power and polarization beam-splitters, mirrors, and integrated interferometers based on air-hole...

Power and polarization beam-splitters, mirrors, and integrated interferometers based on air-hole photonic crystals and lateral large index-contrast

waveguides Pierre Pottier, Sara Mastroiacovo, and Richard M. De La Rue

Optoelectronics Research Group, Department of Electronics & Electrical Engineering, University of Glasgow, Rankine Building, Oakfield Avenue, Glasgow G12 8LT, Scotland, UK

[email protected]

Abstract: Air hole 2D photonic crystals (PhC) and air slots have been used in association with semiconductor ridge waveguides to produce highly compact beam-splitters (less than 10 µm ×10 µm) for power or polarization separators and mirrors. An efficiency of 99 % (in both 2D and 3D formulations) has been obtained for the power beam-splitter using finite-difference time-domain (FDTD) simulations – and around 95 % has been measured experimentally for structures realized in silicon-on-insulator (SOI) waveguides. In the polarization splitter, an extinction ratio as large as 11 dB was also reached experimentally. Examples of combinations of these elements in the form of interferometers are also presented.

©2006 Optical Society of America

OCIS codes: (230.1360) Beam splitters; (999.9999) Photonic crystal; (230.7380) Waveguides, channeled; (230.5440) Polarization-sensitive devices; (260.6970) Total internal reflection; (230.4040) Mirrors; (230.3120) Integrated optics devices; (250.5300) Photonic integrated circuits; (120.3180) Interferometry

References and links

1. T. F. Krauss, R. M. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699-702 (1996).

2. J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143-149 (1997); J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, “Erratum: Photonic crystals: putting a new twist on light,” Nature 387, 830 (1997).

3. C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol. 17, 1682-1692 (1999).

4. G. P. Nordin, S. Kim, J. Cai, and J. Jiang, “Hybrid integration of conventional waveguide and photonic crystal structures,” Opt. Express 10, 1334-1341 (2002).

5. L. Li, G. P. Nordin, J. M. English, and J. Jiang, “Small-area bends and beamsplitters for low-index-contrast waveguides,” Opt. Express 11, 282-290 (2003).

6. S. Kim, G. P. Nordin, J. Cai, and J. Jiang, “Ultracompact high-efficiency polarizing beam splitter with a hybrid photonic crystal and conventional waveguide structure,” Opt. Lett. 28, 2384-2386 (2003).

7. S. Kim, G. P. Nordin, J. Jiang, and J. Cai, “Microgenetic algorithm design of hybrid conventional waveguide and photonic crystal structures,” Opt. Eng. 43, 2143–2149 (2004).

8. S. Shi, A. Sharkawy, C. Chen, D. M. Pustai, and D. W. Prather, “Dispersion-based beam splitter in photonic crystals,” Opt. Lett. 29, 617-619 (2004).

9. L. Wu, M. Mazilu, J.-F. Gallet, T. F. Krauss, A. Jugessur, and R. M. De La Rue, “Planar photonic crystal polarization splitter,” Opt. Lett. 29, 1620-1622 (2004).

10. G. Erwin, A. C. Bryce, and R. M. De La Rue, “Low-threshold oxide-confined compact edge-emitting semiconductor laser diodes with high-reflectivity 1D photonic crystal mirrors,” in International Congress on Optics and Optoelectronics (ICOO), K. M. Abramski, A. Lapucci, E. F. Plinski; eds., Proc. SPIE 5958, 96-102 (2005).

11. M. Gnan, “Systematic investigation of mis-alignment effects at photonic crystal channel waveguide to feeder waveguide junctions,” Degree Thesis, Università degli Studi di Bologna, Facoltà di Ingegneria (2003).

#68815 - $15.00 USD Received 9 March 2006; revised 14 May 2006; accepted 15 May 2006

(C) 2006 OSA 12 June 2006 / Vol. 14, No. 12 / OPTICS EXPRESS 5617

1. Introduction

Integration, in optoelectronics technologies as well as in other fields, is an area where much effort has been spent. Indeed, it provides simultaneously several advantages, such as cost reduction, size reduction, performance and reliability enhancement. Photonic crystals and high index contrast guiding elements provide possible solutions to the problem of achieving photonic integrated circuits (PICs) [1-3]. In this paper, we have used them both to create devices capable of splitting a beam into two (in power or polarization)–or reflecting a beam. Such devices are building blocks for optical circuits – and have been studied in some detail in recent years [4-7]. Other versions of PhC beam-splitters, using wide regions of PhC to guide or to separate light, can be found in ref. [8, 9]. Here, we focus on 2D triangular and square lattices of air holes in semiconductor waveguides. This configuration should minimize the losses in the third (vertical) direction, by providing robust vertical confinement. It also provides compatibility with “traditional” on-chip guided optics and substantially avoids the problems of coupling of light into and out of active elements. It is also compatible with standard microelectronics planar fabrication techniques, requiring only a single step lithography/etching process. The results of simulation are presented here for power splitters, polarization splitters and mirrors for TE and TM polarizations, using PhC structures and/or slots–and a comparison is then undertaken. The combination of several of these elements is consequently considered in interferometer arrangements, namely Michelson and Mach-Zehnder interferometers. Finally, the fabrication and characterization of a power and polarization splitter realized on a silicon-on-insulator (SOI) wafer is presented and discussed.

