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Abstract
Polarization rotation and wavelength filtering are key functionalities used to build complex photonic integrated circuits. Both these functionalities have been demonstrated in various material and device platforms. We propose, for the first time, a fully passive wavelength selective polarization rotation in silicon nitride/amorphous silicon hybrid waveguide. We demonstrate TE0 → TM0 and TM0 → TE0 wavelength selective polarization rotator-cum-filter with a measured 3dB bandwidth of 14.8 nm. Further, we experimentally demonstrate a proof of concept for simultaneous coarse wavelength division multiplexing and polarization rotation for the first time in a passive configuration. We also show the feasibility of bandwidth engineering from 0.59 nm to 81 nm, enabled by the unique flexibility of the proposed hybrid waveguide.
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1. Introduction
On-chip polarization handling is among the crucial functionalities used for complex optical signal processing in photonic integrated circuits (PIC). As demanded by the application, a particular state of polarization may be more suitable than others. An example can be of using TE mode for propagation due to better confinement and using TM mode for high-performance filters and sensing [1,2].
Further, structural birefringence inherently present in waveguides causes polarization-dependent phase response, detrimental to wavelength division multiplexing (WDM) applications. A polarization-insensitive waveguide operating in a single mode region with zero birefringence is ideal for wavelength division multiplexing (WDM) [3]. Such a response is reported using rib waveguide and specialized platforms like Triplex [4–6]. However, it puts design constraints on waveguide geometry and dimensions, making such solutions restrictive. Therefore, on-chip polarization manipulation is highly desirable, and a polarization diversity scheme can be utilized for this purpose.
Polarization beam splitters (PBS) and polarization rotators (PR) are the primary components to achieve polarization diversity. A polarization splitter is used to split the arbitrary incoming polarization states, and the rotator converts it into a desired polarization to be processed throughout the chip.
A PR can work in either active or passive configuration. An active PR requires an external field for polarization conversion, putting constraints on material systems [7,8]. A passive PR operates through geometrical perturbation, making its implementation universal and energy efficient.
Polarization conversion in passive PR can either be done through mode evolution or mode coupling. Mode evolution based PR transforms a propagating mode adiabatically through geometrical evolution along the propagation direction [9–11]. The PR based on mode evolution shows broadband response but has long device lengths for adiabatic conversion and requires additional PBS for obtaining required extinction [11]. Polarization rotation can also be realized by transforming the input TM0 mode into intermediate TE1 mode using a tapered waveguide and demultiplexing it into TE0 mode through MMI, asymmetric Y-splitters, asymmetric directional coupler (ADC) or recently using inverse design [12–15]. Mode coupling based PR couples the orthogonal polarization by introducing asymmetry through geometrical perturbation that excites a hybrid mode. The asymmetry can be introduced using overlay structures, etching a corner of the waveguide or through double core [16–18]. An asymmetric directional coupler (ADC) based rotator is another reported structure that is easy to design and fabricate as the concept is similar to a directional coupler [19–21]. It has been modified with sub-wavelength structures with short coupling length and is also used to implement polarization rotation in the ALIG platform due to simplicity [22,23].
Wavelength filtering is another key component used in PIC. Coarse WDM and dense WDM require wavelength filters with appropriate bandwidth. Such functionalities are traditionally realized on chip using echelle gratings and arrayed waveguide gratings (AWGs) [24].
All the passive PR have inherently high bandwidth, and active PR have shown narrow bandwidth. The passive PR can offer narrow bandwidth through Bragg reflection in the counter propagation direction [25,26]. The bandwidth in all these configurations has been reported to be fixed without any further discussion about bandwidth engineering, restricting their applications.
Both wavelength filtering and polarization rotation are realized separately using different sets of devices. A polarization rotator whose bandwidth can be engineered through design changes should be an ideal way to combine both functions in a single device. Bandwidth engineering implies designing the polarization rotator to realize a desired bandwidth that can potentially open new areas of study and applications.
