Mode conversion in tapered submicron silicon
ridge optical waveguides
Daoxin Dai,1,2,* Yongbo Tang,2 and John E Bowers2 1Centre for Optical and Electromagnetic Rearch, State Key Laboratory for Modern Optical Instrumentation, Zhejiang Provincial Key Laboratory for Sensing Technologies, Zhejiang University, Zijingang Campus, Hangzhou
310058, China
2Department of Electrical and Computer Engineering, University of California, Santa Barbara, California 93106,
USA
*dxdai@zju.edu
Abstract: The mode conversion in tapered submicron silicon ridge optical
waveguides is investigated theoretically and experimentally. Two types of
optical waveguide tapers are considered in this paper. One is a regular
姚明捐款lateral taper for which the waveguide width varies while the etching depth
is kept the same. The other is a so-called “bi-level” taper, which includes
two layers of lateral tapers. Mode conversion between the TM fundamental
mode and higher-order TE modes is obrved in tapered submicron silicon-
on-insulator ridge optical waveguides due to the mode hybridization
resulting from the asymmetry of the cross ction. Such a mode conversion
could have a very high efficiency (clo to 100%) when the taper is
designed appropriately. This enables some polarizer,
polarization splitting/rotation, etc. It is also shown that this kind of mode
conversion could be depresd by carefully choosing the taper parameters
锂电池原理(like the taper width, the etching depth, etc), which is important for the
applications when low-loss propagation for the TM fundamental mode is
needed.
©2012 Optical Society of America
OCIS codes: (130.0130) Integrated optics; (230.5440) Polarization-lective devices.
References and links
1. Y. Shani, C. Henry, R. Kistler, K. Orlowsky, and D. Ackerman, “Efficient coupling of a miconductor lar to
an optical fiber by means of a tapered waveguide on silicon,” Appl. Phys. Lett. 55(23), 2389–2391 (1989).
2. R. Smith, C. Sullivan, G. Vawter, G. Hadley, J. Wendt, M. Snipes, and J. Klem, “Reduced coupling loss using a
tapered-rib adiabatic-following fiber coupler,” IEEE Photon. Technol. Lett. 5, 1053–1056 (1993).古代后宫
3. R. Zengerle, H. Bruckner, H. Olzhaun, and A. Kohl, “Low-loss fiber-chip coupling by buried laterally tapered
InP/InGaAsP waveguide structure,” Electron. Lett. 28(7), 631–632 (1992).
4. K. Kasaya, O. Mitomi, M. Naganuma, Y. Kondo, and Y. Noguchi, “A simple laterally tapered waveguide for
low-loss coupling to single-mode fibers,” IEEE Photon. Technol. Lett. 5(3), 345–347 (1993).
5. T. Schwander, S. Fischer, A. Kramer, M. Laich, K. Luksic, G. Spatschek, and M. Warth, “Simple and low-loss
fiber-to-chip coupling by integrated field-matching waveguide in InP,” Electron. Lett. 29(4), 326–328 (1993). 6. L. Yang, D. Dai, B. Yang, Z. Sheng, and S. He, “Characteristic analysis of tapered lens fibers for light focusing
and butt-coupling to a silicon rib waveguide,” Appl. Opt. 48(4), 672–678 (2009).
7. D. Dai, S. He, and H. K. Tsang, “Bilevel mode converter between a silicon nanowire waveguide and a larger
waveguide,” J. Lightwave Technol. 24(6), 2428–2433 (2006).
8. A. Barkai, A. Liu, D. Kim, R. Cohen, N. Elek, H.-H. Chang, B. H. Malik, R. Gabay, R. Jones, M. Paniccia, and
N. Izhaky, “Double-stage taper for coupling between SOI waveguides and single-mode fiber,” J. Lightwave Technol. 26(24), 3860–3865 (2008).
9. Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and K. J. Orlowsky, “Integrated optic adiabatic devices on
silicon,” IEEE J. Quantum Electron. 27(3), 556–566 (1991).
10. R. S. Fan and R. B. Hooker, “Tapered polymer single-mode waveguides for mode transformation,” J. Lightwave
Technol. 17(3), 466–474 (1999).
