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Abstract
A high-performance integrated silicon TE-pass polarizer is proposed and demonstrated. The polarizer uses a series of adiabatic waveguide bends that yield high extinction ratio for the TM polarization and low insertion loss for the TE polarization, and does not require special materials or complex fabrication steps. The polarizer, implemented on a silicon-on-insulator platform with a 220 nm silicon thickness, is measured to have insertion loss ≤ 0.37 dB (average 0.12 dB) and extinction ratio ≥ 27.6 dB (average 36.0 dB) over a 1.5 μm to 1.6 μm wavelength range, with a footprint of 63 μm × 9.5 μm. The trade-off between the footprint of the polarizer and its performance is established. While the analysis was done for a silicon-on-insulator platform, the concept is applicable to other waveguide geometries and integrated photonic platforms.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Silicon photonics has emerged as a promising technology to integrate compact optical circuits on a silicon chip, driven by applications in low-energy high-bandwidth interconnects and by its compatibility with complementary metal-oxide semiconductor (CMOS) processes [1]. The large refractive index contrast enables strong confinement of light in a submicron silicon waveguide, and allows sharp bends with negligible loss. In most planar waveguide cross-sections, the (quasi-) transverse electric (TE) and transverse magnetic (TM) modes have different mode profiles, confinement factors, and effective and group indices. For this reason, silicon photonic devices are normally optimized and designed to operate with one of the two polarizations (usually the TE polarization). Any unwanted fraction of the cross polarization may lead to performance degradation, and should ideally be blocked [2].
The undesired polarization can be introduced into the silicon chip from an optical fiber where the polarization is not well controlled. This is usually not a problem when fiber-to-chip grating couplers are used, since the gratings themselves act as polarizers. However, fiber-to-chip edge couplers based on inverse tapers are almost polarization-independent, and will couple any polarization state present in the fiber into the silicon waveguide. The undesired polarization can also result from an imperfect operation of other on-chip components, such as polarization splitters and rotators used in polarization diversity schemes [3–7]. In both cases, on-chip polarizers can be used to remove any unwanted polarization components, eliminating polarization crosstalk.
Several types of silicon-based polarizers have been proposed in the literature, including photonic crystals [8] and plasmonic-based structures [9–12]. Polarizers based on photonic crystals usually transmit the selected polarization state with relatively high insertion loss, and their fabrication is challenging. Plasmonic-based polarizers can achieve high extinction ratios in small footprints, but they require specific metals and the insertion loss is still significant. Polarizers exploiting different waveguide cross-sections have also been developed [13–17]. In [13], a TE-pass polarizer is designed using a shallowly etched ridge waveguide, which uses the TM mode lateral leakage to increase the polarization-dependent loss. However, this design results in a long device (1 mm). In [14], both TE- and TM-pass polarizers are designed using polarization-dependent resonant tunneling into a silicon layer placed within the silica substrate. Alternatively, polarizers can be designed by engineering the waveguides to have different cut-off conditions for the two polarization states; this has been shown in symmetric shallowly etched waveguides (TE- and TM-pass) [15], in narrow waveguide sections sandwiched between two tapered waveguides (TM-pass) [16], and in sub-wavelength grating waveguides (TM-pass) [17] (where a compact polarizer, shorter than 10 μm, with extinction ratio above 26 dB has been demonstrated). In addition to the standalone devices, any polarization splitter can also operate as a polarizer if only one of the split components is utilized. However, the extinction ratio of these devices is usually not optimized.
In this work, we demonstrate a TE-pass polarizer based on cascaded adiabatic bends, where the TM mode radiates out of the waveguide while the TE mode propagates with low loss. The polarizer design closest to the one proposed in this work was realized in an ultra-low loss Si3N4 platform, with constant-radius waveguide bends [18,19]. TE-pass polarizers were created either as single or multiple mm-scale radii S-bends, resulting in cm-scale long devices, or as a 1 m-long waveguide spiral. All these designs lead to an ultra-high TM loss, but at an expense of a significant TE loss. We recently used this concept to create on-chip silicon photonic polarizers [20], and further extended it by utilizing adiabatic waveguide bends in order to reduce the insertion loss and reduce the size of the device [21]. Here, we present numerical and experimental analysis of the proposed polarizer, and show that a high extinction ratio and a low insertion loss can be achieved in a device with a small footprint, which can be fabricated with standard CMOS processes available in current silicon photonics foundries. We start by giving a qualitative description of the proposed polarizer in Sec. 2. The polarizer design optimization and discussion of the trade-offs between footprint and performance are given in Sec. 3. Measurement results are presented and analyzed in Sec. 4, and the results are summarized in Sec. 5.
