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Optical logic gates based on the transverse spin of structured optical fields
Abstract
The transverse spins of guided waves and surface waves are studied in a rigorous and unified manner. In particular, analytical derivations show that the transverse spin of guided waves also depends on the mean direction of propagation, which may have important applications in spin-dependent unidirectional optical interfaces. As an example of which, we propose two optical logic gates related to the transverse spin of guided waves, i.e., the XNOR and XOR gates, which are realized via the Y-shaped and the T-shaped waveguides, respectively. The extinction ratios of XNOR and XOR logic gates are 16 dB and 14 dB respectively. Our results may have potential application value in the design of nanoscale integrated all-optical logic gate devices.
... Many different structures have been proposed for the design of all-optical logic gates. The working mechanism of them is based mainly on the nonlinear optical effect in semiconductor waveguides [17][18][19] or the linear coherence effect in semiconductor or plasmonic waveguides [20,21], such as photonic crystals [19,22], silicon waveguides [6,23], metallic nanowires [24][25][26], metal-insulator-metal (MIM) waveguides [27,28], nanoantenna waveguides [29,30], and graphene waveguides [31,32]. Compared to nonlinear waveguides, linear waveguides can work at arbitrary field intensities, and they have more development potential in functionality and reliability. ...
In the past few years, designing multifunctional all-optical logic devices has attracted more and more attention in integrated optical computing. We report a metal–insulator–metal based four-port all-optical logic gate device containing two parallel straight waveguides and a ring resonator. We employ the scattering matrix method to analyze the coupling mechanisms of the hybrid waveguide and adopt the finite-difference time-domain method to design four fundamental logic functions of AND, OR, XOR, and NOT based on the all-optical coherent control of the four-port system under three symmetrically incident conditions. We demonstrate that these logic functions can be freely modulated by changing the phase difference of the input light at two resonant wavelengths or in a broad band. The logic gate device proposed shows a simple structure with multiple functions, multiple channels, and convenience in fabrication, and can be applied in parallel optical computing based on wavelength division multiplexing technology.
Radiation pressure is associated with the momentum of light, and it plays a crucial role in a variety of physical systems. It is usually assumed that both the optical momentum and the radiation-pressure force are naturally aligned with the propagation direction of light, given by its wavevector. Here we report the direct observation of an extraordinary optical momentum and force directed perpendicular to the wavevector, and proportional to the optical spin (degree of circular polarization). Such an optical force was recently predicted for evanescent waves and other structured fields. It can be associated with the ’spin-momentum’ part of the Poynting vector, introduced by Belinfante in field theory 75 years ago. We measure this unusual transverse momentum using a femtonewton-resolution nano-cantilever immersed in an evanescent optical field above the total internal reflecting glass surface. Furthermore, the measured transverse force exhibits another polarization-dependent contribution determined by the imaginary part of the complex Poynting vector. By revealing new types of optical forces in structured fields, our findings revisit fundamental momentum properties of light and enrich optomechanics.
Silicon-on-insulator Mach-Zehnder interferometer structures that utilize a photonic crystal nanobeam waveguide in each of two connecting arms are proposed here as efficient 2 × 2 resonant, wavelength-selective electro-optical routing switches that are readily cascaded into on-chip N × N switching networks. A localized lateral PN junction of length ~2 μm within each of two identical nanobeams is proposed as a means of shifting the transmission resonance by 400 pm within the 1550 nm band. Using a bias swing ΔV = 2.7 V, the 474 attojoules-per-bit switching mechanism is free-carrier sweepout due to PN depletion layer widening. Simulations of the 2 × 2 outputs versus voltage are presented. Dual-nanobeam designs are given for N × N data-routing matrix switches, electrooptical logic unit cells, N × M wavelength selective switches, and vector matrix multipliers. Performance penalties are analyzed for possible fabrication induced errors such as non-ideal 3-dB couplers, differences in optical path lengths, and variations in photonic crystal cavity resonances.
Maxwell’s equations, formulated 150 years ago, ultimately describe properties of light, from classical electromagnetism to
quantum and relativistic aspects. The latter ones result in remarkable geometric and topological phenomena related to the
spin-1 massless nature of photons. By analyzing fundamental spin properties of Maxwell waves, we show that free-space light
exhibits an intrinsic quantum spin Hall effect—surface modes with strong spin-momentum locking. These modes are evanescent
waves that form, for example, surface plasmon-polaritons at vacuum-metal interfaces. Our findings illuminate the unusual transverse
spin in evanescent waves and explain recent experiments that have demonstrated the transverse spin-direction locking in the
excitation of surface optical modes. This deepens our understanding of Maxwell’s theory, reveals analogies with topological
insulators for electrons, and offers applications for robust spin-directional optical interfaces.