In this work, we design and experimentally demonstrate an intermediate bandwidth polarization rotator with a 3 dB bandwidth of 14.8 nm. We next report, for the first time to our knowledge, a wavelength-selective passive polarization rotator with the potential for bandwidth engineering, spanning a 3 dB bandwidth from 0.59 nm to 81 nm by appropriately designing the waveguide structure. We use coupled mode theory and simulations to analyse and design the polarization rotator with the required bandwidths. Further, we demonstrate a proof-of-concept for simultaneous polarization rotation and coarse WDM. We use the recently reported "Sandwiched hybrid waveguide" owing to the flexibility offered for realizing the rotator with wavelength selective characteristics [27].
2. Design and simulation study
This work uses an ADC scheme for polarization rotation based on the principle of mode-coupling. The fundamental TE and TM modes of a waveguide are mutually orthogonal and generally have significant phase mismatch due to birefringence. Thus, power coupling from one to another requires both phase match and mode profile overlap. Phase matching requires appropriate design of TE and TM waveguides forming the ADC that matches the propagation constants. Further, a good mode profile overlap is essential for efficient power transfer, which is done by introducing both horizontal and vertical asymmetry. The ADC ensures horizontal asymmetry, as the waveguides forming the directional coupler have different widths naturally by design. Vertical asymmetry is created by choosing different cladding materials below and above the core, generally achieved using asymmetric core or air clad on top. In the effective index calculations, this asymmetry shows as a hybrid mode, where both TE and TM fractions are present in equal proportions [19].
Figure 1(a) shows a cross-section of the sandwiched hybrid waveguide (SHW) used in this work with its geometrical parameters. Width and height in the SHW can be varied to control the various properties: effective index, confinement, and birefringence, similar to a wire waveguide. The SHW has an additional parameter defined as ‘f,’ where f = Thickness of high index/Total height (‘H’). This ratio ‘f’ provides flexibility to control the waveguide properties, as discussed in detail in [27]. Figure 1(b) shows the electric field profile for TE and TM mode, where the field confinement in TE is primarily in the high index (a-Si) and for TM, it is more in the medium index (SiN). In this work, the value of ‘H’ is fixed as 500 nm, and the value of ‘f’ is 20% unless mentioned otherwise. The resulting thickness of the top and bottom SiN is 200 nm, and the a-Si thickness is 100 nm due to the values of ‘H’ and ‘f’. The refractive index of $a-Si$ is considered as 3.48, $SiN$ as 2, and $SiO_2$ as 1.44 at a wavelength of 1550 nm in all the simulations unless stated otherwise [28–30].
Fig. 1. (a) Cross-section of sandwiched hybrid waveguide core to realize the PR using ADC and (b) electric field profile of TE0 and TM0 mode of the hybrid waveguide.
Figure 2(a) shows the top view of the proposed ADC scheme for polarization rotation, and Fig. 2(b) shows the cross-sectional view of the PR with various geometrical parameters. The value of $W_{TE}$ and $W_{TM}$ pair is determined by matching the propagation constants through a modal simulation at 1550 nm wavelength.
Fig. 2. (a) Top-view of the PR showing coupling region and coupling length $L_C$. (b) Cross-section of the ADC based PR on the SHW platform showing various geometrical parameters.
The effective index ($n_{eff}$) evolution with the width of an isolated waveguide is calculated to find the waveguide width range that ensures single mode operation as shown in Fig. 3(a). For the TM waveguide, which is broader, any width that is in the shaded region, indicating single-mode operation can be considered for design. However, operating the device away from the cut-off width is recommended, as a smaller TM waveguide width will result in an even narrower TE waveguide that can decrease the mode confinement, resulting in higher scattering losses [31]. Therefore the broad waveguide width ($W_{TM}$) is fixed at 730 nm, and keeping a gap ‘g’ of 250 nm, the narrow waveguide width ($W_{TE}$) is varied as shown in Fig. 3(b). At $W_{TE}$ = 415 nm, there is the existence of a hybrid mode necessary for mode conversion between the orthogonally polarized modes. The field plot of this hybrid mode is shown in Fig. 3(c).