2. Principle of operation
The integrated polarizer design studied in this work is based on the idea that the radiation loss in bent waveguides can differ significantly for the TE and TM modes if the waveguide height and width are different. In this work, we consider a common choice for the silicon waveguide geometry, where the silicon core is 220 nm high and 500 nm wide. The field profiles (at a wavelength of 1550 nm) of the fundamental TE and TM modes of such a waveguide geometry are illustrated in Figs. 1(a) and 1(b) for a 1 μm bend radius, indicating a much higher degree of confinement for the TE mode. Snapshots of TE- and TM-polarized pulses propagating through a 90° bend with a 1 μm bend radius, obtained through 3D finite-difference time-domain (FDTD) simulations, are shown in Figs. 1(c) and 1(d), pointing to significantly larger radiation losses for the TM-polarized light. The design concept behind the proposed polarizer is to exploit the difference between the TM and TE bend losses, selecting a bend radius such that the loss for the TM mode is substantial while the loss for the TE mode is low.
Fig. 1 Bend-induced radiation losses in a 500 nm × 220 nm silicon waveguide with a 1 μm bend radius, for a wavelength of 1550 nm: (a,b) magnitude squared of the electric fields (|E|2) of the fundamental TE and TM modes; (c,d) temporal snapshots of |E|2 (top view) obtained with 3D FDTD simulations for TE- and TM-polarized pulses passing through a 90° bend.
A high-performance on-chip polarizer must have the following characteristics: (1) high extinction (in the case of a TE-pass polarizer, high loss for the TM polarization relative to TE); (2) low insertion loss (i.e. low loss for TE polarization); and (3) a small on-chip footprint. This section discusses how to create a high-performance on-chip polarizer starting from the basic idea of a bend with radiation loss higher for the TM mode than for the TE mode.
While a single bend with a properly selected radius can function as a simple TE-pass polarizer, it is not enough to achieve both high (> 30 dB) extinction ratio and low (≪ 1 dB) insertion loss. In the next sections, we show that by concatenating multiple bends, as illustrated in Fig. 2, one can achieve a high TM mode loss without excessive loss for the TE polarization. A similar concept has been explored before in low-confinement Si3N4 waveguides, but using bends with constant radius [18]. However, the design with constant radius bends [Fig. 2(a)] suffers from high insertion loss for the TE mode due to scattering at the junctions, where the curvature of the waveguide section changes its sign. This scattering is a well-known phenomenon which is explained by the mode discontinuity at these junctions. Specifically, as can be seen in Fig. 1(a), the mode of a bent waveguide is not symmetric with respect to the center of the waveguide, but is shifted towards the outer sidewall. At the junction where the curvature changes its sign, the modes are shifted towards opposite sidewalls, which leads to scattering loss due to the mode discontinuity. These losses can, in fact, exceed radiation losses, leading to an increased TE mode insertion loss.
Fig. 2 Layouts of integrated TE-pass polarizers considered in this work: (a) polarizer composed of bends with constant radius, with |R| = 2 μm and N = 8; (b,c) polarizers proposed in this work which use adiabatic (clothoid-shaped) bends, where the waveguide curvature changes linearly with the waveguide length. In (b), Rmin = 1 μm, θ = 75°, and N = 7, and in (c), Rmin = 1 μm, θ = 105°, and N = 6.
The loss at the junctions can be reduced by introducing a transversal offset between the two bends in order to improve the mode overlap [22, 23]. Alternatively, at the junctions where the waveguide curvature changes abruptly, one can use adiabatic transitions with the curvature (the inverse of the bend radius) changing gradually. Such adiabatic bends have previously been implemented as cosine bends [24], spline bends [25], and clothoid bends (also known as Euler spirals) [26–30]. In this work we use clothoid adiabatic bends, where the waveguide curvature changes linearly with the waveguide length.
By replacing the constant-radius bends of Fig. 2(a) with clothoid bends, we arrive at the polarizer design proposed in this work, which is illustrated in Figs. 2(b) and 2(c). In this polarizer, the waveguide curvature starts at 0 at the input and changes in a piecewise linear fashion back and forth between −1/Rmin and 1/Rmin, going back to 0 at the output of the polarizer. The angle of the waveguide with respect to its initial direction changes between θ and −θ, with the angles θ and −θ corresponding to the zero curvature points in the bends. The number of times the waveguide bends up and down is referred to as the number of bends N. As shown in the following section, by optimizing the radius Rmin, the angle θ, and the number of bends N, one can make a high-performance on-chip polarizer with high loss for the TM mode and low loss for the TE mode.
