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Abstract
We report the design of a chip-scale and highly efficient polarization rotator (PR) based on an asymmetric directional coupler geometry involving a horizontal slot waveguide (WG) and a strip WG on a silicon-on-calcium-fluoride (SOCF) platform for the mid-IR regime. In particular, we have optimized it for rotations of both the polarizations at the operating wavelength of 4.47 µm in two configurations, which relied on single and double-slot WG geometries. Power coupling through appropriate phase matching between the quasi-TM mode of a horizontal slot WG and the quasi-TE mode of a strip WG has been exploited for realizing polarization rotation. Numerical simulations demonstrate that achievable maximum power coupling efficiency (Cm) is as high as ~95% (with a device length of ~0.57 mm) for the single slot WG geometry and ~97% (with an even shorter device length of ~0.47 mm) for the PR based on double-slot WG geometry for both the polarizations. Both the designed PRs exhibit relatively large bandwidth of 50 nm with reasonably high Cm of ~80%. A study on fabrication tolerances show that Cm remains ~80% for variation in width Δw from -2 to +3 nm and -6 to +5 nm for single and double-slot based PRs, respectively.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, mid-IR (mid-infrared) silicon photonics (spanning 2-10 µm wavelengths) has become a vibrant field of research for industrial and scientific communities because of its wide ranging applications in bio and chemical sensing, environmental pollution monitoring, healthcare, medical diagnostics, defense and security, industrial leak detection and process control, and many more [1–5]. This mid-IR spectrum is also known as the “molecular fingerprint” spectrum as it contains the strong rotational-vibrational absorption lines of several important bio and chemical species such as NO, N2O, NO2, CH4, NH3, CO, CO2, SO2 etc. The strength of these absorption lines in this spectral region is 100-1000 times higher than corresponding strengths in the near-IR spectral region [6], making this regime extremely important for above-mentioned applications. Moreover, this wavelength region exhibits an atmospheric transmission window (3–5 µm), which can be exploited as a new communication window with very large bandwidth to mitigate the problem of “capacity crunch,” which is being currently faced in the popular near-IR wavelength region [7]. So, considering these impressive characteristics of mid-IR silicon photonics, it is attractive to move all optical components/devices to the mid-IR region. To date, many Si-based devices/components have been designed for mid-IR region such as sensors [4,5], photo-detectors [8], grating couplers [9], modulators [10], ring resonators [11], etc. On the one hand, due to high refractive index contrast between silicon (Si) core and its cladding, though it is advantageous to realize low footprint devices, and consequently high density integration of components, but on the other hand, it induces a large polarization birefringence. Consequently, Si-based devices/components are strongly polarization dependent, which is often a challenge in their practical utilization. To mitigate this challenge, a polarization diversity scheme that consists of polarization splitters and polarization rotators/converters has been proposed to realize polarization-independent operation in Si photonics integrated circuits [12]. To that end, polarization rotator (PR) is essential in practical applications of Si photonics-based devices/components. So far, several types of waveguide (WG) geometries based on mode coupling and mode evolution in silicon-on-insulator (SOI) platform for PRs have been proposed in the literature for applications at the near-IR region, such as directional couplers (DCs), Y-junctions, sub-wavelength gratings, photonic crystal structures, and multimode WGs etc. [13–21], but very few [22,23] for the mid-IR region. Barh et al. [22] have reported a DC-type PR by exploiting power coupling through phase matching between the quasi-TM mode of a strip WG and quasi-TE mode of a vertical slot WG for rotation of both the polarizations at the wavelength of 3 µm within a device length of 2 mm. However, in this design, fabrication of nano sized vertical slot with smooth surfaces through the etching technique is relatively difficult. Recently, Wang et al. [23] have reported a polarization splitter-rotator based on a taper and an asymmetric Y-junction at the wavelength of 4 µm and 6.9 µm for which the device lengths were 470 µm and 1 mm, respectively. This design requires precise control of the taper, which makes its fabrication somewhat difficult and complex. Moreover, it can convert only one state of polarization for one input orientation. Therefore, to achieve dense Si photonic integrated circuits for mid-IR Si photonics, it is of great interest to develop a compact PR which is of relatively simple geometry and easier to fabricate.