11. K. W¨orhoff, P. V. Lambeck, and A. Driesn, “Design, tolerance analysis, and fabrication of silicon oxynitride
bad planar optical waveguides for communication devices,” J. Lightwave Technol. 17(8), 1401–1407 (1999).
柳宗元生平简介
12. P. Sewell, T. M. Benson, and P. C. Kendall, “Rib waveguide spot-size transformers: modal properties,” J.
Lightwave Technol. 17(5), 848–856 (1999).
13. K. Sasaki, F. Ohno, A. Motegi, and T. Baba, “Arrayed waveguide grating of 70×60µm2 size bad on Si
photonic wire waveguides,” Electron. Lett. 41(14), 801–802 (2005).
#166272 - $15.00 USD Received 9 Apr 2012; revid 19 May 2012; accepted 22 May 2012; published 31 May 2012 (C) 2012 OSA 4 June 2012 / Vol. 20, No. 12 / OPTICS EXPRESS 13425
14. D. Dai, L. Liu, L. Wosinski, and S. He, “Design and fabrication of ultra-small overlapped AWG demultiplexer
bad on Si nanowire waveguides,” Electron. Lett. 42(7), 400–402 (2006).
15. W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-
on-Insulator Spectral Filters Fabricated With CMOS Technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
16. H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S. Itabashi, “Silicon photonic circuit
with polarization diversity,” Opt. Express 16(7), 4872–4880 (2008).
17. W. Bogaerts, P. Dumon, D. V. Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G.
Baets, “Compact wavelength-lective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top.
Quantum Electron. 12(6), 1394–1401 (2006).
18. M. Soltani, S. Yegnanarayanan, and A. Adibi, “Ultra-high Q planar silicon microdisk resonators for chip-scale
silicon photonics,” Opt. Express 15(8), 4694–4704 (2007).
19. O. Boyraz and B. Jalali, “Demonstration of a silicon Raman lar,” Opt. Express 12(21), 5269–5273 (2004).
20. C. Li, L. Zhou, and A. W. Poon, “Silicon microring carrier-injection-bad modulators/switches with tunable
extinction ratios and OR-logic switching by using waveguide cross-coupling,” Opt. Express 15(8), 5069–5076 (2007).
21. H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon
lar,” Nature 433(7027), 725–728 (2005).
22. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature
435(7040), 325–327 (2005).
23. C. A. Barrios, V. R. Almeida, R. Panepucci, and M. Lipson, “Electrooptic modulation of silicon-on-insulator
submicrometer-size waveguide devices,” J. Lightwave Technol. 21(10), 2332–2339 (2003).
24. Y. Tang, H.-W. Chen, S. Jain, J. D. Peters, U. Westergren, and J. E. Bowers, “50 Gb/s hybrid silicon traveling-
wave electroabsorption modulator,” Opt. Express 19(7), 5811–5816 (2011).
25. K. Mertens, B. Scholl, and H. Schmitt, “New highly efficient polarization converters bad on hybrid
supermodes,” J. Lightwave Technol. 13(10), 2087–2092 (1995).
26. L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Silicon-on-insulator polarization splitting and rotating device for
polarization diversity circuits,” Opt. Express 19(13), 12646–12651 (2011).
27. D. Dai, Z. Wang, N. Julian, and J. E. Bowers, “Compact broadband polarizer bad on shallowly-etched silicon-
on-insulator ridge optical waveguides,” Opt. Express 18(26), 27404–27415 (2010).
28. R. S. Tummidi, T. G. Nguyen, A. Mitchell, and T. L. Koch, “An ultra-compact waveguide polarizer bad on
“anti-magic widths”,” 2011 8th IEEE International Conference on Group IV Photonics (GFP), London, UK, pp.
104–106, 14–16 Sept. 2011.
29. D. Vermeulen, S. Selvaraja, W. A. D. De Cort, N. A. Yebo, E. Hallynck, K. De Vos, P. P. P. Debackere, P.
Dumon, W. Bogaerts, G. Roelkens, D. Van Thourhout, and R. Baets, “Efficient tapering to the fundamental Quasi-TM mode in asymmetrical waveguides,” ECIO 2010 (2010).
