Asymmetric directional couplers based on silicon nanophotonic waveguides and applications

Abstract

Directional couplers (DCs) have been playing an important role as a basic element for realizing power exchange. Previously most work was focused on symmetric DCs and little work was reported for asymmetric directional couplers (ADCs). In recently years, silicon nanophotonic waveguides with ultra-high index contrast and ultra-small cross section have been developed very well and it has been shown that ADCs based on silicon-on-insulator (SOI) nanophotonic waveguides have some unique ability for polarization-selective coupling as well as mode-selective coupling, which are respectively very important for polarization-related systems and mode-division-mulitplexing systems. In this paper, a review is given for the recent progresses on silicon-based ADCs and the applications for power splitting, polarization beam splitting, as well as mode conversion/(de)multiplexing.

Key words： silicon photonics; asymmetric directional couplers (ADCs); polarization-division multiplexing (PDM); mode-division multiplexing (MDM); polarization beam splitter (PBSs)

Introduction

A directional coupler (DC) is one of the most important fundamental elements for photonic integrated circuits (PICs) and has been used very widely for power splitting in many photonic integrated devices, including Mach-Zehnder Interferometers (MZIs), microring-resonators (MRRs), etc. DCs can also be used as polarization splitters [ 1], coarse wavelength-division-multiplexers [ 2], etc. Because of their extreme importance, lots of papers have been published on the theory, modeling, simulation, and analyses for DCs since integrated optics was proposed in 1960s [ 3]. A systematic design rules for DCs have been established. Particularly, the coupled mode theory had been developed very well even at the first decade of integrated optics [ 4]. With the help of coupled mode theory, one can easily calculate the mode coupling in a DC for designing power splitters, wavelength-division-demultiplexers, etc. On the other hand, one should note that most work in the past decades was focused on low-Δ (index-contrast) optical waveguides, e.g., SiO₂-on-Si buried optical waveguides, Ti:LiNbO₃ diffusion optical waveguides, etc, which were used as the most popular options previously. For DCs, most of the previous work is focused on the symmetric design consisting of two identical optical waveguides, in which case light power can be transferred from one waveguide to the other one completely when choosing the length L of the coupling region appropriately. And the power coupling ratio can be adjusted between 0 and 100% arbitrarily by modifying the length L, which is very useful for power splitting.

In contrast, an asymmetric directional coupler (ADC) consists of non-identical waveguides in the coupling region. Since the evanescent coupling in an ADC is usually weak possibly due to the phase mismatching, the application of an ADC is quite limited. A potential application reported for ADCs is to realize an optical switch by tuning the refractive index for one of the coupled waveguides [ 5– 7]. In this way, the fundamental modes of two optical waveguides can satisfy or unsatisfy the phase matching condition and thus the evanescent coupling can be enhanced or depressed. For this application, low-index contrast optical waveguides are usually used [ 5– 7]. In the recent years, submicron silicon-on-insulator (SOI) waveguides have been used widely for ultra-compact CMOS-compatible PICs [ 8– 20]. In this case, the situation becomes very different because of the possibility of large cross-sectional asymmetry, ultra-high birefringence, and large mode discrepancy. As a result, there are some unique characteristics of mode coupling and conversion in these waveguides [ 21, 22], and some novel applications can be explored.

First, ADC can be used to realize some special power splitters. For example, an ADC with two bent waveguides was used successfully to achieve sufficient coupling for realizing a flat-top optical filter based cascaded microrings as a better option than the conventional multimode interference (MMI) couplers or straight DCs. This will be discussed in Section 2.1.

Second, ADCs have also been attracted a lot attention as an excellent candidate for realizing ultracompact and broadband polarization-beam splitters (PBSs) [ 23– 47]. For the application of PBSs using ADCs, one should make the phase matching condition unsatisfied for one polarization mode so that almost no cross-coupling happens. On the other hand, more importantly the ADC should be designed to make the phase matching condition satisfied for the orthogonal polarization mode and consequently this orthogonal polarization mode is cross-coupled completely when choosing the length of the coupling region carefully. In this way, the two orthogonal polarizations (TE and TM) can be separated within a short length (equal to the beat length of the cross-coupled polarization mode). In order to do so, the optical waveguides should have significantly different birefringence. This can be realized by introducing two different types of optical waveguides to form the ADC [ 42– 47], e.g., by using a nano-slot waveguide [ 48] or silicon hybrid plasmonic waveguide [ 49] to work with a SOI nanowire. This will be reviewed in Section 2.2.