In this paper, we report a design for realizing an efficient and compact PR based on an asymmetric DC comprising of a strip and horizontal slot WGs in silicon-on-calcium-fluoride (SOCF) platform by exploiting mode coupling for potential applications at the mid-IR wavelength of 4.47 µm (which is the characteristic absorption peak wavelength of N2O gas). Its fabrication should be relatively easy as it does not require etching of nano-sized vertical slot and any kind of tapering. Furthermore, it can convert/rotate an input quasi-TM polarization in the slot WG to a quasi-TE polarization output from the strip WG, and a quasi-TE polarization input in the strip WG to a quasi-TM polarization output from the slot WG with very high power coupling efficiency of ~95%. We have also optimized it for both the polarizations when asymmetric DC consists of horizontal double-slot WG instead of a single slot horizontal WG. Bandwidth of operations and fabrication tolerances have also been studied for both the PRs based on single as well as double-slot WG geometries. It may be noted that, we have considered SOCF platform in our proposal for developing mid-IR PR instead of traditional SOI platform because SiO2 exhibits high absorption at mid-IR wavelengths > 3.6 μm [24]. Thus, instead of commonly used SiO2, we considered CaF2 of refractive index n ~1.4 and having low loss transmission windows up to ~9 μm [25] because it offers wider transparency window as well as higher index contrast in the mid-IR in comparison to other materials such as sapphire (Al2O3 of n ~1.7) and silicon nitride (Si3N4 of n ~1.9) having spectral transparency window up to ~5.5 μm and ~7μm, respectively [2]. Additionally, we have also tested the applicability of our designed PR at the wavelength of 1.55 μm and found better performance compared to earlier reported PRs based on DCs in the literature (see comparative performance in Table 3).
2. Proposed waveguide design and working principle
The cross-sectional and 3D views of our proposed PR are sketched in Figs. 1(a) and 1(b)
, respectively. It is an asymmetric DC, which is composed of a horizontal slot and strip WGs formed on CaF2 substrate with air as cover and Si as core material. CaF2 was also assumed as the slot filling material. The structural parameters w, w1, h, and h1 correspond to the width of the Si core of the horizontal slot WG, width of the Si core of the strip WG, height of the upper core of the horizontal slot WG, height of the lower core of the horizontal slot WG, and height of the core of the strip WG, respectively. Parameters t and S denote the thickness of CaF2 in the low index slot region and separation between the two WGs, respectively. The modalcharacteristics of PR are investigated by a full-vectorial mode solver FEM (finite element method) using 500 × 500 mesh in commercially available simulation package FIMMWAVE©. Calculated results are cross checked by another versatile full-vectorial numerical method, FDM (finite difference method). The wavelength dependent refractive indices of Si and CaF2 were obtained by using corresponding Sellmeier’s coefficients. Its propagation characteristics were studied by using eigenmode expansion method-based FIMMPROP©, which is associated with FIMMWAVE. The working principle of our proposed PR is based on mode coupling between the two orthogonal polarized modes i.e. between the quasi-TM mode of slot WG and quasi-TE mode of strip WG when they are phase matched in an asymmetric WG geometry. Breaking of WG symmetry yields excitation of hybrid modes with tilted optical axis, giving rise to polarization rotation of modes after propagation through one coupling length, , where β1 and β2 are the propagation constants of the two hybrid modes. For ease in use of terminology, henceforth we would call quasi-TM (whose Hx component is dominant) and quasi-TE (whose Hy component is dominant) modes as TM and TE modes in the following analysis.3. Results and discussions
As a first step for designing a PR, it is essential to determine the condition(s) for phase-matching between the two orthogonally polarized modes, e.g. between the TM mode of a horizontal slot WG and TE mode of a strip WG. For this reason, we have studied variation of the effective indices (neff) of the fundamental modes of the isolated WGs as a function of their widths for the geometrical parameters of t = 0.02 µm, h = 0.3 µm, and h1 = 0.8 µm. Results are shown in Fig. 2
Fig. 2 Effective refractive indices of the fundamental TE and TM modes of isolated horizontal single slot WG and isolated strip WG as a function of their widths. Here, h = 0.3 µm, h1 = 0.8 µm, and t = 0.02 µm.