3. Polarizer design optimization
This section analyzes the performance of the proposed adiabatic bend polarizer [Figs. 2(b) and 2(c)], as a function of its parameters – the minimum radius of curvature Rmin, the angle θ, and the number of bends N. The purpose of this analysis is to understand the design trade-offs inherent to the proposed polarizer, and arrive at high-performance designs compatible with common silicon photonics platforms.
Before considering polarizers with an arbitrary number of bends N, let us look into the properties of a single-bend polarizer (N = 1), which is the building block of the multi-bend polarizers. Figure 3 plots the performance metrics of a single-bend polarizer (N = 1) as a function of the minimum bend radius Rmin, for different angles θ. Note that the values of the bend radii correspond to the radii of the center of the waveguides. In this work, the simulations were carried out using the 3D finite-difference time-domain method, with a 500 nm × 220 nm silicon waveguide core surrounded by silicon dioxide, and a center wavelength of 1550 nm. The propagation loss in silicon waveguides, which is typically 1.5 dB/cm to 2.5 dB/cm, was not included into the analysis due to the small length of the polarizer.
Fig. 3 Performance of single-bend polarizers (N = 1): (a) TE mode loss (dB), (b) TM mode loss (dB), and (c) ratio of these losses [Eq. (1)], for different adiabatic bend polarizers (solid lines) and a constant-radius polarizer (dashed lines). The x-axis shows the minimum bend radius Rmin in the case of the adiabatic bend polarizers (solid lines), and the bend radius R for the constant-radius polarizer (dashed lines). The losses are calculated with the 3D FDTD method, at λ = 1550 nm.
Figure 3(b) indicates that, as the bend radius decreases, the loss for the TM mode increases, which is desirable for a high-performance TE-pass polarizer. However, the undesirable loss for the TE mode (i.e. the insertion loss) also increases, as seen in Fig. 3(a). This suggests that, by changing the bend radius, one can trade-off extinction ratio for insertion loss. To analyze this trade-off in more detail, we use a “Loss Ratio” figure of merit defined as
where “TM loss (dB)” and “TE loss (dB)” are the losses for the TM- and TE-polarized light, respectively, in dB. A high loss ratio is preferable, since it suggests that the desired loss for the TM mode is much higher than the undesired loss for the TE mode. Figure 3(c) plots the loss ratio for a single-bend polarizer, suggesting that the loss ratio greatly increases for larger bend radii. However, the improved loss ratio is accompanied by low TM loss and poor extinction ratio in a single-bend polarizer. To achieve high extinction, multiple bends can be concatenated together. For example, a single-bend polarizer with Rmin = 2.5 μm and θ = 105° has an excellent loss ratio of around 700, but a low TM extinction ratio of only 2 dB. To reach 30 dB extinction, we need to concatenate approximately 15 bends. This points us to the fundamental trade-off between the performance of the polarizer and its footprint: increasing Rmin and using more bends improves the performance, but leads to a larger device. If a smaller footprint is desirable, we can use bends with smaller Rmin, which have higher loss for the TM mode, so that fewer bends are required to achieve a given extinction level. However, the TE loss will not be as low, due to the lower TM-to-TE loss ratio [Fig. 3(c)]. As a result, the choice of Rmin of the polarizer is dependent on which characteristic is favored: low insertion loss or small device footprint.Figure 3 also compares the performance of adiabatic bend polarizers for different angles θ, suggesting that designs with larger θ offer better performance; this comes at the cost of an increased width (transversal dimension) of the polarizer [compare Figs. 2(b) and 2(c)]. However, while the width increases, the length (longitudinal dimension) goes down because the same extinction ratio can be achieved with fewer bends. For example, the number of bends in polarizers with Rmin = 1.5 μm can be reduced from 20 to 9 when θ increases from 30° to 105°. Moreover, as θ increases past 90°, the length of each bend starts decreasing [compare Figs. 2(c) and 2(b)]. For these reasons, designs with large angles θ are preferred. There is, however, an upper limit for the angle θ: as θ increases, the distance between the upward and downward waveguides shrinks and can lead to coupling between them, which needs to be avoided. For this reason, the maximum angle θ considered in this work is 105°.
Finally, Fig. 3 also compares the performance of adiabatic bend polarizers (solid lines) and a polarizer with constant bend radius (dashed lines). The constant-radius polarizer performs worse than the adiabatic bend polarizers because its loss ratio is lower by 1–2 orders of magnitude compared to the adiabatic polarizers, particularly for Rmin > 1.5 μm. As a result, for the same performance, a constant-radius polarizer will have a much higher footprint than an adiabatic bend polarizer (or, for the same footprint, the adiabatic bend polarizer will perform much better).
