonator
geometry.69
Recent efforts have explored the unique behavior associated with phononic and plasmonic materials at the LO
phonon or plasma frequency, respectively, where the permittivity of the material approaches zero and the material
behaves as an epsilon-near-zero, or ENZ, material. At the ENZ condition, the wavelength of a propagating mode in
the material is dramatically extended, and a quasi-uniform phase is observed across distances larger than multiple
free-space wavelengths.52 A thin film of ENZ material is able to support a unique propagating mode, referred to as
the Berreman mode,47,48,126 which can be thought of as a hybrid EM/bulk excitation polaritonic mode.47,48 Strong
coupling to the Berreman mode can be observed in planar structures,49,50,54 with momentum matching provided only
by the incidence angle of the free-space light, though out-coupling via patterned structures is also possible.127
Thermal emission from such layered structures is then monochromatic,53 due to the narrow spectral band where the
ENZ condition is fulfilled. Furthermore, the resonance frequency and linewidth can also be influenced further within
planar films through implementation of strong coupling between SPPs and ENZ polaritons in adjacent bilayers.49,55
3. Exploring Mid- to Far-IR Polaritons via s-SNOM
Overall, s-SNOM has been used for many of the initial investigations of polaritonic systems, as it provides a tool
that doesn’t require significant processing of the sample being studied to directly measure propagating and/or
localized polariton modes. This means that s-SNOM experiments do not directly study the properties of polaritonic
devices usable for far-field optics, but instead provide invaluable information about electromagnetic near fields and
materials properties. This has been demonstrated for chemical sensing,119 on-chip photonic structures128 and
proposed for photonic circuits based on transformation optics.129 Since its development, s-SNOM has been used for
measuring polaritons in semiconductor and polar dielectrics.20,45,94,95,97 However, while the initial studies provided
significant insights into these polaritonic modes, including propagation lengths, field confinement and the ability to
focus sub-diffractional modes,98 it was following the discovery of graphene130 that the application of this technique
for characterization of polaritonic systems expanded dramatically. Within the basis of two-dimensional van der
Waals materials and corresponding heterostructures,131 a broad array of polaritons have been identified,1 including
31
exciton, Cooper-pair and magnon polaritons in addition to the previously discussed SPPs and SPhPs. For these 2D
materials, the long-free space wavelengths coupled with the typically small-scale (microns to tens of microns) flakes
that result from exfoliation from the bulk crystals, made characterization of polaritonic effects using conventional
MIR spectroscopy difficult. The implementation of s-SNOM provided the means to overcome these limitations,
providing direct imaging of polariton waves at the length scales commensurate with the deeply sub-diffractional
compressed polariton wavelength, .36,132
The implementation of s-SNOM in characterizing polaritonic effects within 2D materials was initiated by the
seminal works of the Basov36 and Koppens/Hillenbrand groups,34 where SPPs within graphene were probed. While
previously there had been theoretical studies of polariton dispersion within graphene133 and experimental studies in
the far-field using nanoscale fabricated graphene resonators,134 the works by these two groups for the first time
directly imaged the SPP propagation within graphene. It should be noted that in later works,93,128 additional so-
called ‘edge-launched’ modes were observed due to direct launching of the polaritons from scattering of the incident
light off of the flake edge. Surface polaritons have also been preferentially launched in 2D materials such as hBN
via deposition of metallic pads on a portion of the flake, which in turn acts as the scattering site.46,93
In any of these approaches, the polariton decay rate and period can be extracted from the exponential decay of the
oscillating s-SNOM amplitude as a function of distance from the flake edge. This can be used to determine the
polariton propagation length and wavelength, and by extension, the carrier scattering rate and carrier concentration,
following the approaches described earlier (Fig. 5a-d). From these highlighted works, SPP wavelengths were
demonstrated as short as 260 nm, which is approximately 40x shorter than the free-space wavelength of the incident
light at the same frequency.34 Later efforts have demonstrated wavelength compression in excess of 26,000x.135
However, beyond providing a direct image of the SPP wave, the s-SNOM technique provides further diagnostic
insights for polaritonic systems and devices. Specifically, for graphene and doped semiconductors, this polariton
dispersion is directly dependent upon the Fermi energy. Essentially, with changing free carrier density, the slope of
the dispersion changes, becoming steeper with increasing density due to the increased plasma frequency of the
material.43 By controlling the free carrier density in situ, one can extract the Fermi-energy dependent changes in the
dispersion relationship, while also demonstrating the ability to actively tune the SPP response. This was
demonstrated in those seminal works by Chen et al.34 and Fei et al.36 via electrostatic gating, however, in subsequent
works this has also been demonstrated using optical pumping approaches.104 More recently, cryogenic measurement
schemes demonstrated the first observation of ballistic SPP propagation in graphene,136 perhaps approaching the
fundamental limit for graphene SPP performance.
