Polarization management for silicon photonic integrated circuits

Transcription

1 Early View publication on wileyonlinelibrary.com (issue and page numbers not yet assigned; citable using Digital Object Identifier DOI) Laser Photonics Rev., 1 26 (2012) / DOI /lpor LASER & PHOTONICS Abstract Polarization management is very important for photonic integrated circuits (PICs) and their applications. Due to geometrical anisotropy and fabrication inaccuracies, the characteristics of the guided transverse-electrical (TE) and transversemagnetic (TM) modes are generally different. Polarizationdependent dispersion and polarization-dependent loss are such manifestations in PICs. These issues become more severe in high index contrast structures such as nanophotonic waveguides made of silicon-on-insulator (SOI), which has been regarded as a good platform for optical interconnects because of the compatibility with CMOS processing. Recently, polarization division multiplexing (PDM) with coherent detection using silicon photonics has also attracted much attention. This trend further highlights the importance of polarization management in silicon PICs. The authors review their work on polarization management for silicon PICs using the polarization independence and polarization diversity methods. Polarization issues and solutions in PICs made of SOI nanowires and ridge waveguides are discussed. REVIEW ARTICLE Polarization management for silicon photonic integrated circuits Daoxin Dai 1, Liu Liu 2, Shiming Gao 1, Dan-Xia Xu 3, and Sailing He 1,2,* 1. Introduction In recent years, silicon photonics [1 9] has become one of the most promising platforms for photonic integration because of their compatibility with mature CMOS technologies, excellent processing control, low cost, and high volume processing. These advantages allow the use of electronics fabrication facilities to make photonic integrated circuits (PICs). Silicon-on-insulator (SOI) technology provides a very promising platform for silicon photonics. Due to limitations in the fabrication process, people initially focused mainly on SOI optical waveguides with a large cross section in order to achieve low-loss single-mode light propagation [10]. The single-mode condition [11,12], the bending characteristic [13], and the birefringence [14 20] of large SOI ridge waveguides have been well investigated. Various passive elements have also been developed [21 31], e.g., the first arrayed-waveguide grating (AWG) demultiplexer demonstrated by Trinh et al. in 1997 [31]. One of the advantages of large SOI ridge waveguides is that accurate phase control is easier than that for small SOI waveguides (e.g., SOI nanowires discussed below), leading to their continued use in commercial applications. For example, Kotura recently announced a 100 Gb/s optical engine, which is based on their 3-µm thick SOI platform. On the other hand, for large ridge waveguides, the bending radius is usually at the order of µm [13], which is too large to realize ultracompact photonic integrated devices. A possible solution to obtain a sharp bending is using a total internal reflection mirror [32, 33]. However, high-quality mirrors are difficult to fabricate. More recently, SOI nanowire waveguides enabling ultrasharp bending with a radius as small as 1 2 µm have been developed by utilizing the high refractive index contrast [34], enabling highly compact photonic integrated devices, e.g., AWG [35 37], microrings [38], etc. Even though silicon itself is not a good option for active PICs with lasers as well as photodetectors (for the wavelength window around 1550 nm), several technologies have been developed to solve this issue, such as the III-V/Si hybrid integration [7, 8]. All these efforts make it more and more feasible to realize largescale PICs on a silicon substrate, especially for the demands of optical network-on-chip in the future. Another direct consequence of the high index-contrast between the silicon core and the cladding (SiO 2 or air) is that SOI waveguides generally have a considerable birefringence. For large SOI ridge waveguides (with a ridge height of 1 5 µm), the birefringence is on the order of , while the birefringence of SOI nanowires can be several orders of magnitude higher [36]. This birefringence intro- 1 Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang University (ZJU), Zijingang, Hangzhou , China 2 Centre for Optical and Electromagnetic Research, ZJU-SCNU Joint Research Center of Photonics, South China Academy of Advanced Opto-electronics, South China Normal University (SCNU), Guangzhou, China 3 Institute for Microstructural Sciences, National Research Council Canada, Building M50, 1200 Montreal Road, Ottawa, Ontario, Canada, K1A 0R6 * Corresponding author: sailing@zju.edu.cn

2 LASER & PHOTONICS 2 D. Dai et al.: Polarization management for silicon photonic integrated circuits duces significant polarization dependence to SOI PICs [36]. For fiber optical communication applications, the light from an optical fiber usually has a random polarization state and consequently the signal-to-noise ratio will degrade seriously after it goes through a polarization-sensitive PIC. Therefore, polarization-insensitive PICs are extremely desired. In theory it is possible to achieve a nonbirefringent SOI optical waveguide by optimizing the waveguide dimensions [14 20, 31]. This simple approach works for the case with large SOI ridge waveguides, because the typical dimensional variations caused by fabrication inaccuracies generate an acceptable birefringence. In [31], the demonstrated AWG demultiplexer made of 5-µm thick SOI ridge waveguides is almost polarization-independent by simply optimizing the waveguide dimension. For the case of using thinner SOI ridge waveguides, it is also possible to minimize the birefringence by controlling the stress generated from an oxide cladding [19, 20, 39]. The details about this approach will be reviewed in Sect In comparison with the case of large SOI ridge waveguides, it is much harder to achieve a nonbirefringent SOI nanowire experimentally by controlling the waveguide dimensions as desired because of the stringent fabrication tolerance. Due to the large structural birefringence of SOI nanowires [40], the photonic integrated devices usually suffer significant polarization dependence, as shown by the experimental results given in [36]. Furthermore, the polarization-dependent properties can be quite different from those devices based on the micrometer optical waveguides. For example, for a SOI-nanowire AWG device, not only the channel wavelength but also the channel spacing are polarization sensitive. This makes conventional polarization-compensation approaches ineffective [41], and novel solutions are desired. In [41 46], several special approaches are proposed to reduce the polarization sensitivity of SOI-nanowire-based photonic integrated devices including multimode interference (MMI) couplers, microring resonators, and AWG (de)multiplexers, which will be reviewed in Sect A general solution to eliminate the polarization sensitivity of photonic integrated devices based on SOI nanowires is using the so-called polarization-diversity technology [38, 47]. The basic principle is described as follows: The input light is separated by a polarization beam splitter (PBS) and two polarized beams are obtained (i.e. TE and TM). One polarized beam (e.g., TM) is then converted into the orthogonal one (TE) with a polarization rotator. Then the two beams with the same polarization state enter two identical PICs separately and two identical outputs are expected. One of the outputs is then converted back to its original polarization state using a second polarization rotator. Finally, one obtains two orthogonal beams, which are then combined with a polarization beam combiner. In such a polarizationdiversity circuit, the PBS and polarization rotator are the most important elements [38, 47], which have been studied for many years. In particular, the giant birefringence of SOI nanowires makes it possible to realize novel photonic devices for polarization management, including ultrasmall PBSs as well as polarization rotators. This is the reason for the recent surge of attention to the polarization-management devices on silicon, which will be reviewed in Sect. 3. In addition, polarization-management technologies are not only essential for solving the polarization issues of SOI PICs, but also the key for many applications, e.g., coherent optical communications, which has attracted much attention for long-haul optical fiber communications because it improves the spectral efficiency and consequently the communication capacity. Similar coherent technology may also be used in the future network-on-chip for optical interconnects. Thus, high-performance polarization-management devices with small sizes are also very interesting for coherent optical applications. In Sect. 4.1, we will give a review on the polarization management for coherent receivers. Finally, the strong confinement and the high nonlinear coefficient of SOI nanowires also enable efficient lowthreshold on-chip nonlinear photonic effects and applications [48]. For example, by using four-wave mixing (FWM) in silicon nanowires, various highly integrated all-optical signal processing components such as wavelength conversion [49 51], wavelength multicasting [52], and logic gates [53], have been developed. However, one should note that FWM is polarization sensitive and the efficiency is greatly related to the incident signal polarization state [54, 55]. The polarization dependence of the nonlinear photonic effects will be discussed and summarized in Sect Some specific solutions for polarization-insensitive silicon PICs In this section, several specific polarization-compensation approaches to achieve polarization-insensitive silicon PICs based on large SOI ridge waveguides as well as SOI nanowires are discussed and summarized Polarization management in SOI ridge waveguides and devices Waveguide birefringence: geometrical and stress-induced effects In planar optical waveguides, the modal birefringence (the difference in the effective index for the TM and TE polarizations n eff = n TE eff ntm eff ) results from a combination of geometrical, compositional and stress-induced effects. In high index contrast SOI waveguides, the cross-sectional geometry has the largest impact on the waveguide effective index and consequently on the birefringence. For optical waveguides of micrometer size, ridge structures as illustrated in Fig. 1 are generally used. By respecting the proper ratios between the ridge height H, width W and the etch depth D, single-mode-like operation can be achieved [11, 12]. There has been extensive work that shows both polarization degeneracy and single-mode conditions can be simultaneously fulfilled at specific waveguide aspect ratios [14 17]. The