Third, an ADC can also be used to realize efficient mode coupling/conversion between two types of optical waveguides, which is beneficial for seamless integration between different types of optical waveguides [ 50]. Furthermore, according to the coupled mode theory, in principle an efficient mode conversion can be achieved between any eigenmodes of two optical waveguides of an ADC when the phase matching condition is satisfied for the two eigenmodes to be coupled so that it is possible to realize mode-selective coupling, which is useful for mode-division-multiplexing (MDM) optical interconnects [ 51]. This will be discussed in Section 2.3.

These ADCs can be further integrated with other elements to realize some photonic integrated circuits (PICs), which will be reviewed briefly in Section 3.

In this paper, we give a review and summary for the recent progresses on ADCs based on SOI nanowires with ultra-high Δ and their applications for power splitting, polarization beam splitting, as well as mode conversion/(de)multiplexing.

ADCs for different applications

ADCs for power splitting

Power splitting is a one of the most fundamental application for DCs and has been playing an important role for various photonic integrated devices like MRRs. For MRRs, the coupling ratio is usually chosen according to the requirement for the 3 dB bandwidth. However, the regular DCs might not be a good option for some specific cases, even though it is easy to realize an arbitrary power splitting ratio (or coupling ratio) by choosing the length of the coupling region. For example, when MRRs are used as an optical filter, a box-like filtering response is often desired so that it can tolerate a wavelength shift due to any environmental change. This response for optical filters based on MMRs can be synthesized with multiple rings [ 52– 55]. When using multiple microrings to achieve a box-like filtering response, all the couplers involved should be designed optimally to achieve the coupling coefficients as desired [ 56]. For example, for the ultra-compact 5th order MRR optical filters demonstrated in Ref. [ 57], the power coupling ratios k² for all the couplers are chosen as 0.45, 0.09, 0.05, 0.05, 0.09, and 0.45, respectively. In order to achieve the sufficient power coupling coefficient as high as 0.45, one usually has to use the design of race-track resonators with long coupling region or narrow gap w_gap in the coupling region. However, a longer coupling region causes a smaller free-spectral range (FSR), which limits the channel number available in wavelength-division-multiplexing (WDM) systems. When choosing a narrow gap (e.g., ~20 nm), the beating length becomes small. However, the fabrication (e.g., the lithography and etching processes) becomes difficult and the coupling ratio is very sensitive to the beating length variation [ 57]. In order to overcome these issues, MMI couplers were used as the coupler with a power ratio of 45%:55% in Ref. [ 57]. One should realize that the design with MMI couplers has some disadvantages. First, an MMI coupler usually has a few percent of excess loss due to the non-perfect self-imaging in the multimode section [ 57], and there is also mode conversion loss between the straight section and the bending section of a microring (particularly when the bending radius is ultrasmall). As a result, some notable excess loss will be introduced for an MRR filter. Second, the power splitting ratio of an MMI coupler is fixed [ 58] and thus it is not flexible to choose any other power splitting ratios in order to achieve a desired 3 dB bandwidth. Third, the length L_MMI of the MMI section is usually several microns (e.g., L_MMI=~3.5 mm [ 57]), which makes the cavity length increased by 2L_MMI and thus reduces the FSR. These problems can be solved by using bent DCs, as shown in Fig. 1(a) [ 59].

Fig.1 (a) SEM image of the present five-microring filter with bent couplers; (b) SEM image of the bent coupler used here [59]

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With bent couplers (which is a kind of ADC, as shown in Fig. 1(b)), there is no excess loss in theory and the cavity length is the same as a regular microring (which has the minimal bending radius). This bent coupler consists of two parallel bent waveguides in the coupling region, i.e., the bent access waveguide and the microring waveguide, which should be designed to be with different widths (w₁, w₂) according to the phase matching condition [ 40], n_eff1R₁=n_eff2R₂, where n_eff1 and n_eff2 are the effective indices of the fundamental modes of the two bent waveguides, respectively, R₁ and R₂ are the corresponding bending radii, and R₁=R₂ + (w₁+w₂)/2+w_gap. The design with the phase matching condition also helps minimize the excitation of higher-order modes in the microring waveguides (which might be multimode). As the coupling ratio can be sufficient as long as the length of the coupling region is long enough, a relatively large gap is allowed (w_gap>150 nm) so that the fabrication is not difficult.

