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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 12 — Jun. 4, 2012
  • pp: 13425–13439
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Mode conversion in tapered submicron silicon ridge optical waveguides

Daoxin Dai, Yongbo Tang, and John E Bowers  »View Author Affiliations


Optics Express, Vol. 20, Issue 12, pp. 13425-13439 (2012)
http://dx.doi.org/10.1364/OE.20.013425


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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 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 observed in tapered submicron silicon-on-insulator ridge optical waveguides due to the mode hybridization resulting from the asymmetry of the cross section. Such a mode conversion could have a very high efficiency (close to 100%) when the taper is designed appropriately. This enables some applications e.g. polarizer, polarization splitting/rotation, etc. It is also shown that this kind of mode conversion could be depressed by carefully choosing the taper parameters (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 OSA

1. Introduction

2. Structure and analysis

In this paper, we consider tapered submicron SOI rib waveguides, which has been used very widely for silicon optoelectronics [19

19. O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12(21), 5269–5273 (2004). [CrossRef] [PubMed]

24

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). [CrossRef] [PubMed]

]. 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

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). [CrossRef]

8

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). [CrossRef]

, 32

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). [CrossRef]

33

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). [CrossRef]

]. In the present example, the SOI wafer has a 400nm-thick top Si layer and the refractive indices of Si and SiO2 are nSi = 3.455, and nSiO2 = 1.445, respectively. A finite-difference method (FDM) mode-solver (from Fimmwave) is used to calculate the mode field profiles and the effective indices for all eigenmodes.

A. Regular lateral taper

Figure 2(a)
Fig. 2 The calculated effective indices for the eigen modes of SOI rib waveguide with different etching depths. (a) het = 0.4H; (b) het = 0.5H; (c) het = 0.6H. Here the total height of the Si layer is H = 400nm.
-2(c) show the effective indices for SOI rib waveguides with different etching depths het as the core width wco increases from 0.5μm to 3μm. Here the etching depth is chosen as het = 0.4H, 0.5H, and 0.6H, respectively. Particularly, for the case of het = 0.4H, one should note that the TM0 mode becomes leaky and is to be cutoff in the range of wco<0.95μm and thus the curve for the TM0 mode in Fig. 2(a) stops at w0 = 0.95μm. Here het is given with a ratio in respect to H just to understand that the case considered here is with an etching depth around half of the total height (which is used very often).

Since a SOI rib waveguide is asymmetrical in the vertical direction, mode hybridization is observed in some special ranges of the rib width, e.g., around wco0 = 1μm, and 2.45μm, as shown by the circles labeled in Fig. 2(a)-2(c). Due to the mode hybridization around wco = wco0, mode conversion between the two hybridized modes will happen when the light propagates along an “adiabatic” (long) taper structure whose end-widths (w1, and w2) satisfy the condition: w1<wco0<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

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).

]. In order to avoid the undesired mode conversion, one can choose 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 seen that the mode hybridization region shifts when choosing different etching depths het. One has a smaller wco0 (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 het, which makes the design flexible. For example, when reducing the etching depth from 0.6H to het = 0.4H, the first and second mode hybridization regions shift from around wco0 = 1.1μm and 2.55μm to around wco0 = 0.9μm and 2.35μm, respectively, as shown in Fig. 2(a). Then one can choose 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 case of het = 0.4H. Particularly, regarding that the TM0 mode becomes leaky when wco<0.95μm, one should choose 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 case of tapered SOI nanowires [30

30. 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]

].