Engineering photon emission and scattering is central to modern photonics applications ranging from light harvesting to quantum-information processing. To this end, nanophotonic waveguides are well suited as they confine photons to a one-dimensional geometry and thereby increase the light-matter interaction. In a regular waveguide, a quantum emitter interacts equally with photons in either of the two propagation directions. This symmetry is violated in nanophotonic structures in which non-transversal local electric-field components imply that photon emission and scattering may become directional. Here we show that the helicity of the optical transition of a quantum emitter determines the direction of single-photon emission in a specially engineered photonic-crystal waveguide. We observe single-photon emission into the waveguide with a directionality that exceeds 90% under conditions in which practically all the emitted photons are coupled to the waveguide. The chiral light-matter interaction enables deterministic and highly directional photon emission for experimentally achievable on-chip non-reciprocal photonic elements. These may serve as key building blocks for single-photon optical diodes, transistors and deterministic quantum gates. Furthermore, chiral photonic circuits allow the dissipative preparation of entangled states of multiple emitters for experimentally achievable parameters, may lead to novel topological photon states and could be applied for directional steering of light.
We show that the spin angular momentum (SAM) carried by a surface mode can be linked to the expectation value, with respect to the distribution of optical power flow, of its decay constant by itself or divided by the product of permittivity and permeability of the medium. Rewriting the formulas for the SAM of a surface mode using the relation between the SAM density and the Poynting vector and then normalizing the light field so that the surface mode carries unit power, we derive novel formulas that show the linear relation between the SAM and those expectation values. The effect of propagation loss is also discussed briefly.
Light carries spin and orbital angular momentum. These dynamical properties
are determined by the polarization and spatial degrees of freedom of light.
Modern nano-optics, photonics, and plasmonics, tend to explore subwavelength
scales and additional degrees of freedom of structured, i.e.,
spatially-inhomogeneous, optical fields. In such fields, spin and orbital
properties become strongly coupled with each other. We overview the fundamental
origins and important applications of the main spin-orbit interaction phenomena
in optics. These include: spin-Hall effects in inhomogeneous media and at
optical interfaces, spin-dependent effects in nonparaxial (focused or
scattered) fields, spin-controlled shaping of light using anisotropic
structured interfaces (metasurfaces), as well as robust spin-directional
coupling via evanescent near fields. We show that spin-orbit interactions are
inherent in all basic optical processes, and they play a crucial role at
subwavelength scales and structures in modern optics.
We show the existence of an inherent property of evanescent electromagnetic waves: spin-momentum locking, where the direction of momentum fundamentally locks the polarization of the wave. We trace the ultimate origin of this phenomenon to complex dispersion and causality requirements on evanescent waves. We demonstrate that every case of evanescent waves in total internal reflection (TIR), surface states, and optical fibers/waveguides possesses this intrinsic spin-momentum locking. We also introduce a universal right-handed triplet consisting of momentum, decay, and spin for evanescent waves. We derive the Stokes parameters for evanescent waves, which reveal an intriguing result—every fast decaying evanescent wave is inherently circularly polarized with its handedness tied to the direction of propagation. We also show the existence of a fundamental angle associated with TIR such that propagating waves locally inherit perfect circular polarized characteristics from the evanescent wave. This circular TIR condition occurs if and only if the ratio of permittivities of the two dielectric media exceeds the golden ratio. Our work leads to a unified understanding of this spin-momentum locking in various nanophotonic experiments and sheds light on the electromagnetic analogy with the quantum spin-Hall state for electrons.
