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Abstract
Multimode based polarization independent (PI) wavelength division multiplexing (WDM) devices are proposed and experimentally demonstrated. The key concept is to utilize two different order modes for the orthogonal polarizations, ith-order mode for TE and jth-order mode for TM (i ≠ j) polarization respectively to extend the flexibility for designing devices. PI coupler composed of a multimode directional coupler and mode converters is introduced as a basic device. Then, we apply PI coupler to Mach Zehnder interferometer (MZI) and Bragg grating bandpass filters. PI MZI is achieved by optimizing the combination of two phase shifters in the interferometer arms. PI bandpass uses 3dB-PI coupler and polarization rotate Bragg gratings that induce mode coupling between the polarizations. Each device showed good matching in the spectrum between TE and TM polarizations in term of operation wavelength. The proposed concept can be a promising approach to realize PI WDM functions without introducing polarization diversity scheme in which a polarization beam splitter, two devices designed for each polarization and a polarization beam combiner are required.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The advent of 5G mobile and internet of things (IoT) have enhanced the demand for increasing bandwidth required in the access network, making wavelength division multiplexing (WDM) system increasingly important to avoid inflating the infrastructure cost and the physical volume of the optical components. The optical transceivers need to be low-cost and small enough to be placed everywhere inside the buildings because the radio-wave frequency used in 5G is hard to penetrate the concrete walls. Si photonics have been expected as a promising platform for its potential to reduce the cost due to mass production with CMOS equipments and to shrink the optical circuit size using the waveguide composed of Si core and SiO2 clad with high refractive index contrast [1–6]. However, such high index contrast waveguide tends to suffer from polarization dependence. At the receiver side in the optical link, where the random polarized signal comes, such polarization dependence induces the crosstalk degradation, even the malfunction, arising from the difference of the transmission spectrum between TE and TM polarizations.
Many researchers have dealt with this polarization issue by introducing the polarization diversity technique into the optical circuit that requires a polarization beam splitter, twice the number of the devices designed for each polarization and a polarization beam combiner, leading to large and complex circuit layout [7–10]. While we chose the approach to make the device itself polarization independent to simplify the optical layout with compact size.
One of the major WDM devices is Mach Zehnder interferometer (MZI) composed of some directional couplers and interferometer arm waveguides sandwiched by them, because arbitrary spectrum characteristics can be obtained by serially connecting several MZI devices [11–15]. Here, as mentioned above, MZI devices used in the receiver side must be independent of light polarizations, which means each element such as the directional couplers and the arm waveguides must be polarization independent individually. Polarization independent arm waveguides have been demonstrated by several design approaches [14,15]. However, to the best of our knowledge, making the directional coupler independent of light polarizations still remains a challenge due to the limitation of Si core thickness determined by the host wafer [15–17] and there are few reports that include experiment data. In fact, thinner silicon on insulator (SOI) thickness is preferable for low-loss waveguide [18], but it becomes more difficult to make the coupler independent to the light polarizations.
In this paper, we present the novel polarization independent directional coupler based on following concept. We utilize two different order modes for the orthogonal polarizations, $i$th-order mode for TE (TEi) and $j$th-order mode for TM (TMj) ($i \ne j$) polarization respectively as shown in Fig. 1. At the input side, the mode converter excites TEi and TMj modes from the fundamental modes of each polarization and send them to the multimode device that is designed to be insensitive to the polarizations. By using the various combinations of different order modes, polarization independent condition required for the multimode device can be extended compared with the conventional method in which only fundamental mode is used. By placing the identical mode converter at the output side as input side, the converted high order modes are back-converted to the fundamental modes, which means the multimode device acts as a single-mode device and is compatible with the other single-mode devices. All the waveguides sandwiched by the input and output mode converters are formed by multimode waveguides that transmit TEi and TMj simultaneously.
Fig. 1. Multimode device concept. TEi and TMj mean the ith-order mode for TE and the jth-order mode for TM polarization including the case where i or j equals to 0 (fundamental mode).