2. Design

The devices simulated consisted of ridge-waveguide junction structures in one-, two-, three- and four-port configurations with reflecting/transmitting/splitting elements located at the junctions, as shown schematically in Fig. 1. “Reflection” should be understood to mean the lateral (or side-ways) reflection that is a desired feature of these device structures. The reflection back towards the source is specifically mentioned as “back-reflection”. However, for the one-port configuration, there is only the single type of reflection (back towards the source). By transmission is meant the light that continues in the same direction, after crossing the device–and splitting corresponds to selective partial transmission and reflection. The ridge waveguides are 3 µm wide and deeply etched (i.e. below the core, see Fig. 2), inducing a high lateral index contrast. This width is not chosen smaller because it would lead to higher losses by diffraction of the light in the beam-splitter region were the beam is no more guided, and higher propagation losses (due to sidewall roughness). In addition, one needs at least several holes to provide a plane for the wave front to be reflected laterally. A monomode waveguide, in this high lateral index contrast configuration, would be too narrow and only one hole could be placed laterally. The FDTD method was used to compute the transmission and reflection of these devices. The vertical layer arrangement, used for 3-D simulations, is shown in Fig. 2. For 2-D simulations, a refractive index of 2.77 corresponding to the effective index (neff) of the planar slab waveguide for TM polarization (E-field vector normal to the plane), was used. An index of unity, i.e., that of air, was taken for the etched regions. All the devices studied hereafter are ordered first by function and then by technology used. They are summarized in Fig. 3.



a) b) c) d)a) b) c) d) Fig. 1. (a) to (d): one- to four-port configuration beam-processing elements. (a): frontal mirror, (b): 45° mirror, (c): power or polarization splitter, (d): power splitter for interferometer.

SiO2

Si

SiO2

Si

100 nm

340 nm

3 µm

substrate

d=490 nmn=1.45

n=3.45

n=1.45

SiO2

Si

SiO2

Si

100 nm

340 nm

3 µm

substrate

d=490 nmn=1.45

n=3.45

n=1.45

Fig. 2. Vertical layer configuration, with refractive indices and layers thicknesses, after dry etching has taken place. On the top right are depicted holes, waveguides or slots etched down to the depth d.

Device function

TechnologyPhC Air slot/region

Power splitter

Polarization splitter

Mirrors

Interferometers

90° (bend)

180° (frontal)

Device function

TechnologyPhC Air slot/region

Power splitter

Polarization splitter

Mirrors

Interferometers

90° (bend)

180° (frontal)

Fig. 3. List of devices studied, classified by function and technology used, with schematics.

2.1 Power splitter structure

The first device considered was designed to split the power between two output branches, either equally or unequally. It was simulated as a three-port configuration (T-junction) [see Fig. 1(c)]. One row of holes at 45° was chosen and proved a posteriori to be sufficient to



achieve the desired splitting. Having a thin splitting element (one row of holes thick) is also beneficial through producing a more symmetrical device (with respect to the waveguide axes) in the case of a four-port configuration, avoiding the need to shift waveguides. The question of the choice of lattice configuration (triangular or square) also disappears–and the two key parameters remain the period and filling-factor f, defined as the ratio of the area of the air discs to the total area. Because of the scalability of photonic crystals, the problem is reduced to the dependence of transmission and reflection on the filling-factor alone. This parameter was therefore scanned. The results for TM polarization are compiled in Fig. 4 and were obtained by simulation in 2-D “free space,” meaning that a gaussian beam that was 4 µm wide at its 1/e points was used, without explicit lateral confinement by the boundaries of a ridge wave-guide. Figure 4 shows that various splitting ratios can be obtained, depending on the normalized frequency and that they evolve with changing filling-factor. Two main regions appear: (i) below a certain normalized frequency, the back reflection goes to zero and the incident power is completely split between transmission and reflection and (ii) above this frequency, some light is lost (i.e. is neither transmitted nor reflected). These results can be understood in terms of diffraction grating behavior, since the PhC can be regarded as forming a diffracting element of period a. It can be shown that only the 0th order of diffraction exists for this grating, at angle θ, if the following condition applies:

( ) ceff

a

n

a⎟⎠

⎞⎜⎝

⎛=+

<λθλ sin1

1 (1).

