Abstract—Very strong resonant polarization conversion is
observed in the reflectivity properties of one-dimensional lattices
of air trenches deeply etched in AlGaAs surface waveguides. The
symmetry properties and the magnitudes of the observed effects
are found to be in very good agreement with the results of
scattering matrix calculations.
Index Terms—Photonic Crystals, Photonic Band Structure,
Reflectivity, Polarization, Waveguide, Electromagnetic Coupling.
HOTONIC crystal waveguides constitute a class of photonic
crystal structures which exhibit band structure effects for
guided modes  and in addition several novel external
coupling properties for leaky modes [2-8]. Surface external
coupling occurs under phase matching conditions when both
the energy and the in-plane wave vector of incident light match
those of the folded band structure of the photonic crystal
modes. Such external coupling to leaky modes above the light
line is manifested in external reflectivity spectra by the
appearance of sharp resonant features and polarization mixing
[4,7-11] and anticrossing between bands; by contrast in two
dimensional (2D) photonic crystals of infinite vertical extent,
without vertical waveguide confinement, such bands are pure
transverse electric (TE) or transverse magnetic (TM)
eigenstates of the electromagnetic field .
The polarization mixing of bands, leading to TE modes of
the 2D crystal appearing in TM polarized reflectivity spectra
[4,7] or vice versa, arises from the effects of zone folding and
the vertical confinement. Band states which would otherwise
lie outside the light cone, are folded back into the first
Brillouin zone by the effects of the lattice potential. Since the
lattice potential contains off diagonal components which mix
pure TE and TM states, bands become observable in
'oppositely' polarized reflectivity spectra [4,7,13]. Two of us
have also predicted that polarization conversion of incident
TEin (TMin) polarized light into outgoing TMout (TEout) may
This work is funded by the EPSRC.
A. D. Bristow, V. N. Astratov, R. Shimada, I. S. Culshaw, D.M. Whittaker
and M. S. Skolnick, are with the Department of Physics and Astronomy,
University of Sheffield, Sheffield,
V. N. Astratov is also with the Department of Physics, University of North
Carolina at Charlotte, Charlotte, North Carolina 28223, U.S.A.
R. Shimada is also with the Department of Physics, Japan Women’s
University, Tokyo 112-8681, Japan
A. Tahraoui and T. F. Krauss are with the School of Physics & Astronomy,
University of St. Andrews, St. Andrews, Fife, KY16 9SS, U.K.
S3 7RH, U.K. (e-mail:
occur when light is incident away from the main symmetry
directions of the photonic lattice . Such polarization
conversion was recently observed for 2D triangular lattices of
air cylinders , with relatively modest polarization of the
outgoing light, β=TMout/TEout of order of ~1.
In the present paper we report very strong polarization
conversion effects in the reflectivity of a one-dimensional
lattice of air trenches etched into an AlGaAs surface
waveguide structure, of the type employed in refs [5,6]. We
observe very strong polarizations of the outgoing beam of
order β = 4, for directions of incidence away from the main
symmetry directions of the lattice, with high efficiencies
(TMout/TMin) of order 30%. We also show theoretically that
the strength of the polarization conversion is a strong function
of the depth of the lattice, and is negligibly small for e.g.
shallow etched Bragg gratings.
The paper is organized as follows. After description of the
samples and the measurement techniques in Section II, we
present the determination of the photonic band structure in
Sec. III. The polarization conversion effects are presented in
Sec. IV. Finally we summarise the main conclusions in Sec. V.
The samples studied in this work are surface waveguides
with a 1D lattice of air trenches deep etched through the
waveguide, as shown in Fig 1, to give rise to photonic band
structure effects for the guided modes. The planar waveguides
were grown using molecular beam epitaxy (MBE) and had
Al0.08Ga0.92As core thickness of d = 240nm, and were clad by
air on the top side and Al0.9Ga0.1As, of thickness dcl = 790nm
on the lower side.