Furthermore, the proposed multimode concept can be applied to WDM devices such as a MZI or a grating bandpass filter. We experimentally demonstrated the performances of the fabricated multimode directional coupler, MZI and grating devices, verifying that each device operated at the same wavelength for both polarizations.
2. Device structure of polarization independent coupler
We first explain how to design the polarization independent (PI) coupler. In the coupling region, PI condition is defined as the situation where the perfect coupling lengths of ${L_{cTE}}$ for TE and ${L_{cTM}}$ for TM polarizations match each other, which is given by ${L_c} = {\raise0.7ex\hbox{$\lambda $} \!\mathord{\left/ {\vphantom {\lambda {2({{n_{even}} - {n_{odd}}} )}}} \right.}\!\lower0.7ex\hbox{${2({{n_{even}} - {n_{odd}}} )}$}}$ associated with the difference of the effective indices between even and odd supermodes in the directional coupler [16]. Assuming 300 mm SOI wafer whose SOI layer is 220 nm in thickness as a host material, we set Si core height ($H$) to 220 nm. The remaining parameters are the width (${W_{DC}}$) and the gap ($\textrm{G}$) of two waveguides placed to parallel as shown in Fig. 2. We used finite element method (FEM) to calculate the effective indices of even and odd supermodes, estimating the perfect coupling lengths for both polarizations. Figure 3 shows the relationship between the waveguide width (${W_{DC}}$) on the horizontal-axis and the perfect coupling length (${L_C}$) of TE and TM polarizations on the left vertical-axis or ${\raise0.7ex\hbox{${{L_{cTE}}}$} \!\mathord{\left/ {\vphantom {{{L_{cTE}}} {{L_{TM}}}}} \right.}\!\lower0.7ex\hbox{${{L_{TM}}}$}}$ on the right vertical-axis at the central wavelength of 1550 nm, with the gap fixed to be 400 nm. The cross-point of ${L_{cTE}}$ and ${L_{cTM}}$ corresponds to the PI condition in which the identical power distribution ratio can be obtained for both polarizations. As can be seen from Fig. 3(a), in this case, we apply only fundamental modes for TE and TM (TE0 and TM0), nearly PI condition is achieved at ${W_{DC}}$ around 250 nm. However, the cross-sectional size of Si core is too small to confine the light strongly enough within the core resulting in the bending loss or the leakage loss into the Si substrate. It should be noted that even though the gap G is varied from 400 nm, ${W_{DC}}$ for PI condition only slightly changes. Meanwhile, if we expand the width to the multimode waveguide region [Fig. 3(b)], the PI condition is achieved at the width around 740-750 nm between TE 1-order mode (TE1) and TM0, and the corresponding perfect coupling length is 52 $\mu $m around the wavelength of 1550 nm. In this case, TE1 and TM0 modes propagate and contribute to the power distribution in the directional coupler for each polarization.
Fig. 3. Relationship between the waveguide width (${W_{DC}}$) and the perfect coupling lengths (${L_c}$) for TE (solid line) and TM (dashed line) polarizations. The gap is fixed to 400 nm.
Figure 4 shows the schematic top view of proposed PI coupler device. It is composed of mode converters placed at input and output sides and the multimode directional coupler (MMDC). One of the key elements is the mode converter that exchanges the fundamental mode(s) to the higher order mode(s) for TE or (and) TM polarization(s). As mentioned above, we assume the case in which TE fundamental mode (TE0) is converted to TE 1-order mode (TE1), on the other hand TM fundamental mode (TM0) is maintained. TE0 must be suppressed as small as possible because it may become noise component.
Fig. 4. Top view of the polarization independent coupler. Each path of the modes is drawn by solid line and dashed line for TE and TM polarization, respectively. Each converted mode is attached with apostrophe.