For this condition there can only be specular reflection. The critical value for neff = 2.77 (with

θ = 45°) is 211.0=⎟⎠

⎞⎜⎝

⎛

c

a

λ – a value that matches with the graphical results. The region of

interest for efficient splitting is therefore below this value. It should be noted that, for a given normalized frequency, the ratio of reflection to transmission increases with the filling-factor, which is intuitively understandable since more low index material is required to produce reflection of the light. Also, for a given filling-factor, the reflection decreases and the transmission increases when the normalized frequency decreases. Again, the result can be understood intuitively since there is less low-index material (because the ratio a/λ is smaller). Simulations with the effects of lateral confinement included, in a waveguide configuration (3 µm width), were carried out and gave very similar results to those for the “free space” configuration. The target device at this stage is an equal power splitter for TM-polarized light.

A filling-factor of 0.60 satisfies this requirement at 145.0=λa , in the low-loss region. The

period is then a = 0.22 μm for the wavelength of interest, which is λ = 1.518 μm. The transmission and reflection are both 49.4 % , while the back-reflection is 0.2 %. A small amount of light (no more than 1 %) is lost through radiative scattering at the edges of the waveguide junction – probably because the beam is not laterally confined in the beam-splitter region. The use of low index-contrast waveguides could reduce this already small loss. Maps of the field-distribution and power-spectrum of the device are shown in Fig. 5. This calculation of the spectrum has been obtained using a 20 nm grid in the FDTD simulations (at a wavelength of 1.518 μm). Although the transmission and reflection vary with frequency, it should be noted that, over the limited window typically used in telecommunications, they remain relatively flat. For example, over the 1530 nm - 1565 nm band, reflection and transmission will vary by only 1.3 % between the middle and the edges of that wavelength band.



0.1 0.2 0.3 0.4 0.50.0

0.2

0.4

0.6

0.8

1.0

f = 0.75

f = 0.75

f = 0.25

f = 0.75

f = 0.25

f = 0.25

Tra

nsm

issi

on &

Ref

lect

ion

Normalised frequency a/λ

transmission reflection back reflection

Fig. 4. Transmission, reflection and back-reflection of a PhC beam-splitter (without lateral confinement), vs. the normalized frequency a/λ, for a set of filling-factors (f) ranging from 0.25 to 0.75 by step of 0.05, for TM polarization (2D FDTD simulations).

0.10 0.15 0.20 0.250.0

0.2

0.4

0.6

0.8

1.03 2.5 2 1.5 1

Tra

nsm

issi

on &

Ref

lect

ion



Wavelength (µm)

(a) (b)0.10 0.15 0.20 0.25

0.0

0.2

0.4

0.6

0.8

1.03 2.5 2 1.5 1

Tra

nsm

issi

on &

Ref

lect

ion



Wavelength (µm)

0.10 0.15 0.20 0.250.0

0.2

0.4

0.6

0.8

1.03 2.5 2 1.5 1

Tra

nsm

issi

on &

Ref

lect

ion



Wavelength (µm)

(a) (b)

Fig. 5. Intensity map of the field (a) and transmission, reflection and back-reflection (b) of a PhC beam-splitter, vs. the normalized frequency a/λ, for TM polarization (2D FDTD simulations, a = 0.22 μm, f = 0.60). (N.B.: the additional air holes drawn outside the waveguides – air region – have no effect.)

For the case of TE polarization, similar results were obtained in terms of behavior, i.e.

total efficiency, splitting ratio variation with filling-factor and normalized frequency – but with a smaller fraction of the light being reflected, as opposed to transmitted.

Further refinements of the PhC beam-splitter structure were carried out in simulation, addressing the resolution issue. The way in which the structure was initially created was modified to allow index smoothing at the air-hole/semiconductor interface in the discretisation process, giving greater precision and the grid size was simultaneously reduced to 11 nm.



Although these modifications changed substantially the calculated values for the transmission and reflection, their general behavior did not change with, for example, only a shift in the

crossing point of the two curves (from 1450.0=λa to 0.1751 for TM polarization). In this

situation, a further reduction of the grid size did not affect the results (e.g. only a 0.2 % change in the total transmission plus reflection in going from an 11 nm to a 1 nm grid size). These PhC structures (i.e. the beam-splitters) showed themselves to be more sensitive to discretisation issues than other structures (e.g. the transmission of PhC channel waveguides). The original dimensions of the PhCs were however kept constant for the work described in following sections.