As an example, when considering SOI nanowires with a 220 nm-thick top-silicon, the following parameters are chosen as w₁=0.35 mm, R₁=5.455 mm, w₂=0.425 mm, and R₂=4.886 mm for the bent coupler so that the gap is as large as w_gap=~182 nm. Figure 2(a) shows the calculated power coupling ratios of the designed bent coupler as the angle q of the coupling region increases. It can be seen that one obtains the coupling ratio of ~0.45 as required when choosing q=13.7° and the theoretical excess loss of this structure is almost zero in theory. For the inter-ring coupler between two adjacent microrings, the coupling coefficients can be controlled by adjusting the gap between them, as shown in Fig. 2(b). For example, the gap widths are about 116 and 156 nm to achieve the power coupling ratios of 0.09 and 0.05, respectively. It has also been shown that the power coupling ratio for the bent coupler is not sensitive to the deviation Dw, which is an advantage and has been also proposed to realize a broad band 3 dB coupler in Ref. [ 60] recently. In contrast, the inter-ring coupler is more sensitive to the deviation Dw (see the curves with squares and circles). The spectral response is still box-like even when the deviation Dw is as large as±20 nm. One should note that the 3 dB bandwidth changes and the ripples increases slightly.

Fig.2 (a) Simulated power coupling ratio of the bent coupler as the angle q of the coupling region increases when w₁=0.35 mm, R₁=5.455 mm, w₂=0.425 mm, and R₂=4.886 mm; (b) coupling ratio of the inter-ring coupler as the gap width w_gap varies when choosing R₂=4.886 mm and w₂=0.425 mm [59]

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Fig.3 Measured (thin curves) and simulated (thick curves) responses of the optical filters with (a) three microrings and (b) five microrings. The insets are the SEM images of the filers [59]

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Figures 3(a)−3(b) show the measured spectral responses of the fabricated optical filters with three and five microrings (see the thin curves). The measured responses agree well with the calculated results. Their FSRs are about 18.4 nm and the 3-dB bandwidths are 2.6 and 2.38 nm, respectively. The measured out-of-band rejection ratios for the fabricated three-microring and five-microring filters are about 30 and 36 dB, respectively. It can be seen that higher out-of-band rejection ratio is obtained by introducing more microrings. From the measured spectral responses, one can also see that the fabricated three-microring and five-microring filters have an excess loss of<1.0 dB (@1550 nm), which is beneficial from the low excess loss of the bent couplers in comparison with the MMI couplers or traditional straight-bend coupler used in race-track resonators demonstrated in e.g., Ref. [ 61].

ADCs for PBS

A PBS is a basic functional element for many applications when polarization control is needed. Many kinds of on-chip PBSs have been reported by using various structures, e.g., MZIs [ 26, 62], MMI structure [ 28, 29, 31], ADCs [ 1, 25, 27, 32, 33, 42], and photonic-crystal (PhC)/grating structures [ 27, 37, 38, 63]. Among them, an ADC has been proved to be an excellent option for realizing ultra-short PBSs with an ultra-broad band [ 24]. When designing an ADC to work as a PBS, the waveguide dimension is required to be optimized so that the phase matching condition can be satisfied to have a complete cross-coupling for one polarization only. For the other polarization, the phase matching condition usually is not satisfied due to the strong birefringence of the waveguides, and thus no cross-coupling happens almost. In order to form an ADC, a straightforward way is making the core widths of the two straight optical waveguides in the coupling regions different. However, the phase matching condition won’t be satisfied because their fundamental modes are different for any polarization. In the following parts, we give a summary for four types of ADCs used popularly.

ADCs with three waveguides

Fig.4 (a) Schematic configuration of the PBS based on an ADC with three optical waveguides; (b) effective indices of the guided-modes in a SOI nanowire with h_co=220 nm. The simulated light propagation when the light is launched into the PBS (c) for TE polarization and (d) for TM polarization, respectively. The calculated wavelength dependence of the designed PBS when the input is (e) the TM₀ mode, and (f) the TE₀ mode. The parameters are: h_co=220 nm, w₁=410 nm, w₂=1.195 mm, w_g=300 nm, L_c1=11.3 mm, L_c2=12.7 mm, and L₀= –3 mm [39]