30. D. Dai and J. E. Bowers, “Novel concept for ultracompact polarization splitter-rotator bad on silicon
nanowires,” Opt. Express 19(11), 10940–10949 (2011).
31. M. Kohtoku, T. Hirono, S. Oku, Y. Kadota, Y. Shibata, and Y. Yoshikuni, “Control of higher order leaky modes10月5号
in deep-ridge waveguides and application to low-crosstalk arrayed waveguide gratings,” J. Lightwave Technol.
22(2), 499–508 (2004).
32. D. Dai, J. He, and S. He, “Elimination of multimode effects in a silicon-on-insulator etched diffraction grating
demultiplexer with bi-level taper structure,” IEEE J. Sel. Top. Quantum Electron. 11(2), 439–443 (2005).
33. J. H. Schmid, B. Lamontagne, P. Cheben, A. Delâge, S. Janz, A. Densmore, J. Lapointe, E. Post, P. Waldron,
and D.-X. Xu, “Mode Converters for coupling to high aspect ratio silicon-on-insulator channel waveguides,”
IEEE Photon. Technol. Lett. 19(11), 855–857 (2007).
34. FIMMWAVE/FIMMPROP, Photon Design Ltd,
35. D. Dai, Z. Wang, J. Peters, and J. E. Bowers, “Compact polarization beam splitter using an asymmetrical Mach-
Zehnder Interferometer bad on silicon-on-insulator waveguides,” IEEE Photon. Technol. Lett. 24(8), 673–675 (2012).
1. Introduction
Optical waveguide taper is a fundamental element for photonic integrated circuits (PIC’s). It is often ud to change the light spot size in order to have better coupling efficiency between two ctions with different cross ctions (e.g., a planar optical waveguide and a singlemode or lens fiber) [1–8]. In order to achieve a low-loss taper, one usually makes the taper long enough to be adiabatic so that higher-order modes are not excited [9–12]. This design rule works well usually especially for low index-contrast (∆) optical waveguides (e.g., SiO2-on-Si buried waveguides). However, the situation becomes complicated for small-sized high-∆optical waveguides, e.g., submicron silicon-on-insulator
(SOI) waveguides, which have been ud widely for ultra-compact CMOS-compatible PIC’s in the recent years [13–24]. In a high-∆optical waveguide, the mode hybridization is significant at some special waveguide widths [25–30] and conquently mode conversion may happen in a tapered structure [29,30]. In Ref [29,30], the authors give a discussion on the mode conversion in a tapered SOI strip #166272 - $15.00 USD Received 9 Apr 2012; revid 19 May 2012; accepted 22 May 2012; published 31 May 2012 (C) 2012 OSA 4 June 2012 / Vol. 20, No. 12 / OPTICS EXPRESS 13426
nanowire. When a SOI nanowire has a SiO2 under-cladding and an air upper-cladding, which makes the SOI nanowire asymmetrical in the vertical direction, the mode conversion between the TM fundamental mode and the first-order TE mode is obrved when light propagates along a taper structure. Such a mode conversion is not desired usually becau it introduces some rious excess loss as well as crosstalk due to the excited higher order modes, e.g., in AWG (arrayed-waveguide grating) demultiplexer [31]. Such undesired mode-conversion could be minimized by using veral kinds of modified tapered structures suggested in Ref [29]. A simple and easy way to depress such a mode conversion in a SOI-nanowire taper is to introduce a SiO2 upper-cladding (instead of air) to make the SOI nanowire symmetrical in the vertical direction [30]. On the other hand, such a kind of
mode conversion could be very uful. For example, in our previous paper a SOI-nanowire taper was designed to have an almost 100% mode conversion efficiency from the TM fundamental (TM0) mode to the first higher-order TE (TE1) mode so that polarization splitter-rotators could be realized with a very simple design and easy fabrication process [30].