4. Far-IR tunable ENZ Modulators
32
Numerous demonstrations of passive SPhP-supporting structures often offer lower loss analogs of plasmonic
phenomena, though at longer wavelengths (extending out to the FIR for traditional III-V materials).12,137 Ultimately,
the creation of active IR devices is much more technologically significant. Currently there are extremely limited
options for active modulation and control of MIR to FIR light, so the realization of such devices using polaritonic
modes would be of immediate importance. The development of active SPhP-based devices, however, can be
challenging, as they often require modulating relatively fixed quantities, such as the phonon energies or the
geometry of the polaritonic material or structure, respectively. However, the total permittivity of a polar material
will contain contributions from not only the phonon response, but also from the free carrier response and optical
transitions between electronic states. Thus, the permittivity of a phononic material can be controlled by increasing
the carrier density in the structure through the longitudinal optic phonon plasmon coupling (LOPC) effect,23,24
modulating the carrier populations of bound states in a QW, and thus the contributions from intersubband transitions
(ISBTs) to the dielectric tensor.
Leveraging the modulation from ISBTs requires a significant spatial overlap between the SPhP and the QW, which
for a single interface SPhP is difficult, as the spatial extent of SPhPs is at least an order of magnitude larger than
QW dimensions required for ISBTs at or near phonon energies.138 To overcome the lack of overlap in traditional
QW structures, the Greffet group took advantage of the ENZ polaritons within thin polar films.47 An ISBT in an
AlGaAs/GaAs QW between these interfaces is then used to electrically modulate the SPhP dispersion. Coupling to
the ENZ mode is achieved using the grating approach discussed in previous sections, and the dynamic control of
the near-ENZ permittivity via accumulation/depletion of the QW is observed by FTIR reflection spectroscopy from
the grating-coupled device. This work demonstrated significant modulation of reflectance, evidence for active
control of an optoelectronic device at the FIR phonon frequency of GaAs.
The experimental parameters in this example study demonstrate the significant challenges associated with FIR
measurements of polaritonic structures and devices. As stated in the supplemental material of Ref. 139, scans were
collected with the slowest FTIR scanner velocity and averaged over 512 scans, with each measurement taking over
3 hours. Considering the required single-beam reference spectrum for each sample spectrum and that a new sample
spectra and reference spectra is needed for every reflectance curve, a substantial amount of time is invested into
characterizing a single sample. Furthermore, if the device produces a significant amount of heat, long scan times
could further obfuscate the measurement spectra.
The realization of active SPhP devices demonstrates the unique opportunities available for new classes of devices
operating at FIR frequencies, where (relatively) small changes in carrier concentrations and the large oscillator
strength of ISBTs can dramatically alter the permittivity of a material. While SPhPs are ultimately relegated to the
rather narrow frequency range between or near the optic phonon frequencies, the hybridization of phononic, ISBT,
33
and free carrier responses43 does offer an opportunity to cover a broad range of FIR wavelengths with new classes
of optoelectronic devices.
V. CONCLUSION/SUMMARY
In this tutorial we have provided an overview of the various techniques available for characterizing surface
polaritons within the MIR to FIR. Specifically, we have detailed the methodology by which the polariton dispersion
and dependence upon various material properties can be quantified. The increased complexities that result for such
measurements in the MIR, and the increased complications that result in the FIR have been highlighted, with the
hope that this provides a more complete understanding for researchers entering this exciting area of science and
engineering, thereby shortening the learning curve. The manner in which these various techniques have been
implemented have been summarized for a few key examples, with the goal of providing direct context in how these
approaches can be realized. In conclusion, it is the authors’ hope that this tutorial can expand the basis of researchers
working in this field and thus increase the potential for advanced technologies and new physical insights in the
coming years.
ACKNOWLEDGEMENTS
JDC and TGF gratefully acknowledge support from the Office of Naval Research (N000141812107). The authors
(LN and DW) gratefully acknowledge support from the National Science Foundation (Award ECCS-1609912).
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