1D lattices of air stripes of width w = 45nm were fabricated
by electron beam lithography and deep reactive ion etching
(RIE), see Fig.1 (c). The air trenches were deep etched through
the core into the cladding to depths de ~450nm (aspect ratio
~10) to reduce scattering [5,6]. In this paper we focus on a
lattice period of a = 295nm and air fill factor f = 22% as
determined by SEM (Fig.1 (b)), although lattices of several
other periods and fill fractions were also investigated. The size
of the lattices was 80µm x 80µm.
Polarization Conversion in the Reflectivity Properties
of Photonic Crystal Waveguides
Alan D. Bristow, Vasily N. Astratov, Ryoko Shimada, Ian S. Culshaw, Maurice S. Skolnick,
David M. Whittaker, Abbes Tahraoui, and Thomas F. Krauss
Fig 1. (a) Experimental geometry (b) Scanning electron micrograph of the
surface of 1D lattice with period a = 295nm and f=22%. (c) Cross-sectional
schematic (d) Depth dependent mode profile for 1st and 2nd order modes.
B. Experimental Geometry
Surface reflectivity spectra were obtained using linearly
polarized TE incident light from a broadband tungsten-halogen
lamp. To select the angle of incidence (θ, the polar angle, see
Fig.1 (a)), the sample was illuminated with a highly collimated
beam with angular spread <1°. The angle of incidence was
varied in a broad range from 00 to 70°.
The samples were positioned on a mount which could be
rotated about a vertical axis, permitting additional control of
the direction of incidence relative to the symmetry directions
of the lattice, as defined by the azimuthal angle φ, see Fig.1(a).
Incidence perpendicular to the air trenches corresponds to φ=0
and incidence along the trenches to φ=900.
To access the reflectivity properties of individual lattices,
the image of the sample was strongly magnified (1:20) and
brought to an intermediate focus on a pinhole with a 0.5mm
radius aperture. The transmitted light was then refocused on
the slits of a spectrometer, dispersed and then detected by a
cooled Ge photodiode. A polarisation rotator and a linear
polariser were placed before the spectrometer to enable
detection in both TEout as well as TMout polarizations.
III. DETERMINATION OF PHOTONIC BAND STRUCTURE
The photonic band structure of the lattices was first
determined from the positions of sharp coupling features in the
reflectivity spectra as a function of both polar θ and azimuthal
φ angles see Fig.1 (a). The measurements in this section were
performed in the polarizing conserving geometry (TEin, TEout).
The results were compared with theoretical spectra obtained
by numerical solution of Maxwell’s equations by scattering
matrix techniques  and with band structures calculated by
standard plane wave techniques [4,12].
A. Polar Angle Dependence
Reflectivity spectra as a function of polar angle are
presented in the left side of Fig.2(a) for incidence
perpendicular to the air trenches (φ = 0°). The polar angle is
varied in the range 15° ≥ θ ≥ 60° in 5° steps. Two sharp
resonant features (5-10 meV linewidth), superimposed on a
slowly oscillating background are observed, arising from
coupling to TE modes of the photonic band structure. Both
bands shift down in energy by approximately 150meV from 15
to 60° as a function of angle, as indicated by the dashed lines
on the figure.
Fig 2. (a) Experimental and theoretical reflectivity as a function of polar
angle θ for incidence perpendicular to the air trenches, φ = 0°. (b) Schematic
of the band structure along two main symmetry directions: positive k-vectors
represent the first photonic Brillouin zone for incidence perpendicular to the
air trenches, negative k-vectors represent dispersions for incidence along the
air trenches, φ = 90°. Dashed construction lines show the accessible light
cone with external coupling techniques. The points labelled A and B
correspond to the polar angle of 25o, and azimuthal angles 0 and 90o in Fig 3.
Along the symmetry directions all modes are either pure TE or TM.
Therefore no polarisation conversion occurs.
Fig 3. Experimental and theoretical reflectivity as a function of azimuthal
angle in the range 0° ≤ φ ≤ 180° in 10° steps for a fixed polar angle θ = 25°.
The lower energy mode is 1st order and the higher energy mode 2nd order.
Simulations of the reflectivity spectra were carried out with
the values of the parameters a, f, d and dcl given in Sec. II.A.
