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Abstract
An ultra-sharp multimode waveguide bend (MWB) based on a multimode waveguide corner-bend (MWCB) is proposed and realized. With the present MWCB, total internal reflection (TIR) happens and the light propagation direction of all the mode-channels can be modified with low excess losses (ELs) and low inter-mode crosstalk (CT) in the optical communication bands from 1260 nm to 1680 nm. For the MWCB designed for the TE0 and TE1 modes, the ELs are less than 0.18 dB and the inter-mode CTs are less than −36 dB in the wavelength range of 1260-1680 nm. The measurement results show the fabricated MWCB works very well as predicted by the theory. It is very flexible to extend the present MWCB for more mode-channels by simply adjusting the core width. For example, the MWCB designed with a 35 µm-wide core has an EL less than 0.54 dB and inter-mode CT less than −24 dB for the ten TE-polarization modes (i.e., TE0∼TE9) in the wavelength-band of 1260-1680 nm. For the present MWCB, the fabrication is also very convenient because no tiny nano-structure and no additional fabrication steps are needed. It also shows that the present MWCB is not sensitive to the sidewall angles even when the angle is up to 8°. The proposed MWCB is promising for multimode silicon photonics because of the simple structure, easy design, easy fabrication as well as excellent performances in an ultra-broad wavelength-band.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the recent years, various advanced multiplexing technologies have been developed to satisfy the increasing demands of high-capacity optical interconnects [1–7], such as wavelength-division-multiplexing (WDM), polarization-division-multiplexing (PDM) and mode-division-multiplexing (MDM). Among them, the MDM technology using different mode-channels in a multimode waveguide is becoming an attractive way to increase the link capacity for a single wavelength-carrier in optical interconnects. One should notice that not only the fundamental mode but also the higher-order modes are involved in MDM systems. As a result, the development of multimode photonic integrated devices is extremely important to manipulate all the involved modes (including the higher-order modes). As it is well known, silicon photonics has been developed rapidly in the past decade as a very popular technology for realizing photonic integrated devices because of the CMOS compatibility and the high integrated-density [8]. Various passive and active silicon photonic devices have been realized with excellent performances. More recently, multimode silicon photonics has been recognized as a new direction in order to satisfy the demands for MDM systems as well as some other emerging applications [9].
For multimode photonic integrated circuits (PICs), sharp multimode waveguide bends (MWBs) are usually needed for changing the direction of light propagation. When operating with singlemode silicon-on-insulator (SOI) nanophotonic waveguides, which has an ultra-high refractive index-contrast between the core and the claddings, it is very easy to achieve ultra-sharp waveguide bends for realizing compact photonic devices and high-density photonic circuits [10]. However, for multimode waveguide bends, the situation becomes very different because the mode fields are squeezed to the outside sidewall and become very asymmetric when the bend is sharp [11–15]. This introduces not only the mode-mismatching loss but also the inter-mode crosstalk [10,11]. As a result, a very large bending radius is usually required for MWBs when using regular arc-bends. For example, the bending radius for a 4 µm-wide regular arc-bend should be in millimeter scale [12]. Consequently, it becomes a challenge to realize sharp multimode waveguide bends.
Nevertheless, tremendous efforts have been made to develop novel structures for MWBs in the past years. There are three typical methods to achieve compact MWBs. The first one is modifying the effective refractive index profile of the bent section to minimize the mode mismatch between the straight and bent sections. In this case, some special fabrication processes or some special structures are needed. For example, the grayscale lithography is needed to vary the core-height of the MWB in [12], which is not easy for fabrication. More recently, the structure with shallowly-etched non-uniform subwavelength-gratings was introduced on the top-surface of the MWB [13], so that the effective refractive index of the MWB is engineered. In this way, the bending radius is as small as 10 µm for the case with thee mode-channels [13]. The second one is utilizing some trajectory designs in the bent section so that the mode can be transmitted adiabatic. For example, an MWB based on modified Euler curves is proposed with an effective radius of 45 µm to support four TM modes with low excess losses and low inter-mode crosstalk [14]. The third one is introducing a special mode converter between the straight- and bent-sections [15,16], so that the mode field in the straight waveguide will vary gradually to match that in the bent waveguide. One might notice that the design for most of the previous designs needs lots of optimizations to find the optimal geometrical parameters. Furthermore, the parameters should be re-optimized carefully when the bending radius changes or more mode-channels are involved. Currently, the demonstrated MWBs have no more than four mode-channels, and it is still not easy to design low-loss and low-crosstalk ultra-broadband MWBs with more than four mode-channels.