We review basic physics and novel types of optical angular momentum. We start
with a theoretical overview of momentum and angular momentum properties of
generic optical fields, and discuss methods for their experimental
measurements. In particular, we describe the well-known longitudinal (i.e.,
aligned with the mean momentum) spin and orbital angular momenta in polarized
vortex beams. Then, we focus on the transverse (i.e., orthogonal to the mean
momentum) spin and orbital angular momenta, which were recently actively
discussed in theory and observed in experiments. First, the recently-discovered
transverse spin angular momenta appear in various structured fields: evanescent
waves, interference fields, and focused beams. We show that there are several
kinds of transverse spin angular momentum, which differ strongly in their
origins and physical properties. We describe extraordinary features of the
transverse optical spins and overview recent experiments. In particular, the
helicity-independent transverse spin inherent in edge evanescent waves offers
robust spin-direction coupling at optical interfaces (the quantum spin Hall
effect of light). Second, we overview the transverse orbital angular momenta of
light, which can be both extrinsic and intrinsic. These two types of the
transverse orbital angular momentum are produced by spatial shifts of the
optical beams (e.g., in the spin Hall effect of light) and their Lorentz
boosts, respectively. Our review is underpinned by a unified theory of the
angular momentum of light based on the canonical momentum and spin densities,
which avoids complications associated with the separation of spin and orbital
angular momenta in the Poynting picture. It allows us to construct
comprehensive classification of all known optical angular momenta based on
their key parameters and main physical properties.
It has been known for a long time that light carries both linear and angular
momenta parallel to the direction of propagation. However, only recently it has
been pointed out that beams of light, under certain conditions, may exhibit a
transverse spin angular momentum perpendicular to the propagation direction.
When this happens, the electric field transported by the light rotates around
an axis transverse to the beam path. Such kind of fields, although deceptively
elusive, are almost ubiquitous in optics as they manifests in strongly focused
beams, plasmonic fields and evanescent waves. In this work we present a general
formalism describing all these phenomena. In particular, we demonstrate how to
mathematically generate a wave field possessing transverse spin angular
momentum density, from any arbitrarily given scalar wave field, either
propagating and evanescent.
In this paper, we have proposed an ultra-compact surface plasmonic two-mode interference (SPTMI) coupler having a silicon core, silver upper and lower cladding, and GaAsInP left and right cladding for basic logic gate operations. By modulating the refractive index of the GaAsInP cladding with incidence of optical pulse energy, we have shown coupling characteristics depending on additional phase change between the excited surface plasmon polariton modes propagating through the silicon core. By using applied optical pulse dependent coupling behavior of the proposed SPTMI device, the operations of NOT, AND, and OR logic gates are shown. It is also seen that the coupling length of the proposed device is 32.3 times more compact than that of a multimode interference-directional coupler.
The spin of light in subwavelength-diameter waveguides can be orthogonal to the propagation direction of the photons because of the strong transverse confinement. This transverse spin changes sign when the direction of propagation is reversed. Using this effect, we demonstrate the directional spontaneous emission of photons by laser-trapped caesium atoms into an optical nanofibre and control their propagation direction by the excited state of the atomic emitters. In particular, we tune the spontaneous emission into the counter-propagating guided modes from symmetric to strongly asymmetric, where more than % of the optical power is launched into one or the other direction. We expect our results to have important implications for research in quantum nanophotonics and for implementations of integrated optical signal processing in the quantum regime.
The spin Hall effect leads to the separation of electrons with opposite spins in different directions perpendicular to the electric current flow because of interaction between spin and orbital angular momenta. Similarly, photons with opposite spins (different handedness of circular light polarization) may take different trajectories when interacting with metasurfaces that break spatial inversion symmetry or when the inversion symmetry is broken by the radiation of a dipole near an interface. Here we demonstrate a reciprocal effect of spin-orbit coupling when the direction of propagation of a surface plasmon wave, which intrinsically has unusual transverse spin, determines a scattering direction of spin-carrying photons. This spin-orbit coupling effect is an optical analogue of the spin injection in solid-state spintronic devices (inverse spin Hall effect) and may be important for optical information processing, quantum optical technology and topological surface metrology.
It is well-known, since the seminal works by J.H. Poynting, that light
carries momentum and angular momentum (AM). Typical plane-wave or Gaussian-beam
states exhibit longitudinal momentum associated with the wave vector and also
longitudinal spin AM associated with the degree of circular polarization
(helicity). Locally, optical momentum and angular-momentum densities can
demonstrate unusual features which have recently attracted considerable
attention: `super-momentum' with values higher than \hbar*k per photon,
transverse helicity-independent spin AM, and transverse helicity-dependent
momentum. So far, such abnormal momentum and spin properties have appeared only
in special field configurations, namely, evanescent waves and optical vortices.