The mode converter is decomposed into two polarization beam splitters (PBS)s connected serially for two-step mode transition. The first one (PBS1) translates TM0 to the adjacent waveguide as TM0, and the latter (PBS2) converts TE0 into TE1. The first PBS1 is a standard directional coupler whose cross-section has low aspect ratio to ensure the large difference of the perfect coupling length between TE0 and TM0 modes so that the coupling strength of TM0 gets to be much larger than that of TE0. While the second PBS2 is considered as an asymmetric directional coupler and it must be satisfied that the effective index of TE0 in the single-mode waveguide (${n_{TE0}}$) matches to that of TE1 in the adjacent multimode waveguide (${n_{TE1}}^{\prime}$), where TM0 is already transferred to. The effective indices of TM0s do not match between two waveguides due to the asymmetric structure, leading to the operation as a PBS for only TE polarization. In order to broaden the operating range of second PBS2, the widths of each waveguide are tapered along the opposite direction.
In these ways, TE1 can be generated from the fundamental mode and TM0 is preserved. Designed parameters of the mode converter are summarized in Table 1 (see Fig. 5 as the structure model). Figure 6 is the performance of the designed mode converter obtained by three-dimensions finite difference time domain (FDTD) simulation. Mesh sizes of each direction were set to 0.03 $\mu $m. The boundary condition was set to the perfectly matched layer with thickness of 0.5 $\mu $m. Input lights were set to the fundamental modes for each polarization simulation. From this result, we can expect low loss transmission for TE1 and TM0 modes while undesirable TE0 is sufficiently suppressed at below 20 dB around the center wavelength of 1550 nm. The 3-dB operating range is over 1500 nm to 1600 nm wide enough to cover C-band fully.
Fig. 6. Spectrum characteristic of the mode converter obtained by FDTD simulation. Solid lines and dashed lines indicate the cases in which TE fundamental mode (TE0) or TM fundamental mode (TM0) is input respectively.
Table 1. Design parameters of the mode converter.
Furthermore, we verified how each mode propagates through designed 3-dB coupler by semi-vector beam propagation method (BPM). Mesh sizes were set to 0.02 $\mu $m for each direction and wavelength was set at 1550 nm. Considering some coupling at the bending waveguides, coupling length was set to 23$\; \mu $m which was slightly shorter than the half of the perfect coupling length of 52 $\mu $m. Figure 7 shows polarization independent power distribution as we expected. Output powers to Bar and Cross ports were 3.9 dB and 3.8 dB for TE, and 3.4 dB and 3.0 dB for TM respectively. Although excess loss of TE is slightly larger than that of TM, power imbalance between Bar and Cross ports is within 0.4 dB for both polarizations.
Fig. 7. How each mode propagates through proposed coupler designed as 3-dB coupler obtained by beam propagation method, (a) for TE0 input and (b) for TM0 input respectively.
3. Design of MZI device
In this section, we design MZI device using the PI coupler discussed in the previous section. What is essential is to ensure the matching of the optical phases between TE1 and TM0 at the interferometer arm waveguides. As shown in Fig. 8, by combining two waveguide regions with different width as the phase shifters and aligning the length ratio of each region, the phase difference between TE1 and TM0 in the arm waveguides can be compensated. Considering only the center wavelength around 1550 nm, the phase difference $\Delta \phi $ between upper and lower arm waveguides is given by
Here, ${n_a}({{n_b}} )$ and ${L_a}({{L_b}} )$ are the effective index and the optical path length at the phase shifter A (or B) respectively. $\lambda $ is wavelength. Separating TE1 and TM0 modes, and setting them into the Eq. (1) to be equal, following Eq. (2) is derived.