3-D simulations were also carried out using the parameters: f = 0.60, a = 0.22 μm, λ = 1.518 μm with the configuration shown in Fig. 2, for a grid size of 11 nm in the plane of the slab waveguide and 20 nm along the vertical direction. The simulations give an estimated efficiency of 49.6 % for both transmission and reflection at the crossover point, for TM polarized light – and 49.8 % for TE polarized light. In total only 0.4 to 0.8 % of the light is lost, a clear indication of the high performance quality of the device. In particular, the simulation shows that the limited etch depth of the holes (just below the core) does not affect the performance significantly. A fraction of the estimated light loss is due to limitations in the accuracy of the simulations – and the losses could also be further decreased by shifting the position of the output waveguide to take into account the Goos-Hänchen shift arising from the reflection of the beam at the interface. The transmission and reflection results calculated using the 3D simulation are close to the 2D ones in term of behavior, but a substantial shift in

frequency is observed (with the cross-over occurring at 1356.0=λa instead of 0.1751, for TM

polarized light). The evolution of the transmission and reflection with the filling-factor is presented in Fig. 6, for both polarizations. The results confirm what has been said earlier – and show that almost all combinations of splitting ratios between complete reflection and complete transmission can be achieved.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.00.20.40.60.81.0

TE

Tra

nsm

issi

on&

Ref

lect

ion

Filling factor


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.00.20.40.60.81.0

TM

Tra

nsm

issi

on&

Ref

lect

ion

Filling factor

Fig. 6. Evolution of the transmission, reflection and back-reflection of a PhC beam-splitter, vs. the area filling-factor, for TM and TE polarizations (3D FDTD simulations, a = 0.22 μm, λ = 1.518 μm).



A power splitter was also tested in an air-slot configuration, working in a frustrated total internal reflection (FTIR) regime. The slot was orientated at 45° and had the same etch depth as for the previous case (cf. Fig. 2). The air slot gap was adjusted to modify the ratio of transmitted and reflected light. For an equal splitting, it was found to be 104 nm wide for TM and 35 nm for TE (see Fig. 7). The difference between the effective indices of the TM and TE modes, on which the exponential decay of the evanescent wave depends, is considered likely to be the cause of this significant difference. In this situation, the transmission and reflection were 49.6 % for TM simulation and 49.8 % for TE (3D FDTD). All ratios of splitting could also be obtained, by adjusting the slot width. The levels of transmission and reflection were the same as for the hole-PhC beam-splitter – and could possibly be increased slightly for the same reasons. From this point of view, both devices were equally efficient. The air-slot configuration had the advantage over the PhC configuration of providing a slightly more perfectly shaped mode after reflection and transmission. But it had the disadvantage of being narrower and hence more sensitive to fabrication errors. Because of their shape and size, larger holes (typically 170 nm in diameter) are easier to produce than narrower slots (typically 70 nm in width). The sensitivity in the fabrication was estimated by taking into account a typical absolute error Δx of 10 nm in the size. It led, for the 50/50 splitter, to a relative error in

the transmission (or reflection) T

TΔ ⎟⎠

⎞⎜⎝

⎛ Δ≈R

R of 14 % (for TM light) and 29 % (for TE light)

for the hole-PhC structure and 11 % (TM) and 64 % (TE) for the air-slot configuration.

0 20 40 60 80 100 120 1400.00.20.40.60.81.0

TE

Tra

nsm

issi

on&

Ref

lect

ion

Slot width (nm)


0 20 40 60 80 100 120 1400.00.20.40.60.81.0

TM

Tra

nsm

issi

on&

Ref

lect

ion

Slot width (nm)

Fig. 7. Evolution of the transmission, reflection and back-reflection of an air slot beam-splitter, vs. the slot width, for TM and TE polarizations (3D FDTD simulations, λ = 1.518 μm).

2.2. Polarization splitter structure

This second device structure makes it possible to separate TE and TM polarized light controllably between the two distinct output branches. It has, ideally, to fulfill four conditions simultaneously: i) not to transfer TE polarized light into branch 1, ii) to transfer all TE polarized light into branch 2, iii) not to transfer TM polarized light into branch 2, and iv) to transfer all TM polarized light into branch 1. The structure was simulated in a three-port configuration (i.e. as a T-junction) [see Figs. 1(c) & 15(b)]. Three rows of holes (inclined at 45°) were chosen to increase the reflection and thereby to increase the polarization discrimination. The filling-factor dependence was scanned for the two principal types of