In order to show the mode hybridization which causes the mode conversion in a tapered SOI rib waveguide, we consider the case of het = 0.5H as an example. From Fig. 2(b), it can be seen that there are two regions (i.e., wco0 = 2.45μm, and 1.0μm) where mode hybridization happens. In the region around wco = 2.45μm, the mode hybridization happens between the TM0 and the third-order TE (TE3) mode. The mode profiles for these two modes are shown in Fig. 3(a)
Fig. 3 The field profiles (Ex and Ey) for modes #1 and #2 of a SOI ridge waveguide with wco = 2.45μm, (a) mode #1; (b) mode #2. The total height of the Si core layer is H = 400nm, and the etching depth het = 0.5H. Here modes #1 and #2 are the two hybridization modes in the region around w = 2.45μm.
-3(b), respectively. It can be seen that the minor-component (Ex or Ey) is comparable to the corresponding major-component (Ey or Ex). In this case, it is hard to distinguish these two modes. When wco = 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)
Fig. 4 The field profiles (Ex and Ey) for modes #1 and #2 of a SOI ridge waveguide with wco = 1.0μm, (a) mode #1; (b) mode #2. The total height of the Si core layer is H = 400nm, and het = 0.5H. Here modes #1 and #2 are the two hybridization modes in the region around w = 1.0μm.
-4(b).

As mentioned above, there are two regions (around wco0 = 1.0μm, and 2.45μm) where mode conversions happen when the core width is tapered from 3μm to 0.5μm. Therefore, here we examine two types of tapers. For the first one, the taper end-width is chosen as w1 = 2μm, and w2 = 2.7μm (w1<2.45μm<w2). The second one has taper end-widths w1 = 0.8μm, and w2 = 1.5μm (w1<1μm<w2).

A commercial software (FIMMPROP, Photon Design, UK) employing an eigenmode expansion and matching method [34

34. FIMMWAVE/FIMMPROP, Photon Design Ltd, http://www.photond.com.

] is then used to simulate the light propagation in the defined taper structure. Figure 5
Fig. 5 The mode conversion efficiency η as the taper length Ltp varies when the TM0 mode is launched. The parameters are het = 0.5H, w1 = 2.7μm, and w2 = 2μm.
shows the mode conversion efficiencies coupled to the TM0 mode and the TE3 mode after the launched TM0 mode propagates along the linear lateral taper with w1 = 2.7μm, and w2 = 2.0μm. From this figure, it can be seen that one could realize a very high efficiency (>90%) from the TM0 mode to the TE3 mode when choosing the taper length Ltp appropriately.

From Fig. 5, one can also see that the mode conversion could be very slight by choosing a very short non-adiabatic taper. For example, for a 10μm -long taper, the mode conversion from TM0 to TE3 is about 5% only and such a low loss is acceptable for some applications. Figure 7(a)
Fig. 7 The light propagation in the designed short (non-adiabatic) taper when the launched field is TE polarization (a), and TM polarization (b), respectively. The parameters are: H = 400nm, het = 0.5H, w1 = 2.7μm, w2 = 2μm, and Ltp = 10μm.
and 7(b) show the simulation results for light propagating along a 10μm-long taper for the case with the TE0 and TM0 modes launched, respectively. From these two figures, it can be seen that there are some small ripples due to the multimode-interference effect. For the case when the TE0 mode is launched, the TE2 mode is excited slightly because the taper is not adiabatic. In this case, the dominant mode is the TE0 mode which has a power ratio of 99.66% while the excited TE2 mode has a low power ratio of about 0.26%.

Figure 8
Fig. 8 The mode conversion efficiency η as the taper length Ltp varies when the TM0 mode is launched. The parameters are het = 0.5H, w1 = 1.5μm, and w2 = 0.8μm.
shows the mode conversion efficiencies to the TM0 and the TE1 mode after the launched TM0 mode propagates along a linear lateral taper with w1 = 1.5μm, and w2 = 0.8μm, between which there is a mode hybridization region round wco0 = 1μm (see Fig. 2 (b)). From this figure, it can be seen that the mode conversion efficiency from the TM0 mode to the TE1 mode is close 100% when choosing the taper length Ltp appropriately.