Having analyzed the transmission through a single bend, we now turn our attention to multi-bend polarizers. Figure 4 plots the transmission for the TE polarization (which is the negative of the insertion loss) and the extinction ratio for polarizers with radii Rmin = 1 μm, 1.3 μm and 1.5 μm, with the number of bends N shown as the curve parameter. The angle θ is 105° for all polarizers, as discussed above. To arrive at specific usable designs, we require the polarizer extinction ratio to be at least 30 dB over the whole 1.5 μm to 1.6 μm wavelength range. To achieve such extinction, N = 8, 8, and 10 bends are selected for Rmin = 1, 1.3 and 1.5 μm, respectively. In this work, these three designs are referred to as designs “A”, “B”, and “C”. The parameters and performance of these designs are summarized in the “Summary and conclusions” section, and the coordinates of the polygons defining these designs can be found in Design Files 1–3 (from [31–33], respectively). As expected, increasing Rmin helps to significantly reduce the insertion loss, with the peak loss going from 2.24 dB for design A with Rmin = 1 μm, down to 0.24 dB for design C with Rmin = 1.5 μm. On the other hand, the device footprint increases from 34 μm × 6.5 μm for design A, to 44 μm × 8.2 μm for design B, and 63 μm × 9.5 μm for design C. Note that the polarizer widths given above are the distances between the outermost sidewalls of the waveguide bends. In a practical layout, no other structures can be placed within 0.5 μm to 1 μm of the bends, which will slightly increase the effective footprint of the device. For example, the effective width for design A will be 8.5 μm if 1 μm keep-out regions are added on each side of the 6.5 μm-wide bends.
Fig. 4 TE transmission (insertion loss) and extinction ratio of adiabatic bend polarizers with (a) Rmin = 1 μm, (b) 1.3 μm, and (c) 1.5 μm, as a function of the wavelength, calculated with the 3D FDTD method. The number of bends N is shown as the curve parameter. The angle θ is 105° for all designs.
The alternative design, where the radius of the bends is constant [Fig. 2(a)], does not perform nearly as well as the design with adiabatic bends. This is illustrated in Fig. 5, which plots the extinction ratio and insertion loss of a constant-radius polarizer with |R| = 2 μm and 3 μm, for a varying number of bends N. To achieve 30 dB extinction with |R| = 2 μm, N = 8 bends are required, with the associated insertion loss being as high as 2 dB. The insertion loss can be reduced by using |R| = 3 μm; with N = 10 bends (and a 130 μm × 7 μm footprint), one can achieve 30 dB extinction with about 1.2 dB insertion loss. However, this performance is achieved only in the 1.53 μm to 1.6 μm spectral region, with an abrupt drop in extinction ratio for wavelengths below 1.53 μm. To achieve high extinction below 1.53 μm, we would need to increase N further, which would lead to even higher values for the insertion loss and the footprint. This confirms that the polarizer design based on adiabatic bends is superior to the design based on bends with constant radius.
Fig. 5 TE transmission (insertion loss) and extinction ratio of constant-radius polarizers with (a) |R| = 2 μm and (b) |R| = 3 μm, as a function of the wavelength. The number of bends N is shown as the curve parameter.
4. Experimental results
Several versions of the proposed TE-pass polarizers were fabricated at the Institute of Microelectronics (Singapore), on a silicon-on-insulator platform with a 220 nm-thick silicon layer and a 2 μm-thick buffered oxide layer. The structures were patterned using 248 nm optical lithography, and covered with a 2 μm-thick oxide overcladding layer. Optical images of the fabricated designs A and C are shown in Figs. 6(a) and 6(b), respectively.
A tunable laser (1.5 μm to 1.6 μm) was used as the light source, and an electronic polarization controller was used to switch between the TE and TM polarizations. Light was edge coupled from a standard tapered lensed fiber into the silicon chip, through input and output inverse taper-based spot size converters to improve the coupling efficiency. The transmitted light was collected with a second lensed fiber and its power was measured using an InGaAs photodetector. To get a reliable measurement of the insertion loss, test structures with 20 cascaded polarizers were used, which significantly reduced the impact of measurement errors caused by fiber misalignment and instability of the measurement setup. The transmission through the 20 cascaded polarizers was compared to the transmission through a reference straight waveguide without polarizers, in order to subtract the input/output coupling insertion loss; the latter was obtained by averaging the measured transmission of 4 identical straight waveguides located in different parts of the chip. Figures 7 and 8 show the measured and simulated transmission spectra for the TE and TM polarizations of adiabatic bend polarizers with Rmin = 1 μm and 1.5 μm, respectively. In Fig. 7, N = 8 and the angle θ is 30°, 45°, 90° and 105°, while in Fig. 8, N = 10 and θ = 105°. The results from designs A and C described in the previous section correspond to Figs. 7(d) and 8, respectively; design B was not implemented. The peak and average values of the measured and simulated transmission curves of all the fabricated devices are summarized in Table 1.