lattice: i.e. triangular and square. The rows of holes have respectively the directions ΓK and ΓX, to provide a smooth interface. Since it was practically not possible to satisfy all the four desired conditions simultaneously, we have chosen to focus on two devices: one with the best contrast between polarizations in one branch and the other with the best separation of polarizations. For the first case, the triangular lattice was chosen to provide a wide TE photonic band gap (PBG), making it possible to operate in a guaranteed small TE transmission

situation. A ratio between TM and TE transmission ⎟⎟⎠

⎞⎜⎜⎝

⎛

TE

TM

T

T of 375 (= 25.7 dB) was obtained

in this way for a “free space” simulation and 133 (= 21.2 dB) for a laterally wave-guided configuration (a = 0.429 μm, f = 0.35, λ = 1.518 μm) [Fig. 8(a)]. For the second case, with a triangular lattice, a TM reflection (RTM) of 88 % and a TE transmission (TTE) of 70 % were obtained in “free space”, while RTM = 75 % and TTE = 60 % were obtained for the wave-guided configuration (a = 0.506 μm, f = 0.25, λ = 1.518 μm) [Fig. 8(b)]. The alternative of using a square lattice gave inferior results. For the first case, the contrast could still be increased by adding more rows of holes. To further increase the spatial separation, it would be interesting to make the PBG region coincide with the zeroth order-only diffraction regime. Unfortunately

this coincidence does not appear to be possible, since 189.0=⎟⎠

⎞⎜⎝

⎛

c

a

λ (for a TE mode with

neff = 3.10) is slightly below the bottom of the first TE PBG region (at 218.0=λa ). This

objective may however be made possible by decreasing the reflection angle (θ), which would

increase c

a⎟⎠

⎞⎜⎝

⎛

λ (see Eq. 1). The objective of coincidence with the zeroth order-only diffraction

regime would also be made possible by using guiding in air (or a low index material) with

semiconductor rods, since neff will be reduced significantly and c

a⎟⎠

⎞⎜⎝

⎛

λ will consequently

increase, but this configuration is not considered in the present work.

(a)

(b)0.1 0.2 0.3 0.4 0.5

0.0

0.20.40.60.8

1.0

Tra

nsm

issi

on&

Ref

lect

ion


TE transmission TM reflection

0.1 0.2 0.3 0.4 0.50.00.2

0.40.6

0.81.0

Tra

nsm

issi

on


TE transmission TM transmission

(a)

(b)0.1 0.2 0.3 0.4 0.5

0.0

0.20.40.60.8

1.0

Tra

nsm

issi

on&

Ref

lect

ion


TE transmission TM reflection

0.1 0.2 0.3 0.4 0.50.00.2

0.40.6

0.81.0

Tra

nsm

issi

on


TE transmission TM transmission

Fig. 8. Transmission for TE & TM polarization (a), and transmission (for TE) & reflection (for TM) (b), vs. the normalized frequency a/λ, of a PhC polarization splitter (2D FDTD simulations, a = 0.429 μm, f = 0.35 (a), and a = 0.506 μm, f = 0.25 (b)).



Concerning the air-slot configuration, both TE and TM polarized light are reflected, as already observed for the power splitter – up to the situation of total reflection, if the slot is sufficiently wide. (See the next section concerned with mirrors). So there is insufficient discrimination between TE and TM polarized light to make a polarization splitter possible using the air slot configuration.

2.3. Mirror structure

This third device is required to reflect a beam, either into another direction (at 90°), or back towards the incoming direction (180°). It was simulated in a two-port (bend) or a one-port configuration. For the bend, three rows of holes (at 45°) were chosen to provide sufficient reflection. The filling-factor dependence was scanned for the two principal lattices: triangular and square. The rows are oriented along the ΓK and ΓX directions respectively. The triangular one gave better results. The performance was then improved by adding a row of smaller holes as the first row of the lattice (the lattice structure is retained), to provide a smoother transition. Its filling-factor was also optimized (by scanning). The results are a reflection of 85 % for TE polarization, and 80 % for TM, in a wave-guided configuration (a = 0.541 μm, f = 0.35, λ = 1.518 μm) (Fig. 9). This device has the attractive feature of being able to provide performance close to these values over a wavelength band as large as 100 nm centered on 1520 nm.

0.1 0.2 0.3 0.4 0.50.0

0.2

0.4

0.6

0.8

1.05 4 3 2

Ref

lect

ion


TM reflection TE reflection

Wavelength (µm)

Fig. 9. Reflection vs. the normalized frequency a/λ, for TM and TE polarization, of a PhC mirror (2D FDTD simulations, a = 0.541 μm, f = 0.35).