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Figure 4(a) shows the ADC based on three waveguides for realizing a PBS. In this structure, there are two narrow waveguides and a wide waveguide inserted between them. The waveguide widths are chosen optimally so that the phase matching condition is satisfied for TM polarization between the fundamental mode in the narrow optical waveguide and the higher-order mode in the wide optical waveguide (i.e., n_eff0(1)=n_eff1(2)) [ 39], which can be done easily according to the calculated effective indices for all the eigenmodes as shown in Fig. 4(b). Therefore, the TM₀ mode launched at the input port of the narrow waveguide will be cross-coupled to the higher-order mode in the wide waveguide very efficiently when the length of the coupling region is optimized. Another narrow optical waveguide is placed at the other side of the wide optical waveguide so that an output with a fundamental mode is achieved, as shown in Fig. 4(c). From Fig. 4(b), it can be also seen that the phase-matching condition is not satisfied for TE polarization due to the high birefringence of SOI nanowires. As a consequence, when the TE₀ mode is launched, no coupling happens almost, as shown in Fig. 4(d). Figures 4(e)−4(f) show the calculated wavelength dependence of the output powers at the cross port and the through port when the input is the TM₀, and the TE₀ modes, respectively. It can be seen that the output is not sensitive to the wavelength variation when the TE₀ mode is launched and the extinction ratio is higher than 35 dB over a very broad wavelength range from 1.45 to 1.65 mm. In contrast, for the case when the TM₀ mode is input, the response is more sensitive to the wavelength due to the wavelength dependences of the evanescent coupling length. Nevertheless, the designed PBS still has a relatively large bandwidth ranging from 1.53 to 1.58 mm for an extinction ratio of 15 dB.

ADCs with bent waveguides

Figure 5 shows an ADC based on bent waveguides, which consists of two bent waveguides with different core widths. In this structure, the phase matching condition is given by n_eff0(1)R₁=n_eff0(2)R₂, where R₁ and R₂ are the bending radii of the narrow and wide optical waveguides. As a result, it is possible to satisfy the phase matching condition for these two bent waveguides with different core widths by choosing the bending radius appropriately. Generally the narrow optical waveguide should have a larger bending radius than the wide optical waveguide (i.e., R₁>R₂) [ 40]. Figures 6(a) and 6(b) respectively show the calculated optical path lengths (OPL) (with q=1 rad and R₂=20 mm) for the TE₀ and TM₀ modes as the waveguide width varies. From Fig. 6(a), one can easily obtain a pair of optimal widths (w₁, and w₂) satisfying the phase matching condition for the TM₀ modes in waveguides #1 and #2. For example, one can choose (w₁, w₂)=(0.534 mm, 0.46 mm) as indicated by the dashed line in Fig. 6(a). On the other hand, for the TE₀ mode, there is a notable phase mismatching when choosing the optimal widths (w₁, w₂), as shown in Fig. 6(b). Figures 6(c) and 6(d) show the simulated light propagation in the designed bent ADC when the input is with the TM₀ and TE₀ modes, respectively. From these figures, it can be seen that the launched TM₀ mode is coupled completely almost from the narrow optical waveguide to the wide optical waveguide while the TE₀ mode propagates along the narrow input waveguide with negligible cross-coupling. Such a polarization-dependent evanescent coupling enables an ultra-short PBS [ 40, 41].

Fig.5 An bent ADC consisting of two bent waveguides with different core widths [40]

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Figures 7(a) and 7(b) respectively show the schematic configuration and the SEM picture for the PBS based on the bent ADC. In order to decouple the two bent waveguides, an S-bend section is cascaded. The S-bend has a sharp bending so that it also works as a TE-passed polarization filter regarding that the TM polarization has a much higher loss than the TE polarization when the bending radius is ultrasmall. Figures 7(c) and 7(d) show the simulated light propagation in the designed PBS for TM and TE 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 cross-coupling. The total length for the PBS is only 9.5 mm, which is one of the smallest PBS for the case without nanoplasmonic structures involved. Further numerical analyses also show that the present PBS has a very large bandwidth (>200 nm for an extinction ratio of 10 dB) and a large fabrication tolerance (>±60 nm). Figures 7(e) and 7(f) show the measured transmission responses at the through port and the cross port of the fabricated PBS when TM and TE polarized light are launched respectively. The responses are normalized by the transmission of a straight waveguide. From these figures, it can be seen that the excess losses for both TE and TM polarizations are low at the central wavelength (close to zero). In Figs. 7(e)−7(f), the finite-difference time-domain (FDTD) simulation results for the fabricated PBS are also shown. It can be seen that the simulation and measurement results agree well with each other in the measurement wavelength range. The PBS has a high extinction ratio (ER) (>15 dB) for TE polarized light in a broad band. In contrast, for the TM polarized light, the response is wavelength-dependent which agrees with the theoretical prediction because of the intrinsic wavelength-dependence of the evanescent coupling. The ER for TM polarization increases from 6 to 20 dB when the wavelength increases from 1520 to 1600 nm. According to the simulation, one can increase the length of the coupling region appropriately so that the central wavelength (~1620 nm) moves back to the design value (1550 nm). It can be seen that TM polarization has the highest ER (~23 dB) at around 1620 nm. Such an ultra-compact PBS with ultra-broad band and large fabrication tolerance will be useful for many PICs.

