Compact Bragg gratings for long-range surface plasmon polaritons

Abstract

By introducing periodic thickness modulation of thin metal stripes embedded in a dielectric, compact and efficient Bragg gratings for long-range surface plasmon polaritons (LR-SPPs) operating around 1550 nm are realized. Reflection and transmission spectra of the gratings having different lengths (from 20 to 160 μm), heights (tens of nanometers), and widths of the metal ridges forming the grating were measured, and the reflectivity of up to 60% and bandwidths ranging from 5 to 40 nm are demonstrated. By using a simple lossless-uniform-grating description, the effective refractive-index modulation in LR-SPP gratings is estimated to be of the order of 10^-2, and two different approaches for these calculations are compared. The LR-SPP loss incurred in the investigated gratings is also discussed.

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912 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 2, FEBRUARY 2006
Compact Bragg Gratings for Long-Range
Surface Plasmon Polaritons
Alexandra Boltasseva, Sergey I. Bozhevolnyi, Thomas Nikolajsen, and Kristjan Leosson
Abstract—By introducing periodic thickness modulation of
thin metal stripes embedded in a dielectric, compact and effi-
cient Bragg gratings for long-range surface plasmon polaritons
(LR-SPPs) operating around 1550 nm are realized. Reflection
and transmission spectra of the gratings having different lengths
(from 20 to 160 µm), heights (tens of nanometers), and widths
of the metal ridges forming the grating were measured, and the
reflectivity of up to 60% and bandwidths ranging from 5 to 40 nm
are demonstrated. By using a simple lossless-uniform-grating de-
scription, the effective refractive-index modulation in LR-SPP
gratings is estimated to be of the order of 10−2, and two different
approaches for these calculations are compared. The LR-SPP loss
incurred in the investigated gratings is also discussed.
Index Terms—Integrated optics devices, multiple scattering,
surface plasmons.
I. INTRODUCTION
I
so-called surface plasmon polaritons (SPPs) [1], have attracted
much interest in the context of highly integrated photonic de-
vices and nanooptics [2]. For these waves, the electromagnetic
field amplitudes are strongly enhanced at the interface and
decay exponentially into both of the neighboring media [1].
These features make SPPs very sensitive to surface features
allowing one to efficiently control the SPP propagation in
the surface plane by using different types of surface metal
nanostructures[2]–[7].However,SPPssufferfromratherstrong
damping due to absorption in metals (ohmic loss) so that their
propagation length is limited to micrometer distances (∼ 30 µm
in visible and ∼ 300 µm in near infrared, for a silver–air
interface). Moreover, SPPs are rather difficult to excite by the
conventional end-fire coupling of radiation with single-mode
fibers; and more elaborate schemes (grating or prism coupling)
are to be used.
The SPP characteristics change drastically in the symmetric
configuration of two very close metal–dielectric interfaces, e.g.,
the surfaces of a thin metal film embedded in dielectric. Such
a structure supports propagation of the field-symmetric modal
N RECENT years, surface-bound electromagnetic excita-
tions propagating along the metal–dielectric interface, the
Manuscript received June 21, 2005; revised September 21, 2005.
A. Boltasseva is with the Department of Communications, Optics, and
Materials, COM DTU, Nano DTU, Technical University of Denmark, Kongens
Lyngby DK-2800, Denmark (e-mail: aeb@com.dtu.dk).
S. I. Bozhevolnyi is with the Department of Physics and Nanotechnol-
ogy, Aalborg University, Aalborg Øst DK-9220, Denmark (e-mail: sergey@
physics.aau.dk).
T. Nikolajsen is with the Crystal Fibre A/S, Birkerød DK-3460, Denmark
(e-mail: tni@crystal-fibre.com).
K. Leosson is with the Science Institute, University of Iceland, Reykjavik
IS-107, Iceland (e-mail: k.leosson@raunvis.hi.is).
Digital Object Identifier 10.1109/JLT.2005.862470
solution, the so-called a long-range SPP (LR-SPP), whereby
a coupling of SPPs at two metal–dielectric interfaces results
in a very small field concentration within the central metal
film and, hence, low propagation loss for the LR-SPP [8]–[10].