Next, we studied the variation of neff of the first and the second supermodes with w1 using above structural parameters (w = 0.95 µm, h = 0.3 µm, h1 = 0.8 µm, and t = 0.02 µm) for three different values of S and results are shown in Fig. 3
Fig. 3 Effective refractive indices of the first and the second supermodes as a function of strip WG width (w1) for three different values of S = 0.45 µm, 0.5 µm, and 0.55 µm.
Fig. 4 Variation of the modal hybridness with strip WG width (w1) for three different values of S = 0.45 µm, 0.5 µm, and 0.55 µm; (a) for the first supermode (b) for the second supermode.
Thereafter, we have calculated the Lc for different values of S and corresponding maximum power coupling efficiency, Cm, between the two orthogonal polarized modes and results are tabulated in Table 1
Table 1. Values of phase matching width w1, Lc and Cm for different S values at λ = 4.47 µm with WG dimensions: w = 0.95 µm, h = 0.3 µm, h1 = 0.8 µm, and t = 0.02 µm for PR based on single slot WG geometry
Fig. 5 The color and surface plots of field distributions of the Hx and Hy components of the first and the second supermodes with WG dimensions: w = 0.95 µm, w1 = 1.148 µm, h = 0.3 µm, h1 = 0.8 µm, t = 0.02 µm, and S = 0.5 µm.
Fig. 6 The light propagation in the designed PR based on single slot WG geometry when (a) TM mode is input in the slot WG (b) TE mode is input in the strip WG.
Fig. 7 The normalized power variations as a function of the device length of TM mode in the slot WG (red curve) and TE mode in the strip WG (black curve).
We have also optimized the double-slot WG-based structure (see Fig. 8 (a)
Fig. 8 (a) Schematic cross-sectional view of the proposed PR based on double-slot WG geometry, (b) its 3D view.
Table 2. Values of phase matching width w1, Lc and Cm for different S values at λ = 4.47 µm with WG dimensions: w = 0.95 µm, h1 = 0.8 µm, h2 = 0.35 µm, h3 = 0.05 µm, and t = 0.02 µm for PR based on double-slot WG geometry
Fig. 9 The color and surface plots of field distributions of the Hx and Hy components of the first and the second supermodes of double-slot WG-based PR.
Fig. 10 The normalized power variations of TM mode in the slot WG (red curve) and TE mode in the strip WG (black curve) as a function of the device length for PR based on double-slot WG geometry.
Fig. 11 The light propagation in the designed PR based on double-slot WG geometry with TM mode in the slot WG and TE mode in the strip WG, (a) when TM is input in the slot WG (b) when TE is input in the strip WG. Here, w = 0.95 µm, w1 = 1.221 µm, h1 = 0.8 µm, h2 = 0.35 µm, h3 = 0.05 µm, and t = 0.02 µm.
We have also checked applicability of our approach and model for the proposed double-slot based PR design for the popular telecom wavelength of 1.55 μm. The optimized structural parameters were found to be w = 0.31 µm, w1 = 0.394 µm, h1 = 0.26 µm, h2 = 0.16 µm, h3 = 0.05 µm, and t = 0.02 µm. For these parameters, the values of Cm for two separations S = 150 nm and S = 200 nm were as high as 94.3% and 95.6%, respectively. Corresponding calculated values of Lc were 82.0 µm and 119.7 µm, respectively. Here, we would like to mention that we have taken minimum value of S = 150 nm for realizable device in practice because fabrication with separation ≤ 100 nm is difficult to control in the CMOS fabrication technology [27]. These results revealed that our proposed double-slot-based PR yields better performance than earlier reported PRs based on DCs at the wavelength of 1.55 μm [13–15] (see Table 3
Table 3. Comparison of proposed double-slot based PR with earlier reported DCs based PRs
To determine the bandwidth of operation, the wavelength dependence of Cm has also been studied for both the designed PRs based on single as well as double-slot WG geometries and shown in Fig. 12
Fig. 12 Variations of maximum power coupling efficiency (Cm) with wavelength for both the PRs based on single and double-slot WG geometries. Inset shows the mode profiles of the Hy component of the first supermode of double-slot WG-based PR at two sample values of λ = 4.45 µm and 4.50 µm.