3 REVIEW ARTICLE Laser Photonics Rev. (2012) 3 Figure 1 Schematic cross section of a SOI ridge waveguide. The inplane stress component in the uniform cladding film far from the ridge is denoted as σ film. drawback of this exclusively geometrical approach is that the conditions are rather restrictive, particularly for waveguides with a ridge height of less than 3 µm. These designs also require narrow waveguide widths and deep etching, resulting in high sensitivity to dimensional fluctuations. As an example, Fig. 2a (dashed lines) shows the geometrical birefringence n geo as a function of the etch depth D for waveguides with H = 2.2 µm. For a given W, n geo = 0 may be achieved at a specific value of D. At the birefringence-free point for W = 1.6 µm, the change of n geo with the fluctuation in the etch depth is for D = ± 10 nm. When W = 2.5 µm, n geo is less sensitive to the fluctuations in the etch depth ( for D = ± 10 nm near D = 1.5 µm), however the birefringence-free condition cannot be achieved. To reduce the birefringence below the required level ( n eff < 10 4 ) by controlling only the ridge aspect ratio W/D, dimension control on the order of 10 nm is required [19,20,39]. Using contact-print lithography, waveguide width variations of the order of 100 nm can be expected. Using state-of-the-art high-resolution lithogra- Figure 2 (online color at: (a) Calculated modal birefringence n eff for waveguides as a function of the etch depth D. Here, H = 2.2 µm, width W = 1.6 and 2.5 µm, cladding thickness t c = 0.7 µm and film stress σ film = 100 MPa. The dashed curves show the geometrical birefringence n geo (i.e. in the absence of stress), the solid curves show n eff, which includes both the geometrical and the stress-induced components. phy methods such as e-beam direct write or deep-uv steppers, dimensional control of the order of 10 nm is possible but still very challenging [56]. This sensitivity to waveguidesize variations increases as the core size decreases. The fabrication of a birefringence-free submicrometer wire waveguide requires a size control of better than 1 nm, which is not achievable with the current fabrication technologies [57]. Another source of birefringence can originate from the stress present in commonly used cladding layers such as silicon dioxide (SiO 2 ). Due to the different thermal expansion coefficients between Si ( K 1 ) and SiO 2 ( K 1 ), the oxide cladding, usually deposited at elevated temperatures, is under compressive stress at room temperature. This stress imparts anisotropic forces on the silicon ridge and causes corresponding material birefringence due to the photoelastic effect, given by [58 60]: n y n x = (C 2 C 1 )(σ y σ x ). (1) Here, σ i (i = x, y, z) is the stress tensor, n i is the material refractive index in the corresponding directions, and C 1 and C 2 are the stress-optic constants. For silicon, C 1 = Pa 1, and C 2 = Pa 1. Since these two constants have the opposite polarity, stress anisotropy is particularly effective in modifying the birefringence in silicon. The stress distributions in a SOI ridge waveguide are shown in Figs. 3a and b. The silicon ridge is under a compressive stress in the horizontal direction but under a high tensile stress in the vertical direction. The corresponding local material birefringence (n y n x ) is shown in Fig. 3c, with values as large as This material birefringence in turn causes a stress contribution n s to the modal birefringence, and the total modal birefringence is n eff = n TE n TM = n geo + n s. As shown in Fig. 4, n s increases monotonically with the oxide thickness t c until it reaches a plateau when the cladding layer is thick enough to bury the entire ridge. It also scales linearly with the stress level σ film [19, 20]. The stress-induced index variations resulted from commonly used oxide cladding films (with a stress of 100 MPa to 400 MPa) are of comparable magnitude to the geometrical birefringence found in typical SOI ridge waveguides ( 10 3 ) of micrometer size. By controlling t c and σ film, n s can be effectively tuned to adjust the total modal birefringence and advantageously employed in many applications [60, 61]. Polarization-independent operation has been achieved in a variety of components, including AWGs, ring resonators and MZIs. The same effect has also been used to achieve broadband polarization splitting. A few examples are described below. One should also note that this method is no longer effective for SOI nanowires where the birefringence is typically on the order of Polarization-independent AWGs based on SOI ridge waveguides In AWGs the polarization-dependent wavelength shift λ = λ TE λ TM mainly arises from the birefringence of

4 LASER & PHOTONICS 4 D. Dai et al.: Polarization management for silicon photonic integrated circuits Figure 3 (online color at: Stress distributions in the (a) x-direction and (b) y-direction. The ridge height is 2.2 µm, the width is 1.8 µm and the etch depth is 1.47 µm. The cladding oxide is 1 µm thick with a compressive stress of σ film = 320 MPa. (c) Stress-induced material birefringence (n y n x ) corresponding to the stress distributions shown in (a) and (b). Figure 4 Total modal birefringence n eff as a function of the cladding thickness t c and its stress level σ film. the arrayed waveguides and can be expressed as λ λ n eff /n g, where n g is the waveguide group index and λ is the operating wavelength in vacuum [62]. Prism-shaped polarization compensators in the combiner or the array regions have been used to reduce λ. These methods are effective in reducing λ, but both are accompanied with a penalty in the insertion loss [63, 64]. Using cladding stress engineering, a blanket upper cladding oxide film is deposited on the entire AWG without causing excess loss (Fig. 5a). As shown in Fig. 5b, SiO 2 cladding layers with different thicknesses can modify λ over a 2-nm wavelength range [19, 39]. The TE and TM spectra of a wet-etched AWG before and after polarization compensation are shown in Figs. 5c and d. The noncompensated AWG device has a polarizationdependent wavelength shift of λ 0.6 nm, arising from the geometrical birefringence of n geo in the arrayed waveguide. With an oxide upper cladding film of 0.6 µm in thickness, λ was reduced to below 0.04 nm for all channels (corresponding to n eff < ). The polarization-dependent loss (PDL) was also found to be negligible in these devices after the compensation. Figure 5 (online color at: (a) Optical image of a fabricated AWG. (b) Polarization-dependent wavelength shift λ as a function of the cladding thickness t c for AWGs fabricated using wet (waveguide top width W 1 = 1.1 µm and bottom width W 2 = 3.8 µm) and dry (W 1 = 1.85 µm and W 2 = 2.0) etching to a depth of D = 1.47 µm. The ridge height is H = 2.2 µm, and the cladding stress is σ film = 320 MPa. Measured spectra for an SOI AWG (c) without the oxide upper cladding, and (d) compensated using a 0.6-µm thick SiO 2 cladding. TM (solid) and TE (dashed).

5 REVIEW ARTICLE Laser Photonics Rev. (2012) 5 Figure 6 (a) Layout of the Mach-Zehnder delay interferometers (DIs), showing five DIs and test structures. The insert shows a 2 2 MMI coupler as a part of one DI. (b) PDF shift for two temperatures (T = 35 C and 70 C). (c) PDL of the filter curve maxima for TE and TM mode across the C-band. (d) Port imbalance of TE and TM light. (After Voigt et al., [67].) Polarization-independent couplers, interferometers and ring resonators based on SOI ridge waveguides Couplers, Mach-Zehnder interferometers (MZI) and ring resonators are basic building blocks frequently employed in a diverse range of applications, including optical communications, optical interconnect and optical sensing. However, polarization sensitivity has often been an obstacle that demands considerable efforts to mitigate [23, 29, 65]. In all these devices, the waveguide birefringence can be corrected using cladding stress similar to the case in AWGs (see Sect ). In a triplexer fabricated in 3-µm thick SOI, two layers of thin films are applied on top of the device to compensate the polarization dependence in the coupler splitting ratio. The coupling length difference between TE and TM was reduced from 25% to 2%, and the polarizationdependent loss (PDL) was reduced to less than 0.1 db by choosing the appropriate cladding thickness [66]. For ring resonators and MZIs that have a periodic spectral response, the birefringence can also be adjusted so that the TE response overlaps with the TM response of an adjacent interference order. An MMI-coupled Mach-Zehnder delay interferometer realized in 4-µm thick SOI waveguide technology (Fig. 6a) has been used for 40 GB/s differential phase shift keying (DPSK) demodulation where very precise birefringence control ( 10 5 ) is a key requirement [67]. A silicon nitride film was used as the cladding layer, so that the tensile stress in the cladding shifts the TE response by one free spectral range (FSR) relative to that of TM, therefore achieving apparent polarization independence. The measured performance is shown in Figs. 6b d. These devices also showed a very low temperature dependence (polarization dependent frequency shift PDF < 1 GHz) for chip temperatures up to 70 C. In ring resonators, apart from the birefringence in the cavity waveguides that can be corrected using the cladding stress, the polarization dependence of the evanescent coupling between the bus and cavity waveguides also needs to be minimized. MMI couplers are less sensitive to polarizations, making it a suitable alternative to achieve polarization independent light transfer. In the device shown in Fig. 7a, we used a restricted interference coupler that is 7.5 µm wide and 84 µm long to obtain a splitting ratio of 50:50 for both polarizations with a similar excess loss of 0.2 db [29]. Measured transmission spectra for a ring resonator with a radius of 200 µm are shown in Fig. 7b for both polarizations. Over the 4-nm scan range, the polarization-dependent wavelength shift is below 2 pm, demonstrating the effective- Figure 7 (online color at: (a) SEM image of a MMIcoupled ring resonator; (b) TE and TM transmission spectra of the ring resonator, with an upper SiO 2 cladding 0.8 µm thick, and film stress of σ film = 250 MPa.