Then, leading to following length relation:
Although any combination of the two phase shifters can be applied according to Eq. (3), we need to take the difference of the chromatic dispersion between TE1 and TM0 into account and to find the optimum combination of phase shifter A and B. We introduce an index D as the difference of phase dispersion between TE1 and TM0 as follow,
An example as a function of the combination of Wa and Wb for the widths at the phase shifter A and B is shown in Fig. 9. When two widths exceed 620 nm, the value D does not converge to zero, so we keep one width below 620 nm. To minimize D, we chose 850 nm for Wa and 580 nm for Wb as the shifter A and B respectively, and the length ratio $\textrm{k} = {\raise0.7ex\hbox{${{L_b}}$} \!\mathord{\left/ {\vphantom {{{L_b}} {{L_a}}}} \right.}\!\lower0.7ex\hbox{${{L_a}}$}}$ between the phase shifter A and B is 1.473595527 given by Eq. (3). For flattening the passband, the interferometer waveguides are connected serially forming two stage MZI so that the phase relation at the second stage gets to be -2times of that at the first stage ($- 2\Delta \phi $) [11]. Thus, each optical path length of phase shifter A and B at second arm is twice of that at first stage.
The width steps between different waveguides are eased by inserting the same taper structures between them into each arm waveguide so that the phases generated at the tapers are canceled. Some examples of predicted spectra are shown in Fig. 10 for (a) coarse WDM (CWDM) and (b) dense WDM (DWDM) applications, based on the mode calculation using FEM. Each parameter is summarized in Table 2. It is shown that the MZI device operates at the same wavelength for TE and TM polarization nevertheless apart from the center wavelength of 1550 nm, even when channel spacing gets much finer up to 0.8 nm(b). In case of Ref. [15], wavelength responses diverge between TE and TM as the operation point leaves from the central wavelength. It should be noted that in these calculations, only TE1 and TM0 are taken into the consideration and the noise effect from undesirable TE0 is ignored, which depends on the performance of the mode converters. A slight difference in the isolation between TE and TM originates from the difference of the coupling dispersion in MMDC, which does not matter as long as sufficient isolation is obtained.
Fig. 10. Calculated spectrums of 2stage-MZI device aimed for (a) CWDM and (b) DWDM, using PI couplers. As the phase shifters, two kind of waveguides are adopted whose widths are 850 and 580 nm respectively.
Table 2. Design parameters of 2-stage MZI devices aimed for CWDM or DWDM applications. ${\kappa }({L} )$ (= ${si}{{n}^2}\left( {\frac{{\pi }}{2} \cdot \frac{{L}}{{{{L}_{c}}}}} \right)$) means coupling strength at each MMDC considering some coupling at the bending waveguides.
4. Design of Bragg grating bandpass filter
In this section, we propose PI bandpass filter using the polarization rotate (PR) Bragg gratings. Figure 11 shows the schematic model of the PI bandpass filter. It is composed of PI 3-dB coupler and two Bragg gratings which exchange TE1 for TM0 as a polarization rotator. Input signal is divided into the upper and lower Bragg grating respectively with the same power and the phase offset of ${\raise0.7ex\hbox{$\pi $} \!\mathord{\left/ {\vphantom {\pi 2}} \right.}\!\lower0.7ex\hbox{$2$}}$ between two separated signals. Then two diffracted signals via mode conversion between TE1 and TM0 at each Bragg grating combine at 3-dB coupler in the contra-direction of input light and output from the output port. The cross-section of PR Bragg grating is shown in the inset of Fig. 11, being rib structure for breaking the orthogonality between TE1 and TM0 to induce the mode coupling between them [19,20]. Due to its mutual coupling between TE1 and TM0, Bragg wavelength matches perfectly between TE and TM polarizations and polarization dependence is omitted.
Fig. 11. Top view of PI bandpass filter using polarization rotate Bragg gratings. Bird view of PR Bragg grating is in the Balloon.