Here we find that the simplest propagating non-singular field -- two
interfering plane waves -- also exhibits a variety of extraordinary spin and
momentum properties. Despite the seemingly planar and thoroughly-studied
character of the two-wave system, we discover that such field possesses a
transverse (out-of-plane) helicity-independent spin AM, and also a transverse
polarization-dependent momentum with unusual physical properties.
Nanophotonic structures are routinely used to enhance light matter
interactions by modifying the density of virtual photon states. This is often
simplified to a scalar quantity, the local density of states (LDOS). However we
show that the virtual photons also contain phase information. We show that the
phase information of an emitter interacting with a modified density of virtual
photon states has a non-trivial, non-intuitive behaviour. This extra phase
information is vital in practical design of integrated quantum photonic
circuits. We consider a quantum dot (QD) electron spin transition in a photonic
crystal waveguide (PhCWG). The mode of a PhCWG is complex with local
polarization variation across the crystal lattice. By placing the QD at a
polarization singularity in the photonic mode, we show unidirectional emission,
with a one-to-one correlation of spin orientation to path. We show a range of
new functionalities suited to integrated photonic circuits, including
spin-photon interfaces and photonic cluster state generation.
Momentum and spin represent fundamental dynamic properties of quantum particles and fields. In particular, propagating optical waves (photons) carry momentum and longitudinal spin determined by the wave vector and circular polarization, respectively. Here we show that exactly the opposite can be the case for evanescent optical waves. A single evanescent wave possesses a spin component, which is independent of the polarization and is orthogonal to the wave vector. Furthermore, such a wave carries a momentum component, which is determined by the circular polarization and is also orthogonal to the wave vector. We show that these extraordinary properties reveal a fundamental Belinfante's spin momentum, known in field theory and unobservable in propagating fields. We demonstrate that the transverse momentum and spin push and twist a probe Mie particle in an evanescent field. This allows the observation of 'impossible' properties of light and of a fundamental field-theory quantity, which was previously considered as 'virtual'.
Metal surfaces structured at a scale below the wavelength of light create devices that control plasmon beam direction through their polarization.
We present a space-time generalization of the known spatial (monochromatic) wave vortex beams carrying intrinsic orbital angular momentum (OAM) along the propagation direction. Generic spatiotemporal vortex beams are polychromatic and can carry intrinsic OAM at an arbitrary angle to the mean momentum. Applying either (i) a transverse wave-vector shift or (ii) a Lorentz boost to a monochromatic Bessel beam, we construct a family of either (i) time-diffracting or (ii) nondiffracting spatiotemporal Bessel beams, which are exact solutions of the Klein-Gordon wave equations. The proposed spatiotemporal OAM states are able to describe either photon or electron vortex states (both relativistic and nonrelativistic) and have potential applications in particle collisions, optics of moving media, quantum communications, and astrophysics.
We consider a p-polarized surface electromagnetic wave (a classical surface polariton) at the interface between the vacuum and a metal or left-handed medium. We show that the evanescent electromagnetic waves forming the surface polariton inevitably possess a backward spin energy flow, which, together with a superluminal orbital energy flow, form the total Poynting vector. This spin energy flow generates a well-defined (but not quantized) spin angular momentum of surface polaritons which is orthogonal to the propagation direction. The spin of evanescent waves arises from the imaginary longitudinal component of the electric field which makes the polarization effectively elliptical in the propagation plane. We also examine the connection between the spin and chirality of evanescent modes.
The concept of angular momentum is ubiquitous to many areas of physics. In
classical mechanics, a system may possess an angular momentum which can be
either transverse (e.g., in a spinning wheel) or longitudinal (e.g., for a
fluidic vortex) to the direction of motion. Photons, however, are well-known to
exhibit intrinsic angular momentum which is longitudinal only: the spin angular
momentum defining the beam polarization and the orbital angular momentum
associated with a spiraling phase front. Here we show that it is possible to
generate a novel state of light that contains purely transverse angular
momentum, the analogue of a spinning mechanical wheel. We use an optical
nano-probing technique to experimentally demonstrate its occurrence in our
setup. Such a state of light can provide additional rotational degree of
freedom in optical tweezers and optical manipulation.
In this paper, we have introduced optically controlled two-mode interference (OTMI) coupler having silicon core and GaAsInP cladding as an all-optical switch. By taking advantage of refractive index modulation by launching optical pulse into cladding region of TMI waveguide, we have shown optically controlled switching operation. We have studied optical pulse-controlled coupling characteristics of the proposed device by using a simple mathematical model on the basis of sinusoidal modes. The device length is less than that of previous work. It is also seen that the cross talk of the OTMI switch is not significantly increased with fabrication tolerances () in comparison with previous work.