6 LASER & PHOTONICS 6 D. Dai et al.: Polarization management for silicon photonic integrated circuits ness of this method of polarization control. The measured free spectral range (FSR) is 0.46 nm, and the quality factor Q [68] Polarization management in SOI nanowires and devices The birefringence of SOI nanowires Figure 8a shows the cross section of a typical SOI nanowire, which has a submicrometer rectangular Si core on a SiO 2 insulator. The upper cladding is usually SiO 2 (or polymer) for protection or quasi-symmetry in the vertical direction. For the application of optical sensing, the upper cladding is usually gas or liquid. Here, we focus on the case with a SiO 2 upper cladding as an example. Figure 8b and c, respectively, show the mode profiles of the TE and TM fundamental modes for the case of w co = 500 nm, h co = 300 nm and h cl = 2 µm as an example. It can be seen that there are distinct differences between the polarization modes because of the discontinuity of the normal E-field at the boundaries and consequently a large birefringence is expected. Figure 9a shows the calculated birefringence B as the core width w varies for different heights h. The birefringence B is defined as the difference in the effective refractive indices between TE and TM modes, i.e. B = n eff = n TM eff n TE eff. Here, both the SiO 2 upper cladding and buried oxide layers are assumed to be infinitely thick (i.e. h cl = ). One sees that the geometrical birefringence of a nonsquare SOI nanowire is very large due to the small cross section and the ultrahigh index contrast. For example, when h co = 300 nm and w co = 500 nm, which are the parameters often chosen in the published literature to achieve a low scattering loss as well as to satisfy the single-mode condition, the birefringence B is approximately 0.4 (which is 10 3 times Figure 8 (online color at: (a) Schematic cross section of a SOI nanowire; The mode profiles of the TE mode (b) and the TM mode (c) for the case of w co = 500 nm, h co = 300 nm, and h cl = 2 µm. Figure 9 (online color at: (a) The birefringence B when h cl = ; (b) the birefringence B as the uppercladding thickness h cl increases [40].

7 REVIEW ARTICLE Laser Photonics Rev. (2012) 7 more than that in a large SOI ridge waveguide). Zero birefringence is possible to obtain in principle by simply choosing a square Si core (e.g., 300 nm 300 nm [69]), which, however, usually gives a high scattering loss than a wide and thin SOI nanowire [70, 71]. More importantly, it can be seen from Fig. 9 that the nonbirefringent SOI nanowire is very sensitive to the variations of the waveguide dimension. The slope of the curve at the nonbirefringent point is larger when the size of the core is smaller. This indicates that a nonbirefringent design is more sensitive to the size variation of the core for a smaller SOI nanowire, which results in a more stringent control in the fabrication process. Therefore, it is of interest to use postcompensation approaches to adjust the birefringence. For a very small adjustment range, the stress approach discussed in Sect. 2.1 might be useful. It is also possible to adjust the birefringence by modifying the thickness h cl of the SiO 2 upper cladding through a postetching process. Figure 9b shows the variation of the birefringence [B(h cl ) B(h cl = )] as the thickness h cl of the SiO 2 upper cladding varies. It can be seen that one can accurately adjust the birefringence of an SOI nanowire by controlling the upper-cladding thickness with a good fabrication technology. This should be useful to compensate the residual birefringence due to fabrication errors. However, even when nonbirefringent SOI nanowire is obtained using advanced fabrication processes and postcompensation methods (though still difficult), the corresponding SOI-nanowire PICs may still be polarization sensitive. For example, for an AWG (de)multiplexer based on a square SOI nanowire (e.g., 300 nm 300 nm), only the central wavelength could become polarization independent, while the channel spacing is still polarization dependent, due to the huge birefringence of the nanoslab region [41]. Therefore, special methods are needed for reducing the polarization sensitivity of SOI-nanowire PICs, which will be discussed below. Figure 10 (online color at: (a) The schematic configuration of an MMI coupler; (b) the beat length difference L π as a function of the MMI width w MMI for different core heights h co [43] The polarization dependence and compensation of PICs based on SOI nanowires A Polarization-insensitive MMI couplers Fig. 10a shows the schematic configuration of an MMI coupler based on SOI nanowires [43]. According to the self-imaging theory for the case of symmetric interference (e.g., a 1 N MMI coupler), the first N-fold image is formed at L MMI = 3L π /4N, where the beat length L π = π/(β 0 β 1 ) (in which β 0 and β 1 are the propagation constants for the two lowest-order modes). For a polarization-insensitive MMI coupler, the difference between the beat lengths of the two polarizations should be zero, i.e. L π = L π(te) L π(tm) = 0. Figure 10b shows the difference L π as the MMI width w MMI increases for different core heights h co. According to this figure, an optimal width w MMIo can be obtained to make L π = 0 for a chosen core height [43]. For example, the optimal MMI width is w MMIo = 3.86 µm and the corresponding MMI length is L MMI = 15.3 µm when h co = 400 nm. Figures 11a and b show the simulated light propagation in Figure 11 (online color at: The light propagation in an optimized 1 2 MMI splitter with h co = 400 nm and w MMI = 3.86 µm. (a) TE polarization; (b) TM polarization [43]. this optimized polarization-insensitive 1 2 MMI splitter for the TE and TM polarizations, respectively. From these figures, it can also be seen that a polarization-insensitive

8 LASER & PHOTONICS 8 D. Dai et al.: Polarization management for silicon photonic integrated circuits 1 N (2 < N < 6) splitter could be realized easily by choosing the MMI length as L MMI = 3L π /4N. For example, one has the length L MMI = 7.65 µm for a 1 4 MMI splitter. Another way to realize a polarization-insensitive MMI coupler is to use a sandwiched structure [72], which has a center layer (with a low refractive index n s ) between two Si layers with high refractive indices n H, as shown in Fig. 12. There is an optimal refractive index n s0 for the center layer that leads to identical beat lengths L π for both polarizations, and thus a polarization-insensitive design is achieved. The analysis given in [72] shows that the performance of such a sandwiched MMI splitter is especially sensitive to the index n s and the thickness h s of the center layer. On the other hand, this also implies that the propagation properties in these waveguides can be easily modulated using external effects such as thermo-optical and electro-optical effects, showing the possibility of realizing efficiently tunable/ switchable optical functional devices with low operating powers. This Si sandwich nanowire is also used for realizing a polarization-insensitive microring resonator (MRR) filter [73]. Figure 13 (online color at: (a) The topview image of the fabricated SOI-nanowire AWG (de)multiplexer; (b) the measured spectral responses for the TE and TM polarizations. Figure 12 (online color at: The cross section of a Si sandwiched nanowire. B Polarization-insensitive AWG (de)multiplexers An AWG demultiplexer is one of the most important devices in a dense wavelength-division-multiplexing (WDM) system for optical communications. Ultracompact AWG demultiplexers have been demonstrated previously by using SOI nanowires whose width is larger than the height [35 37]. Figure 13a shows the fabricated ultrasmall AWG (de)multiplexer based on 500 nm 250 nm amorphous silicon nanowires, and the measured spectral responses for the TE and TM polarizations are shown in Fig. 13b. It can be seen that the SOI-nanowire AWG device suffers a significant polarization-sensitivity due to the high birefringence of SOI nanowires and the measured polarization-dependence wavelength (PDλ) is as large as 35 nm for the present example. Instead, when choosing square SOI nanowires, one could eliminate the polarization-dependent wavelength (PDλ) of the central channel. However, the FPR (free propagation region) of an AWG still has a significant positive birefringence (n TE > n TM ), which makes the channel spacing of an SOI-nanowire AWG very polarization dependent. Consequently, those polarization-compensation methods for a large AWG based on micrometric waveguides become unavailable because they compensate the PDλ of the central channel only [74, 75]. The polarization diversity approach is one of the most effective methods [38, 47], which will be discussed in Sect. 3. In this section, we focus on the specific technique without polarization diversity for compensating the polarization dependence of SOI-nanowire AWGs. According to the formulas for the central wavelength and the channel spacing [76], the procedure to design a polarizationinsensitive AWG demultiplexer is given as follows [41]. a) In order to make the channel spacing λ ch polarization insensitive, i.e. λ ch(te) = λ ch(tm), optimize the width w co and the height h co of the arrayed waveguides. b) In order to eliminate the PDλ ( = λ 0(TE) λ 0(TE) ) of the central channel, one should choose appropriate diffraction orders m TE, and m TM for TE and TM polarizations. c) Finally, choose an appropriate position for the input waveguide so that the residual PDλ is compensated by the small PDλ introduced by the polarization dependence of the FPR effective index. A similar approach was proposed to compensate the polarization dependency of an SOI-nanowire AWG by using an oblique incident angle and different diffraction orders for TE and TM polarization with an upper cladding