Very good agreement with experiment is obtained, as seen by
comparison of the left and right sides of Fig.2(a). Calculations
of the electromagnetic energy density in the vertical direction
further show that the lower and higher energy bands
correspond to 1st and 2nd order modes (see the field profiles
in Fig.1(d)), respectively. As mentioned in the introduction,
the features observed in surface reflectivity arise from
coupling to leaky modes, due to scattering into the cladding
and air. However, the 1st order mode only leaks very weakly,
due to its better vertical confinement, thus leading to the
observed sharper features in reflectivity. In order to obtain
confinement of the higher order mode in the calculations, a
reduced average refractive index 2.6 for the high Al
concentration cladding layer was employed, to account for the
expected presence of low index AlxOy around the air trenches
The band structures shown in Fig.2 (b), both parallel and
perpendicular to the trenches, were calculated using standard
plane wave techniques, employing a simplified model of two
perfectly reflecting mirrors with effective separation d*, which
is varied to account for vertical confinement to obtain the best
fit to the data [4-6]. Values selected for the effective thickness
were d* = 315nm for the 1st order and d* = 200nm for the 2nd
order modes. The dispersions for incidence perpendicular to
the trenches are determined by the photonic lattice potential.
The dispersions parallel to the trenches can be understood
physically as arising from a combination of the k = 0 quantized
energies from the photonic lattice, together with an additional
contribution from free propagation along the trenches, as
the mode at k=0 and neff is an effective refractive index. Use of
this simple perturbation treatment gives a good fit (not shown
, where Em is the energy of
here) to the data for incidence parallel to the trenches.
Coupling to the resonance features occurs at the phase
matching condition with conservation of in-plane wavevector
. Using this correspondence between k
and θ, the angular dispersions of Fig.2(a) can then be plotted
directly on the band structures of Fig.2(b) (the dots), with good
agreement again being obtained between experiment and
B. Azimuthal Angle Dependence
The dependence of the reflectivity spectra on azimuthal
angle is shown in the left hand part of Fig.3 for φ from 0 to
180° in 100 steps for a fixed polar angle θ = 25°;
corresponding theoretical spectra are shown on the right hand
side. The sharp coupling features exhibit a shift by ~100meV
to higher energy as φ increases from 0° to 900 followed by a
symmetrical shift to lower energy for further increase of φ up
to 180°, behavior expected from the symmetry properties of
the lattice (see Fig 2(b) insets). The variation from φ = 0ο to φ
= 90o, at a fixed θ of 25o, corresponds to azimuthal rotation
between points A and B on the polar-angle-variation band
structure diagram of Fig 2(b). It is interesting to note that for
arbitrary direction of incidence (φ), the modes excited in the
waveguide have propagation direction different from that of
the incident wave, an example of the very strong refractive
properties of photonic crystals . The direction of
propagation is determined by the phase-matching condition in
vector form  kw = ki + G, where kw is the wavevector in the
guide, with magnitude (2π/λ)neff, ki is the in-plane incident
wavevector of magnitude ki=(ω/c)sinθ , and G is the reciprocal
lattice vector of the grating of magnitude 2π/a. The direction
of kw coincides with ki only in the case of incidence
perpendicular to the trenches at φ=0, 1800.
Fig 4. Experimental and theoretical azimuthal dependence of the polarization
conversion (η(E)=TMout/TEin) spectra for a polar angle of θ = 25°. The
azimuthal angle is varied from 0° ≤ φ ≤ 180° in 5° steps. There is no
polarization conversion along crystal symmetry directions at φ = 0°, 90° and
Fig 5. (a) Experimental and theoretical dependence of (a) the energy and (b)
the amplitude of the main peak in the polarization conversion efficiency η
(from Fig.4) as a function of azimuthal angle.
The calculated spectra in Fig.3 reproduce all the important
features of the experiment, including the energy shift of the
resonances with φ, the energy difference between the 1st and
2nd order features and even the spectral shape of the
resonances. The good agreement with the calculations,
together with that in Fig 2(a), clearly indicates that the
theoretical model describes very well the band structures and
coupling properties of the photonic crystal waveguides under
Fig 6. Experimental spectra for normalized reflectivity R=TEout/TEin,
polarization conversion efficiency η(E)=TMoutITEin and polarization degree
β(E)= TMout/TEout at φ=450 and θ = 25°. The results of scattering matrix
calculations for β(E) are shown for direct comparison.