We develop the quantum theory of transverse angular momentum of light beams.
The theory applies to paraxial and quasi-paraxial photon beams in vacuum, and
reproduces the known results for classical beams when applied to coherent
states of the field. Both the Poynting vector, alias the linear momentum, and
the angular momentum quantum operators of a light beam are calculated including
contributions from first-order transverse derivatives. This permits a correct
description of the energy flow in the beam and the natural emergence of both
the spin and the angular momentum of the photons. We show that for collimated
beams of light, orbital angular momentum operators do not satisfy the standard
commutation rules. Finally, we discuss the application of our theory to some
concrete cases.
In this paper, an optical controlled surface plasmonic two mode interference (SPTMI) structure based on silicon waveguide has been proposed for all optical switching. We have shown cross and bar state switching characteristics depending on additional phase between the excited SPP modes propagating through the silicon core obtained due to refractive index modulation of GaAsInP cladding with incidence of optical pulse of width ∼1 ps. It is also seen that the coupling length of the proposed device is ∼33 times compact than that of the existing multimode interference-directional coupler. The deviation of crosstalk of the SPTMI switch with increase of fabrication tolerances (±δw) is also almost to that of previously reported all optical switch.
Scientists have known for more than a century that light possesses both linear and angular momenta along the direction of propagation. However, only recent advances in optics have led to the notion of spinning electromagnetic fields capable of carrying angular momenta transverse to the direction of motion. Such fields enable numerous applications in nano-optics, biosensing and near-field microscopy, including three-dimensional control over atoms, molecules and nanostructures, and allowing for the realization of chiral nanophotonic interfaces and plasmonic devices. Here, we report on recent developments of optics with light carrying transverse spin. We present both the underlying principles and the latest achievements, and also highlight new capabilities and future applications emerging from this young yet already advanced field of research.
Evanescent electromagnetic waves possess spin-momentum locking, where the
direction of propagation (momentum) is locked to the inherent polarization of
the wave (transverse spin). We study the optical forces arising from this
universal phenomenon and show that the fundamental origin of recently reported
non-trivial optical chiral forces is spin-momentum locking. For evanescent
waves, we show that the direction of energy flow, direction of decay, and
direction of spin follow a right hand rule for three different cases of total
internal reflection, surface plasmon polaritons, and mode of an
optical fiber. Furthermore, we explain how the recently reported phenomena of
lateral optical force on chiral and achiral particles is caused by the
transverse spin of the evanescent field and the spin-momentum locking
phenomenon. Finally, we propose an experiment to identify the unique lateral
forces arising from the transverse spin in the optical fiber and point to
fundamental differences of the spin density from the well-known orbital angular
momentum of light. Our work presents a unified view on spin-momentum locking
and how it affects optical forces on chiral and achiral particles.
Light emitted near an optical waveguide is captured and equally split into two modes with opposite directions of propagation. By controlling the dipole spin of the emitter, it is possible to break this symmetry and select only one direction.
We generate tightly focused optical vector beams whose electric fields spin
around an axis transverse to the beams' propagation direction. We
experimentally investigate these fields by exploiting the directional
near-field interference of a dipole-like plasmonic field probe, placed adjacent
to a dielectric interface, which depends on the transverse electric spin
density of the excitation field. Near- to far-field conversion mediated by the
dielectric interface enables us to detect the directionality of the emitted
light in the far-field and, therefore, to measure the transverse electric spin
density with nanoscopic resolution. Finally, we determine the longitudinal
electric component of Belinfante's elusive spin momentum density, a solenoidal
field quantity often referred to as 'virtual'.
Controlling the flow of light with nanophotonic waveguides has the potential of transforming integrated information processing.
Because of the strong transverse confinement of the guided photons, their internal spin and their orbital angular momentum
get coupled. Using this spin-orbit interaction of light, we break the mirror symmetry of the scattering of light with a gold
nanoparticle on the surface of a nanophotonic waveguide and realize a chiral waveguide coupler in which the handedness of
the incident light determines the propagation direction in the waveguide. We control the directionality of the scattering
process and can direct up to 94% of the incoupled light into a given direction. Our approach allows for the control and manipulation
of light in optical waveguides and new designs of optical sensors.