In this paper, we propose a novel ultra-compact MWB based on a multimode waveguide corner-bend (MWCB), where total internal reflection (TIR) happens for all the modes. The present MWCB can change the light propagation direction of all the modes, while the excess losses (ELs) and the inter-mode crosstalk (CT) for all the M mode-channels are very low over all the optical communication bands from 1260 nm to 1680 nm. Here, for the MWCB designed for two mode-channels, the EL is less than 0.18 dB and the inter-mode CT is less than −36 dB in an ultra-broadband from 1260 nm to 1680 nm for the TE0 and TE1 modes. The measurement results show the fabricated MWCB works very well as predicted by the theory, while the bandwidth is limited by the mode (de)multiplexers and the grating couplers used here. It is also possible to easily handle more mode-channels as desired by using the present MWCB. As an example, the designed MWCB with a 35 µm-wide core has an EL less than 0.54 dB and inter-mode CT less than −24 dB for all the ten TE-polarization modes (i.e., M = 10).
2. Structure and design
Figure 1(a) shows the three-dimensional schematic configuration of the proposed MWCB with uniform wide core-width wco. In particular, Goos-Hanchen (GH) effect is considered at the TIR surface. As a result, the reflecting interface is displaced slightly from the original geometric interface [17]. In this design, there is a small displacement ΔwGH at the corner for the input waveguide and output waveguide, as shown in Fig. 1(b). According to the optical TIR principle, the launched guided-modes are reflected totally with an angle (which is the double of the incident angle). As it is well known, light confinement becomes stronger when the core width is larger. And one can easily increase the core width of the waveguide corner-bend when more modes are involved, so that all these modes are confined well in the silicon core. In this case, all these modes tend to have similar effective refractive indices and similar behaviors for reflection. The details about the design procedure for determining the core width wco and the displacement ΔwGH are described below.
Fig. 1. Schematic configuration of the proposed MWCB. (a) Three-dimensional view; (b) Enlarged view for the GH-shift; (c) Cross section of the waveguide.
Here a silicon-on-insulator (SOI) photonic waveguide with a 220 nm-thick top-silicon layer is used (i.e., hco=220 nm). As it is desired to achieve an ultra-broadband MWCB, we consider the design for the wavelength range from 1260 nm to 1680 nm, which covers all the optical communication bands (e.g., O-, E-, S-, C-, L-, and U-bands). Figures 2(a)–2(d) shows the mode field Ex(x, y) of the TE0-TE3 modes with the same core width wco (e.g., 2 µm). The field profiles along the x-axis at y = 0 are also shown. It can be seen that the higher-order mode has stronger evanescent field than the lower-order mode, indicating that the mode confinement is lower for the higher-order mode has, as it is well known according the guided-wave theory. Figures 2(e) and 2(f) shows the calculated effective indices neff(wco, m) of the m-th guided-modes in an SOI waveguide when operating at the wavelengths of 1.26 µm and 1.68 µm, respectively. Here we consider the lowest ten guided-modes (i.e., m = 0, 1, …, 9). From Figs. 2(e) and 2(f), one can see that the effective index neff(wco, m) of the m-th guided-mode tend to be very close to the effective index neff(wco, 0) for the fundamental mode when the core width wco is much larger than the wavelength. This indicates that these guided-modes have very similar mode confinement and thus similar TIR behaviors when reflected at the core-bend. Therefore, one can easily predetermine the core width wco for the MWCB according to the calculated dispersion curves shown in Figs. 2(e) and 2(f), so that the effective indices for the mode-channels propagating