Fig.6 Optical path lengths (OPL) as the waveguide width varies when R₂=20 mm: (a) TM, (b) TE; light propagation in the designed bent coupler with R₁=19.3 mm, R₂=20.0 mm, w₁=0.534 mm, w₂=0.46 mm, and w_g=203 nm: (c) TM, (d) TE. The SOI wafer has a silicon thickness of h_co=220 nm, and the refractive indices of Si, SiO₂, and air are assumed to be n_Si=3.455, n_SiO2=1.445, and n_air=1.0 respectively [40]

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Fig.7 An ultra-short PBS based on a bent ADC. (a) Schematic configuration; (b) SEM picture. The light propagation in the designed PBS with L_dc=4.5 mm, R₁=19.3 mm, R₂=20.0 mm, w₁=0.534 mm, w₂=0.46 mm, and w_g=203 nm: (c) TM, (d) TE. The wavelength dependence of the PBSs: (e) TM, (f) TE [40]

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ADCs with nano-slot waveguides

An ADC can also be formed by introducing some special optical waveguide, e.g., silicon nano-slot waveguide [ 48], as shown in Figs. 8(a)−8(b) [ 42– 44]. In the coupling region, these two waveguides are designed according to the phase-matching condition for TM polarization. Figure 8(c) shows the calculated effective indices for the TE- and TM-polarization modes of a SOI nanowire and a nano-slot waveguide as the waveguide core widths (w_Si, w_co) varies when the core height is chosen as h_co=250 nm. It can be seen that these two different types of waveguides have similar effective indices for the TM polarization mode, and consequently it is easily to make the phase matching condition 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 mm, w_Si =0.26 mm and w_slot=60 nm. As a result, the TM₀ mode can be coupled completely to the cross port when the length of the coupling region is also chosen appropriately (see Fig. 8(d)). In contrast, there is a significant phase mismatch for the TE polarization mode. Thus the evanescent coupling is negligible possibly, and finally the TE polarized light is then output from the through port (see Fig. 8(d)). In order to minimize the footprint, the mode converter between a SOI nanowire and a nano-slot waveguide is merged with the S-bend. With this mode converter, low-loss connection between a SOI nanowire and a nano-slot waveguide is realized, the present design merges the mode converters between the nano-slot waveguide and the regular SOI nanowire into the S-bends at the side of the nano-slot waveguide, as shown in Fig. 8(a). With such a design, the PBS is as short as 6.9 mm.

Fig.8 PBS based on an ADC consisting of a SOI nanowire and a nano-slot waveguide: (a) SEM picture; (b) cross section; (c) calcualted effective indices of a SOI nanowire and a nano-slot waveguide as the core width (w_Si, w_co) varies; (d) light propagation in the designed PBS with w_co=0.4 mm, w_Si=0.26 mm, h_co=250 nm, w_slot=60 nm, and w_g=100 nm [43]

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ADCs with silicon hybrid plasmonic waveguides