We evaluate optical forces and torques induced by a surface plasmon to a
sphere of arbitrary size, i.e. beyond the point-like dipolar limit. Through a
multipolar decomposition of the plasmonic field, we demonstrate that the
induced torque is purely transverse to the plasmon propagation direction. Our
approach removes the inherent ambiguities of the dipolar regime with respect to
rotations and emphasizes the crucial role played by dissipation in the onset of
the plasmonic torque. We also give realistic estimates of such plasmon-induced
spinning of gold spheres immersed in water or air.
We present a method for exciting surface plasmon polaritons (SPPs) caused by a magnetic field component perpendicular to the direction of slit. The excitation mechanism is based on the spatially oscillating induced current along the edges of the slit under obliquely incident electromagnetic waves. Our finding distinguishes itself from previous mechanisms based on transverse electric fields and unveils the missing point of the SPP-excitation problem in a nanoslit. The use of a magnetic field for SPP excitation can be highly efficient and even comparable to that with an electric field, so that their composition can lead to selective unidirectional excitation.
The optical constants n and k were obtained for the noble metals (copper, silver, and gold) from reflection and transmission measurements on vacuum-evaporated thin films at room temperature, in the spectral range 0.5-6.5 eV. The film-thickness range was 185-500 Å. Three optical measurements were inverted to obtain the film thickness d as well as n and k. The estimated error in d was ± 2 Å, and that in n, k was less than 0.02 over most of the spectral range. The results in the film-thickness range 250-500 Å were independent of thickness, and were unchanged after vacuum annealing or aging in air. The free-electron optical effective masses and relaxation times derived from the results in the near infrared agree satisfactorily with previous values. The interband contribution to the imaginary part of the dielectric constant was obtained by subtracting the free-electron contribution. Some recent theoretical calculations are compared with the results for copper and gold. In addition, some other recent experiments are critically compared with our results.
Controlling Light Propagation
Surface plasmons are light-induced collective electronic excitations in a metal that offer the possibility of manufacturing optoelectronic devices at nanometer scale. Before such shrinking can be achieved, the propagation direction and lifetime of the plasmonic excitations have to be controlled (see the Perspective by Miroshnichenko and Kivshar ). Rodríguez-Fortuño et al. (p. 328 ) show how this is done using polarized light. Alternatively, using an array of metallic nanoantennae (in this case, slits) patterned into a thin gold film, Lin et al. (p. 331 ) present a further improvement on current plasmonic coupling schemes that has the potential to encode information contained in both the intensity and polarization of light.
The polarization state of a surface mode is a hybrid between linear and elliptical states, meaning that although one of its electric- and magnetic-field components is linearly polarized, the other rotates on the transverse-longitudinal plane, effectively in its elliptical polarization state. We show that the rotation of the electric-field component can induce transverse spin angular momentum of the surface mode. The rotation of the magnetic-field component, however, cannot generate the spin. We argue that this results from the fact that the rotation direction of the magnetic field is invariant under time reversal.
We demonstrate tunable frequency-converted light mediated by a chi-(2)
nonlinear photonic crystal nanocavity. The wavelength-scale InP-based cavity
supports two closely-spaced localized modes near 1550 nm which are resonantly
excited by a 130 fs laser pulse. The cavity is simultaneously irradiated with a
non-resonant probe beam, giving rise to rich second-order scattering spectra
reflecting nonlinear mixing of the different resonant and non-resonant
components. In particular, we highlight the radiation at the sum frequencies of
the probe beam and the respective cavity modes. This would be a useful,
minimally-invasive monitor of the joint occupancy state of multiple cavities in
an integrated optical circuit.
We present a novel fundamental phenomenon occurring when a polarized beam of light is observed from a reference frame tilted with respect to the direction of propagation of the beam. This effect has a purely geometric nature and amounts to a polarization-dependent shift or split of the beam intensity distribution evaluated as the time-averaged flux of the Poynting vector across the plane of observation. We demonstrate that such a shift is unavoidable whenever the beam possesses a nonzero transverse angular momentum. This latter result has general validity and applies to arbitrary systems such as, e.g., electronic and atomic beams.
Optical diode based on the chirality of guided photons
- C Sayrin
- C Junge
- R Mitsch
- B Albrecht
- D Shea
- P Schneeweiss
- J Volz
Nanophotonic control of circular dipole emission: towards a scalable solid-state to flying-qubits interface
- Feber