Fig. 13 Variations of confinement factor of cover and substrate regions of double-slot WG-based PR with wavelength for the (a) first supermode (b) second supermode.
Our designed PRs based on single and double-slot based WG geometries should be possible to fabricate with the mature technology of CMOS (complementary metal oxide semiconductor). Figure 14
Fig. 14 Fabrication process flow: (a) Grow Si and CaF2 layers epitaxially on a CaF2 substrate and then spin-coat it with the resist; (b) pattern the resist through E-beam lithography; (c) dry etch Si and CaF2 up to the substrate; (d) again spin-coat with the resist; (e) pattern the resist; (f) dry etch Si and CaF2 which are unrelated to the device and remove the resist.
Fig. 16 Dependence of maximum power coupling efficiency (Cm) on WGs widths variation Δw for both the PRs based on single as well as double-slot WG geometries.
Fig. 17 Dependence of maximum power coupling efficiency (Cm) on slot thickness variation Δt for the double-slot based PR.
4. Conclusions
In summary, we have proposed a silicon-on-calcium-fluoride based asymmetric directional coupler comprising of a horizontal slot waveguide and a strip waveguide for realizing a very efficient and compact mid-IR PR by exploiting power coupling through phase matching between the TM mode of a horizontal slot WG and TE mode of a strip WG. We have optimized it for operation at the wavelength of 4.47 µm (characteristic absorption wavelength of N2O gas) for both polarization conversions in two configurations. In one configuration, horizontal slot waveguide of asymmetric directional coupler consists of single slot, and for another configuration, it consists of double-slot. Numerical studies revealed that with the length of ~0.576 mm of PR based on single slot waveguide structure maximum power coupling efficiency of ~95% is realizable and that of ~97% is realizable with device length of just ~0.468 mm for the PR based on double-slot waveguide structure from an input TM mode to output TE mode and vice versa. In order to achieve a robust PR design, bandwidth of operation and fabrication tolerances of both the designed PRs have also been investigated. Both the PRs have broad band width of 50 nm with appreciable power coupling efficiency of ~80%. Analysis of fabrication tolerances has shown that PR based on double-slot waveguide geometry exhibits larger tolerance to fabrication errors as compared to PR based on single slot waveguide geometry. Thus, our proposed designed PR based on double-slot waveguide structure should have excellent potential to make an efficient polarization diversity scheme for mid-IR silicon photonics which contains several potential applications in various fields like sensing, bio-photonics, etc.
Acknowledgment
This work was partially supported by Department of the Navy Grant N62909-10-1-7141 issued by Office of Naval Research Global. The United States Government has royalty-free license throughout the world in all copyrightable material contained herein.
References
1. Y. Zou, S. Chakravarty, C. J. Chung, X. Xu, and R. T. Chen, “Mid-infrared silicon photonic waveguides and devices,” Photon. Res. 6(4), 254–276 (2018). [CrossRef]
2. H. Lin, Z. Luo, T. Gu, L. C. Kimerling, K. Wada, A. Agarwal, and J. Hu, “Mid-infrared integrated photonics on silicon: a perspective,” Nanophoton. 7(2), 393–420 (2017). [CrossRef]
3. R. Shankar and M. Lončar, “Silicon photonic devices for mid-infrared applications,” Nanophoton. 3(4–5), 329–341 (2014).