Fig. 3. (a) Effect of waveguide (shown in inset) width on the effective index showing phase matching width for TE and TM modes along the single-mode region. (b) The effective index of the ADC structure (shown in inset) for fixed $W_{TM}$(730 nm) and gap (250 nm) as a function of $W_{TE}$. The encircled region shows the hybrid mode necessary for polarization conversion. (c) $E_X$ and $E_Y$ field plot showing the super-mode of the directional coupler.
The coupling length ‘$L_C$’ is the minimum length at which maximum polarization conversion occurs. It is related to propagation constants of the participating modes as ‘$L_C = \pi$/$\Delta \beta _0$.’ Here, $\Delta \beta _0$ is the difference of propagation constants of the participating hybrid modes at the phase-matched wavelength ($\lambda = 1550 \ nm$). The spectral response of the PR can be analytically obtained from coupled mode theory [32]:
Here, ‘$\kappa$ = $\pi /2L_C$’ is the coupling coefficient considered constant, although the actual value depends on the overlap integral of the interacting fields of the two waveguides forming the ADC and ‘$\delta$ = $\sqrt {(\Delta \beta /2)^2-|\kappa |^2}$’ is the wavelength dependent phase mismatch. The wavelength dependent phase mismatch ‘$\delta$’ is primarily responsible for the spectral response as the other quantities are considered constants with wavelength [32].
Figure 4(a) shows the ratio of phase mismatch and coupling coefficient ‘|$\delta /\kappa |$’ as a function of wavelength. The slope of this ratio around the phase-matched wavelength is an indicator of the bandwidth of the polarization rotator that is crucial to bandwidth engineering. The value of ‘$L_C$’ is 130 $\mu m$ at a wavelength of 1550 nm and corresponding coupling coefficient ‘$\kappa \approx 0.0121 \mu m^{-1}$’. The semi-analytical spectral response shown in Fig. 4(b) is obtained by using the values of $\delta, \kappa$ and $L_C$, and plugging them in Eq. (1). The spectral shape is the characteristic "Sinc" function with a 3dB bandwidth of 13.8 nm and a 1dB bandwidth of 8.2 nm.
Fig. 4. (a) Phase mismatch to coupling coefficient ratio (‘$\delta /\kappa$’) as a function of wavelength showing minima at the phase-matched wavelength. (b) Semi-analytical spectral response of the PR using Eq. (1)
The propagation constants are derived from modal simulations using a finite difference method (FDM) that are substituted in Eq. (1) [33]. Hence, the response is termed as semi-analytical. It is an approximate response as it ignores power lost due to coupling into radiation modes but is quite resourceful for quick design. The efficiency is thus shown incorrectly as 100%, and therefore, a full propagation simulation is done using the eigenmode expansion (EME) method for exact results. From here on, the term analytical will be used to imply semi-analytical for brevity.
Based on the geometrical data acquired from modal simulations, the spectral response of the rotator is obtained through propagation simulations. Fig. 5(a) shows the intensity plot of the PR along with the cross-sectional field profile at different lengths. Fig. 5(b) shows the spectral response at the cross-port (XP) and through-port (TP) of the PR. The input mode is TM, and the output at the cross port is the converted TE mode. The output at the through port is the residual TM mode. The maximum transmission at the cross port is −0.29 dB at 1550 nm, and the maximum extinction is −33 dB at the through port. The 3 dB bandwidth is $\sim$14 nm, and the 1 dB bandwidth is 8 nm, close to values predicted analytically. The simulation results and parameters are summarized in Table 1.
Fig. 5. (a) Top-view of the intensity profile and cross-section electric field at different lengths showing the mode coupling over length. (b) Simulated spectral response of the PR at cross-port (XP) and through port (TP) for input as TM0.