For the frontal mirror (180°) a sufficient number of rows of holes (10), in a triangular

lattice (rows oriented along ΓK), was chosen to provide complete reflection of light using the TE PBG. (See the schematic in the Michelson interferometer section below, where this device is used). There is some freedom in the choice of the filling-factor, which was taken as 0.35 for ease of fabrication and limitation of out-of-plane scattering losses. By operating around the middle of the bandgap, a reflection around 100 % was obtained (using 2D FDTD simulation, TE polarization, a = 0.375 μm, f = 0.35). In this configuration, the angle of incidence θ = 0

and neff = 3.10, so for λ = 1.518 μm, 323.0247.0 =⎟⎠

⎞⎜⎝

⎛<=c

aa

λλ. Therefore only specular



reflection occurs (i.e. only zeroth order diffraction) – at normal incidence in this case, which is why the reflection can be complete.

A mirror was also simulated using total internal reflection (TIR) with a semi-infinite air gap at 45°) (see inset Fig. 10). The Goos-Hänchen shift was investigated (by shifting the output waveguide), but only a very small difference in the reflection (a maximum of 0.15 %) was observed, as compared with the un-shifted position used thereafter. Estimated values for reflection of 98.8 % for TE and 98.5 % for TM were obtained from 3D FDTD simulation. The wavelength response is quite flat (see Fig. 10), which makes this device structure a good candidate for application in ultra-short bends.

1.45 1.50 1.55 1.600.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0R

efle

ctio

n

Wavelength (µm)

TM TE

1.45 1.50 1.55 1.600.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0R

efle

ctio

n

Wavelength (µm)

TM TE

Fig. 10. Reflection vs. wavelength, for TM and TE polarization, of a total internal reflection mirror (3D FDTD simulations). Inset: intensity map of the field (TE polarization). (N.B.: the lines drawn outside the corner waveguide have no effect.)

Frontal mirrors can also be realized with a 1D array of air gaps in the waveguide, in the

well-known Distributed Bragg Reflector (DBR) configuration, and can provide high reflection (see, e.g. ref. [10]).

Another frontal mirror, using TIR, was investigated. It consists of a waveguide with the end beveled at 45° from each side (see the inset in Fig. 11), and forms a corner reflector. The reflection is substantial: 92 % for TE and 80 % for TM (as indicated by 3D FDTD simulations) and takes place over a wide range (Fig. 11). But some of the light (up to 8-20 %) is lost at the tip, where it is radiated (inset in Fig. 11).



1.45 1.50 1.55 1.600.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Ref

lect

ion

Wavelength (µm)

TM TE

1.45 1.50 1.55 1.600.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Ref

lect

ion

Wavelength (µm)

TM TE

Fig. 11. Reflection vs. wavelength, for TM and TE polarization, of a corner reflector frontal mirror (3D FDTD simulations). Inset: intensity map of the field (TE polarization). The light is launched upwards at z = 0. Picture taken at a maximum of the standing wave occurring above z = 0. (N.B.: the lines drawn outside the beveled waveguide have no effect.)

2.4 Association in systems

Having studied the properties of these building blocks, it now becomes possible to combine them and form more complex device structures and sub-systems. The following devices are simulated with 2D FDTD with an 11 nm grid size. The first example that we shall consider is a Michelson interferometer, which is made up from a PhC beam-splitter (in a four-port configuration) and two PhC mirrors (each in a one-port configuration) (as shown in Fig. 12). The PhC beam-splitter was first optimized to give the maximum total transmission into the two output branches, taking into account the Goos-Hänchen shift that occurs in reflection. With the objective of maximizing the total transmission, the waveguides were shifted, while retaining their symmetry with respect to the beam-splitter plane. This shift also produces the detrimental effect of slightly reduced transmission for light passing through the beam-splitter, but an acceptable compromise can be reached. The parameters of the optimization are then the lattice constant a, the filling-factor f, and s (the shift of the waveguide axis: arm 1 is shifted by -s along x, arm 2 by +s along x, arm 3 by +s along z and arm 4 by -s along z). The total amount of usefully transmitted and reflected light, R+T, is optimized, while retaining R = T. The results are high transmission and reflection values, each 49.4 %, for the following parameters: s = +35 nm, a = 0.216 μm and f = 0.655, for λ = 1.518 μm, with TE polarization and neff = 3.10. The beam-splitter is then integrated with the two PhC mirrors designed previously (with a = 0.375 μm and f = 0.35), in a symmetrical manner. In order to explore the behavior of the interferometer, the position of one of the mirrors was scanned and the output and input monitored. This scanning process could, for example, be applied in an actual device by applying a mechanical deformation or by using micro-electro-mechanical systems (MEMS). Alternatively, the refractive index can be modified locally (e.g. by using thermo-optic or electro-optic effects) in one arm, effects that can readily be simulated. The mirror in arm 3 was moved from its original position, p = 0, and the results for transmission and reflection are shown in Fig. 13. As expected, the relationship is sinusoidal, depending on the phase difference between the two beams when they recombine. The total amount of useful light leaving the device is predicted to be 97.9 %, and the contrast between the two arms to be 14.1 (= 11.5 dB). Incomplete superposition of the beams leads to imperfect cancellation, but nevertheless the separation is sufficient to monitor a variation (e.g. of length, index) in one



arm. A field map for the situation where the mirrors are at equal distances from the beam-splitter is shown in Fig. 12.