in the MWCB are very similar. Accordingly, one should have neff(wco, M)−neff(wco, 0)≤ɛ, where ɛ<<1, and neff(wco, M) is the effective index of the highest-order mode-channel propagating in the MWCB. As an example, we choose ɛ=0.01 for the design of the MWCB in this case with the TE0 and TE1 mode-channels, indicating that the difference of neff(wco, 1)−neff(wco, 0) should be less than 0.01. Definitely, one can freely choose another different value ɛ according to the requirements of the MWCB performance. According to Figs. 2(e)–2(f), the core-width is chosen as wco=7 µm so that one has neff(wco, 1)−neff(wco, 0) ≤ 0.01 in the wavelength-band of 1260-1680 nm. A three-dimensional finite-difference time-domain (3D-FDTD) method with non-uniform grid sizes (Lumerical FDTD) was then used to simulate the light propagation in the designed structures. In order to evaluate the EL and inter-mode CT quantitatively, we calculate the transmissions Tij (i = 1, 2, 3) from the i-th guided-mode launched at the input end to the j-th guided-mode at the output end. The EL and the inter-mode CT for the i-th guided-mode are then calculated by
Fig. 2. The mode fields of the TE0 (a), TE1 (b), TE2 (c), and TE3 (d) modes when wco = 2 µm; Calculated dispersion curves for the TE0-TE9 modes at the operating wavelength of 1260 nm (e) and 1680 nm (f).
In this simulation, we focus on the mode-channel with the weakest mode confinement in the core regarding that it usually is the worse one. In the present case with two mode-channels, we focus on the EL of the TE1 mode and the inter-mode CT from the TE1 mode to the TE0 mode. First, we investigate the dependence of the EL and the inter-mode CT on the core width wco by initially choosing ΔwGH=0, because the displacement ΔwGH related to the GH-shift is usually as small as ∼0.1 µm (Note the displacement ΔwGH will be optimized below). Figure 3(a) shows the calculated ELs of the TE1 mode and the inter-mode CT from the TE1 mode-channel to the TE0 mode-channel in the ultra-broad wavelength-band of 1260-1680 nm. Here the core-width is chosen as wco=5, 6, 7, 8 and 9 µm. It can be seen that the EL and the CT decrease monotonously as the core-width wco increases. The MCWB works very well with very low ELs and very low CTs when the core-width is sufficiently large. For example, when choosing wco=7 µm, the inter-mode CT for the launched TE1 mode is lower than <−25 dB and the ELs is lower than <0.23 dB in the broadband from 1260nm to 1680nm, which is excellent enough for most applications of multimode silicon photonics. When really needed for some specific application, the performance of the MCWB can be even near-perfect in theory by further increasing the core width. However, the improvement is insignificant. Instead, the performance will be limited by the fabrication process in reality. On the other hand, a narrow core-width is really preferred to achieve a compact footprint and to be connected conveniently with other photonic devices on the same chip. Therefore, here we choose the core-width wco=7 µm be making the trade-off as example.
Fig. 3. (a) Calculated ELs and inter-mode CTs of the TE1 mode in the wavelength range of 1260-1680nm for different core widths wco (=5, 6, 7, 8, and 9µm) when initially choosing ΔwGH=0; (b) Calculated ELs and inter-mode CTs of the TE1 mode for the designs with different displacements ΔwGH ( = 0.07-0.17 µm) when wco=7 µm.
In order to improve the performance further, the displacement ΔwGH due to the GH shifting should be optimized. For the TE-polarization mode, the GH-shift ΔwGH in a TIR structure is given approximately by [18]
Fig. 4. Simulated light propagation in the designed MWCB (@1550 nm) when the TE0 (a) and TE1 (b) is launched; Calculated wavelength-dependent transmissions of the designed MWCB when the TE0 (c) and TE1 (d) is launched. Here the MWCB is designed with wco = 7 µm and ΔwGH = 0.11 µm.