Table 1. Summary of simulated parameters
An important feature of the PR in this platform is the ability to place the central wavelength as required by the design. The spectral shift can be designed through the width of the waveguides forming the ADC. Fig. 6(a) shows the spectral response for a fixed $W_{TM}$ and varying $W_{TE}$. There is a red shift of 4.9 nm/nm of $W_{TE}$, and this is 5 times better fabrication tolerance compared to similar SOI based PR [19]. Similarly, a blue shift of 0.475 nm/nm can be achieved by keeping $W_{TE}$ fixed and varying $W_{TM}$ as shown in Fig. 6(b). The spectral shift is summarized through a linear fit in Fig. 6(c). Thus, a coarse control of spectral shift is possible through $W_{TE}$ and a fine control through $W_{TM}$.
Fig. 6. (a) Red shift with fixed TM waveguide width and varying TE waveguide width for coarse control. (b) Blue shift with fixed TE waveguide width and varying TM waveguide width for fine control. (c) Comparison of slope of spectral shift.
3. Fabrication and characterization
Figure 7(a) shows the top view of the schematic of the PR as implemented in this work. Fig. 7(b) shows the microscopic image of the fabricated device. The TM/TE gratings and waveguides are fabricated as reported in [27]. A broadband superluminescent diode is used for exciting the TM mode through the curved grating couplers. It is routed through bends to the directional coupler section, enabling polarization conversion into TE mode. The through and cross port outputs are fed into an optical spectrum analyzer (OSA) for the spectral response. A similar experiment was done, considering TE grating as input.
Fig. 7. (a) Schematic of the polarization rotation scheme. (b) Microscopic image of the fabricated device.
Figure 8(a) shows the measured normalized spectral response of the PR at the cross port (XP) for TE and TM inputs. Figure 8(b) shows the measured normalized spectral response of the PR at the through port (TP) for TE and TM inputs. The raw data is normalized to the straight waveguide to extract the PR response. The spectral shape of both TE and TM input shows good agreement with differences in insertion loss due to polarization dependent propagation loss in the propagating modes. The maximum transmission is observed for a TM input at 1551 nm with an insertion loss of −2.25 dB at the cross port. The 3-dB bandwidth is 14.8 nm, in good agreement with the simulation. An intermediate bandwidth is obtained for the first time in any PR. Fig. 8(c) shows the cross port spectral response (TM input $\rightarrow$ TE output) of analytical, simulated and experimental data for comparison. Table 2 shows the summary of experimental bandwidth reported in previously reported PR compared with present work.
Fig. 8. (a) Spectral response after polarization conversion at the cross port for both TE0 and TM0 input. (b) Spectral response after polarization conversion at the through port for TE0 and TM0 input. (c) Comparison of analytical, simulated and measured spectral response at the cross-port for TM to TE conversion.
Table 2. Comparison of measured PR response with literature
The efficiency of the polarization rotator is less than optimal. Also, the phase-matching parameters in this experiment are different from the simulations. The ‘$W_{TE}$ = 440 nm’ and ‘$W_{TM}$ = 680 nm’ with a ‘g = 250 nm’ are the experimental values for the response shown in Fig. 8. This deviation is possible due to the refractive index values considered in our simulations that can be significantly different from actual deposited materials. We are limited by our tools and unable to measure the refractive index at 1550 nm. Hence, we have considered standard values. Further, the measured a-Si thickness is 93 nm, which is lower than the desired thickness of 100 nm compared to the design, that can change the phase matching condition and coupling coefficient. The phase matching is strongly sensitive to effective index. Thus, it is possible to have this deviation without affecting the spectral shape in any significant way.
Further, to show the sensitivity to index change, we measure the thermo-optic response of the PR using a Peltier element and a temperature controller. The temperature was increased from 29 $^\circ$C to 51 $^\circ$C in steps of 2 deg. Fig. 9(a) shows the spectral shift of the PR response for three different temperatures, and Fig. 9(b) shows the linear fit with the calculated spectral shift as 104 pm/$^\circ$C. This shows a higher temperature sensitivity compared to the corresponding ring resonator that shows 69 pm/$^\circ$C [27]. Thus, we conclude a strong refractive index dependence on the spectral response of the PR.