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Fig. 12. Intensity map of the field of a Michelson interferometer (2D FDTD simulation). The light is launched upwards at z = -3. Arms are numbered from 1 to 4. (N.B.: the additional air holes drawn outside the waveguides – air region – have no effect.)

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The second example of a combined structure is a Mach-Zehnder interferometer that comprises two PhC beam-splitters (in a four-port configuration) and two TIR mirrors (in a two-port configuration) (as shown in Fig. 14). The optimized PhC beam-splitter configuration of the Michelson interferometer was used. The TIR mirrors were optimized to give the maximum reflection, taking into account the Goos-Hänchen shift. For this optimization, the mirrors were shifted along the incoming waveguide axis by an amount s2. The results are a reflection of 98.7 %, for s2 = -90 nm (λ = 1.518 μm, with TE polarization and neff = 3.10). The optimized beam-splitters and mirrors were then brought together to form the complete device structure. The total amount of light leaving through the two output branches is 93.8 %, and the contrast between the two branches is 18.5 (= 12.7 dB). A field map can be seen in Fig. 14. Here also, imperfect overlap of imperfectly shaped beams is a partially limiting issue but, nevertheless, the contrast may be sufficient, depending on the application. Switching between one output branch and the other can subsequently be obtained by locally modifying the refractive index in one arm (e.g. by using the electro-optic effect).

Fig. 14. Intensity map of the field of a Mach-Zehnder interferometer (2D FDTD simulation). The light is launched upwards at z = -3. (N.B.: the additional air holes drawn outside the waveguides – air region – have no effect; the lines drawn outside the corner waveguides have no effect neither.)

3. Fabrication and characterization

Experimental device structures were realized on an SOI wafer that consisted of a silicon substrate, a 3 µm thick silica buffer layer (as bottom cladding) and a 340 nm silicon core (as shown in Fig. 2). A 200 nm thick layer of silica was then deposited on top of the silicon core by a plasma enhanced chemical vapor deposition (PECVD) process. Electron-beam lithography was used to write the patterns into a 200 nm thick polymethyl-methacrylate (PMMA) resist layer. A first pattern transfer process into the deposited silica layer was then performed, using reactive ion etching with CHF3 gas. Then, using this intermediate mask, the silicon waveguide core layer was etched using SiCl4 to create the finite-width waveguides (3 µm wide) and the PhC holes of the beam-splitters and mirrors. Finally, oxygen plasma-



ashing was used to remove the PMMA resist residue. Around 100 nm of the deposited silica layer remained after etching and formed part of the upper cladding of the waveguide structure. Scanning electron microscope (SEM) images of the beam-splitters are shown in Fig. 15.

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Fig. 15. SEM micrographs of the power (a) and polarization (b) splitter on SOI ridge waveguides (T-junction).

Characterization was carried out using the end-fire technique with a tunable diode laser.

The transmission was normalized by reference to an identical ridge waveguide without holes. For the reflection, an additional step was used to take into account the bend and tapers used to bring the output branch to the same output facet. Due to the low transmission levels of the reference bend structure at long wavelengths, in TM polarization, part of the spectrum has been removed to avoid erroneous normalization. The wavelength spectral data have been processed by low-pass filtering (using a cut-off “frequency” of 0.2 nm-1) before normalization, in order to eliminate the Fabry-Pérot oscillations caused by facet reflections. Both the raw (unfiltered) and filtered data are presented in the following figures. Ultimately, a solution that would avoid these unwanted Fabry-Pérot oscillations would be to apply anti-reflection coatings to the facets. Other alternatives could be to use inverse tapers to couple light in or to use angled waveguides.