It is well known that the mode behavior in surface plasmon polariton (SPP) nanostructures usually have very strong polarization dependence because SPP effect occurs for the polarization mode whose electrical field is perpendicular to the metal-dielectric interface only. Therefore, using nanoplasmonic waveguides provides a good option for realizing ultra-compact polarization-handling devices. Among various nanoplasmonic waveguides, the hybrid plasmonic waveguides developed recently [ 49, 64– 67] are considered as an excellent candidate because it is possible to achieve a nano-scale light confinement as well as relatively long propagation distance simultaneously. In particular, SOI-compatible hybrid plasmonic waveguide shown in Fig. 9(a) [ 49] is even more attractive because the design and fabrication technologies for silicon photonics can be available compatibly. As shown in Fig. 6(a), a silicon hybrid nanoplasmonic waveguide consists of a SOI nanowire, a metal cap and an ultra-thin SiO₂ layer (h_d) between them. Due to the surface plasmonic effect, a silicon hybrid nanoplasmonic waveguide has very different birefringence from a SOI nanowire. Therefore, it is easy to form an ADC for realizing PBSs by combining a silicon hybrid nanoplasmonics waveguide and SOI nanowires [ 45– 49]. For example, a small PBS is proposed by using an ADC consisting of two SOI nanowires with a silicon hybrid plasmonic waveguide between them [ 45, 46]. The PBS length is about 5−10 mm when the waveguides are optimized to make the TM polarization cross-coupled. It is possible to simplify the three-waveguide ADC into an ADC with two waveguides, as shown in Fig. 9(b) [ 47]. In addition, the waveguides for the ADC can be designed optimally to make the phase-matching condition satisfied for TE polarization (instead of TM polarization in Ref. [ 47]). In this way, both two waveguides have relatively large widths (w₁, w₂ ~ 300 nm) and the length of the coupling region is as short as 2.2 mm even when choosing the gap width as large as w_gap=200 nm. Such a relatively large gap makes the fabrication not difficult. Figure 9(d) shows the simulated light propagation in the designed ADC with L_c=2.2 mm and R=1.3 mm when the TE₀ and TM₀ modes are launched. It can be seen that the TE and TM polarizations are separated within the coupling region as short as 2.2 mm and the total length for the PBS is 3.7 mm only.

Fig.9 (a) Cross section of a silicon hybrid plasmonic waveguide with field enhancement in the low index region [49]; (b) schematic configuration of an ADC with a hybrid nanoplasmonic waveguide [47]; (c) cross section of the coupling region of the ADC; (d) 3D-FDTD simulation result for the light propagation in the designed PBS when the input is TE or TM respectively

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ADCs for MDM

MDM is a new technology developed recently to expand the capacity of an optical communication/interconnect link. In order to realize MDM, it is well known that mode multiplexer play an important role as a key component in such a system. In comparison with those mode multiplexers realized with optical fiber couplers [ 68, 69], on-chip mode multiplexers are desired regarding the compactness and the potential to be integrated with other elements on the same chip. Waveguide-grating couplers have been demonstrated to synthesize the desired field profiles and excite a few linearly polarized (LP) fiber modes [ 70– 73]. However, the configuration is quite complicated and the excess loss is relatively large. Recently several kinds of structures for mode (de)multiplexers have been proposed to enable mode multiplexing by using e.g. multimode interferometers [ 74], adiabatic mode-evolution DCs [ 75– 77], Y-junctions [ 78– 84], as well as ADCs [ 51, 85– 91]. Among them, the ADC-based mode (de)multiplexers have the advantages including the broad wavelength band, the ultra-compact footprint and the flexible scalability for more mode channels.

As demonstrated above, an efficient coupling from the TM₀ mode in a narrow input waveguide to the TM₁ mode in a wide middle waveguide was realized with a three-waveguide ADC in Ref. [ 39]. Similarly, the other higher-order mode in a wide waveguide can also be excited selectively by the fundamental mode in a narrow waveguide. The condition is that the widths (w_a and w_b) of the narrow and wide waveguides should be chosen optimally according to the phase matching condition, i.e., n_eff0(w_a)= n_effi(w_b), where n_eff0(w_a) and n_effi(w_b) are the effective indices of the fundamental mode of the narrow access waveguide and the ith higher-order mode of the bus waveguide, respectively. On the other hand, those undesired eigenmodes will hardly be excited due to the significant phase mismatching. Therefore, one can realize a mode (de)multiplexer with multiple channels [ 51, 86] by cascading ADCs working for different mode-channels. In Refs. [ 51, 86], a 4-channel silicon mode converter-multiplexer with low loss (<0.1 dB), low crosstalk (<−25 dB) as well as small footprint was proposed and demonstrated for the first time. A grating-assist ADC was also designed to construct a 4-channel narrow-band mode converter-multiplexer in Ref. [ 88]. In Ref. [ 89], a three-channel converter-multiplexer combining ADCs and microrings for simultaneous mode- and WDM has also been recently realized to expand the link capacity.