Furthermore, for a metal stripe embedded in the dielectric,
the dimensions of the metal stripe can be chosen so that the
LR-SPP field distribution matches that of a single-mode fiber,
facilitating the efficient end-fire excitation with the coupling
loss being less than 1 dB per facet [11], [12].
LR-SPP stripe waveguides thereby constitute a new alter-
native for integrated optical (IO) circuits with one unique
feature—the possibility of using the same metal-stripe circuitry
for both guiding optical radiation and transmitting electri-
cal signals that control its guidance. Different LR-SPP-based
passive IO components, including straight and bent wave-
guides, Y-splitters, and directional couplers, have been recently
experimentally demonstrated [12], [13]. In addition, efficient
LR-SPP-based dynamic devices with low power consump-
tion, including various modulators and switches, have been
also realized utilizing the thermooptic effect in the polymer
cladding [14], [15]. After different passive and active LR-SPP-
based components for IO have been demonstrated, it seems
natural to study Bragg gratings based on LR-SPP-supporting
configurations, having in mind great interest in Bragg grat-
ings for broad range of applications in distributed feedback
(DFB) and distributed Bragg reflection (DBR) lasers, Bragg fil-
ters, (de)multiplexers, etc. Our preliminary investigations have
verified the feasibility of realization of efficient Bragg gratings
for LR-SPP stripe waveguides [16]. Recently, another approach
for making Bragg gratings for LR-SPPs, which is different from
the one described in [16] and here, was reported [17].
In this paper, we report in detail on the fabrication and optical
characterization at telecom wavelengths of compact LR-SPP
ridge gratings formed by the periodical thickness modulation
of metal stripes and present a simple analysis of the results
obtained. We investigate the LR-SPP transmission through and
reflection from gratings with different parameters at telecom
wavelengths and compare the performance of the gratings
with the behavior of a lossless uniform grating. The paper is
organized as follows. In Section II, the fabrication procedure
for making metal ridge gratings is described. Section III is
devoted to the experimental part of our work. First, the ex-
perimental setup is described. Secondly, experimental spectra
for the LR-SPP transmission through and reflection from grat-
ings are shown for different grating parameters. Experimental
results for losses introduced by such gratings are also presented
and discussed. Comparison with a lossless uniform grating is
presented in Section IV, where the effective refractive-index
0733-8724/$20.00 © 2006 IEEE
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BOLTASSEVA et al.: COMPACT BRAGG GRATINGS FOR LONG-RANGE SURFACE PLASMON POLARITONS913
Fig. 1.
periodic symmetric ridges protruding from a metal film embedded in dielectric.
Schematic (side view) of the ridge grating for LR-SPPs formed by
modulation in investigated metallic gratings is calculated using
two different methods. Finally, we summarize the results and
offer our conclusions in Section V.
II. DESIGN AND FABRICATION
The investigated grating structures for LR-SPPs were fab-
ricated using the electron-beam lithography (EBL). First, a
silicon substrate was first spin coated with a 15-µm-thick ben-
zocyclobutene (BCB) polymer layer followed by soft baking of
the polymer. Prior to the EBL, the wafer with polymer cladding
was coated with positive electron beam followed by resist
prebaking. Then the designed grating pattern was transferred
into the resist by EBL exposure and development processes.