9 REVIEW ARTICLE Laser Photonics Rev. (2012) 9 of SU-8 polymer [42]. As an example of the design of a polarization-insensitive SOI-nanowire AWG, the parameters are chosen as follows: L FPR = 36 µm, d g = 1.6 µm, λ ch = 1.6 nm, and the channel number N ch = 4. By following the steps given above, the optimal parameters are: h co = 362 nm, w co = 297 nm,x i = µm, m TE = 61, and m TM = 72. Figure 14 shows the simulated spectral responses of the central and edge channels. It can be seen that the peaks of the spectral responses for the TE and TM polarizations are almost the same. This indicates that both the channel spacing and channel wavelengths are polarization insensitive, as predicted. Figure 14 (online color at: The simulated spectral responses (for the TE and TM polarizations) of the designed polarization-insensitive AWG [41]. (a) the central and edge channels; (b) the enlarged view. 3. Polarization-diversity technology: a general solution for polarization-insensitive silicon PICs As a general solution to eliminate the polarization sensitivity of silicon photonic integrated devices, the so-called polarization-diversity technology has attracted considerable attention in recent years [38, 47]. Polarization diversity is also very important for many other applications, such as coherent receiver systems [77]. The most important elements for realizing the polarization-diversity technology include PBS and polarization rotator. In [78], a smart design for a polarization-diversity system was demonstrated to realize polarization-insensitive AWG by using a two-dimensional (2D) grating coupler with circular holes. This 2D grating coupler simultaneously serves as a fiber-chip coupler, a polarization splitter and a rotator. The 2D grating has a period of 605 nm, and the circular holes have a diameter of 390 nm. The waveguides of the fiber coupler were etched through the silicon top layer, while the grating holes were etched only 70 nm deep. The 2D grating coupler first introduced in [79] can be seen as a superposition of two 1D grating couplers. Consequently, the polarization of the light at the fiber is decomposed into two linear polarizations, which then get coupled to two 10-µm wide on-chip waveguides. In order to avoid a cavity response in the waveguides due to the strong second-order reflections of the grating, the 2D grating is detuned and the fiber is tilted with a 10 angle from the normal direction. As a result, the two on-chip waveguides are no longer perpendicular to each other, but angled inward at 3.1. The experimental results show that the 2D fiber couplers can enable a polarization-independent circuit. However, the polarization-dependent loss (PDL) might still be an issue because some careful alignment is required for different input polarizations in order to obtain balanced coupling efficiencies to both on-chip waveguides [78]. In order to reduce the PDL of the 2D-grating coupler, a method of introducing a phase shifter in one of the arms of the polarization-diversity circuit was proposed and demonstrated experimentally [80]. In this way the PDL is effectively reduced to 0.15 db, and the low-pdl bandwidth also increases. Therefore, such a polarization-diversity system is very suitable for realizing polarization-insensitive devices that can be directly connected to fibers for, e.g., the fiber-to-the-home (FTTH) applications. However, it does not work for the case when the device (e.g., AWG) needs to be integrated with other components in the same chip. Therefore, inplane polarization-management devices are desired for future large-scale PICs. The high birefringence of SOI nanowires and Si nanoslot waveguides makes it possible to realize novel ultrasmall polarization-management devices, including PBSs as well as polarization rotators, which will be reviewed in the following sections Polarization beam splitter (PBS) Since a PBS is a basic functional element for many applications when polarization control is desirable, many kinds of waveguide-type PBSs have been reported in various material systems by using various structures, e.g, MMI structures [81 85], directional couplers (DCs) [86 91], Mach- Zehnder interferometers (MZIs) [94 96], and photonic crystal (PhC) structures [97 100]. Some of our work on siliconbased PBSs is summarized here PBS based on MMI structures For conventional MMI-based PBS, the device length is usually chosen as the common multiple of the self-imaging lengths for the TE and TM polarizations. Consequently, the total length for the PBS is quite long because the selfimaging length difference between the two polarizations in a MMI section is generally not significant. In order to shorten the device length, a design with two cascaded MMI sections is presented [82]. As shown in Fig. 15, there is a slight shift between the self-imaging positions of the TE and TM polarizations due to the birefringence. Then, one can put a receiving waveguide at the top side for the polarization (e.g., TM here) which has a

10 LASER & PHOTONICS 10 D. Dai et al.: Polarization management for silicon photonic integrated circuits Figure 15 (online color at: The numerical simulation results for the light propagation in a straight MMI section for (a) TM polarization, and (b) TE polarization. longer self-imaging length. For the other polarization, a second narrow MMI section is cascaded to collect and focus the light. Figure 16a shows the PBS based on the cascaded MMI structure, which could also be used as WDM demultiplexers [101]. The SEM picture of the fabricated PBS is shown in Fig. 16b. Figure 17 (online color at: A PBS based on a PC-assisted MMI coupler, (a) the schematic structure [97]; (b) the SEM image [102] Grating-based PBS (a) (b) Figure 16 (online color at: A PBS based on cascaded MMI sections, (a) the schematic structure; (b) the SEM picture. Another approach to achieve short MMI-based PBS is introducing a polarization-selective photonic-crystal (PhC) structure in the middle of the MMI section [97], as shown in Figs. 17a and b. This 2 2 MMI coupler works similarly to a regular MMI coupler, while only one polarization is reflected and the other one goes through the PhC structure. In this way, the length Lt of the MMI section is as short as the beat length of the through polarization (TM here), i.e. Lt = LπTM. The distance Lr between the PhC structure and the input end of the MMI section is half of the beat length of the reflective polarization, i.e. Lr = LπTE /2. As discussed in Sect , a PhC structure is polarization sensitive and therefore can be utilized to separate two orthogonal polarizations. In [98, 99], a bidirectional grating coupler is demonstrated to serve as a PBS as well as a grating coupler to optical fibers, as shown in Fig. 18. Figs. 19a and b show the two-dimensional finite-difference time-domain (2D-FDTD) simulation results for light propagation in the optimized grating structure. The related parameters are given as follows: the etching depth a = 70 nm, the period Λ = 630 nm, the period number N = 16, the tilt angle θ = 15, the distance p1 = 3.9 µm, the top silicon thickness tsi = 260 nm and the BOX thickness tbox = 1.95 µm. From these figures, it can be seen that the polarization-splitting behavior is observed clearly. The calculated wavelength dependence of the coupling efficiencies for both polarizations is also shown in Fig. 20. It is shown that the coupling efficiencies for both polarizations are about 50%, while there is a very broad 3-dB bandwidth of more than 70 nm. Furthermore, the polarization crosstalk is lower than 22 db (refer to the inset of Fig. 20). Fig. 21a shows the structure and setup for measurements, where the grating in the center is used as the input coupler while the other two are output couplers. The input fiber is tilted by 15, while the two output fibers are tilted by 15. The measured coupling efficiencies of the two orthogonal polarizations are shown in Fig. 21b. It can be seen that a coupling efficiency as high as 43% for TM polarization is achieved, while the efficiency for TE polarization is lower (33%). The difference is mainly caused by fabrication errors. The measured extinction ratio between the two orthogonal

11 REVIEW ARTICLE Laser Photonics Rev. (2012) 11 Figure 18 The schematic configuration of the grating structure serving as a PBS as well as a grating coupler. Figure 19 (online color at: (a) The field distribution (E x ) for the TE polarization; (b) the field distribution (H x ) for the TM polarization at λ = 1550 nm. The design parameters are a = 70 nm, Λ = 630 nm, N = 16, θ = 15, p 1 = 3.9 µm, t Si = 260 nm and t BOX = 1.95 µm. Figure 20 (online color at: The wavelength dependence of the coupling efficiency for the optimized polarization splitter. The inset shows an enlarged view inside the dotted box.

12 LASER & PHOTONICS 12 D. Dai et al.: Polarization management for silicon photonic integrated circuits Figure 21 (online color at: (a) The structure and setup for measurements; (b) the measured coupling efficiency for both polarizations; (c) the measured extinction ratio. polarizations is shown in Fig. 21c. It can be seen that the extinction ratio is as high as 20 db in the whole C-band, which agrees well with the theoretical prediction. Such a grating-based PBS is very suitable for coupling the chip with optical fibers, but not for use within a chip PBS based on evanescent coupling structures As an alternative, an evanescent coupling structures is a popular structure for PBSs because of its simplicity and easy design. When using a symmetrical DC consisting of two identical coupling waveguides for PBS, one should design the coupling region to satisfy the following condition: pl π TE = (p + m)l π TM, where p is an integer, m = ± 1, 3, 5,..., L π TE and L π TM are the coupling lengths for the TE and TM polarizations, respectively. Then, the length of the coupling region for the DC-PBS is chosen as L = pl π TE = (p+m)l π TM, which is usually quite long [86,87]. Recently, several versions of PBSs based on symmetric SOInanowire DC s have been reported [88, 91, 103], employing the large birefringence of SOI nanowires [40] and nanoslot waveguides [91]. However, one should note that this type of DC-PBS is intrinsically long, regarding the principle of choosing the length as L = pl π TE = (p + m)l π TM. In addition, such a DC-PBS behaves like a series-cascaded DC filter, which has a smaller wavelength-bandwidth than a single-stage DC. In order to achieve a compact, broadband and fabricationtolerant PBS, it is desired to have an improved coupling system, in which only one polarization has a strong crosscoupling, while the other polarization is almost not coupled. With such an improved coupling system, the length of the coupling region of the PBS could be as short as the beat length of TE or TM polarizations, i.e. L = L π TE, or L = L π TM. Such an improved coupling system could be achieved in the following two ways. One is using a strongly polarization-dependent coupling system, in which L π TE L π TM or L π TM L π TE. In [92], a 7 16 µm 2 PBS was demonstrated by using a DC based on two identical 400 nm 200 nm SOI nanowires. The DC is designed to obtain L π TE L π TM by choosing the gap width appropriately and the length of the coupling region is chosen as short as L = L π TM. However, slight coupling for the TE polarization still occurs, which is not beneficial to achieving a high extinction ratio. A solution to improve the extinction ratio is to use a cascaded structure, which, however, makes the PBS longer and also reduces the bandwidth. The other way is using an asymmetrical coupling system, in which the waveguide dimension is optimized to satisfy the phase-matching condition for only one polarization so that a complete crosscoupling occurs. In contrast, for the other polarization, there is almost no crosscoupling caused by the phase mismatching due to the strong birefringence. Then, one could separate the two orthogonal polarizations within a short length (i.e. equal to the coupling length of the crosscoupled polarization). In [93], a PBS with a 16-µm long coupling region including two parallel SOI nanowires and a nanoslot waveguide in between is presented. This coupling system behaves like two parallelly cascaded asymmetrical couplers consisting of a SOI nanowire and a nanoslot waveguide. In contrast, a single-stage asymmetrical coupling system is more compact as well as broadband. In the following, two types of ultrashort PBSs based on single-stage asymmetrical couplers are reviewed. A PBS based on an asymmetrical coupler consisting of a SOI-nanowire and a nanoslot waveguide [105] Figs. 22a and b show an asymmetrical coupling system for PBSs, consisting of a SOI-nanowire and a nanoslot