Bragg condition is given by following the equation [20,21]:
Here, $\mathrm{\Lambda }$ is the period of the refractive index perturbation in the grating and ${\lambda _{bragg}}$ is Bragg wavelength. In order to broaden the reflection range of Bragg wavelength, the grating adopts chirped structure where the pertubation period changes linealy by $\Delta \mathrm{\Lambda }$ along the propagating direction [21]. We set the parameters of Bragg grating as summarized in Table 3. $\Delta \mathrm{\Lambda }$ is set to 9 nm corresponding to the reflection band of 20 nm. Then we verified the spectrum characteristic of the PR Bragg grating by FDTD simulation. Mesh sizes were 0.03 $\mu $m. It should be noted the simulation was implemented with only single PR graring having just only 400 periods without mode converters and 3-dB MMDC to save the calculation memories of CPU. TE1 or TM0 is input to the PR Bragg grating and the reflected signal is monitored by TM0 or TE1 respectively. The calculated spectrum is shown in Fig. 12. The same wavelength responses are observed for TE1 and TM0, indicating PI bandpass operation. Although full grating length was shorten to 400/2500 in terms of number of periods, sufficient coupling strength is obtained.
Fig. 12. Spectrum characteristic of the polarization rotate Bragg grating obtained by FDTD simulation.
Table 3. Design parameters of PR Bragg grating.
5. Fabrication and measurement of the devices
The proposed devices were fabricated by 300 mm SOI wafer process whose thicknesses were 220 nm for SOI layer and 3 $\mu $m for buried oxide layer respectively. The process included the photolithograpy using the immersion ArF excimer laser ($\lambda = $193 nm) and the dry etching to define the waveguide patterns. Then the patterned waveguides were covered by SiO2 clad by chemical vapor deposition. Finaly, device patterned wafer was diced into the chip by dicing. Figure 13 shows some examples of the cross section of the fabridated waveguides, (a) for channel and (b) for rib structure. Figure 14 shows optical microscope image of the fabricated PI directional coupler and MZI devices. Device sizes are 360 ${\times} $150 $\mu $m2 for the PI coupler and 570 ${\times} $ 150 $\mu $m2 for MZI respectively including mode converters.
Fig. 13. Scanning electron microscope images of the cross-sections for the fabricated waveguide, (a) channel waveguide (b) rib waveguide.
Measurement was conducted with the single mode fiber alignment system. The super luminescent diode (SLD) as a broad band white light source sends CW light to the device patterned chip via the rotatable polarizer to define TE or TM polarization using the polarization maintaining fiber whose end facet is lens-shaped for efficient coupling to the inversed tapered spot size converter (SSC) on the chip [22]. The light traveling the chip is received by the lens shaped fiber as the input side and sent to the spectrum analyzer. The device performance is defined as the transmission spectrum of the device pattern by subtracting one of the reference waveguide with the same length as the device pattern, whose cross-section size is 440 nm ${\times} $ 220 nm for the singlemode condition. The propagation loss of the fabricated singlemode waveguide is 0.09 dB/mm for TE and 0.14 dB/mm for TM respectively around the wavelength of 1550 nm.
First, we tried to grasp the characteristic of the mode converter as a key element of the PI multimode devices. Since the measuremt was implemented in the single mode system where the converted high order mode is omitted, what we can verify about the mode converter is only the transmission loss but it is important factor to know. Figure 15 shows the transmission spectrum of two mode converters located at the opposite side each other as shown in the inset. The length of the intermediate waveguide sandwiched by them is just 200 $\mu $m which is short enough to neglect the propagation loss of it. From this figure, mode conversion losses are estimated to be 0.9 dB for two times mode conversion that are broken down into TE0 to TE1 and TE1 to TE0, or 0.5 dB for TM0 around the wavelength of 1550 nm.
Fig. 15. Transmission spectrum of mode converters. The inset shows the test pattern in which two mode converters are located at opposite side. Intermediate waveguide is 200 $\mu $m in length.