As an example, Fig. 10(a) shows the calculated dispersion curves for an SOI strip nanowire with e.g. h_co=220 nm. Figures 10(b)−10(d) shows the simulated light propagation in the designed ADCs when choosing different core widths for the bus waveguide. It can be seen that an efficient mode excitation is achieved from the TM₀ mode in the narrow access-waveguide to the desired higher-order mode in the wide bus-waveguide, with very little power left in the access waveguide. When these ADCs are cascaded by inserting an adiabatic taper between two adjacent stages, a mode multiplexer with N mode-channels is realized as shown in Fig. 10(e) [ 51, 86].

Fig.10 (a) Calculated effective indices of the guided-modes in an SOI strip nanowire with h_co=220 nm; the FDTD simulated light propagation in the designed ith stage ADC with (b) i=1, (c) i=2, and (d) i=3; (e) schematic configuration of the mode converter-multiplexer with 4 channels [86]

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Fig.11 (a) SEM picture for the 4×1 mode multiplexer and 1×4 mode demultiplexer integrated on the same chip; measured responses at output ports (O₁, O₂, O₃, and O₄) when light is input from the port of (b) I₁, (c) I₂, (d) I₃, and (e) I₄ [86]

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Figure 11(a) shows the fabricated PIC including a mode multiplexer (with input ports I₁₋I₄), and a mode demultiplexer (with output ports O₁₋O₄), which is used to characterize the mode convert-(de)multiplexer. Figures 11(b)−11(e) show the measured transmission responses at all output ports O₁, O₂, O₃, and O₄ when light is input from port I₁, I₂, I₃, and I₄ respectively. It can be seen that one has the maximal output from the jth input port to the jth output port as desired. The fabricated device has low excess loss (<0.5 dB) and low crosstalk (<−20 dB) over a broad band around the central wavelength. The total insertion loss of about 12−13 dB is mainly from the butt-coupling loss between the fiber and the chip, which can be reduced by introducing grating couplers or inversed tapers. The ADC-based mode multiplexer can also be further extended to deal with the modes for both polarizations so that the link capacity is doubled. Figure 12(a) shows the proposed ADC-based (de)multiplexer for both polarizations [ 91]. Here the TE₀ and TM₀ modes combined/separated by using a PBS based on a three-waveguide coupler [ 25] while the high-order modes (TE₁, TE₂, TE₃, TM₁, TM₂, and TM₃) are (de)multiplexed by using six cascaded ADCs. Figure 12(b) shows the fabricated 8-channel hybrid multiplexer. The present hybrid (de)multiplexer works well (with low crosstalk and low loss) over a broad wavelength band [ 91]. The performance can be improved by introducing polarizers to filter out the polarization crosstalks [ 92]. The broad-band performance makes the ADC-based mode multiplexers available for WDM systems so that it is possible to realize the hybrid multiplexing technology combining WDM and MDM.

Fig.12 (a) 8-channel hybrid multiplexer enabling mode- and polarization-division-(de)multiplexing simultaneously; (b) the fabricated 8-channel hybrid multiplexer [91]

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PICs with ADCs

Hybrid (de)multiplexer enabling PDM and WDM

Fig.13 A 18-channel PDM-WDM hybrid (de)multiplexer (a) and the measurement responses of all the channels (b)

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A polarization-diversity circuit including PBSs and polarization rotators (PRs) enables polarization-insensitive PICs as well as PICs working for dual-polarizations. For example, the polarization-diversity circuit can be realized by including a PBS based on a bent ADC [ 40, 41], and a PR based on a SOI nanowire with a cut corner [ 93]. When a polarization-diversity circuit working with an arrayed waveguide grating (AWG), it is possible to realize the hybrid (de)multiplexing technology combining WDM as well as PDM, as shown in Fig. 13(a). The bi-directional AWG has N+1 access optical waveguides at both sides. The input 2N channels of optical signals are separated into the TE-polarization group and the TM-polarization group by a broadband PBS. Each group has N wavelength channels (l₁, l₂,..., l_N). The TM-polarization group is then rotated and converted to be TE polarization by using a broadband PR. These two groups of signals are then input to the two input waveguides of the bi-directional AWG and then demultiplexed respectively by the bi-directional AWG. In this way, there are 2N output waveguides to receive 2N channels carried by N wavelengths (l₁, l₂,..., l_N) and two polarizations (TE and TM), respectively. Figure 13(b) shows the measured spectral responses for the whole structure including a polarization beam combiner (PBC), PBS, PR, and bi-directional AWG. Here both the PBC and PBS are based on a bent ADC. The solid curves and the dashed curves are for the channels output from the ports at the right side (TM polarization) as well as at the left side (TE polarization). It can be seen that these two groups of channels are aligned very well with nearly zero polarization dependent wavelength (PDl), which is guaranteed intrinsically by such a bi-directional AWG working as two AWGs sharing the identical dispersion waveguide grating.