IV. POLARIZATION CONVERSION EFFECTS
Experimental Results, Modelling and Discussion
Reflectivity spectra for TMout detection (for TEin incident
polarization) are shown in the left part of Fig.4 for azimuthal
angles φ from 0° to 180°, for the polar angle θ of 25° as in
Fig.3. Once again theoretical spectra are shown for
comparison in the right half of the figure. The TMout signal
was normalized to the incident intensity (TEin) by replacing the
sample with a mirror and measuring TEout (=TEin for the
mirror). The normalized data in Fig.4 thus represent the
polarization conversion efficiency (η(E)) as a result of
reflection by the photonic lattice, with η(E) given by the ratio
The important points of Fig.4 are as follows:
i) The energies and angular dependence of the peaks in
Fig.4 are the same as for the resonances in Fig.3, thus showing
that the polarization conversion arises from coupling to the
photonic band structure modes. The angular variation of the
energy of the main feature of Fig.4 is shown in Fig.5(a).
ii) There is no polarization conversion for incidence along
the main lattice symmetry directions (η=0° for φ=0°, 90° and
180°), as seen in Fig.5(b).
iii) The conversion efficiency η(E) is maximum at φ∼450
from the main symmetry directions. Along these directions it
reaches the high level of η(E)~40% at the resonant energies, as
seen from Fig.5(b).
iv) Most importantly, at these resonant energies, and at
φ=45°, the outgoing light is very strongly polarized, with the
degree of polarization of the reflected light (β(E)=
TMout/TEout) reaching very high levels up to 4 (i.e. 80%
polarized). This is illustrated in the spectra of Fig.6 where TE
reflectivity, R=TEout/TEin, η(E) and β(E) are presented.
Inspection of Fig 6 shows that the very large values of β, the
polarization of the reflected light arises partly because of the
efficient conversion (high η), but also because the spectral
feature in TEout reflectivity exhibits a very strong resonant
minimum (as opposed to the TMout maximum).
All the results of Fig.4-6 were again modelled using
scattering matrix calculations , with the theory results
presented on the figures for direct comparison with
experiment. As for the polar and azimuthal dependences for
TEin/TEout, the calculations are found to describe very well the
symmetry properties, spectral dependence and magnitudes of
the polarization conversion effects.
The observed effects arise from the phenomenon of
polarization mixing of TE/TM bands occurring for directions
of incidence away from the symmetry directions of the 1D
lattice. This effect, which results in TEin incident light being
reflected in TMout polarization, is strongly enhanced at
resonance frequencies where strong coupling to the photonic
As mentioned briefly in the introduction, TE and TM states are
pure, unmixed eigenstates in infinite 2D lattices. Along main
symmetry directions, the introduction of symmetrical vertical
waveguide confinement (as in an air bridge structure) leads to
TE/TM mixing between bands of differing vertical parity (i.e.
between 1st and 2nd order modes), as we discuss in ref . In
asymmetric structures with air above and dielectric cladding
below, the modes no longer have definite parity and TE/TM
mixing can occur between e.g. two 1st order modes. This is the
origin of the weak anti-crossings between TE and TM bands
we have reported along main symmetry directions for 2D
lattices, and the observability of TE bands in TM polarization
and vice versa . However, by going away from the main
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polarization mixing and conversion becomes allowed, as we
report here for the 1D lattices.
directions (φ ≠ 0° or 90o), much stronger
We have carried out simulations of the degree of
polarization of the reflected light (β) as a function of etch
depth. For shallow 1D gratings, as employed in e.g. grating
couplers or fibre Bragg gratings, we find β of only 0.01 at
10nm etch depth, and 0.08 at 50nm, showing clearly that in
order to achieve strong polarization conversion, deep etched
photonic lattices, with strong modulation of refractive index
must be employed.