13 REVIEW ARTICLE Laser Photonics Rev. (2012) 13 Figure 23 (online color at: The effective indices of a SOI-nanowire and a nanoslot waveguide as the core width (w Si, w co ) varies. Figure 22 (online color at: The PBS based on an asymmetrical coupler consisting of a SOI-nanowire and a nanoslot waveguide: (a) the schematic configuration; (b) the SEM picture; (c) the cross section of the waveguides in the coupling region. waveguide. In order to integrate them conveniently with other components in the same chip, the S-bend section for the nanoslot waveguide plays a role as a mode converter between the input/output SOI-nanowire and the nanoslot waveguide (similar to that in [106]), which also makes the PBS very compact. In the coupling region, these two waveguides are designed to satisfy the phase-matching condition for TM polarization so that it is completely coupled to the cross-port when choosing the length of the coupling region appropriately. On the other hand, the phase-matching condition is not satisfied for TEpolarized light and consequently it goes through the SOInanowire almost without coupling. Consequently, the TE- and TM-polarized light are separated within a very short length. Fig. 23 shows the calculated effective indices of a SOInanowire and a nanoslot waveguide as the waveguide core width (w Si, w co ) varies for the case with h co = 250 nm. It can be seen that the effective indices of the TM-polarization mode for the two different types of waveguides are close, and consequently the phase- Figure 24 (online color at: Light propagation in the designed PBS with w co = 0.4 µm, w Si = 0.26 µm, h co = 250 nm, w slot = 60 nm, and w g = 100 nm. (a) TM; (b) TE. matching condition can be satisfied (i.e. n eff TM1 = n eff TM2 ) by choosing the core width w co and w Si appropriately, e.g., w co = 0.4 µm, w Si = 0.26 µm and w slot = 60 nm. Therefore the TM-polarized light is completely coupled to the cross-port when choosing the length of the coupling region appropriately (see Fig. 24a). On the other hand, there is a serious phase mismatch for the TE-polarized light, and consequently the evanescent coupling is negligible. The TE-polarized light is then output from the through port, as shown in Fig. 24b. Such a design was independently proposed in [107] and a 13.6-µm long PBS was demonstrated experimentally. The average extinction ratios are about 21 db and 17 db over the entire C-band for the TE and TM polarizations, respectively.

14 LASER & PHOTONICS 14 D. Dai et al.: Polarization management for silicon photonic integrated circuits Figure 25 (online color at: The configuration of the ultrashort PBS based on a bent DC, (a) a 3D view; (b) the SEM picture for top view; (c) the schematic configuration (top view). B PBS based on a bent directional coupler [108] Fig. 25a shows the 3D view of an ultrashort PBS [108], which consists of a bent coupling section with two bending waveguides and an S-bend section with a sharp bend of radius R0. Figure 25b and c, respectively show the SEM picture of the fabricated PBS and the schematic configuration with the parameters labeled. The S-bend section is not only for decoupling the two bent waveguides, but also functions as a TE-passed polarization filter by choosing a small radius R0 for which the TM polarization has a much higher loss than the TE polarization. Such a cascaded compact polarizer enables a high extinction ratio in a broad wavelength range and also leads to large fabrication tolerances. The bent coupling section is designed to make the phase-matching condition satisfied for one polarization (e.g., TM) by choosing different core widths (w1 and w2 ) for the two bent waveguides and consequently a complete crosscoupling occurs when choosing the length of the coupling region [109]. For the other polarization (e.g., TE), there is no coupling almost because the phase-matching condition is not satisfied due to the strong waveguide birefringence. Figs. 26a and b, respectively show the calculated optical path lengths (OPL) for the TE and TM fundamental modes as the waveguide width varies. In this example, the parameters are chosen as R2 = 20 µm, and R = R2 R1 = 700 nm to have a gap width around 200 nm since the Si core width is chosen as wco 500 nm to be single mode. It is designed to make the phasematching condition satisfied for TM polarization that has a much shorter coupling length than the TE polar- Figure 26 (online color at: The optical path lengths (OPL) as the waveguide width varies when R2 = 20 µm, (a) TM; (b) TE. ization for 500 nm 220 nm SOI nanowires. The dashed line in Fig. 26a gives the optimal widths (w1, w2 ) for the two waveguides to be phase matched, e.g., (w1, w2 ) = (0.534 µm, 0.46 µm). For the TE polarization, there is a significant phase mismatch, as shown in Fig. 26b. The S-bend section is designed so that the bending loss is negligible for TE polarization and the end separation ( 2 µm) of the two output ports is large enough to be decoupled. The S-bend section is also designed to include a sharp bent section (R0 = 3 µm) to be the TE-passed polarizer, which helps to filter out the residual TM polarization at the through port and consequently improve the extinction ratio. Figure 27a and b show the light propagation in the designed PBS for TE and TM polarizations, respectively. It can be seen that the TM polarization is coupled and output from the cross-port, while the TE polarization is output from the through port with negligible crosscoupling. The total length for the PBS is only 9.5 µm, which is one of the smallest PBS reported until now. Further numerical analyses also show that the present PBS has a very large bandwidth (>200 nm for an extinction ratio

15 REVIEW ARTICLE Laser Photonics Rev. (2012) 15 Figure 27 (online color at: The light propagation in the designed PBS with L dc = 4.5 µm, R 1 = 19.3 µm, R 2 = 20.0 µm,w 1 = µm, w 2 = 0.46 µm, and w g = 203 nm. (a) TM; (b) TE. of 10 db) and a large fabrication tolerance (>± 60 nm). The ultrabroad band and the large fabrication tolerance is attributed to the cascaded TE-pass polarizer based on the sharp bending section Polarization rotators In comparison with PBSs, it is even more difficult to realize waveguide-type polarization rotators because a planar waveguide usually has a very good ability to maintain polarization and it is not easy to rotate its optical axis. Great efforts have been made to realize polarization rotators in the past by introducing specific anisotropy in the waveguide structure. In [110, 111], the structure with periodic sections of asymmetrical loads is presented to realize polarization rotators. The problem is that the device is quite long (e.g., 3 mm) and the excess loss is relatively large due to the scattering and mode-mismatching at the junctions between alternating sections. Similarly cascaded bent sections have also been used for polarization rotators [112, 113], whose length could be greatly shortened with the help of slanted waveguide sidewalls (e.g., 117 µm [112]). However, the design and fabrication are quite complex. Recently, great efforts have been made to realize a simple polarization rotator with a Figure 28 (online color at: (a) The schematic configuration of the present polarization rotator; (b) the cross section of the asymmetrical SOI nanowire for the polarizationrotation section. single straight section [ ]. In [114], a compact (as short as 150 µm) GaAs-AlGaAs polarization rotator is realized by utilizing the reactive ion-etch lag effect. Another type of short polarization rotator ( 50 µm) with a low insertion loss ( 1 db) is designed and fabricated by using angled InP/InGaAsIn waveguides [115]. For silicon photonics, polarization rotators using micrometric SOI ridge waveguides with slanted sidewalls have also been demonstrated [ ], but they are as long as several hundred micrometers. Furthermore, the fabrication of such slanted sidewalls is obviously difficult [120]. Silicon photonic wirebased polarization rotators have also been demonstrated, although they generally involve significant modifications to the wire waveguide structures [38, 121]. In [122], a novel design for polarization rotators is proposed by using an SOI nanowire with a cut corner, as shown in Figs. 28a and b. The proposed polarization rotator consists of an input section, a polarization-rotation section, and an output section. The input and output sections are based on standard square SOI nanowires, while the polarizationrotation section is formed by an SOI nanowire with a cut corner (see Fig. 1b). In the polarization-rotation section, the asymmetrical waveguide has two lowest-order modes that are almost fully hybridized, i.e. the overlap between the dominant and nondominant field components of these

