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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 Optical Society of America
1. Introduction
Optical waveguide taper is a fundamental element for photonic integrated circuits (PIC’s). It is often used to change the light spot size in order to have better coupling efficiency between two sections with different cross sections (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 used 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 consequently 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 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 observed when light propagates along a taper structure. Such a mode conversion is not desired usually because it introduces some serious 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 several 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 useful. 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-based 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 TM0 mode and the higher-order TE mode for the case 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 section due to the mode hybridization by simply choosing the same material for the upper-cladding and the under-cladding. Such a mode conversion will introduce a significant excess insertion loss as well as some channel crosstalk due to the excited higher-order modes(e.g., in AWG demultiplexers [31]).
In the following section, we give a detailed analysis for light propagation in SOI rib waveguide tapers and present the mode conversion numerically. The experimental observation for the mode conversion has also been presented. 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 consequently a double-etching process is needed for the fabrication. A bi-level taper is often used to connect two sections 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 useful for the case when a singlemode rib waveguide is needed at the input/output ends of a chip while a strong confinement is desired for e.g., 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 used 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 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 1(a) and 1(b) show the 3D-view for the regular lateral taper and the cross section for the SOI rib waveguide. In this taper section, the waveguide width varies while the etching depth is kept the same. Such a taper is often used 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 our calculation we give a modal analysis for a SOI rib waveguide whose 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 section for a SOI rib waveguide.
Figure 2(a) -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).
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.
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]. 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].
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) -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) -4(b).
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.
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.
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] is then used to simulate the light propagation in the defined taper structure. Figure 5 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.
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.
For example, here we choose Ltp = 1500μm. When the launched field is chosen as the TE0 or TM0 modal field, the simulated light propagation along the designed taper are shown in Fig. 6(a) and 6(b), respectively. It can be seen that the mode conversion happens as predicted when the input filed is the TM0 mode, while there is no mode conversion for the case with the TE0-mode input. When one choose a shorter taper (e.g., 350μm), the launched TM0 mode is then converted to the TE3 mode partially. Consequently two-mode interference happens, which introduces some undesired ripples when measuring the wavelength dependence of the output power.
Fig. 6 The light propagation in the designed long 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, Ltp = 1500μm.
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) 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%.
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.
Figure 8 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.
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.
For example, here we choose Ltp = 215μm. Figure 9(a) and 9(b) show the simulation results for light propagating along the designed taper when the launched field is chosen as the TE0 and TM0 modal field, respectively. It can be seen that the mode conversion happens for the input TM0 modal field, while there is no mode conversion for the input TE0 modal field, as predicted. When one chooses a shorter taper, the launched TM0 mode is converted to the TE1 mode partially. For example, when Ltp = 22.4μm, the mode conversion from the TM0 mode to the TE1 mode is about 50%, and a significant multimode-interference effect is observed as shown in Fig. 10(a) -10(b). Particularly, when choosing Ltp = 0 (i.e., no taper), the mode conversion from the TM0 mode to the TE1 mode is about 25% and more power (~75%) is preserved to the TM0 mode as shown in Fig. 8. One could design a discontinuous taper structure by optimizing the widths w1 and w2 further to improve the preservation efficiency for the TM0 mode, in a way similar to that suggested for the design of SOI strip nanowire tapers in Ref [29].
Fig. 9 The light propagation in the designed taper when the input is the TE0 modal field (a), and the TM0 modal field (b), respectively. The parameters are: H = 400nm, het = 0.5H, w1 = 1.5μm, w2 = 0.8μm, Ltp = 215μm.
Fig. 10 Light propagation in the taper when the input is the TE0 modal field (a), and the TM0 modal field (b), respectively. The parameters are: H = 400nm, het = 0.5H, w1 = 1.5μm, w2 = 0.8μm, Ltp = 22.4μm.
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 [7–8, 32–33, 35]. 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) 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 [7–8, 32–33].
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.
Figure 12(a) -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) 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) 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.
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.
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.
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.
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.
In order to show the mode conversion in a tapered SOI double-rib waveguide, the case of het = 0.5H is considered as an example. We use a commercial software (FIMMPROP, Photon Design, UK) [34] to simulate the light propagation in the present structure. Figure 15 shows the mode conversion efficiencies to the TM0 mode and the TE1 mode after the launched TM0 mode propagates along the bi-level taper. Here the side-rib width at the input end of the bi-level taper is chosen as wside1 = 3.0μm (see the inset in Fig. 15).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 (e.g., >300μm). For example, here we choose Ltp = 300μm. Figure 16(a) -16(b) show the simulation results for light propagating along the designed taper when the launched field is chosen as the TE0, and TM0 modal field, respectively. It can be seen that there is a very efficient mode conversion observed between the TM0 mode and the TE1 mode as predicted, while there is no mode conversion when the TE0 modal field is launched. The efficient mode conversion between the TM0 mode and the TE1 mode enables the realization of a polarization splitter-rotator with the assistance of an asymmetrical directional coupler as proposed in Ref [30]. Note that the taper length could be shortened greatly by choosing a smaller side-rib width wside for the input end of the bi-level taper (e.g., wside1 = 1.0μm) since the mode conversion happens at the region very close to the output end of the bi-level taper (see Fig. 16(b)).