Then we measured the performance of the PI coupler designed as 3-dB coupler at the wavelength of 1550 nm. As discussed in the session2, the cross-sectional width of MMDC is set to 744 nm with gap being 400 nm. Coupling length is set to 23 $\mu $m. Bending radius is set to 25 $\mu $m to suppress the bending loss of TE1. Figure 16 shows the transmission spectrum of the fabricated PI coupler. A slight ripple is on TM spectrum as the same case of Fig. 15. Cross-point wavelengths of Bar and Cross states are 1552 nm for TE and 1550 nm for TM. Such little difference of the operating wavelength does not matter as long as the couplers are incorporated in the application deveices such as MZI or band pass filters. Excess loss is slightly larger in TE than TM by 0.6 dB, which can be explained by the difference of the excess loss between TE and TM at the mode converters. Needless to say, arbitrary power distribution ratio can be obtained by adjusting the length of coupling region of the MMDC. As this result shows, we experimentally verified the operating principle as a PI coupler based on multimode concept.
Fig. 16. Transmission spectrum of fabricated PI coupler designed as 3 dB coupler. Cross point of Bar and Cross state indicates 3 dB operation wavelength.
Further we tested the characteristic of the fabricated 2stage MZI device using three MMDCs and two type of phase shifters as interferometer waveguides whose combination is determined by Eqs. (3) and (4). Detail parameters are in Table 2 for CWDM one and its calculated spectrum is shown in Fig. 10(a). Measured result of MZI device exhibits good agreement with the calculated spectrum as shown in Fig. 17. The operation wavelengths match between TE and TM polarization as we expected, although excess loss about 4 dB occurs for TE polarization. The longer wavelength becomes, the larger excess loss gets to be. We attribute the major reason for the excess loss to the bending loss of 25 $\mu $m radius at the interferometer arm waveguide because we applied 580 nm width waveguide as one of the phase shifters where the light confiment is weaker for TE1 than TM0. To confirm it, we implemented FDTD simulations of the bending loss at 180 degree curve whose width was set to 580 nm. Calculated loss resulted in 0.3 dB for TE1 propagation. In the 2stage MZI structure having the connection of two 180 degree curves, the excess loss is estimeted to be 0.6 dB as two times of 0.3 dB. Although the loss value can not explain the total loss about 4 dB including mode conversion loss of 1 dB, we think the losses can be improved by increasing the width or radius of the bending waveguide at the sacrifice of device size. One clue is to apply another combination of two phase shifters. Fortunately, another best combination is found around 1200 nm for Wa and 600 nm for Wb as shown in Fig. 9.
Figure 18 shows the measured spectrum from the output port of the PI bandpass device. Device size is 1200 ${\times} $ 150 $\mu $m2, which is dominantly occupied by the Bragg grating length for efficient coupling between TE1 and TM0. Bragg wavelengths matches between TE and TM polarizations perfectly. Bragg reflection bandwidth is extended to 10 nm by adapting charp structure into grating perturbations, which is narrower than 20 nm we designed. It may be explained as follow; the coupling strength between TE1 and TM0 is weaker than that obtained by the FDTD simulation because of the shape blunting of the sidewall in the grating tooth through the incomplete etching process. We can also see PDL in the reflection band. The possible reason is that it originates from PDL in SSC as the optical interface on the deveice chip because the output polarization differes from the input polarization in PR bandpass structure and it can not be removed by the reference waveguide in which PR effect does not occur.
Finally, we summarized PI coupler and MZI characteristics to compare our devices with other works in Table 4. Although, it is difficult to compare simply due to the difference of the design policy such as channel frequency spacing, our work shows good experimental date with small device size. As we have discussed, our proposed multimode concept devices can be a promising approach for CWDM applications without introducing the polarization divesity functions.
Table 4. Comparison with other PI coupler or MZI devices except Ref. [23], which is not PI designed and referred as a multimode device. Hyphen means no experimental data.
6. Conclusion
In this paper, we have proposed novel polarization independent (PI) coupler using two different modes for TE and TM polarizations and applied it to PI wavelength division multiplexing (WDM) devices such as Mach Zehnder interferometer (MZI) and Bragg Grating bandpass filter based on the multimode concept. Each device was theoretically analyzed and experimentally demonstrated to exhibit good agreement with the predicted spectra and polarization independent property.