Surface coupling techniques have been applied to study
propagation and scattering phenomena in deep etched photonic
crystal waveguides. Strong TE/TM polarization conversion of
the reflected beams, arising from the periodic patterning and
the vertical waveguide confinement of the photonic lattices has
been reported. Polarization of the outgoing light of up to 80%,
of opposite polarization to that of the incident light, has been
found in non-optimized structures. These effects have a
resonant character with finesse up to 102-103 and angular
selectivity of ~1°, both desirable properties for integrated
optoelectronics applications. Furthermore, the experimental
and theoretical techniques developed in this work are direct
means to obtain in-depth information on photonic band
structures, fabrication non-uniformities, and scattering and
waveguiding properties of photonic crystal structures.
 T. F. Krauss, R. M. De La Rue and S. Brand, “Two-dimensional
photonic-bandgap structures operating at near-infrared wavelengths”,
Nature (London), Vol. 383, pp.699-702 (1996)
 V. N. Astratov, R M Stevenson, M S Skolnick, D M Whittaker, S. Brand,
I Culshaw, T. F. Krauss, R. M. De La Rue, O. Z. Karimov, “Experimental
technique to determine the band structure of two-dimensional photonic
lattices”, Inst. Elec. Eng. Proc. Optoelectron., Vol 145 pp398-402
 T. Fujita, Y. Sato, T. Kuitani and T. Ishihara, “Tunable polariton
absorption of distributed feedback microcavities at room temperature”,
Phys Rev B Vol. 57, pp.12428-12434 (1998).
 V. N. Astratov,, D M Whittaker, I S Culshaw, R M Stevenson, M S
Skolnick, T F Krauss and R M De La Rue, “Photonic Band Structure
Effects in the Reflectivity of Periodically Patterned Waveguides”, Phys.
Rev. B, Vol.60, No.24, pp.R16255-16258 (1999).
 V. N. Astratov, I S Culshaw, R M Stevenson, D M Whittaker, M S
Skolnick, T F Krauss and R M De La Rue, “Resonant coupling of near-
infrared radiation to photonic band structure waveguides”, J. Lightwave
Technol. Vol. 17, No.11, pp.2050-2057, 1999.
 V. N. Astratov, R M Stevenson, I S Culshaw, D M Whittaker, M S
Skolnick, T F Krauss and R M De La Rue, “Heavy Photon Dispersions in
Photonic Crystal Waveguides” Appl. Phys. Lett., v.77, No.2, pp.178-180
 D. M. Whittaker and I. S. Culshaw, “Scattering-matrix treatment of
patterned multiplayer photonic structures”, Phys. Rev. B, Vol. 60, No.4,
 V. Pacradouni, W. J. Mandeville, A. R. Cowan, P. Paddon, J. F. Young
and S. R. Johnson, “Photonic band structure of dielectric membranes
periodically textured in two dimensions” Phys. Rev. B, Vol. 62, No 3, pp
 S. G. Johnson, S Fan, P R Villeneuve, J D Joannopoulos and L A
Kolodziejski, “Guided modes in photonic crystal slabs”, Phys. Rev. B,
Vol.60, No.8, pp.5751-5758 (1999).
 P. Paddon and J. F. Young, “Two-dimensional vector-coupled-mode
theory for textured planar waveguides”, Phys. Rev. B, Vol.61, No.3,
 D. M. Whittaker, I S Culshaw, V N Astratov and M S Skolnick.,
“Photonic bandstructure of patterned wave-guides with dielectric and
metallic cladding”, Phys. Rev. B, Vol 65, No. 7, pp073102 (2001).
 J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals
(Princeton University Press, Princeton, New Jersey, 1995)
 M. C. Netti, A Harris, J J Baumberg, D M Whittaker, M B D Charlton,
M E Zoorob and G J Parker, “Optical trirefringence in photonic crystal
waveguides” Phys. Rev. Lett. Vol. 86, No.8, pp.1526-1529 (2001).
 Y. Zhao, I. Avrutsky, and B. Li, “Optical coupling
between monocrystalline colloidal crystals and a planar
waveguide”, Appl. Phys. Lett., Vol.75, No.23, pp.3596-