In a short summary, for a regular lateral taper whose widths ranges from w1 to w2 (w1<w2), the mode conversion between the TM0 mode and higher-order TE modes (e.g., TE1, TE3) happens when there is a mode hybridization region in the range of w1<w<w2 according to the simulation given above. Such a mode conversion could be very efficient (close to 100%) when the taper length is long enough, which is very useful some applications, e.g., polarization rotation. On the other hand, it is also possible to design a taper to minimize the mode conversion by choosing the etching depth (het) or the range for the taper end-widths (w1, and w2) when it desired to achieve a low-loss waveguide taper. For example, one can choose the taper end-widths (w1, and w2) so that there is no a mode hybridization region in the range of w1<w<w2. In this way, there will not be mode conversion when light propagates along a long taper. Generally speaking, the mode evolution in a gradually-varying taper structure is insensitive to the variation of the taper dimension (e.g., the height, the width) when the taper is long enough. However, when there are mode-hybridization regions as discussed here, one should choose the taper end-widths carefully to be tolerant to the taper dimension variation because the mode hybridization region shifts slightly as the taper dimension changes. For example, one can choose the taper end-widths not to be close to the mode hybridization regions (around wco0), which can make the taper tolerant to the dimension variation.

Bi-level taper is another type of taper structure used often to connect two sections with different etching depth [7

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). [CrossRef]

8

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). [CrossRef]

, 32

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). [CrossRef]

33

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). [CrossRef]

, 35

35. D. Dai, Z. Wang, J. Peters, and J. E. Bowers, “Compact polarization beam splitter using an asymmetrical Mach-Zehnder Interferometer based on silicon-on-insulator waveguides,” IEEE Photon. Technol. Lett. 24(8), 673–675 (2012). [CrossRef]

]. Usually it is assumed that no higher-order mode is excited when light propagates along a long bi-level taper, so that one achieves a low-loss smooth transition between the fundamental modes of the SOI ridge waveguide and the silicon strip waveguide. However, our simulation shows that higher-order modes might be generated even in a long bi-level taper for submicron SOI ridge waveguides. It is very essential to understand this issue when designing the waveguide taper. In the following part, we give a detailed analysis for the mode conversion in bi-level taper.

B. Bi-level taper

Figure 11(a)
Fig. 11 (a) The schematic configuration of a bi-level lateral taper; (b) the cross section for an SOI double-rib waveguide in the taper section.
and 11(b) show the 3D-view for the bi-level taper and the cross section for the SOI double-rib waveguide. Such a taper is often used to connect two sections with different etching depths previously [7

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). [CrossRef]

8

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). [CrossRef]

, 32

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). [CrossRef]

33

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). [CrossRef]

].

Figure 12(a)
Fig. 12 The calculated effective indices for the eigen modes of SOI double-ridge waveguides with different rib widths wco: (a) wco = 0.85μm, and het = 0.5H; (b) wco = 1.0μm, and het = 0.5H; (c) wco = 1.2μm, and het = 0.5H; (d) wco = 1.0μm, and het = 0.6H. Here H = 400nm.
-12(c) show the effective indices for an SOI double-rib waveguide with het = 0.5H as the side-rib width wside decreases from 3μm to 0 when the central-rib width is chosen as wco = 0.85, 1, and 1.2μm, respectively, so that the SOI rib waveguide is quasi-singlemode. Since a SOI double-rib waveguide is not symmetrical in the vertical direction, mode hybridization might happen. The mode hybridization in a SOI double-rib waveguide depends a lot on the central rib width wco. For the present case (het = 0.5H), it is found that mode hybridization and conversion happen as the side-rib width wside varies from 3μm to 0 when the central rib width wco = 1.0μm according to Fig. 12(b) and the mode profiles e.g. shown in Fig. 13(a)-(b)
Fig. 13 The field profiles (Ex and Ey) for modes #1 and #2 of a double ridge waveguide with: (a) wside = 0.5μm; (b) wside = 0.5μm. The parameters are: wco = 1μm, H = 400nm, and het = 0.5H. Here modes #1 and #2 are the two lowest order modes except the TE0 mode.
below. In contrast, when choosing wco = 0.85μm, and 1.2μm, there is no mode hybridization and conversion according to Fig. 12(a)-(c), and Fig. 14(a)-(b)
Fig. 14 The field profiles (Ex and Ey) for modes #1 and #2 of a double ridge waveguide with the following parameters: (a) wco = 0.85μm, (b) wco = 1.2μm. The parameters are: wside = 0.5μm, H = 400nm, and het = 0.5H. Here modes #1 and #2 are the two lowest-order modes except the TE0 mode.
below. The mode hybridization and conversion can be also avoided by choosing a deeper etching depth het. For example, when choosing het = 0.6H (see Fig. 12(d)), there is no mode conversion observed.