Fig. 9. (a) Thermo-optic shift of the PR spectra. (b) Linear fit for the normalized shift of the spectral response as a function of temperature.
4. Bandwidth engineering of the PR
The sandwiched waveguide offers unique flexibility to control the various properties like effective index, birefringence and confinement [27]. This flexible behaviour can be exploited to engineer the bandwidth of the PR for various applications not reported in any previous work involving uniform core waveguides. This is indicated in Table 2, which shows our device with an intermediate bandwidth compared to high bandwidth passive platforms and narrow bandwidth active platforms. It hints towards the possibility of spanning the bandwidth from narrow to high.
Equation (1) shows the dependence of the conversion efficiency as a function of coupling coefficient ‘$\kappa$’ and phase mismatch ‘$\delta$’. Changing the ‘$\delta$’ and ‘$\kappa$’ appropriately, large (>80 nm) and narrow (< 1nm) 3dB bandwidths can be obtained. It is shown both analytically and using propagation simulations.
A large bandwidth can be realized through a smaller slope of ‘|$\delta /\kappa$|’ near the phase-matching wavelength. This can be satisfied for a larger refractive index cladding like $SiO_2$. However, a uniform cladding will make the ADC vertically symmetric, making the coupling modes orthogonal, as shown in Fig. 10(a). Thus, to maintain the asymmetry, the oxide cladding is made in the shoulders with air cladding on top, resulting in the hybrid mode necessary for polarization rotation, as shown in Fig. 10(b). This can be fabricated by depositing oxide and planarizing through chemical mechanical polishing (CMP).
Fig. 10. (a) Effective index vs width for uniform oxide clad showing mode orthogonality. (b) Effective index vs width for top air and oxide clad on shoulders showing the hybrid mode.
Low bandwidth can be realized by increasing the slope of ‘|$\delta /\kappa$|’ near the phase-matching wavelength. This can be achieved with a high value of ‘f’ to increase ‘$\delta$’ and an increased gap to decrease the coupling coefficient ‘$\kappa$’. Figure 11(a) shows the ratio ‘|$\delta /\kappa$|’, Fig. 11(b) shows the analytically derived polarization converted power, and Fig. 11(c) shows the simulated transmission at the cross port. The oxide clad at ‘f = 20%’ with 250 nm gap (numbered 1 in red) gives a 3 dB bandwidth of 81 nm, at ‘f = 20%’ with 250 nm gap (numbered 2 in green) and air clad the 3 dB bandwidth is 14 nm and at ‘f = 35%’ with 400 nm gap (numbered 3 in blue) and air clad the 3 dB bandwidth is 0.59 nm. This flexibility in bandwidth engineering for any PR is reported for the first time, which can open possibilities for several applications like wavelength division multiplexing and sensing. The results are summarized in Table 3 for comparison.
Fig. 11. In all three parts ((a), (b), (c)) "Red 1" indicates PR with oxide cladding on the shoulders and air cladding on top with ‘f = 20%’ and ‘g = 250 nm’; "Green 2" indicates PR with air cladding, ‘f = 20%’ and ‘g = 250 nm’; "Blue 3" indicates PR with air cladding, ‘f = 35%’ and ‘g = 400 nm’. (a) The ratio ‘|$\delta /\kappa$|’ as a function of normalized wavelength for different configuration. (b) Analytical spectral response derived from Eq. (1) for different configurations. (c) Simulated spectral response for different configurations. (d) $L_C$ and 3 dB bandwidth as a function of fraction ‘f’.