Fig. 15 The mode conversion efficiency η as Ltp varies when TM0 modal field is launched. The parameters are wco = 1.0μm, wside = 3.0μm, and het = 0.5H.
Fig. 16 The light propagation in the taper when the input field is TE polarization (a), and TM polarization (b), respectively. The parameters are: H = 400nm, het = 0.5H, wco = 1.0μm, Ltp = 300μm.
In order to give a comparison, we also calculate the mode conversion efficiencies for the cases of wco = 0.85, and 1.2μm, as shown in Fig. 17(a) and Fig. 17 (b), respectively. From these figure, it can be seen that the mode conversion could be eliminated almost by choosing the taper length appropriately when the rib width is chosen as 0.85 or 1.2μm. As an example, Fig. 18(a)-(b) show the simulated light propagating in the taper with wco = 1.2μm when the launched field is the TE0, and TM0 modal fields, respectively. Here the taper length is Ltp = 100μm. It can be seen that there is no mode conversion observed between the TM0 mode and the TE1 mode as predicted. Therefore, one has to be careful when design a bi-level taper for TM polarization. It also indicates that the mode conversion between the TM0 mode and the higher-order TE mode could be cancelled or enhanced by choosing the rib width or etching depth appropriately.
Fig. 17 The mode conversion efficiency η after light propagating the taper section as Ltp varies when the TM0 mode is launched. (a) wco = 0.85μm; (b) wco = 1.2μm. Here het = 0.5H.
Fig. 18 The light propagation in the designed adiabatic taper when the input field is TE polarization (a), TM polarization (b), respectively. The parameters are: H = 400nm, het = 0.5H, wco = 1.2μm, Ltp = 100μm. Here het = 0.5H.
2. Experimental observation
We fabricated some straight waveguides with tapered structures, as shown in Fig. 19(a) , by using a simple fabrication process including UV lithography, and ICP (inductively coupled plasma) etching. The etching depth of the fabricated SOI rib waveguide is hrib = 0.5H, and H = 400nm. The taper structure has a 1μm-wide straight waveguide in the middle while there are tapers at both ends, which have been used often to obtain better coupling to singlemode fibers. All the parameters for the widths of the tapers are: w1 = 1μm, w2 = 1.5μm, and w3 = 3μm, as shown in Fig. 19(a). The taper length Ltp = 100μm. Our simulation in Fig. 5 indicates that the mode conversion in the section tapering from w2 = 3μm to w3 = 1.5μm is not significant since the taper length is not long. Furthermore, since the TE3 mode is going to be cutoff (see Fig. 2(b)), it is reasonable to assume that there is only TM0 mode left in the 1.5μm-wide section after light goes through the taper section at the input end. In contrast, as shown in Fig. 8, the mode conversion between the TM0 mode and the TE1 mode is expected to be quite significant in the second taper from w2 = 1.5μm to w1 = 1μm. Therefore, two-mode interference happens between the TM0 mode and the TE1 mode in the 1μm-wide straight section, which has been observed theoretically (see Fig. 10(a)-10(b)).
Fig. 19 (a) The structure of the lateral taper in our experiments; (b) the measured spectral responses for taper structures when the TM0 modal field is launched; (c) the measured spectral responses for taper structures when the input TE0 modal field is launched; (d) the measured and calculated quasi-FSR. H = 400nm, and het = 0.5H.
Figures 19(b) and 19(c) shows the measured light transmissions of a series of taper structures when the TM0 and TE0 modes are launched respectively. The length L1 of the 1μm-wide straight section in the middle varies from 0 to 1020μm. From these figures, it can be seen that the spectral response is quasi-periodical due to the two-mode interference as expected when the launched field is the TM0 mode. In contrast, there is no quasi-periodical responses when the TE0 modal field is launched, which is also consistent with our prediction.
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
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.
For bi-level tapers, the mode conversion could be removed by choosing a relatively deep rib, e.g., het = 0.6H, as indicated in Fig. 12(d). Figure 20(a) and 20(b) show the measured light transmissions of straight waveguides with bi-level taper structures at the input/output ends when the TM0 and TE0 mode are launched, respectively. Here het = 0.6H. The central-rib width is wco = 1μm. From these figures, it can be seen that the spectral response is quite smooth, which indicates that no mode conversion is observed for the case with a TM0 launched field, as the theoretical calculation predicted. Such a design has been used in a MZI-based PBS successfully in our previous paper [35].
Fig. 20 (a) The measured spectral responses for bi-level taper structures when the TE0 modal field is launched; (b) the measured spectral responses for taper structures when the TM0 modal field is launched; The parameters are: H = 400nm, wco = 1μm, H = 400nm, and het = 0.6H.
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].
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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