In order to transfer the pattern into the BCB layer, a reactive
ion etching (RIE) technique was used. After RIE of the BCB
layer with the electron-beam resist as a mask, ridges were
formed by metal (gold) deposition [deposited gold thickness
htotal(see Fig. 1) from 10 to 60 nm] and lift-off. Since vertical
symmetry of the structure is very important for the LR-SPP
propagation [8] and scattering, the etch depth was measured
using an atomic force microscope (AFM). This allowed to
choose the appropriate gold thickness as doubled etch depth
to obtain ridges of different heights (htotal/2) placed symmet-
rically above and below the LR-SPP propagation plane. After
metal deposition, the profile of the gold ridges was studied
using AFM [Fig. 2(a)] in order to obtain the precise values
of the ridge heights on each side of the waveguide plane
[28 nm above and 32 nm below for the structure in Fig. 2(a)
where 60 nm of gold was deposited] as well as to estimate
the roughness of the metal surface (of the order of a few
namnometers). For fabricated grating structures, the asymmetry
of the ridges with respect to the waveguide plane was be-
low 15%. 40-µm-long ridges of different widths from 125 to
375 nm (filling factors, defined as a ratio between the ridge
width and the grating period, w/Λ, from 0.25 to 0.75) were
arranged in 500-nm-period gratings of different lengths having
from 20 to 160 periods. For the approximate value n ≈ 1.53 of
the BCB refractive index found in the BCB data sheet [18], this
period (Λ) was expected to result in the efficient reflection oc-
curring at the Bragg wavelength λB≈ 2nΛ ≈ 1.53 µm. After
thegratingfabrication,LR-SPPstripewaveguides,placedinthe
middleofthegratings[Fig.2(b)],werepatternedusingstandard
ultraviolet (UV) lithography. Gratings were made wide enough
(the length of the ridges, as mentioned above, was 40µm) to en-
sure the full overlap with the LR-SPP mode propagating along
the 8-µm-wide stripe and to increase tolerance for aligning the
Fig. 2.
using atomic force microscopy (the total height of the ridges is approximately
60 to 32 nm below the waveguide plane and 28 nm above) together with the
(b) optical microscope image showing the top view of the 40-µm-wide and
80-µm-long ridge grating placed in the middle of an 8-µm-wide stripe.
(a) Profile of the ridges on one side of the waveguide plane obtained
UV mask with stripe waveguides with respect to EBL-patterned
gratings. A second metallization and lift-off was used to pattern
gold stripes, being approximately 15 nm in thickness (t) (see
Fig. 1) and typically 8 µm in width, which ensured low-loss
LR-SPP propagation and efficient radiation (in/out) coupling
with single-mode fibers [11], [12]. The last processing step
consisted of spin coating the wafer with another 15-µm-thick
BCB layer. After final polymer curing, the wafer was cut into
individual samples.
III. EXPERIMENTAL RESULTS
A. Experimental Arrangement
Optical characterization of the fabricated LR-SPP gratings
was carried out using standard spectrally resolved transmis-
sion and reflection measurements (Fig. 3). The light from a
broadband source based on edge-emitting light-emitting diode
(EE-LED) (1.55 µm) was sent through a polarization con-
troller (to adjust the electric field polarization perpendicular
to the stripe-waveguide plane) and launched into the LR-SPP
waveguide via butt coupling from a polarization-maintaining
single-mode fiber. In order to strip off all light coupled into the
fiber cladding, 1 km of coiled standard single-mode fiber was
used as out-coupling fiber. The output signal was detected by
an optical spectrum analyzer.
The grating transmission spectra were normalized to the
reference stripe transmission, thereby canceling out the prop-
agation and coupling losses. The reflection spectra were nor-
malized to the reflection from the mirror and corrected by
the approximate values of coupling and propagation loss for
LR-SPP waveguides. This was done in the following manner.
First, the coupling loss was measured independently for 8-µm-
wide stripe waveguides (which did not contain any gratings on
them) and found to be 0.6 ± 0.1 dB per facet. After that, for
each set of the grating parameters (ridge height, filling factor,
and grating length), the reflection spectra from four identical
gratings placed at four different distances (2, 4, 6, and 8 mm)
from the input plane to the grating were measured. This allowed
to estimate the value of the propagation loss for each particular
sample that was found to be of the order of 8 dB/cm. As a
final step, for each set of the grating parameters, the reflection
from a grating placed 2 mm from the input plane was first
corrected by the reflection from the mirror (100% reflection),
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914JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 2, FEBRUARY 2006
Fig. 3.Scheme of the experimental arrangement for the reflection and transmission measurements (PC: polarization controller; OSA: optical spectrum analyzer).
Fig. 4.
long gratings with different heights of the ridges (htotal). Grating period is
500 nm and filling factor is 0.45.
Measured (a) reflection and (b) transmission spectra for the 40-µm-
then the correction was made for doubled coupling loss and the
propagation loss over 4 mm of the stripe waveguide.