We chose the combination of first-order mode for TE (TE1) and the fundamental mode for TM (TM0) respectively to achieve PI coupling condition. PI coupler composed of mode converters and a multimode directional coupler (MMDC) was designed as 3-dB coupler and cross point wavelengths of Bar and Cross states matched between TE and TM polarizations. MZI device having 2stage interferometers adoped two region phase shifters to compensate the phase difference between TE1 and TM0 modes. By optimizing the combination of the phase shifters, the difference of optical phase and chromatic disperion between TE1 and TM0 at arm waveguides were minimized. Remaining challenge is to improve excess loss for TE1 mode that originates from the bending waveguides by changing the device layout such as the bending radius. The polarization rotate (PR) bandpass device using two PR Bragg gratings shows good matching in both spectrum for TE and TM due to the mutual coupling between TE1 and TM0.
These multimode concept gives the flexibility to the design of various devices that are required to be independent of light polarizations without introducing the polarization diversity approach into the circuit.
Funding
Ministry of Internal Affairs and Communications (JPMI00316).
Disclosures
The authors declare no conflicts of interest.
References
1. T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, “Microphotonics devices based on silicon microfabrication technology,” IEEE J. Sel. Top. Quantum Electron. 11(1), 232–240 (2005). [CrossRef]
2. H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Si photonic wire waveguide devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1371–1379 (2006). [CrossRef]
3. H. Hao Chang, Y. Hao Kuo, H. Wen Chen, R. Jones, A. Barkai, M. J. Paniccia, and J. E. Bowers, “Integrated triplexer on hybrid silicon platform,” OSA Technical Digest (Optical Society of America, 2010), paper OThC4
4. A. Alduino, L. Liao, R. Jones, M. Morse, B. Kim, W. Z. Lo, J. Basak, B. Koch, H. F. Liu, H. Rong, M. Sysak, C. Krause, R. Saba, D. Lazar, L. Horwitz, R. Bar, S. Litski, A. Liu, K. Sullivan, O. Dosunmu, N. Na, T. Yin, F. Haubensack, I. Hsieh, J. Heck, R. Beatty, H. Park, J. Bovington, S. Lee, H. Nguyen, H. Au, K. Nguyen, P. Merani, M. Hakami, and M. Paniccia, “Demonstration of a high speed 4-channel integrated silicon photonics WDM link with hybrid silicon lasers,” IEEE Hot Chips 22 Symposium (HCS), 2010
5. G. Li, J. Yao, Y. Luo, H. Thacker, A. Mekis, X. Zheng, I. Shubin, J. H. Lee, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow-loss, high-density SOI optical waveguide routing for microchip interconnects,” Opt. Express 20(11), 12035 (2012). [CrossRef]
6. H. Ito, Y. Terada, N. Ishikura, and T. Baba, “Hitless tunable WDM transmitter using Si photonic crystal optical modulators,” Opt. Express 23(17), 21636–21629 (2015). [CrossRef]
7. R. Hereth and G. Schiffner, “Broad-band optical directional couplers and polarization splitters,” J. Lightwave Technol. 7(6), 925–930 (1989). [CrossRef]
8. H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Polarization beam splitter and rotator for polarization-independent silicon photonic circuit,” 2007 4th IEEE International Conference on Group IV Photonics, 19-21 Sept. 2007