Table 3. Summary of bandwidth engineering analysis
Equation (1) suggests that the coupling coefficient ‘$\kappa$’ is among the determining factors for the bandwidth as the Sinc function depends on it. Thus, it looks as if by increasing ‘$\kappa$’, the ‘$L_C$’ can be decreased, and bandwidth can be increased and vice-versa. However, we did a simulation study with a fixed gap of 250 nm to find the variation of both ‘$L_C$’ and bandwidth as a function of ‘f’ to decide the optimum ‘f’ for low ‘$L_C$’ and also lower bandwidth. Fig. 11(d) shows the variation of ‘$L_C$’ and 3 dB bandwidth as a function of ‘f.’ The figure shows that ‘$L_C$’ is almost flattened from ‘f = 15%’ to ‘f = 20%’, and the bandwidth is monotonically decreasing with increasing ‘f’. This also shows that the bandwidth is not strongly related to coupling length but rather to ‘|$\delta /\kappa$|’. Thus, a simple change in the coupling coefficient is insufficient for bandwidth engineering; rather, the ratio ‘|$\delta /\kappa$|’ needs to be designed. A uniform core waveguide can probably be used for minor changes in bandwidth by varying the coupling coefficient through gap changes. However, such vast changes require the ability to change the ratio ‘|$\delta /\kappa$|’ enabled by the sandwiched waveguide. Therefore, the SHW provides a clear advantage over uniform core waveguides.
5. Polarization rotating wavelength multiplexer
We propose the wavelength selective SHW based PR for WDM. Simultaneous coarse wavelength division multiplexing (CWDM) and polarization rotation can be realized by appropriately designing the phase matching condition through a combination of $W_{TE}$ and $W_{TM}$ pair. Fig. 6 indicates that the $W_{TE}$ provides coarse and $W_{TM}$ provides the fine control of the spectral position. This can be exploited for CWDM by fixing the $W_{TE}$ and varying the $W_{TM}$ that will span the required wavelength range. Fig. 12 shows a possible schematic for the implementation of CWDM. The broadband input light is coupled through TM grating couplers to excite the TM mode that is filtered and rotated using the ADC at different wavelengths. The minimum recommended spacing between different channels is 20 nm [34]. The wavelength spacing for different channels can be realized through fixed $W_{TE}$ and different $W_{TM}$ as shown in the CWDM schematic.
Proof of concept is provided by superimposing the spectral response of various individual PR as shown in Fig. 7 with fixed $W_{TE}$ and different $W_{TM}$ and a similar response is expected by using the proposed schematic in Fig. 12. The simulated response is shown in Fig. 13(a), while Fig. 13(b) shows the measured data with a 300 nm gap. The insertion loss is more than Fig. 8 due to the increased gap. Fig. 13(c) shows the normalized peak separation as a function of $\Delta W_{TM}$ for measured and simulated devices. The measured slope is 0.506 nm/nm, which is in good agreement with the simulated 0.473 nm/nm. The required peak wavelength separation of 20 nm can be easily achieved with $\Delta W_{TM}$ as 40 nm.
Fig. 13. (a) Simulated CWDM implemented with fixed $W_{TE}$ and varying $W_{TM}$ with ‘$\Delta W_{TM}$ = 20 nm’ for 300 nm gap. (b) Measured CWDM implemented with fixed $W_{TE}$ and varying $W_{TM}$ with ‘$\Delta W_{TM}$ = 20 nm’ for 300 nm gap. (c) Linear fit of normalized spectral shifts comparing measured and simulated data as a function of $\Delta W_{TM}$.
6. Conclusion
We have demonstrated a wavelength-selective polarization rotator on a hybrid waveguide platform. We presented design, simulation, fabrication and characterisation of the polarisation rotator. We demonstrated wavelength selective polarisation rotation and filtering characteristics of the proposed device with tunable bandwidth. Using the rotator as a unit, we demonstrated a proof of concept for coarse WDM that can be implemented through appropriate design. For the first time, we have shown the possibility of bandwidth engineering in any polarization rotator that can enable a wide variety of applications, including sensing and quantum photonic circuits.