Since the sidewalls of the silicon core is not perfectly vertical due to the non-perfect fabrication process, some additional EL and inter-mode CT might be introduced [19] in the present MWCB. Regarding that the sidewall angle θside is usually less than 10°, here we assume that the sidewall angle θside = 0°, 4° and 8° as an example. Figure 5 shows the calculated ELs and the maximal inter-mode CTs for the two mode-channels in the MWCB with wco = 7 µm and ΔwGH = 0.11 µm. It can be seen the EL increases as the sidewall angle θside increases. When θside<4°, the EL increases very slightly. When the sidewall angle θside varies from 4° to 8°, the EL increases from 0.18 dB to 0.19 dB at 1680 nm and increases from 0.11 dB to 0.16 dB at 1260 nm. One has an EL lower than 0.19 dB in the ultra-broad bandwidth from 1260 nm to 1680 nm when 0°<θside<8°. Meanwhile, the inter-mode CT varies greatly as the sidewall angle increases from 0° to 8°. In particular, the specific wavelength λ0 corresponding to the minimal CT has a blue-shift as the sidewall angle increase. For example, the wavelength λ0 shifts from 1560 nm to 1360 nm when the sidewall angle θside varies from 0° to 8°. Fortunately, the CT is still very low (<−35 dB) in the ultra-broad bandwidth from 1260 nm to 1680 nm when 0°<θside<8°. Therefore, the requirement for the sidewall angle is not critical, which makes the fabrication easy.
Fig. 5. (a) Cross section of the waveguide with angled sidewall; The calculated EL (b) and inter-mode CT (c) when the TE1 mode is launched in the MWCB with wco = 7 µm and ΔwGH = 0.11 µm. Here the sidewall-angle is assumed to be θside = 0°, 4° and 8°.
The proposed approach for MWCB is also very flexible for the cases with more than two mode-channels. As discussed above, the core width wco for the MWCB can be predetermined conveniently from the calculated effective indices of the mode-channels propagating in the MWCB [see Figs. 2(e) and 2(f)]. One should choose the core width wco appropriately for achieving a small difference between the effective indices of the highest-order mode-channel and the fundamental mode-channel, i.e., neff(wco, M) − neff(wco, 0) ≤ɛ (e.g., ɛ=0.01) . In this way, these mode-channels propagating in the MWCB should have similar confinement factors and similar TIR behaviors when reflected at the core-bend. As an example, for the MWCBs with 4, 6, 8, and 10 mode-channels considered in this paper, the core widths for the MWCBs are chosen wco=14, 21, 28, and 35 µm, respectively. Definitely, some deviation for the core width is allowed because the present MWCB is robust and is not sensitive to the core width (see the result in Fig. 3(a) for the MWCB with two mode-channels). Furthermore, one should note that it is able to design the MWCB for more than 10 mode-channels by simply choosing a wider core-width. Here the parameter ΔwGH for the MWCB is chosen as ∼0.11 µm (similar to the case with two mode-channels). Figures 6(a)–6(d) shows the simulated light propagation for the TE3, TE5, TE7, and TE9 modes, which are respectively the highest-order modes considered in these designed MWCBs with wco = 14, 21, 28 and 35 µm. We also calculated the transmissions Tij from the TEi mode launched at the input multimode waveguide to the TEj mode at the output multimode waveguide, as shown in Figs. 6(e)–6(h). It can be seen that the ELs for these highest-order modes (TE3, TE5, TE7, and TE9) propagating in the corresponding MWCBs are as low as 0.3 dB, 0.4 dB, 0.46 dB, and 0.54 dB in the ultra-broad wavelength-band from 1260 nm to 1680 nm. Meanwhile, the inter-mode CTs are also as low as <−24 dB in this ultra-broad wavelength-band.