Figure 13(a)-13(b) shows the field profiles (Ex and Ey) for mode #1 and #2 in the case of wco = 1.0μm when wside = 0.5μm and 0μm, respectively. Here modes #1 and #2 are the two lowest order modes except the TE0 mode. When wside = 0, the double-rib waveguide becomes a rectangular waveguide, which is symmetrical in the vertical direction and consequently no mode hybridization is observed. In contrast, for the case of wside = 0.5μm, it can be seen that the eigen-modes have significant major as well as minor components (Ex and Ey) due to the hybridization as shown in Fig. 13(a)-13(b). This mode hybridization between the TM0 mode and the TE1 mode makes a mode conversion between them when light propagates along an adiabatic taper. In order to check the mode hybridization for the cases of wco = 0.85μm and 1.2μm, we also consider the waveguide with wside = 0.5μm and show the filed profiles (Ex and Ey) for mode #1 and #2 in Fig. 14(a)-14(b), respectively. Note that the color scale are different for Ex and Ey. According to the field profiles, it can be seen that both mode #1 and #2 have a major components (Ex or Ey), which indicates the mode hybridization is not significant.

2. Experimental observation

When the TM0 mode is launched, the beat length Lπ of the two-mode interference in the 1μm-wide straight section is then given by Lπ = π/[(neff_TM0-neff_TE1)k0], where neff_TM0 and neff_TE1 are the effective indices of the TM0 mode and the TE1 mode, respectively, k0 is the wavenumber in vacuum. Correspondingly, the free-spectral range (FSR) of the spectral response of the taper structure is given by
λFSR=λ2(ng_TE1ng_TM0)L1+λ,
where ng_TM0 and ng_TE1 are the group indices for the TM0 mode and the TE1 mode, respectively and they are given by ng_TM0 = neff_TM0–λ(∂neff_TM0/∂λ), and ng_TE1 = neff_TE1–λ(∂neff_TE1/∂λ), respectively.

With this formula, the calculated quasi-FSR of the spectral response for the taper structure as the length L1 varies, is shown in Fig. 19(c). The quasi-FSR extracted from the measured spectral responses in Fig. 19(b) is also shown in order to give a comparison. From Fig. 19(c), it can be seen that the theoretical and experimental results agree with each other very well.

From the measurement results shown here, one should realize that the mode conversion in a taper structure might be very serious and influence the performances of optical waveguides and devices. It is necessary to design the taper very carefully to avoid the undesired mode conversions.

3. Conclusions

In this paper, the mode conversion in tapered submicron SOI rib optical waveguides has been studied. We have considered two typical optical waveguide tapers (i.e., regular lateral tapers, and bi-level tapers) for submicron SOI rib optical waveguides. For a SOI rib waveguide, it is still asymmetrical in the vertical direction even when choosing the same material for the upper-cladding and the under-cladding. Therefore, in a tapered SOI rib optical waveguide, mode conversion between the TM0 mode and higher-order TE modes might happens due to the mode hybridization in some waveguide width ranges, which has been observed for both types of waveguide tapers in our simulation. Our experimental results have also been demonstrated to give the evidence of mode conversions. Such a mode conversion is not desired usually because some excess loss and crosstalk is introduced in some photonic integrated circuits. It has also been shown that such harmful mode conversion effect can be removed almost for both types of waveguide tapers by carefully designing the taper parameters (e.g., the width and length of the taper, the etching depth, etc). On the other hand, our simulation results have also shown that a very high mode-conversion efficiency (close to 100%) could be achieved in both SOI rib optical waveguide tapers. Such an efficient mode conversion could be useful for some applications, e.g., polarization rotation [30

30. 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]

].

Acknowledgments

This research is supported by DARPA MTO under the CIPhER contract No: HR0011-10-1-0079, the National Nature Science Foundation of China (No. 61077040), a 863 project (Ministry of Science and Technology of China, No. 2011AA010301), Zhejiang provincial grant (Z201121938) of China, and also supported by the Fundamental Research Funds for the Central Universities. The authors thank Dr. Di Liang for useful discussions and Jon Peters for fabrication.