For the power splitter, in both TM and TE polarizations (Fig. 16), the transmission and reflection are relatively constant over the range accessible experimentally (a range of 105 nm centered on a wavelength of 1518 nm), although some ripples appear in the spectrum. Only a small change in the transmission and reflection are expected over this range, as shown by the simulation data (Fig. 16). The total amount of the transmitted and reflected signals adds up experimentally to between 90 and 100 % on average, implying that only a small amount of light is lost in the splitting process. Estimated transmission levels can locally exceed 100 %: this point is discussed in Appendix. The experimentally measured levels of transmission and reflection match well, for both polarizations, with those obtained from 3D FDTD simulations. For example, a simulated reflection-to-transmission splitting-ratio of 5.7 % is observed, for TE polarization, that is closely reproduced experimentally – at 5.9 % (using a value averaged over the wavelength range). The parameters used in the simulations presented in Fig. 16 are extracted from SEM images (Fig. 15) of the device actually measured, in order to obtain a close comparison between 3D simulations and experiment. These PhC power splitters work with a high efficiency and as predicted, except for exhibiting ripple in the spectral response that can possibly be attributed to imperfections in the fabrication, such as imperfect roundness of the holes, and also to an excitation of undesired higher order modes, that make the overall response wavelength dependent.



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Fig. 16. Experimental (raw and filtered data) and simulated (3D FDTD) transmission and reflection spectra of the PhC power splitter, for TM (a) and TE (b) polarizations (a = 0.220 µm, f = 0.30).

Turning to the polarization splitter shown in Fig. 17, the level of transmitted TE light is

very low, as expected, since the PhC structure is operating in the PBG regime. The reflected TE light remains globally constant over the range accessible experimentally, although ripples are clearly visible within that range and the behavior is then close to the simulation (i.e. slowly varying), although apparently smaller in magnitude. The transmitted TM light and especially the reflected TM light have a level below that expected from the simulation. This device will also be vulnerable to fabrication errors, which may reveal themselves to be more important for polarization than for power separation issues and experimental performance could therefore deviate significantly from simulation results. Nevertheless, a substantial



average contrast level of 11 dB between the light level in the TM and TE polarizations could be measured in the transmission output branch. The situation in the reflection branch was actually better than expected, in terms of polarization discrimination and this device could also operate as a spatial polarization splitter.

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Fig. 17. Experimental (raw and filtered data) and simulated (3D FDTD) transmission and reflection spectra of the PhC polarization splitter, for TM (a) and TE (b) polarizations (a = 0.400 µm, f = 0.30).

4. Conclusions

We have shown, both in simulation and experimentally, that photonic crystal structures can be used in conjunction with classical ridge waveguides to create beam-splitting elements that occupy only a very small area. PhC-based splitters and mirrors can give significant



advantages over more classical solutions such as the air-gap slot, e.g., for power splitting or they can simply make it possible to separate light, e.g. in polarization splitting. A combination of these elements can be used in the construction of photonic integrated circuits. Additional functionalities such as selective channel dropping should be possible, thanks to the richness of PhC phenomena. Tunability could also be introduced via refractive index change, using thermo-optic or electro-optic effects. An example of realization could be a beam-splitter with tunable splitting ratios.

Acknowledgments

This work was supported by the EPSRC (UK) as part of the Ultrafast Photonics Collaboration. Marco Gnan is also acknowledged for his assistance with the fabrication process.

Appendix

There are several reasons why the estimated transmission can exceed 100 %. First of all, what we measure is the transmission of the device, modulated by the transfer function of the Fabry-Pérot (FP) cavity created by the reflection of the two facets. This transfer function has maxima at 1 and minima as small as 0.35 for semiconductor/air case. The oscillations are closely spaced and when dividing the device spectrum by a reference device spectrum, some values can be as large as 300 % (1/0.35). But this is an artifact of the way the transmission is extracted. Ideally, the oscillation maxima only should be considered. But this again can lead to artifacts when multimode propagation occurs in a waveguide, because it gives rise to beating between the FP oscillations of the different modes, when their periods are close. Moreover, high resolution scans are needed to observe these fine FP oscillations, over a time scale of hour(s), which is not practical and gives rise to drifts in the optical alignment over time. Therefore fast scans are performed that reduce the resolution and consequently imply sub-sampling of the FP oscillations. Aliasing effects will happen when the scan period is a close multiple of the FP oscillation period. In this situation, a slowly varying signal can be measured, too slow to be filtered out by our low-pass filter, and inducing artifacts in the normalized transmission as explained before.

Secondly, the reference device can be imperfect, having a slightly smaller transmission than expected for particular wavelengths or over the entire spectrum. Possible origins can be sidewall roughness, local defects along the waveguide, in particular stitching errors of different blocks exposed during an electron-beam lithography process.

Thirdly, there is error in optimizing the optical alignment, which is carried out manually. We have measured this error on our setup, which is 3-4 % (standard deviation of transmission) [11]. Dividing a device spectrum overestimated by 4 % with a reference device spectrum underestimated by 4 %, for example, will lead to an overestimate in the transmission of 8 %, giving a possible overall value of 1.08.



power and polarization beam-splitters, mirrors, and integrated interferometers based on air-hole...

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