Fig. 6. Simulated light propagation and the spectral responses of the designed MWCBs width different core widths when the highest-order mode (TEi) is launched. (a), (e) i = 3, and wco = 14 µm; (b), (f) i = 5, and wco = 21 µm; (c), (g) i = 7, and wco = 28 µm; (d), (h) i = 9, and wco = 35 µm.
3. Fabrication and measurement
For the present MWCB, the fabrication is very easy because no special processes are required. As an example, the designed MWCB with wco=7 µm was fabricated on an SOI wafer with a 220 nm-thick top-silicon layer and a 2-µm-thick buried-dioxide-layer. The fabrication includes an E-beam lithography process for the resist-patterning and an ICP (inductively coupled plasma) dry-etching process for etching the top-silicon layer. Figures 7(a)-7(b) shows the pictures of the fabricated MWCB. In order to characterize the transmissions of the TE0 and TE1 modes in the MWCB, here we used a photonic integrated circuit consisting of a two-channel mode multiplexer (with the input ports ITE0, ITE1), an input adiabatic taper, cascaded MWCBs, an output adiabatic taper and a two-channel mode demultiplexer (with the output ports OTE0, OTE1), as shown in Fig. 7(a). Here the two-channel mode (de)multiplexers are based on cascaded dual-core adiabatic tapers given in [20]. As discussed above in Figs. 5(a) and 5(b), there is no critical requirement for the sidewall angle and an imperfectly vertical sidewall is allowed for achieving low ELs and low CTs. On the other hand, it would be important to make smooth sidewalls to lower the scattering loss. Fortunately, the present MWCB can be fabricated very well with modern nanofabrication technologies. As show in Fig. 7(b), it can be seen that the sidewall of the waveguide corner is vertical and smooth, which helps achieve high-efficiency reflection with low ELs and low CTs, as verified by the measurement results below.
Fig. 7. (a) Microscope image of the fabricated silicon PIC; (b) Scanning electron microscopic (SEM) images of the fabricated cascaded MWCB.
As it is well known, the bandwidth for grating couplers is usually quite limited. In order to characterize the fabricated MWCBs over the ultra-broad bandwidth, we set the fiber probes with different tilt angles θfiber = 25°, 15° and 5° in the experiments to alleviate the limitation from the bandwidth of grating couplers. Correspondingly, we can measure the transmissions in the wavelength-bands of 1400-1520 nm, 1520-1600 nm and 1600-1680 nm, which however is not as large as the desired bandwidth for charactering the present ultra-broadband MWCB yet. Here we used a supercontinuum source and an optical spectrum analyzer in the measurement. Figures 8(a)-8(b) shows the measured transmissions at the output ports OTE0 and OTE1 of the PIC consisting of eight MWCBs in cascade when launching the TE0 and TE1 modes from the input ports ITE0 and ITE1, respectively. These transmissions are normalized with respect to the transmission of a straight waveguide on the same chip. In order to give a comparison, Figs. 8(c)–8(d) shows the measured transmissions for the PIC without MWCBs. There are some ripples observed for both cases, particularly when θfiber = 25°, and 5°. These ripples are partially due to the reflections occurring at grating couplers and some inter-mode crosstalk introduced by the mode (de)multiplexer. In addition, the bandwidth of the mode (de)multiplexers is quite limited compared to the ultra-broad bandwidth of the present MWCBs, which makes it not easy to characterize the ultra-broadband MWCBs precisely. Nevertheless, the comparison between the results in Figs. 8(a)–8(b) and Figs. 8(c)–8(d) shows that the eight MWCBs inserted in the PIC do not introduce notable excess losses in the broad wavelength-band. From the measurement result, the EL for per MWCB was estimated to be <0.36 dB for the TE0 mode and <0.53 dB for the TE1 mode over the 240-nm bandwidth from 1420nm to 1660 nm. The inter-mode CT for the cascaded MWCBs was measured to be <−15 dB which is mainly due to the intrinsic wavelength dependence of the asymmetric directional couplers used for the mode (de)multiplexers. The MWCB can be better characterized when broadband mode (de)multiplexers with excellent performances are available in the future.