4. B. Kumari, A. Barh, R. K. Varshney, and B. P. Pal, “Silicon-on-nitride slot waveguide: a promising platform as mid-IR trace gas sensor,” Sens. Actuators B Chem. 236, 759–764 (2016). [CrossRef]
5. B. Kumari, R. K. Varshney, and B. P. Pal, “Design of chip scale silicon rib slot waveguide for sub-ppm detection of N2O gas at mid-IR band,” Sens. Actuators B Chem. 255, 3409–3416 (2018). [CrossRef]
6. Y. Chen, H. Lin, J. Hu, and M. Li, “Heterogeneously integrated silicon photonics for the mid-infrared and spectroscopic sensing,” ACS Nano 8(7), 6955–6961 (2014). [CrossRef] [PubMed]
7. T. Hu, B. Dong, X. Luo, T. Y. Liow, J. Song, C. Lee, and G. Q. Lo, “Silicon photonic platforms for mid-infrared applications,” Photon. Res. 5(5), 417–430 (2017). [CrossRef]
8. H. Cong, C. Xue, J. Zheng, F. Yang, K. Yu, Z. Liu, X. Zhang, B. Cheng, and Q. Wang, “Silicon based GeSn pin photodetector for SWIR detection,” IEEE Photonics J. 8(5), 1–6 (2016). [CrossRef]
9. C. Alonso-Ramos, M. Nedeljkovic, D. Benedikovic, J. S. Penadés, C. G. Littlejohns, A. Z. Khokhar, D. Pérez-Galacho, L. Vivien, P. Cheben, and G. Z. Mashanovich, “Germanium-on-silicon mid-infrared grating couplers with low-reflectivity inverse taper excitation,” Opt. Lett. 41(18), 4324–4327 (2016). [CrossRef] [PubMed]
10. M. Nedeljkovic, S. Stankovic, C. J. Mitchell, A. Z. Khokhar, S. A. Reynolds, D. J. Thomson, F. Y. Gardes, C. G. Littlejohns, G. T. Reed, and G. Z. Mashanovich, “Mid-infrared thermo-optic modulators in SoI,” IEEE Photonics Technol. Lett. 26(13), 1352–1355 (2014). [CrossRef]
11. R. Shankar, I. Bulu, and M. Lončar, “Integrated high-quality factor silicon-on-sapphire ring resonators for the mid-infrared,” Appl. Phys. Lett. 102(5), 051108 (2013). [CrossRef]
12. T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007). [CrossRef]
13. B. Wohlfeil, L. Zimmermann, and K. Petermann, “Asymmetric codirectional coupler between regular nanowaveguide and slot-waveguide for polarization conversion,” in Advanced Photonics Congress, OSA Technical Digest (online) (Optical Society of America, Colorado Springs, Colorado, 2012), p. ITu2B.5. [CrossRef]
14. A. Barh, B. M. A. Rahman, R. K. Varshney, and B. P. Pal, “Design and performance study of a compact SOI polarization rotator at 1.55 μm,” J. Lightwave Technol. 31(23), 3687–3693 (2013). [CrossRef]
15. S. Soudi and B. M. A. Rahman, “Design of compact polarization rotator using simple silicon nanowires,” Appl. Opt. 53(34), 8071–8077 (2014). [CrossRef] [PubMed]
16. M. R. Watts and H. A. Haus, “Integrated mode-evolution-based polarization rotators,” Opt. Lett. 30(2), 138–140 (2005). [CrossRef] [PubMed]
17. D. Dai and J. E. Bowers, “Novel concept for ultracompact polarization splitter-rotator based on silicon nanowires,” Opt. Express 19(11), 10940–10949 (2011). [CrossRef] [PubMed]
18. J. Wang, B. Niu, Z. Sheng, A. Wu, W. Li, X. Wang, S. Zou, M. Qi, and F. Gan, “Novel ultra-broadband polarization splitter-rotator based on mode-evolution tapers and a mode-sorting asymmetric Y-junction,” Opt. Express 22(11), 13565–13571 (2014). [CrossRef] [PubMed]
19. Y. Xiong, J. G. Wangüemert-Pérez, D. X. Xu, J. H. Schmid, P. Cheben, and W. N. Ye, “Polarization splitter and rotator with subwavelength grating for enhanced fabrication tolerance,” Opt. Lett. 39(24), 6931–6934 (2014). [CrossRef] [PubMed]
20. M. F. O. Hameed and S. S. A. Obayya, “Design of passive polarization rotator based on silica photonic crystal fiber,” Opt. Lett. 36(16), 3133–3135 (2011). [CrossRef] [PubMed]
21. D. Dai and H. Wu, “Realization of a compact polarization splitter-rotator on silicon,” Opt. Lett. 41(10), 2346–2349 (2016). [CrossRef] [PubMed]
22. A. Barh, B. P. Pal, R. K. Varshney, and B. M. A. Rahman, “Design of a compact SOI polarization rotator for mid-IR application,” in 2012 5th International Conference on Computer and Devices for Communication (CODEC), (IEEE, Kolkata, India, 2012), p. 1.