Funding
Department of Science and Technology, Ministry of Science and Technology, India; Ministry of Electronics and Information Technology; Ministry of Education, India.
Acknowledgments
The authors thank Dr. Siddharth Nambiar for the TM grating design and useful discussions. SKS thanks Professor Ramakrishna Rao chair fellowship. We acknowledge the National Nano fabrication Facility (NNfC) and Micro and Nano Characterisation Facility (MNCF) at the Centre for Nanoscience and Engineering, Indian Institute of Science, Bangalore, India.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. P. De Heyn, B. Kuyken, D. Vermeulen, et al., “High-Performance Low-Loss Silicon-on-Insulator Microring Resonators using TM-polarized Light,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OSA, 2011), paper OThV2.
2. A. Densmore, E. Post, D.-X. Xu, et al., “A Silicon-on-Insulator Photonic Wire Based Evanescent Field Sensor,” IEEE Photonics Technol. Lett. 18(23), 2520–2522 (2006). [CrossRef]
3. P. Trinh, S. Yegnanarayanan, F. Coppinger, et al., “Silicon-on-insulator (soi) phased-array wavelength multi/demultiplexer with extremely low-polarization sensitivity,” IEEE Photonics Technol. Lett. 9(7), 940–942 (1997). [CrossRef]
4. L. Vivien, S. Laval, B. Dumont, et al., “Polarization-independent single-mode rib waveguides on silicon-on-insulator for telecommunication wavelengths,” Opt. Commun. 210(1-2), 43–49 (2002). [CrossRef]
5. D. Dai and S. He, “Analysis of the birefringence of a silicon-on-insulator rib waveguide,” Appl. Opt. 43(5), 1156 (2004). [CrossRef]
6. F. Morichetti, A. Melloni, M. Martinelli, et al., “Box-shaped dielectric waveguides: A new concept in integrated optics?” J. Lightwave Technol. 25(9), 2579–2589 (2007). [CrossRef]
7. R. C. Alferness, “Efficient waveguide electro-optic te/tm mode converter/wavelength filter,” Appl. Phys. Lett. 36(7), 513–515 (1980). [CrossRef]
8. C. Y. Huang, C. H. Lin, Y. H. Chen, et al., “Electro-optic ti:ppln waveguide as efficient optical wavelength filter and polarization mode converter,” Opt. Express 15(5), 2548 (2007). [CrossRef]
9. M. R. Watts and H. A. Haus, “Integrated mode-evolution-based polarization rotators,” Opt. Lett. 30(2), 138 (2005). [CrossRef]
10. Z. S. Hou, X. Xiong, J. J. Cao, et al., “On-chip polarization rotators,” Adv. Opt. Mater. 7(10), 1900129 (2019). [CrossRef]
11. L. Chen, C. R. Doerr, and Y.-K. Chen, “Compact polarization rotator on silicon for polarization-diversified circuits,” Opt. Lett. 36(4), 469 (2011). [CrossRef]
12. Y. Ding, H. Ou, and C. Peucheret, “Wideband polarization splitter and rotator with large fabrication tolerance and simple fabrication process,” Opt. Lett. 38(8), 1227 (2013). [CrossRef]
13. J. Wang, B. Niu, Z. Sheng, et al., “Novel ultra-broadband polarization splitter-rotator based on mode-evolution tapers and a mode-sorting asymmetric y-junction,” Opt. Express 22(11), 13565 (2014). [CrossRef]
14. D. Dai and H. Wu, “Realization of a compact polarization splitter-rotator on silicon,” Opt. Lett. 41(10), 2346 (2016). [CrossRef]
15. X. Ruan, H. Li, and T. Chu, “Inverse-designed ultra-compact polarization splitter-rotator in standard silicon photonic platforms with large fabrication tolerance,” J. Lightwave Technol. 40(21), 7142–7149 (2022). [CrossRef]