B. Reflection and Transmission Spectra
Typical reflection and transmission spectra are presented in
Figs. 4 and 5 for different heights of the ridges and two different
grating lengths. All in all, the investigated gratings showed the
behavior expected from conventional dielectric Bragg gratings
[19], with the Bragg wavelength being close to that estimated
above (a small offset is most probably related to the difference
in the BCB refractive index from the data sheet value as
discussed in [16]). It is also seen that, for the total ridge height
below 40 nm, the grating strength is proportional to the ridge
height (Figs. 4 and 5). For such low ridges, the gap in trans-
mission and the peak in reflection increase with the increase of
the ridge height. As seen in Figs. 4 and 5, one can increase
Fig. 5.
long gratings. All else is as in Fig. 4.
Measured (a) reflection and (b) transmission spectra for the 80-µm-
the grating strength either by increasing the grating length
or making higher ridges (increasing the effective refractive-
index modulation). With the increase of grating length, the
maximum reflection gradually increases until it reaches sat-
uration (Fig. 6). At the same time, the transmission dip also
evolves with the grating length, exhibiting progressively larger
contrast. However, due to simultaneously increasing absorption
and scattering losses, the transmission level decreases at all
wavelengths—also outside the Bragg resonance. For the same
grating length, the gratings become stronger when increasing
the ridge height that leads to both larger effective refractive-
index modulation and larger insertion (scattering and absorp-
tion) losses, resulting, in turn, in broadening of the reflection
peak and faster saturation (Fig. 6). Thus, for the total ridge
height of more than 40 nm, the maximum reflection never
exceeds 60% due to the fact of increased absorption and scat-
tering loss for high ridges, where the out-of-plane scattering
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BOLTASSEVA et al.: COMPACT BRAGG GRATINGS FOR LONG-RANGE SURFACE PLASMON POLARITONS 915
Fig. 6.
ridges (htotal). All else is as in Fig. 4.
Maximum reflection versus grating length for different heights of the
gradually takes over and both transmission and reflection char-
acteristics become progressively distorted (Figs. 4 and 5).
One of the characteristic features in the behavior of the
investigated gratings is an asymmetry in the spectra with re-
spect to the Bragg wavelength. The asymmetry is getting more
pronounced with the increase of heights of the ridges (Figs. 4
and 5). Due to the asymmetry, the Bragg wavelength was
found to shift into shorter wavelengths with the increase in the
grating length [16]. This asymmetry is thought to be related
to two different loss mechanisms in such gratings—absorption
in metal and out-of-plane scattering. These two effects were
described in more detail and compared with the results of
theoretical modeling in [16], where it was shown that the loss
introduced by the grating is dominated by the out-of-plane
scattering. The latter can be decomposed into the coherent
scattering, i.e., the directional LR-SPP diffraction out of the
plane by the grating, and the diffuse LR-SPP scattering by
individual metal ridges. The first process removes the radiation
out of the propagation plane only for the wavelengths below
the Bragg wavelength, while the diffuse scattering occurs at all
wavelengths (though it is expected to gradually increase toward
shorter wavelengths) [16]. The described difference in loss
contributions below and above the Bragg wavelength gives rise
to different transmission loss levels outside the Bragg condition
observed for all investigated gratings (Figs. 4 and 5).
The increase in the grating length not only increases its
maximum reflectivity at the Bragg wavelength but also narrows
the spectral width of Bragg resonance, at least for relatively low
ridges (cf. Figs. 4 and 5). The interplay between the grating
length and the resonance bandwidth for different ridge heights
is most transparent in the dependence of the bandwidth–length
product that is expected to be constant, i.e., δλL ∼ (λB/n)2
∼ 1 µm2, if the efficient Bragg diffraction occurs over the
whole grating length [16]. The bandwidth–length product is,
however, expected to increase once the grating length becomes
longer than the LR-SPP penetration (inside the grating) length
at the Bragg wavelength. It is clear that, for gratings with higher
ridges, this increase should begin for shorter grating lengths,
as indeed was observed in our experiments (Fig. 7). Finally,
we would like to emphasize that changing the total ridge
height from 10 to 60 nm and gratings length from 20 to
Fig. 7.
grating length on the length of the grating for different heights (htotal) of the
ridges. Grating period is 500 nm and filling factor is 0.55.