In this paper, we focus on the mode conversion in submicron SOI rib waveguides (other than SOI nanowires), which is also very popular for silicon-bad integrated optoelectronics [19–24]. One should note that there is a significant difference between an SOI rib waveguide and a SOI strip nanowire. A SOI strip nanowire could be symmetrical or asymmetrical in the vertical direction by simply choosing an appropriate material for the upper-cladding so that the mode conversion could be eliminated or enhanced accordingly [30]. In contrast, for a SOI rib waveguide, it is still asymmetrical in the vertical direction even when having the same material for the upper-cladding and the under-cladding. Therefore, when it is desired to have a mode conversion between the TM0mode and the higher-order TE mode for the ca of using a SOI rib waveguide, it is not necessary to choosing different materials for the upper-cladding and the under-cladding. On the other hand, such an asymmetry also makes that one cannot yet avoid the mode conversion in a taper ction due to the mode hybridization by simply choosing the same material for the upper-clad
ding and the under-cladding. Such a mode conversion will introduce a significant excess inrtion loss as well as some channel crosstalk due to the excited higher-order modes (e.g., in AWG demultiplexers [31]).
In the following ction, we give a detailed analysis for light propagation in SOI rib waveguide tapers and prent the mode conversion numerically. The experimental obrvation for the mode conversion has also been prented. Two types of taper structures are considered here. One is a regular lateral taper for which the waveguide width varies while the etching depth is kept the same. Since the structure and the fabrication are very simple, a regular lateral taper is very popular for modifying the waveguide mode size in the lateral direction. The other is a so-called “bi-level” taper, which includes two layers of lateral tapers and conquently a double-etching process is needed for the fabrication. A bi-level taper is often ud to connect two ctions with different etching depths, e.g., from a shallowly-etched rib waveguide to a deeply-etched rib waveguide [7–8, 32–33]. For example, bi-level taper are very uful for the ca when a singlemode rib waveguide is needed at the input/output ends of a chip while a strong confinement is desired , sharp bending. Our experimental and theoretical results show that one should be very careful when designing an adiabatic lateral taper or bi-level taper with a small-sized high-∆ optical waveguide, e.g., submicron SOI ridge waveguides considered in this paper.
2. Structure and analysis
In this paper, we consider tapered submicron SOI rib waveguides, which has been ud very widely for silicon optoelectronics [19–24]. Two types of taper structures are analyzed here. The first one is a regular lateral taper, and the other is the so-called bi-level taper [7–8, 32–33]. In the prent example, the SOI wafer has a 400nm-thick top Si layer and the refractive indices of Si and SiO2are n Si= 3.455, and n SiO2= 1.445, respectively. A finite-difference method (FDM) mode-solver (from Fimmwave) is ud to calculate the mode field profiles and the effective indices for all eigenmodes.
手麻治疗方法
#166272 - $15.00 USD Received 9 Apr 2012; revid 19 May 2012; accepted 22 May 2012; published 31 May 2012 (C) 2012 OSA 4 June 2012 / Vol. 20, No. 12 / OPTICS EXPRESS 13427
A. Regular lateral taper
Figure 1(a) and 1(b) show the 3D-view for the regular lateral taper and the cross ction for the SOI rib waveguide. In this taper ction, the waveguide width varies while the etching depth is kept the same. Such a taper is often ud when it is needed to modify the mode size, e.g., at the input/output ends of a silicon photonic integrated chip in order to enhance the coupling efficiency between fibers and the chip. Regarding that the spot size of a commercialized lens fiber is usually around 3µm, in o
ur calculation we give a modal analysis for a SOI rib waveguide who core width varies from 3µm to 0.5µm in order to characterize the mode conversion in a waveguide taper to match the lens fiber [6].
Fig. 1. (a) The schematic configuration of a regular lateral taper; (b) the cross ction for a SOI
过年有什么风俗rib waveguide.
Fig. 2. The calculated effective indices for the eigen modes of SOI rib waveguide with
different etching depths. (a) h et = 0.4H; (b) h et = 0.5H; (c) h et = 0.6H. Here the total height of
空白名称the Si layer is H = 400nm.