Fig. 8. Measured transmissions at the output ports OTE0 and OTE1 of the PIC consisting of eight MWCBs in cascade when launching the TE0 (a) and TE1(b) modes from the input ports ITE0 and ITE1, respectively; Measured transmissions for the fabricated PIC without MWCBs when launching the TE0 (c) and TE1 (d) modes.
Table 1 gives a summary for the reported MWBs based on different structures. It can be seen that no MWBs have been reported previously for supporting low-loss and low-crosstalk propagation of more than four mode-channels. For the approach of using a mode converter in [15], it is difficult to be extended for more than two mode-channels. Definitely, some of those reported approaches can be extended for more mode-channels when one carefully designs the structure with, e.g., a non-uniform core-layer [12], shallowly-etched SWGs [13], a Euler-curve bend [14], and a PMMA-SWG mode converters [16]. On the other hand, most of them need special fabrication processes (e.g., the grayscale lithography in [12]) or special structures (subwavelength nanostructures [13,16]), which makes the fabrication not easy. In contrast, the Euler-curve bend proposed in [14] can be extended easily for more mode-channels (e.g., ≥10) with simple design and fabrication. However, the bending radius becomes pretty large. As a summary, it is still very challenging to realize compact MWBs with ≥10 mode-channels even in theory. Furthermore, for those MWBs reported previously, the bandwidth for achieving low-loss (<0.5 dB) and low-crosstalk (<−20 dB) is usually less than 100 nm in theory, as shown in Table 1. As an alternative, the present MWCB can work very well in an ultra-broad bandwidth of >400 nm, which is the best one reported until now. Furthermore, the present MWCB does not need any further special nanostructures and processes, which makes the design and the fabrication very easy. More importantly, it can be extended for more mode-channels very conveniently. Even for the case with M = 10, the designed MWCB can work very well with low ELs and low CTs in an ultra-broad bandwidth. The present MWCB provides an attractive option for realizing compact multimode silicon PICs in the future.
Table 1. Comparison of reported ultra-compact MWBs on silicon (theory).a
4. Conclusion
In conclusion, in this paper we have proposed and realized an ultra-compact and ultra-broadband MWCB for multimode silicon photonics. For example, for the present MWCB with a core-width wco = 7 µm, the ELs are <0.18 dB and the inter-mode CTs are < −36 dB for both TE0 and TE1 modes in an ultra-broad wavelength-band from 1.26 µm to 1.68 µm, which covers the O-, E-, S-, C-, L-, and U-bands. The present MWCB is very flexible to be extended for more mode-channels by simply adjusting the core width according to the dispersion curves. For example, when increasing the core width to e.g. wco=35 µm, the MWCB works very well with a low EL of <0.54 dB and a low inter-mode CT of < −24 dB for the ten TE-polarization modes (i.e., TE0∼TE9) in the ultra-broad wavelength-band of 1.26-1.68 µm. The dependence of the mode-transmissions on the sidewall angle has also been analyzed. It has shown that the present MWCB is not sensitive to the sidewall angles even when the angle is up to 8°, which makes the present design very robust. For the present MWCB, the fabrication is also very convenient because no tiny nano-structure and no additional fabrication steps are needed. The measurement results show that the fabricated MWCB works very well with low ELs and low CTs, as predicted by the simulation. The proposed MWCB is promising for multimode silicon PICs because of the simple structure, easy design, easy fabrication as well as excellent performances in a broadband. In order to be connected conveniently to other elements on the same chip, one can introduce some compact spot-size expander with special structures, e.g., lens-assisted focusing taper [21], subwavelength-grating-based GRINs [22], etc.
Funding
National Major Research and Development Program (No. 2018YFB2200200); National Science Fund for Distinguished Young Scholars (61725503); National Natural Science Foundation of China (6191101294, 91950205); Natural Science Foundation of Zhejiang Province (LD19F050001, LZ18F050001).
Disclosures
The authors declare no conflicts of interest.
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