9. D. Y. Lee, X. Zheng, J. Yao, Y. Luo, J. H. Lee, S. Lin, H. Thacker, J. Bovington, I. Shubin, S. S. Djordjevic, J. E. Cunningham, K. Raj, and A. V. Krishnamoorthy, “Error-free operation of a polarization-insensitive 4λ x 25 Gbps silicon photonic WDM receiver with closed-loop thermal stabilization of Si microrings,” Opt. Express 24(12), 13204 (2016). [CrossRef]
10. S. Chen, Y. Shi, S. He, and D. Dai, “Compact monolithically-integrated hybrid (de)multiplexer based on silicon-on-insulator nanowires for PDM-WDM systems,” Opt. Express 23(10), 12840 (2015). [CrossRef]
11. Q. Wang and S. He, “Optimal design of planar wavelength circuits based on Mach–Zehnder Interferometers and their cascaded forms,” J. Lightwave Technol. 23(3), 1284–1290 (2005). [CrossRef]
12. S. H. Jeong, D. Shimura, T. Simoyama, T. Horikawa, Y. Tanaka, and K. Morito, “Si-nanowire-based multistage delayed Mach–Zehnder interferometer optical MUX/DeMUX fabricated by an ArF-immersion lithography process on a 300 mm SOI wafer,” Opt. Lett. 39(13), 3702–3705 (2014). [CrossRef]
13. S. H. Jeong, “Broadband 1 ( 8 channel silicon-nanowire-waveguide WDM filter based on point-symmetric Mach-Zehnder interferometric optical couplers in the O-band spectral regime,” OSA Continuum 2(12), 3564–3575 (2019). [CrossRef]
14. H. H. Yaffe, C. H. Henry, R. F. Kazarinov, and M. A. Milbrodt, “Polarization-independent silica-on-silicon Mach-Zehnder Interferometers,” J. Lightwave Technol. 12(1), 64–67 (1994). [CrossRef]
15. A. Bois, A. D. Simard, W. Shi, and S. LaRochelle, “Design of a polarization-insensitive WDM demultiplexing lattice filter in SOI,” CLEO2015, © OSA 2015, SM3I.1.pdf
16. V. M.N. Passaro, F. D.’Olio, B. Timotijevic, G. Z. M.ashanovich, and G. T. Reed, “Polarization-insensitive directional couplers based on SOI wire waveguides,” Open Opt. J. 2(1), 6–9 (2007). [CrossRef]
17. N.-N. Feng, D. Feng, H. Liang, W. Qian, C.-C. Kung, J. Fong, and M. Asghari, “Low-Loss Polarization-Insensitive Silicon-on-Insulator-Based WDM Filter for Triplexer Applications,” IEEE Photonics Technol. Lett. 20(23), 1968–1970 (2008). [CrossRef]
18. D. Shimura, T. Horikawa, H. Okayama, S-H. Jeong, M. Tokushima, H. Sasaki, and T. Mogami, “High precision Si waveguide devices designed for 1.31μm and 1.55μm wavelengths on 300mm-SOI,” Group four photonics, WE1, 27-29 August2014
19. H. Okayama, Y. Onawa, D. Shimura, H. Yaegashi, and H. Sasaki, “Polarization rotation Bragg grating using Si wire waveguide with non-vertical sidewall,” Opt. Express 22(25), 31371 (2014). [CrossRef]
20. H. Okayama, Y. Onawa, D. Shimura, H. Yaegashi, and H. Sasaki, “Polarization rotation Bragg grating with high diffraction efficiency using Si waveguide top surface groove grating,” Electron. Lett. 51(23), 1909–1911 (2015). [CrossRef]
21. E. Mortazy, B. L. Drogoff, J. Azana, and M. Chaker, “Chirped Bragg grating in silicon based rib waveguide,” 7th International Workshop on Fibre and Optical Passive Components, 13-15 July (2011).
22. Y. Shoji, K. Kintaka, S. Suda, H. Kawashima, T. Hasama, and H. Ishikawa, “Simple spot-size converter with narrow waveguide for silicon wire circuits,” 15th Microoptics Conference (MOC'09), Tokyo, Japan, 25-28 October2009.
23. A. Fujisawa, J. Takano, Y. Sawada, T. Sakamoto, T. Matsui, K. Nakajima, and K. Saitoh, “A novel Si four-wavelength multiplexer for 100/400GbE using higher-order mode composed of (a)symmetric directional couplers and TE1-TM0 mode converter,” Opt. Express 27(25), 36286 (2019). [CrossRef]