Figure 2(a)-2(c) show the effective indices for SOI rib waveguides with different etching depths h et as the core width w co increas from 0.5µm to 3µm. Here the etching depth is chon as h et = 0.4H, 0.5H, and 0.6H, respectively. Particularly, for the ca of h et = 0.4H, one should note that the TM0 mode becomes leaky and is to be cutoff in the range of w co<0.95µm #166272 - $15.00 USD Received 9 Apr 2012; revid 19 May 2012; accepted 22 May 2012; published 31 May 2012 (C) 2012 OSA 4 June 2012 / Vol. 20, No. 12 / OPTICS EXPRESS 13428
and thus the curve for the TM0 mode in Fig. 2(a) stops at w0 = 0.95µm. Here h et is given with a ratio in respect to H just to understand that the ca considered here is with an etching depth around half of the total height (which is ud very often).
Since a SOI rib waveguide is asymmetrical in the vertical direction, mode hybridization is obrved in some special ranges of the rib width, e.g., around w co0= 1µm, and 2.45µm, as shown by the circl
es labeled in Fig. 2(a)-2(c). Due to the mode hybridization around w co = w co0, mode conversion between the two hybridized modes will happen when the light propagates along an “adiabatic” (long) taper structure who end-widths (w1, and w2) satisfy the condition: w1<w co0<w2. In Fig. 2(a)-2(c), the arrowed curves indicate that the mode conversions between the TM0 mode and the higher-order TE mode as the core width varies. Such a mode conversion is harmful when one expects to have a low-loss adiabatic taper [29]. In order to avoid the undesired mode conversion, one can choo the taper widths (w1, w2) so that there is no mode hybridization in the width range of w1<w<w2. In this way, there will not be mode conversion when light propagates along a long taper. From Fig. 2(a)-2(c), it can be en that the mode hybridization region shifts when choosing different etching depths h et. One has a smaller w co0 (where the mode hybridization region locates) when the optical waveguide is etched less. This indicates that the mode conversion due to the mode hybridization could be modified by slightly adjusting the etching depth h et, which makes the design flexible. For example, when reducing the etching depth from 0.6H to h et = 0.4H, the first and cond mode hybridization regions shift from around w co0 = 1.1µm and 2.55µm to around w co0 = 0.9µm and 2.35µm, respectively, as shown in Fig. 2(a). Then one can choo the taper end-widths in the range of 0.90µm<(w1, w2)<2.35µm so that no mode conversion happens in the designed taper for the ca of h et= 0.4H. Particularly, regarding that the TM0mode becomes leaky when w co<0.95µm, on
e should choo the taper end-widths (w1, and w2) to be larger than 0.95µm, i.e., (w1, w2)>0.95µm. Finally the end-widths of the low-loss taper should be 0.95µm<(w1, w2)<2.35µm. On the other hand, it is also possible to utilize such kind of mode conversion to obtain a polarization rotation, which is similar to the ca of tapered SOI nanowires [30].
Fig. 3. The field profiles (E x and E y) for modes #1 and #2 of a SOI ridge waveguide with w co =
2.45µm, (a) mode #1; (b) mode #2. The total height of the Si core layer is H = 400nm, and the
etching depth h et = 0.5H. Here modes #1 and #2 are the two hybridization modes in the region
around w = 2.45µm.
In order to show the mode hybridization which caus the mode conversion in a tapered SOI rib waveguide, we consider the ca of h et = 0.5H as an example. From Fig. 2(b), it can be en that there are two regions (i.e., w co0 = 2.45µm, and 1.0µm) where mode hybridization happens. In the region around w co= 2.45µm, the mode hybridization happens between the TM0 and the third-order TE (TE3) mode. The mode profiles for the two modes are shown in Fig. 3(a)-3(b), respectively. It can be en that the minor-component (E x or E y) is comparable to the corresponding major-component (E y or E x). In this ca, it is hard to distinguish the two modes. When w co = 1.0µm, the mode hybridization is similar while it happens between the TM0 mode and the first-order TE mode (TE1), as shown in Fig. 4(a)-4(b).
#166272 - $15.00 USD Received 9 Apr 2012; revid 19 May 2012; accepted 22 May 2012; published 31 May 2012 (C) 2012 OSA 4 June 2012 / Vol. 20, No. 12 / OPTICS EXPRESS 13429
