# Polarization conversion in the reflectivity properties of photonic crystal waveguides

**ABSTRACT** Strong resonant polarization conversion is observed in the

reflectivity properties of one-dimensional (1-D) 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

good agreement with the results of scattering matrix calculations

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**ABSTRACT:**We propose and analyze a 90 degrees polarization rotator based on wave coupling through an intermediate, multimode, axially uniform waveguide. The coupling efficiency of the x- and y-polarized fundamental modes between the horizontal and vertical rectangular waveguides is remarkably enhanced with the help of the TE(01) mode in the multimode waveguide. The polarization rotator has a very short (21-microm) conversion length with a 17.22 dB extinction ratio. It also exhibits a 68-nm bandwidth for polarization conversion efficiency above 90%.Optics Express 11/2009; 17(23):20694-9. · 3.55 Impact Factor - Won Hoe Koo, Soon Moon Jeong, Suzushi Nishimura, Fumito Araoka, Ken Ishikawa, Takehiro Toyooka, Hideo TakezoeAdvanced Materials 02/2011; 23(8):1003-7. · 14.83 Impact Factor
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**ABSTRACT:**We demonstrate a system consisting of a two-dimensional photonic crystal slab and two polarizers which has a tunable transmission lineshape. The lineshape can be tuned from a symmetric Lorentzian to a highly asymmetric Fano lineshape by rotating the output polarizer. We use temporal coupled mode theory to explain the measurement results. The theory also predicts tunable phase shift and group delay.Optics Express 09/2013; 21(18):20675-20682. · 3.55 Impact Factor

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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.

I. INTRODUCTION

HOTONIC crystal waveguides constitute a class of photonic

crystal structures which exhibit band structure effects for

guided modes [1] 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 [12].

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,

a.d.bristow@shef.ac.uk)

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 [7]. Such polarization

conversion was recently observed for 2D triangular lattices of

air cylinders [13], 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.

II. EXPERIMENTAL

A. Samples

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

P

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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 [7] 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.

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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

[1,2].

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

represented by:

(

meff

EE hckn

the mode at k=0 and neff is an effective refractive index. Use of

this simple perturbation treatment gives a good fit (not shown

)

1/ 2

2

2

||/ 2

π

=+

, 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

given by

sin

kc

ωθ=

. 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

theory.

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 [14]. The direction of

propagation is determined by the phase-matching condition in

vector form [14] 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

180°.

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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

investigation.

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

TMout/TEin.

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 [7], 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

lattice occurs.

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 [11]. 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 [4]. However, by going away from the main

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symmetry

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.

V. CONCLUSIONS

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.

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