16 LASER & PHOTONICS 16 D. Dai et al.: Polarization management for silicon photonic integrated circuits Figure 30 (online color at: The structure of the PSR consisting of a taper and an asymmetrical directional coupler [124], (a) a 3D view; (b) a top view Polarization splitter-rotator (PSR) Figure 29 (online color at: Optical field contour map of (a) E x and (b) E y in the polarization-rotation section when W e = 240 nm, and H e = 240 nm [122]. modes is very large. When light enters the polarizationrotation section, these two hybridized eigenmodes are both excited and two-mode interference takes place along this section. The length of the polarization-rotation section is then determined by the beat length L π = π/(β 0 β 1 ), where β 0 and β 1 are the propagation constants of these two hybridized modes, respectively. Since these two hybridized modes have very different propagation constants due to the strong confinement and asymmetrical cross section, a very short polarization-rotation section is obtained. Figure 29a and b show the three-dimensional FDTD simulation results for light propagation in an optimized polarization rotator, which has the following parameters: H = 500 nm, W = 500 nm, W e = 240 nm, and H e = 240 nm [122]. It can be seen that the input TE-polarization mode is successfully converted to the TM-polarization mode at the output. With such a design, the length of the polarization-rotation section is L c 7.2 µm, which is much shorter than those previously reported. Recently, a slightly modified polarization rotator configuration was demonstrated experimentally [123] and the measured TE-TM polarization rotation efficiency is 0.51 db over a wavelength range of 80 nm. It has also shown that the design is compatible with CMOS fabrication capabilities. As discussed in Sect. 3.2, regular waveguide-type polarization rotators are usually accompanied by complex and difficult fabrication. In [124, 125], novel designs with a simple fabrication (needing one-step etching only) are proposed and demonstrated. In addition, these designs enable polarization splitting and rotation simultaneously, which is attractive for ultracompact polarization-diversity circuits. In [124], the proposed PSR consists of a taper and an asymmetrical directional coupler, as shown in Fig. 30. The taper section is the key element, which converts the input TM fundamental mode to the higher-order TE mode. The working principle is based on the mode coupling caused by the mode hybridization in a high index-contrast optical waveguide with an asymmetrical cross section. As an example, Figs. 31a c show the effective indices for all the eigenmodes in a SOI nanowire with an air, SiO 2, and Si 3 N 4 upper cladding (n cl = 2.0), respectively, to be asymmetrical or symmetrical in the vertical direction. When the upper cladding is SiO 2, the SOI nanowire becomes vertically symmetrical and consequently the modes are linearly polarized. On the other hand, when the upper-cladding index is not equal to that of the buffer layer (SiO 2 ), the mode properties become more complicated, as shown in Figs. 31a and c. The dashed curves in Figs. 31a and c indicate that an efficient mode conversion might happen between the TM 0 mode and the TE 1 mode when light propagates along a width-varying taper section. Such a mode conversion was also observed theoretically as well as experimentally in submicrometer SOI ridge optical waveguide tapers [126]. One should minimize it when a low-loss adiabatic taper structure

17 REVIEW ARTICLE Laser Photonics Rev. (2012) 17 Figure 32 (online color at: The light propagation in the designed PSR when the input field is TM polarization (a), and TE polarization (b). Here, the taper lengths are: L t p1 = 4 µm, L t p2 = 44 µm, and L t p3 = L t p1 (w 3 w 2 )/(w 1 w 0 ). The other parameters are w 0 = 0.54 µm, w 1 = 0.69 µm, w 2 = 0.83 µm, w 3 = 0.9 µm, w g = 0.15 µm, and L dc = 7.0 µm. Figure 31 (online color at: The effective indices for the eigenmodes of SOI nanowires with (a) air cladding; (b) SiO 2 cladding; (c) Si 3 N 4 cladding. Here, the Si thickness h co = 220 nm [124]. is expected [127], while it can be utilized to achieve a PSR as proposed in [124]. As shown in Fig. 30, an asymmetrical directional coupler is formed by placing a narrow optical waveguide (w 4 ) close to the wide waveguide (w 3 ), so that the TE 1 mode generated by mode conversion in the taper section is then coupled to the TE 0 mode of the adjacent narrow waveguide. As a result, the launched TM 0 mode at the input end is converted into the TE 0 mode at the cross-port of the asymmetrical directional coupler, as shown in Fig. 32a. In contrast, the input TE polarization keeps the same polarization state when it goes through the adiabatic taper structure and is not coupled to the adjacent narrow waveguide because of the serious phase mismatching, as shown in Fig. 32b. This way, the TE- and TM-polarized light are separated while the TM 0 mode is also converted into the TE 0 mode). The simulations show that the designed PSR has a bandwidth of over 70 nm and the tolerance for the width deviation is about 10 nm< w <20 nm for an extinction ratio of 10 db. A larger bandwidth and fabrication tolerance could be achieved by choosing a longer taper [124]. Instead of using a relatively long taper section in the above design, a more compact PSR device can be realized by directly using the polarization mode coupling between two nonidentical SOI nanowires with asymmetrical cross sections [125], as shown in Fig. 33. Adiabatic tapers were used at the input and two output ports for connecting with the standard single-mode SOI waveguide of 450 nm width in the rest of the circuit. The principle is very similar to that presented in Fig. 30, except that it is based on the mode coupling between the TE 0 mode in waveguide #1 and the TM 0 mode in waveguide #2, instead of the coupling between two modes in the same waveguide (Fig. 32). The simulated transmission spectra T i- j t(c) of this structure are presented in Fig. 34, where the subscript t or c indicates the through-port or cross-port spectrum of the device, respectively, and the superscript i- j, where i and j can be either TE or TM, indicates the spectrum from mode i at the input, to mode j at the output. Here, the widths of the two waveguides are 600 nm and 333 nm, respectively; the thickness of the SOI waveguide is 250 nm; the gap between

18 LASER & PHOTONICS 18 D. Dai et al.: Polarization management for silicon photonic integrated circuits Figure 33 (online color at: Schematic (a) and fabricated (b) structure of a compact PSR device using the mode coupling between two SOI waveguides with an asymmetrical cross section [125]. Figure 34 (online color at: Simulated transmission coefficients between differently polarized modes from the input-port to the cross-port (a) and the through-port (b) [125]. The transmission coefficients that are not presented are well below 35 db. the waveguides is 100 nm; the coupling length is 36.8 µm, and we use air cladding to achieve the asymmetrical crosssectional structure. Due to a large mode index mismatch, the TE mode mainly remains in the input waveguide (Tt TE-TE close to 1), and only a small amount of power is coupled to the cross-port (Tc TE-TE ). On the other hand, the TM mode in the input waveguide shows a strong coupling to the TE mode in the cross-port waveguide while passing through the coupling section. This coupling (Tc TM-TE ) reaches the peak value of about 0.46 db around a wavelength of 1550 nm. The remaining TM mode power resides in the through-port Figure 35 (online color at: Measured transmission coefficients between differently polarized modes from the input-port to the cross-port (a), and the through-port (b) [125]. (Tt TM-TM ) and cross-port (Tc TM-TM ), and become the main source of cross talk in the present device. Such a structure is fabricated on a commercial SOI wafer using E-beam lithography (JEOL JBX-9300FS) and dryetching technologies. One such finished device is shown in Fig. 33b. The waveguides were tapered up to a width of 4 µm at the cleaved facets for better coupling with lensed fibers. The measured spectral responses are presented in Figs. 35a and b, which show very similar results to those from the simulations. One can see that the overall insertion

19 REVIEW ARTICLE Laser Photonics Rev. (2012) 19 loss and extinction ratio of this device is < 0.6 db and > 12 db, respectively, in the whole C-band. Fig. 36 shows the measured transmission coefficients for two fabricated PSR devices with the same design parameters on the same die. It can be seen that there is good consistency between them, which indicates good fabrication repeatability for the proposed device. Tc T M T E Figure 37 (online color at: The layout of the designed polarization-insensitive AWG (de)multiplexer. Figure 36 (online color at: The measured transmission coefficient Tc T M T E of two PSR devices with the same parameters on one SOI die. 4. Applications 4.1. Polarization-insensitive silicon photonic circuits with a polarization-diversity system Polarization-diversity technology has been used successfully in ring resonators [38] and AWG (de)multiplexers [78]. Bogaerts et al. [78] presented a polarization-diversity SOInanowires AWG (de)multiplexer using 2D grating fiber couplers as integrated polarization splitters and rotators, resulting in an overall polarization-insensitive circuit. The two polarizations go through the same AWG in the opposite directions. It was the first demonstration of a functional polarization-diversity circuit implemented in SOI nanowires, including interfaces to a single-mode fiber. This is indeed a good solution in some cases, e.g., for an individual AWG chip. However, this is no longer suitable when one wants to integrate an AWG device with other photonic circuits on the same substrate. the other goes through. The polarization that goes through is then reflected by the reflector connected at the end of the second section. In this way, the two polarizations (TE and TM) pass through different light paths. Since both the central channel wavelength and the channel spacing in SOInanowire-based AWG (de)multiplexers are polarization sensitive, one should have at least two adjustable parameters to realize polarization insensitivity. With the present design, one can diminish the polarization dependence of both the central channel wavelength and the channel spacing by adjusting the light-paths, i.e. by optimizing the core width w CO2 and length L 2 j of the second section. Furthermore, such a reflective-type structure is beneficial to achieve a compact AWG (de)multiplexer. Recently, the reflective SOInanowire AWG (de)multiplexer with photonic-crystal (PhC) reflectors has been demonstrated experimentally [129]. The optimized PhC reflector can have a high reflection efficiency and an ultrasmall footprint, as shown in Fig. 38, which Polarization-transparent AWG (de)multiplexer with a polarization-diversity circuit In [128], a novel approach is proposed for a polarizationinsensitive SOI-nanowire AWG (de)multiplexer of the reflective type by introducing an inline PBS in each arrayed waveguide, as shown in Fig. 37. The proposed reflective- AWG consists of an input waveguide (at the edge), an FPR, several output waveguides (on the same side of the FPR as the input waveguide), and many arrayed waveguides. Each arrayed waveguide has two sections divided by an inline PBS. With this PBS, one polarization is reflected and Figure 38 (online color at: The calculated reflection spectral responses for the designed PhC reflector. The inset is the SEM picture for the fabricated PhC reflectors at the end of the arrayed waveguides.