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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). [CrossRef]

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). [CrossRef] [PubMed]

25.

K. Mertens, B. Scholl, and H. Schmitt, “New highly efficient polarization converters based on hybrid supermodes,” J. Lightwave Technol. 13(10), 2087–2092 (1995). [CrossRef]

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). [CrossRef] [PubMed]

27.

D. Dai, Z. Wang, N. Julian, and J. E. Bowers, “Compact broadband polarizer based on shallowly-etched silicon-on-insulator ridge optical waveguides,” Opt. Express 18(26), 27404–27415 (2010). [CrossRef] [PubMed]

28.

R. S. Tummidi, T. G. Nguyen, A. Mitchell, and T. L. Koch, “An ultra-compact waveguide polarizer based 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 based on silicon nanowires,” Opt. Express 19(11), 10940–10949 (2011). [CrossRef] [PubMed]

31.

M. Kohtoku, T. Hirono, S. Oku, Y. Kadota, Y. Shibata, and Y. Yoshikuni, “Control of higher order leaky modes in deep-ridge waveguides and application to low-crosstalk arrayed waveguide gratings,” J. Lightwave Technol. 22(2), 499–508 (2004). [CrossRef]

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). [CrossRef]

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). [CrossRef]

34.

FIMMWAVE/FIMMPROP, Photon Design Ltd, http://www.photond.com.

35.

D. Dai, Z. Wang, J. Peters, and J. E. Bowers, “Compact polarization beam splitter using an asymmetrical Mach-Zehnder Interferometer based on silicon-on-insulator waveguides,” IEEE Photon. Technol. Lett. 24(8), 673–675 (2012). [CrossRef]

OCIS Codes
(130.0130) Integrated optics : Integrated optics
(230.5440) Optical devices : Polarization-selective devices

ToC Category:
Integrated Optics

History
Original Manuscript: April 9, 2012
Revised Manuscript: May 19, 2012
Manuscript Accepted: May 22, 2012
Published: May 31, 2012

Citation
Daoxin Dai, Yongbo Tang, and John E Bowers, "Mode conversion in tapered submicron silicon ridge optical waveguides," Opt. Express 20, 13425-13439 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-12-13425


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References

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  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. Express19(7), 5811–5816 (2011). [CrossRef] [PubMed]
  25. K. Mertens, B. Scholl, and H. Schmitt, “New highly efficient polarization converters based on hybrid supermodes,” J. Lightwave Technol.13(10), 2087–2092 (1995). [CrossRef]
  26. L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Silicon-on-insulator polarization splitting and rotating device for polarization diversity circuits,” Opt. Express19(13), 12646–12651 (2011). [CrossRef] [PubMed]
  27. D. Dai, Z. Wang, N. Julian, and J. E. Bowers, “Compact broadband polarizer based on shallowly-etched silicon-on-insulator ridge optical waveguides,” Opt. Express18(26), 27404–27415 (2010). [CrossRef] [PubMed]
  28. R. S. Tummidi, T. G. Nguyen, A. Mitchell, and T. L. Koch, “An ultra-compact waveguide polarizer based 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 based on silicon nanowires,” Opt. Express19(11), 10940–10949 (2011). [CrossRef] [PubMed]
  31. M. Kohtoku, T. Hirono, S. Oku, Y. Kadota, Y. Shibata, and Y. Yoshikuni, “Control of higher order leaky modes in deep-ridge waveguides and application to low-crosstalk arrayed waveguide gratings,” J. Lightwave Technol.22(2), 499–508 (2004). [CrossRef]
  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). [CrossRef]
  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). [CrossRef]
  34. FIMMWAVE/FIMMPROP, Photon Design Ltd, http://www.photond.com .
  35. D. Dai, Z. Wang, J. Peters, and J. E. Bowers, “Compact polarization beam splitter using an asymmetrical Mach-Zehnder Interferometer based on silicon-on-insulator waveguides,” IEEE Photon. Technol. Lett.24(8), 673–675 (2012). [CrossRef]

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