Hybrid (de)multiplexer enabling MDM and WDM

Mode demultiplexer based on cascaded ADCs is broadband and thus it is WDM-compatible. Therefore, it is possible to enable the MDM and WDM simultaneously [ 94] when a mode demultiplexer works with multiple AWG demultiplexers, as shown in Fig. 14(a). In the present case, there are 64 channels to be demultiplexed in total by using a 1×4 ADC-based mode demultiplexer and four identical 16-channel AWGs with a channel spacing of 3.2 nm. Figure 14(b) show the measured normalized spectral responses for all the channels of the fabricated hybrid demultiplexer when light is launched at input port I₁, I₂, I₃, and I_4, respectively. From these figures, it can be seen that the crosstalk at the output ports of AWG #j (j≠i) from by the undesired mode coupling is about –16~–25 dB. The spectral responses of the wavelength-channels are similar to those of a discrete AWG demultiplexer on the same chip, which benefits from the broadband performance of the ADC-based mode demultiplexer. It proves that the ADC-based mode demultiplexer work together with AWG demultiplexers very well. A simplified version for hybrid MDM-WDM (de)multiplexer can be realized by introducing bi-directional N×N AWGs which can work equally as two 1×N AWG. In this way, less AWGs are indeed and the chip become more compact [ 95].

Fig.14 A 64-channel MDM-WDM hybrid multiplexer (a) and the measurement results (b) [94]

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Conclusions

In summary, we have reviewed our recent work on silicon-based ADCs, which can be constructed with two or three non-identical waveguides in the coupling region. Silicon-based ADCs have some unique performances and applications because of the ultra-high index-contrast and ultra-small cross section of the SOI nanophotonic waveguides. A basic design rule for ADCs is the so-called phase-matching condition. The waveguide dimensions should be chosen optimally to make the phase-matching condition satisfied so that the desired mode coupling happens efficiently. In this paper, we have discussed the applications of ADCs for power splitting, polarization-beam splitting, as well as mode demultiplexing. For example, an ADC with two bent waveguides has been used successfully to achieve sufficient coupling for cascaded microring filters as a better option than the conventional MMI couplers or straight DCs. This kind of bent coupler can be also used to realize an ultra-short PBS because the phase matching condition can be satisfied for one polarization only due to the high birefringence of SOI nanowires. An ADC can be also formed by introducing different types of optical waveguides for the coupling region. For example, the regular SOI nanowire can be used as one of the coupling waveguides while the other waveguide in the coupling region can be made of some special optical waveguide like silicon nano-slot waveguide, silicon hybrid plasmonics waveguides, etc. In this case, the two waveguides can be designed optimally to satisfy the phase-matching condition for only one polarization since they have different birefringence. The strong polarization dependence makes it possible to realize ultra-short PBSs. Another type of ADC is formed by using two waveguides with different core widths, in which case it is to couple the fundamental mode in the narrow optical waveguide to the higher-order mode in the wide optical waveguide by optimizing their widths to make their effective indices equal. This kind of coupling is also polarization dependent, which provides an option to realize a compact PBS. More importantly, this ADC enabling the efficient coupling between the fundamental mode in a narrow waveguide and the higher-order mode in a wide waveguide can be used to realize mode (de)multiplexing, which is very attractive for realizing the mode (de)multiplexer used in mode-division-multiplexed systems. Finally the ADCs in this paper are SOI-compatible so that it is easy and convenient to monolithically integrate these power splitters, PBSs as well as mode (de)multiplexers based on ADCs with other elements on the same chip, like hybrid WDM-PDM (de)multiplexers, and hybrid WDM-MDM (de)multiplexers.

Acknowledgement

We thank Dr. Jian Wang, Dr. Pengxin Chen, Dr. Xiaowei Guan, Dr. Fei Lou, Prof. Lech Wosinski, Dr. Di Liang, Prof. John Bowers, Dr. Yaocheng Shi, Prof. Sailing He, et al for their contributions and the support from the National Natural Science Foundation of China (NSFC) (Grant Nos. 11374263, 6141101056, 61422510), the Doctoral Fund of Ministry of Education of China (No. 20120101110094), and the Fundamental Research Funds for the Central Universities.

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