23. J. Wang, C. Lee, B. Niu, H. Huang, Y. Li, M. Li, X. Chen, Z. Sheng, A. Wu, W. Li, X. Wang, S. Zou, F. Gan, and M. Qi, “A silicon-on-insulator polarization diversity scheme in the mid-infrared,” Opt. Express 23(11), 15029–15037 (2015). [CrossRef] [PubMed]
24. M. Nedeljkovic, A. Z. Khokhar, Y. Hu, X. Chen, J. S. Penades, S. Stankovic, H. M. H. Chong, D. J. Thomson, F. Y. Gardes, G. T. Reed, and G. Z. Mashanovich, “Silicon photonic devices and platforms for the mid-infrared,” Opt. Mater. Express 3(9), 1205–1214 (2013). [CrossRef]
25. “Calcium Fluoride,” http://www.janis.com/Libraries/Window_Transmissions/CalciumFluoride_CaF2_TransmissionCurveDataSheet.sflb.ashx.
26. D. F. G. Gallagher and T. P. Felici, “Eigenmode expansion methods for simulation of optical propagation in photonics: pros and cons,” Proc. SPIE 4987, 69–83 (2003). [CrossRef]
27. C. W. Hsu, T. K. Chang, J. Y. Chen, and Y. C. Cheng, “8.13 μm in length and CMOS compatible polarization beam splitter based on an asymmetrical directional coupler,” Appl. Opt. 55(12), 3313–3318 (2016). [CrossRef] [PubMed]
28. N. I. Filimonova, V. A. Ilyushin, and A. A. Velichko, “Molecular beam epitaxy of BaF2/CaF2 buffer layers on the Si (100) substrate for monolithic photoreceivers,” Optoelectron. Instrum. Data Process. 53(3), 303–308 (2017). [CrossRef]
29. M. Barkai, Y. Lereah, E. Grünbaum, and G. Deutscher, “Epitaxial growth of silicon and germanium films on CaF2/Si,” Thin Solid Films 139(3), 287–297 (1986). [CrossRef]
30. T. Guo, M. J. Deen, C. Xu, Q. Fang, P. R. Selvaganapathy, and H. Zhang, “Observation of ultraslow stress release in silicon nitride films on CaF2,” J. Vac. Sci. Technol. A 33(4), 041515 (2015). [CrossRef]
31. A. Säynätjoki, L. Karvonen, T. Alasaarela, X. Tu, T. Y. Liow, M. Hiltunen, A. Tervonen, G. Q. Lo, and S. Honkanen, “Low-loss silicon slot waveguides and couplers fabricated with optical lithography and atomic layer deposition,” Opt. Express 19(27), 26275–26282 (2011). [CrossRef] [PubMed]
32. A. Matsutani, H. Ohtsuki, and F. Koyama, “Generation of solid-source H2O plasma and its application to dry etching of CaF2,” Jpn. J. Appl. Phys. 47(66S), 5113–5115 (2008). [CrossRef]
33. B. Bai, Q. Deng, and Z. Zhou, “Plasmonic-assisted polarization beam splitter based on bent directional coupling,” IEEE Photonics Technol. Lett. 29(7), 599–602 (2017). [CrossRef]
34. S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010). [CrossRef]