20 LASER & PHOTONICS 20 D. Dai et al.: Polarization management for silicon photonic integrated circuits indicates that a PhC reflector is a good option for reflective AWGs. For the proposed reflective polarization-insensitive SOInanowire AWG (de)multiplexer, the PBS inserted in each arrayed waveguide is a key element. It is possible to use a regular PBS, which usually has one input port and two output ports. However, in this case, one has to introduce two reflectors for each arrayed waveguide, and consequently the photonic circuit becomes much more complex and a large area is occupied. In order to avoid that, an inline PBS based on a Bragg grating is an ideal option, as shown in Fig. 39. Thereafter, the width w CO2 and length difference L 2 between two adjacent arrayed waveguides should be chosen carefully. The design procedure is given as follows. 1. Design an AWG (de)multiplexer by considering only TM polarization first. 2. According to the condition for polarization-independent channel spacing, obtain the optimal length L 2(I) for any given core width w CO2 and plot curve #I of relating L 2(I) and w CO2. 3. According to the condition to have zero PDλ for the central channel, obtain the optimal length L 2(II) for any given core width w CO2, and plot curve #II of relating L 2(II) and w CO2. 4. Get the cross-point of these two curves (i.e. curve #I: L 2(I) w CO2 and curve #II: L 2(II) w CO2 ), which gives the optimal width w CO2 opt and the length difference L 2 opt for the second part. Figure 40 (online color at: (a) The fabricated SOI ring notch filter with polarization diversity employing the proposed PSR in Fig. 33b. Measured transmission responses of the device. The black solid curves indicate the transmissions when using inputs of TE- or TM-polarized light, and the gray region indicates the possible value with an arbitrary input polarization [130]. Figure 39 (online color at: The reflection or transmission spectral responses for the designed inline Bragggrating PBS Polarization-insensitive DPSK demodulator To demonstrate the feasibility of using the PSR device presented in Fig. 36 for polarization-diversity applications on SOI, we further built a notch filter using a SOI ring resonator and two such PSR devices as shown in Fig. 40a [130]. The two optical paths share the same ring, so that the same filter characteristics are ensured. The SOI ring resonator is designed for the TE-polarized light, and it has a free spectrum range of 200 GHz (1.6 nm). Figure 42b shows the measured transmission response of the whole circuit. Clear resonant dips can be observed, which are also kept at any input polarizations. The power variation within the measured wavelength range is about 2 db. This means that the present circuit does actually show polarization-independent characteristics. It is worthwhile to note that the total insertion loss of the circuit (excluding the coupling losses at the cleaved facets) is about 3.5 db, which is higher than expected. This is partially due to slight dimensional variations in the two PSRs, which results in a deviation of the peak coupling wavelength in the curves (cf., Fig. 40a). To verify the polarization-independent characteristics of the polarization-diversity circuit shown above, it is applied for DPSK signal demodulation. A notch filter can be used to demodulate a NRZ-DPSK signal into an AMI signal, so that it can be directly detected [131]. The experimental setup and results are show in Fig. 41. A continuous-wave laser is modulated with a 20-Gb/s NRZ-DPSK format of PRBS. The amplified laser signal is then fed to the polarization-diversity circuit shown in Fig. 33. As a comparison, it is also fed to a single SOI ring resonator (without the PSRs). A polarization scrambler is also inserted in order to randomize the input polarization. The output laser signal is detected by a preamplified receiver. It has been proved that a single SOI ring is able to demodulate the

21 REVIEW ARTICLE Laser Photonics Rev. (2012) 21 Figure 41 (online color at: Experimental setup of the NRZ-DPSK signal demodulated by SOI ring resonator with and without using the polarization-diversity circuit. CW: continuous wave; EDFA: erbium-doped fiber amplifier [130]. DPSK signal when the polarization is well set (i.e. TE polarization) [132]. However, when a random polarized light is used as the input, the eye pattern of the demodulated signal becomes completely closed. This also demonstrates the high polarization-dependent characteristic of the SOI circuit. On the other hand, by introducing the polarization-diversity circuit, the polarization dependency is largely reduced, and a clear eye opening can be observed in the demodulated AMI signal. Further studies show that the power penalty for such a polarization-diversity circuit is about 4 db, which is probably due to the residual polarization-dependent loss resulted from the asymmetry in the two coupling arms of the SOI ring and/or the performance deviation of the two PSRs. This may be improved by using high-accuracy fabrication tools Polarization-insensitive nonlinear effects in silicon photonic circuits. Four-wave mixing (FWM) occurs only between the modes with the same polarization, as shown in Fig. 42. In a silicon waveguide, an angled pump is split in the nanowire to support two FWM processes for the TE and TM modes simultaneously. The incident pump light λ p with a polarization angle θ p and the signal light λ s with a polarization angle Figure 43 (online color at: Required incident pump-polarization angle to realize exact polarization independence versus the signal wavelength in a 500 nm 300 nm waveguide with a pump at 1550 nm. θ s will excite the fundamental modes of TE and TM polarizations. By carefully tuning the polarization angle of the incident pump to satisfy the following relationship [54, 55]: 1 exp [( ) ] jκ TE α p-te L jκ TE + α p-te = γ TMCTM 3/2 [ ] γ TE CTE 3/2 tan 2 (αc-te α c-tm )L θ p exp 2 1 exp [( ) ] jκ TM α p-tm L jκ TM + α p-tm, (2) the converted light power for an arbitrary incident signal polarization becomes polarization independent. Here, L is the waveguide length, C TE,TM is the relative coupling efficiency, γ TE,TM is the nonlinear coefficient, κ TE,TM is the phase mismatch, and α p,c-te,tm are the total losses of the pump and converted waves of the TE and TM modes. Fig. 43 shows the required pump-polarization angle for different signal wavelengths to realize exact polarizationindependent FWM-based wavelength conversion in a 500 nm 300 nm SOI nanowire. It is noted that the required pump-polarization angles are almost the same for a wide signal wavelength range. The inset shows the enlarged illustration in the range from 1530 to 1570 nm and the optimal Figure 42 (online color at: Principle of the polarization-independent FWM with an angled-polarization pump in a silicon waveguide.

22 LASER & PHOTONICS 22 D. Dai et al.: Polarization management for silicon photonic integrated circuits pump-polarization angle θ p (averaged) is calculated to be After determining the incident pump-polarization angle, the polarization dependence can be evaluated by calculating the conversion efficiency (which is defined as the ratio of the converted wave power to the incident signal power) for different incident signal polarization angles. Since the pump-polarization angle is adopted as an average value, a small polarization dependency will still remain for most signal wavelengths. As a result, the conversion efficiency varies in a certain interval as the incident signal angle changes arbitrarily for a given signal wavelength. The efficiency fluctuation can be defined as the difference between the maximum and minimum conversion efficiencies for each signal wavelength. The smaller the efficiency fluctuation, the better the polarization-independent performance. In the 500 nm 300 nm waveguide, the efficiency fluctuation is less than 0.04 db for the signals in the 30-nm range around the 1550-nm pump as the signal polarization varies. The polarization-independent bandwidth is limited by the larger one of the TE- and TM-mode phase mismatch. Therefore, the polarization-independent conversion bandwidth can be enhanced by reducing the dispersion discrepancy between the TE and TM modes [55]. Moreover, the phase mismatch is directly determined by the dimensions of the silicon nanowire used [133, 134]. According to this principle, the silicon nanowire is optimized to be 780 nm 795 nm, for which the effective refractive indices and the group-velocity dispersion (GVD) values for the TE and TM modes are shown in Fig. 44. In this waveguide, the TE and TM GVD curves remain almost the same in a broad wavelength range, with a maximum GVD discrepancy of only 33 ps/(nm km) in the wavelength range from 1300 to 1800 nm. Figure 45 Region and fluctuation value of the conversion efficiency versus the signal wavelength in a 0.8-cm long waveguide that has a 780 nm 795 nm cross section. ciency fluctuation as a function of the signal wavelength in a 0.8-cm long waveguide. The 1-dB polarization-independent bandwidth is as broad as 400 nm. Polarization-division multiplexing (PDM) is another polarization-related technique in optical communications, which is considered as one of the effective multiplexing methods used to double the spectral efficiency by transmitting two different data series using the two orthogonal polarization states with the same wavelength. The wavelength conversion for polarization-multiplexed (Pol-MUX) signals can also be realized by introducing an angled-polarization pump [135]. The pump is split in the nanowire to support two FWM processes for the TE and TM modes separately. In our experiment, wavelength conversion was carried out for a 20-Gb/s Pol-MUX NRZ-ASK signal using FWM in a silicon waveguide. Two channels of 10-Gb/s NRZ-ASK data are modulated on the two orthogonal polarization states of the input signal at nm, and they are converted to the idler at nm by using an angled-polarization pump at nm. The measured optical spectrum of FWM is shown in Fig. 46. The expected temporal waveforms and Figure 44 (online color at: Effective refractive indices and GVD profiles for the TE and TM modes in the optimized 780 nm 795 nm waveguide. Using the optimized silicon nanowire, the polarizationindependent conversion bandwidth can be effectively improved. The shaded region of Fig. 45 indicates the range of the conversion efficiency for arbitrary signal polarization states. Furthermore, Fig. 45 also shows the value of the effi- Figure 46 Measured optical spectrum of the wavelength conversion and multicasting at the end of the silicon waveguide.