Dependence of the product between the reflection peak width and the
Fig. 8.
ridge height (htotal) is 20 nm and the filling factor is 0.35.
Reflection from the 80-µm-long gratings of different periods. The total
160 µm allowed realization of the very broad range of grating
performance—from weak gratings with a bandwidth of only
5 nm for low ridges up to very strong and broadband gratings
with approximately 40 nm of bandwidth.
The reflection spectra were also recorded for five gratings
of the same length and ridge height but with different periods
changing from 480 to 506 nm. These spectra showed very
reproducible shifts in the Bragg wavelength according to the
Bragg condition (Fig. 8). The level of the maximum reflec-
tion stayed within 0.5 dB for all five different-period gratings
(Fig. 8), demonstrating very good reproducibility.
C. Loss Introduced by Grating
In order to study losses introduced by metal ridge gratings,
the spectral dependences of the reflection (R) and transmission
(T) were plotted together with the total power (T + R) spec-
trum (Fig. 9). The most pronounced and somewhat unexpected
feature, which was observed for all investigated gratings is that
the loss level at the Bragg wavelength was found to be smaller
than the loss levels on both sides of the Bragg condition. The
observed decrease in the total loss for the Bragg wavelength
can be due to both reduced out-of-plane scattering and reduced
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916 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 2, FEBRUARY 2006
Fig. 9.
for (a) 80-µm-long grating with a total ridge height (htotal) of 20 nm and
(b) 40-µm-long grating with a total ridge height (htotal) of 40 nm. Grating
period is 500 nm and filling factor is 0.45.
Reflection (R), transmission (T), and total power (R + T) spectra
absorption in metal. The decrease in the out-of-plane scattering
might be connected to the situation when the standing field
pattern at the resonance has minima at the ridge edges giving
less scattering. As for the decrease in the absorption loss, this
can be related to the fact that at the resonance, the field does not
penetratethatdeepintothegratingasatthewavelengthsoutside
the resonance; and less overlap between the LR-SPP field and
metal ridges gives less absorption. Moreover, the roughness
and imperfection of ridges may also contribute similarly to the
absorption loss.
The loss introduced by a grating was found to increase with
the length of the grating and the height of the ridges both
at the Bragg wavelength and outside the resonance due to
both increasing out-of-plane scattering and absorption in metal
(Fig. 10). For example, at 1500 nm for a 40-µm-long grating,
the grating loss increased from ∼ 0.5 dB for a total ridge height
of 10 nm to ∼ 14 dB for 60-nm-high ridges.
There is a tradeoff between the grating strength and loss
introduced by the grating; and for a particular grating perfor-
mance, it is always possible to choose optimal parameters—
for example, ridge height and filling factors that give the most
compact grating. It is seen, for example, from the dependencies
shown in Fig. 6 that by making ridges higher (40 nm instead of
20 nm), one can obtain the same grating strength for a shorter
grating (40 µm long instead of 80 µm).
Fig. 10.
above the resonance for (a) different heights (htotal) of the ridges (40-µm-long
gratings) and (b) different grating lengths (htotalof 20 and 40 nm). Grating
period is 500 nm and filling factor is 0.35.
Loss introduced at the Bragg wavelength and wavelengths below and
IV. COMPARISON WITH LOSSLESS UNIFORM GRATING
In order to estimate the effective refractive-index modulation
in LR-SPP gratings, a simple approach based on comparison
with a lossless uniform Bragg grating is used. In this simple
model, the effective refractive-index modulation ∆n can
be estimated from the maximum reflection Rmax using the
expression [20]
Rmax= tanh2
?2∆nL
λB
?
(1)
where λBis the Bragg wavelength and L is the length of the
grating. Using this expression, the effective refractive-index
modulation can be easily found from the experimental reflec-
tionspectra.However,sincethemaximumreflection,whichcan
be achieved for a given ridge height, is limited by the loss intro-
duced by the grating, this approach can only be relied upon for
low ridge heights. For high ridges, when the loss contribution
is significant, this method will give understated values of ∆n.
Another way of estimating the effective refractive-index
modulation is through reflection spectra zero points. The peak
reflectivity that defines the maximum reflectivity at the Bragg
wavelength can also be written as [21]
Rmax= tanh2(κL)
(2)
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