16. D. Vermeulen, S. Selvaraja, P. Verheyen, et al., “Silicon-on-insulator polarization rotator based on a symmetry breaking silicon overlay,” IEEE Photonics Technol. Lett. 24(6), 482–484 (2012). [CrossRef]
17. Z. Wang and D. Dai, “Ultrasmall si-nanowire-based polarization rotator,” J. Opt. Soc. Am. B 25(5), 747 (2008). [CrossRef]
18. H. Fukuda, K. Yamada, T. Tsuchizawa, et al., “Silicon photonic circuit with polarization diversity,” Opt. Express 16(7), 4872 (2008). [CrossRef]
19. L. Liu, Y. Ding, K. Yvind, et al., “Efficient and compact te–tm polarization converter built on silicon-on-insulator platform with a simple fabrication process,” Opt. Lett. 36(7), 1059 (2011). [CrossRef]
20. L. Liu, Y. Ding, K. Yvind, et al., “Silicon-on-insulator polarization splitting and rotating device for polarization diversity circuits,” Opt. Express 19(13), 12646 (2011). [CrossRef]
21. S. Soudi and B. M. A. Rahman, “Design of compact polarization rotator using simple silicon nanowires,” Appl. Opt. 53(34), 8071 (2014). [CrossRef]
22. Y. Liu, S. Wang, Y. Wang, et al., “Subwavelength polarization splitter–rotator with ultra-compact footprint,” Opt. Lett. 44(18), 4495 (2019). [CrossRef]
23. X. Sun, M. Alam, J. Aitchison, et al., “Polarization rotator based on augmented low-index-guiding waveguide on silicon nitride/silicon-on-insulator platform,” Opt. Lett. 41(14), 3229–3232 (2016). [CrossRef]
24. S. Pathak, P. Dumon, D. Van Thourhout, et al., “Comparison of AWGs and Echelle Gratings for Wavelength Division Multiplexing on Silicon-on-Insulator,” IEEE Photonics J. 6(5), 1–9 (2014). [CrossRef]
25. H. Okayama, Y. Onawa, D. Shimura, et al., “Polarization rotation bragg grating using si wire waveguide with non-vertical sidewall,” Opt. Express 22(25), 31371 (2014). [CrossRef]
26. H. Yun, Z. Chen, Y. Wang, et al., “Polarization-rotating, bragg-grating filters on silicon-on-insulator strip waveguides using asymmetric periodic corner corrugations,” Opt. Lett. 40(23), 5578 (2015). [CrossRef]
27. R. K. Dash and S. K. Selvaraja, “Sandwiched hybrid waveguide platform for integrated photonics application,” Opt. Commun. 550, 129959 (2024). [CrossRef]
28. M. Li, V. A. Yakovlev, J. Wall, et al., “Ellipsometric determination of the thickness and refractive index of silicon films,” J. Vac. Sci. Technol., B: Microelectron. Nanometer Struct.--Process., Meas., Phenom. 11(6), 2102–2106 (1993). [CrossRef]
29. D. S. Kim, S. G. Yoon, G. E. Jang, et al., “Refractive index properties of SiN thin films and fabrication of SiN optical waveguide,” J. Electroceram. 17(2-4), 315–318 (2006). [CrossRef]
30. D. Bulla and N. Morimoto, “Deposition of thick TEOS PECVD silicon oxide layers for integrated optical waveguide applications,” Thin Solid Films 334(1-2), 60–64 (1998). [CrossRef]
31. K. K. Lee, D. R. Lim, H. C. Luan, et al., “Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett. 77(11), 1617–1619 (2000). [CrossRef]
32. J.-m. Liu, Photonic Devices (Cambridge University Press, 2005).
33. P. Lusse, P. Stuwe, J. Schule, et al., “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J. Lightwave Technol. 12(3), 487–494 (1994). [CrossRef]
34. ITU-T, “G.694.2:spectral grids for wdm applications: Cwdm wavelength grid,” International Telecomunication Union, p. 12 (2003).