23 REVIEW ARTICLE Laser Photonics Rev. (2012) 23 In summary, we have given a review of our work on polarization management in silicon PICs, especially the polarization issues and solutions in devices based on nanowires and ridge waveguides. Our results on the design for polarizationinsensitive wavelength division demultiplexers, resonators, MMI couplers, and wavelength converters are discussed. When designing SOI ridge waveguide-based components, the use of cladding stress to correct the waveguide birefringence allows a considerable degree of freedom to meet other performance criteria, such as relaxed dimensional tolerance, reduced loss at waveguide bends and overall improved device performance. This technique is simple to implement, there is no additional process step required other than the conventional cladding layer deposition, and there is negligible associated mode-mismatch loss. The stress-induced birefringence is readily modified by the stress level and the thickness of the upper oxide cladding, allowing precise control of the PD? in a component. Cladding stress engineering has been used to achieve polarization insensitivity in a variety of devices, including AWGs, MZI delay interferometers and ring resonators. For the case with SOI nanowires, the large birefringence caused by the geometrical asymmetry makes the realization of polarization compensation a formidable challenge. Several specific design methods are summarized to show the possibility of achieving polarization-insensitive SOI-nanowire PICs. On the other hand, the polarization-diversity technology is discussed as a general solution to eliminating the polarization dependence of SOI-nanowire PICs, as well as a key technique for coherent receivers. By utilizing the large birefringence of SOI nanowires, several novel ultrasmall key elements have been demonstrated for the polarization-diversity technology, including PBSs, polarization rotators, as well as PSRs. Finally, regarding the efficient nonlinear optical effects in SOI nanonwires, the polarization dependence of nonlinear optical effects (especially FWM) is also discussed. It is shown that FWM-based polarization-insensitive wavelength conversion can be achieved by optimizing the polarization angle of the pump. Figure 47 (online color at: Temporal waveforms (500 ps/div) of the input Pol-MUX signals (a) S x and (b) S y, the output idlers (c) I x and (d) I y, respectively. The corresponding eye diagrams (50 ps/div) are shown in (b), (d), (f), and (h). eye diagrams of the 10-Gb/s demodulated Pol-MUX signals from the generated idlers are successfully observed, as shown in Fig Conclusion Acknowledgements. This research is supported by 863 projects (Ministry of Science and Technology of China, # 2011AA and 2012AA011001), the National Nature Science Foundation of China (# , , and ), Zhejiang provincial grant (Z ) of China, the Guangdong Innovative Research Team Program (# D ), and the Fundamental Research Funds for the Central Universities. The support of the National Research Council Canada is acknowledged. The authors thank Drs. Yaocheng Shi, Yongbo Tang, Di Liang, John E. Bowers, Zhechao Wang, Siegfried Janz, Pavel Cheben and Winnie Ye, et al. for their useful discussions and contributions. Received: 2 May 2012, Revised: 1 August 2012, Accepted: 16 August 2012 Published online: 2 October 2012 Key words: Silicon, polarization, splitter, rotator, waveguide, nonlinear. Daoxin Dai (M 07) received the B. Eng. degree from the Department of Optical Engineering, Zhejiang Univ., China, and the Ph. D. degree from the Royal Institute of Technology, Sweden, in 2000 and 2005, respectively. Then he joined Zhejiang Univ. as an assistant professor and became an associate professor in 2007, and a full professor in He worked at the University of California at Santa Barbara as a visiting scholar from the end of 2008 until His research interests include silicon photonic integrated devices and applications. He has published >90 refereed international journal papers. Liu Liu (S 02 M 06) received the B. Eng. in Information Engineering in 2002 at Zhejiang University, China, and a Ph. D. in Photonics in 2006 at the Royal Institute of Technology (KTH), Sweden. He worked in the Photonics Research Group, Department of Information Technology (INTEC), Ghent University, Belgium, from 2007 to 2009, and in the Department of Photonwww.lpr-journal.org

24 LASER & PHOTONICS 24 D. Dai et al.: Polarization management for silicon photonic integrated circuits ics Engineering, Technical University of Denmark, DTU - Fotonik, Denmark, from He is now with South China Normal University, China, as a full professor, His current research area is heterogeneous integration, and silicon nanophotonic devices. Shiming Gao received the B. E. degree and the Ph. D. degree from Tsinghua University, China, in 2000 and 2005, respectively. Then he engaged in postdoctoral work with Tsinghua University and joined Zhejiang University, China, in He has been engaged as an associate professor since In , he worked at the University of California, Irvine as a visiting scholar. His research interests include nonlinear optics, silicon photonics, all-optical signal processing, and novel fiber lasers. Dan-Xia Xu is a Senior Research Officer with the National Research Council Canada (NRC), and also an adjunct professor with Carleton University. She received her Ph. D. degree from Linköping University, Sweden, in Since joining NRC, her work has encompassed highspeed SiGe HBTs, silicides for submicrometer VLSI, SiGe and silicide photodetectors, and integrated optics. In she was part of the research team at Optenia Inc. that successfully developed the first glass waveguide echelle grating demultiplexer. Her current research interests are in silicon photonics, particularly in ring resonators and other nanophotonic devices for biological sensing and optical communications, as well as polarisation management of SOI components. She has authored over 200 scientific publications, including several book chapters, and holds 5 patents. Sailing He (M 92 SM 98) received the Licentiate of Technology and Ph. D. degree in electromagnetic theory from the Royal Institute of Technology, Stockholm, Sweden, in 1991 and 1992, respectively, and has been in the faculty of the same institute since He is also with the Centre for Optical and Electromagnetic Research, Zhejiang University, China as a distinguished Professor appointed by the central government of China. He also serves as a Chief Scientist at the Joint Research Center of Photonics of the Royal Institute of Technology (Sweden) and Zhejiang University (China). He has first-authored one monograph (Oxford University Press) and authored/coauthored over 400 papers in refereed international journals, as well as been granted a dozen patents in optical communications. References [1] B. Jalali and S. Fathpour, J. Lightwave Technol. 24, 4600 (2006). [2] G. T. Reed, Nature 427, 595 (2004). [3] R. Soref, IEEE J. Sel. Top. Quant. Electron. 12, 1678 (2006). [4] D. Liang and J. E. Bowers, Nature Photon. 4, 511 (2010). [5] M. Lipson, J. Lightwave Technol. 23, 4222 (2005). [6] M. Lipson, Electron. Lett. 45, 576 (2009). [7] D. Liang, G. Roelkens, R. Baets, and J. E. Bowers, Materials 3, 1782 (2010). [8] G. Roelkens, L. Liu, D. Liang, R. Jones, A. Fang, B. Koch, and J. Bowers, Laser Photon. Rev. 4, 751 (2010). [9] P. Dumon, W. Bogaerts, R. Baets, J.-M. Fedeli, and L. Fulbert, Electron. Lett. 45, 581 (2009). [10] R. A. Soref, J. Schmidtchen, and K. Petermann, IEEE J. Quantum Electron. 27, 1971 (1986). [11] R. Soref, J. Schmidtchen, and K. Petermann, IEEE J. Quantum Electron. 27, 1971 (1991). [12] J. Lousteau, D. Furniss, A. Seddon, T. Benson, A. Vukovic, and P. Sewell, J. Lightwave Technol. 22, 1923 (2004). [13] D. Dai and S. He, J. Opt. Soc. Am. A 21, 113 (2004). [14] L. Vivien, S. Laval, B. Dumont, S. Lardenois, A. Koster, and E. Cassan, Opt. Commun. 210, 43 (2002). [15] D. Dai and S. He, Appl. Opt. 43, 1156 (2004). [16] S. Chan, C. Png, S. Lim, G. Reed, and V. Passaro, J. Lightwave Technol. 23, 2103 (2005). [17] G. Mashanovich, M. Milosevic, P. Matavulj, S. Stankovic, B. Timotijevic, P. Yang, E. Teo, M. Breese, A. Bettiol, and G. Reed, Semiconductor Sci. Technol. 23, (2008). [18] M. M. Milošević, P. S. Matavulj, B. D. Timotijević, G. T. Reed, and G. Z. Mashanovich, J. Lightwave Technol. 26, (2008). [19] D.-X. Xu, P. Cheben, D. Dalacu, A. Delage, S. Janz, B. Lamontagne, M. J. Picard, and W. N. Ye, Opt. Lett. 29, 2384 (2004). [20] W. N. Ye, D.-X. Xu, S. Janz, P. Cheben, M. J. Picard, B. Lamontagne, and N. G. Tarr, J. Lightwave Technol. 23, 1308 (2005). [21] A. G. Rickrnan and G. T. Reed, IEE Proc.-Optoelectron. 141, 391 (I994). [22] I. Kiyat, A. Aydinli, and N. Dagli, Opt. Exp. 13, 1900 (2005). [23] I. Kiyat, A. Aydinli, and N. Dagli, IEEE Photon. Technol. Lett. 17, 2098 (2005). [24] P. D. Trinh, S. Yegnanarayanan, and B. Jalali, Electron. Lett. 31, 2097 (1995). [25] D. Dai, J. He, and S. He, IEEE J. Sel. Top. Quant Electron. 11, 439 (2005). [26] D. Dai and S. He, Opt. Commun. 247, 281 (2005). [27] D. Dai, J. He, and S. He, Appl. Opt. 44, 5036 (2005). [28] R. Halir, I. Molina-Fernández, A. Ortega-Moñux, J. G. Wangüemert, -Pérez, D.-X. Xu, P. Cheben, and S. Janz, J. Lightwave Technol. 26, 2928 (2008). [29] D.-X. Xu, S. Janz, and P. Cheben, IEEE Photon. Technol. Lett. 18, 343 (2006). [30] M. R. Pearson and P. E. Jessop, A. Bezinger, A. Delage, J. W. Fraser, S. Janz, and D.-X. Xu, Proc. SPIE 3953, 11 (2000). [31] P. D. Trinh, S. Yegnanarayanan, F. Coppinger, and B. Jalali, IEEE Photon. Technol. Lett. 9, 940 (1997).