Fig. 7 Measured and simulated transmission spectra of TE and TM polarized light for Rmin = 1 μm, N = 8 turns, and angles θ of (a) 30°, (b) 45°, (c) 90°, and (d) 105° (design A).
Fig. 8 Measured and simulated transmission spectra of TE and TM polarized light for Rmin = 1.5 μm, N = 10 and θ = 105° (design C).
Table 1. Summary of the performance of all fabricated devices, with minimum, maximum and average values of TE and TM losses given over the 1.5 μm to 1.6 μm wavelength range.
The bottom plots in Fig. 7 and the right plot in Fig. 8 show a detailed view of the TE transmission for each configuration, and are needed to evaluate the insertion loss of the polarizers. From these, we see that the measured and simulated insertion loss curves match quite well, with about 12 nm spectral shift between them. This shift is likely attributed to a dimensional deviation between the fabricated and designed waveguide widths. This is confirmed with FDTD simulations, where different waveguide widths return similar but shifted spectral responses for the TE transmission. For the extinction ratio, while the measured and simulated profiles have different spectral features, the measured peak and average extinction ratios agree well with the designed values (∼30 dB), as can be seen from Table 1. The only exception is design C (Fig. 8), for which the average measured extinction ratio is lower than simulated by almost 5 dB, but is still well above 30 dB. This is an indication that high extinction, low-loss TE-pass polarizers have been successfully implemented.
5. Summary and conclusions
A high-performance integrated TE-pass polarizer was proposed and experimentally demonstrated on a silicon-on-insulator platform. The polarizer consists of a series of adiabatic waveguide bends, with its parameters carefully chosen to return a high loss for the TM mode and a low insertion loss for the TE mode. It is shown that the performance of such design is superior to the one of a design which uses a series of constant-radius bends, since the adiabatic design eliminates the scattering at the junctions where the waveguide curvature changes its sign, greatly reducing losses for the TE polarization.
A trade-off between the footprint of the polarizer and its performance has been established. It is shown that a better performance (lower insertion loss for a given extinction ratio) can be achieved by using more bends with larger bend radii. Conversely, the footprint of the polarizer can be reduced at an expense of an increased insertion loss. Three polarizer designs, referred to as designs “A”, “B” and “C”, with different performance-footprint trade-offs have been selected. The parameters and performance of these polarizers are summarized in Fig. 9 and Table 2, with the highest-performing design C experimentally showing below 0.37 dB insertion loss (average 0.12 dB), and over 27.6 dB extinction ratio (average 36.0 dB), in the 1.5 μm to 1.6 μm wavelength range. For direct and quick implementation on a 220 nm-thick silicon-on-insulator platform, the coordinates of the polygons corresponding to these designs can be found in Design Files 1–3 (and can be easily imported into a GDSII file for patterning). These coordinates are plotted in Fig. 10.
Fig. 9 Measured and simulated transmission spectra of the fundamental TE and TM modes for polarizer designs A, B and C, as defined in Sec. 3 and Table 2. No experimental data is available for design B, which was not fabricated.
Table 2. Summary of the design parameters and performance characteristics of polarizer designs A, B and C, as defined in Sec. 3, over the 1.5 μm to 1.6 μm wavelength range. Design B was not fabricated, so no experimental data is available.
The proposed polarizer design has important advantages, such as its simplicity of fabrication and compatibility with various waveguide platforms. The polarizers are defined in the same etch step used to form the waveguides, requiring no specialized fabrication, small feature sizes, or partial silicon etch. While in this work the polarizers were implemented in a silicon-on-insulator platform with a 220 nm-thick silicon device layer, the same approach can be used to design high-performance polarizers for other waveguide platforms, such as SiN or InP.
Funding
Mubadala Development Company (Abu Dhabi), Economic Development Board (Singapore) and GlobalFoundries (Singapore), under the framework of the ``Twinlab'' project with A*STAR IME (Singapore).
Acknowledgments
This work was partially funded by Mubadala Development Company (Abu Dhabi), Economic Development Board (Singapore) and GlobalFoundries (Singapore), under the framework of the “Twinlab” project with A*STAR IME (Singapore). The authors acknowledge Dr. Sergio Sanchez Martinez from the Khalifa University Research Computing team for his support with the use of the high-performance computing facilities.
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