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Abstract
The polarizer is a key component for integrated photonics to deal with the strong waveguide birefringence, especially for silicon photonics. A high-performance silicon TE-pass polarizer covering all optical communication bands with low insertion loss (IL) and high polarization extinction ratio (PER) is proposed here. This polarizer is based on anisotropic subwavelength grating (SWG) metamaterials, which maintain the fundamental TE mode as a guided mode but make the fundamental TM mode leaky. Furthermore, based on this working mechanism, the proposed polarizer can work well for any upper cladding material, including air and silicon dioxide (SiO2). The numerical results show that our proposed TE-pass polarizer has a remarkable performance with IL < 0.34 dB over 420 nm (PER > 23.5 dB) or 380 nm (PER > 30 dB) for the air cladding, and IL < 0.3 dB over 420 nm (PER > 25 dB) or 320 nm (PER > 30 dB) for the SiO2 cladding. The fabricated polarizer shows IL < 0.8 dB and PER > 23 dB for the bandwidths of 1.26-1.36 µm and 1.52-1.58 µm (other bandwidths were not measured due to the limited instrument in our research center, but it still covers the most important O-band and C-band).
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In the past two decades, integrated photonics has attracted significant attention due to the possibility of integrating many components on one chip. Among various integrated photonics platforms, silicon-on-insulator (SOI) platform attracts the most attention due to its advantages of high index contrast, compact footprint, and compatibility to the complementary metal oxide semiconductor (CMOS) [1]. Although the high index contrast makes the optical field more confined and the footprint more compact for silicon photonics, it also makes the devices polarization-sensitive. Therefore, the polarization management should be taken to solve this problem [2–7]. As one of the most important devices for the polarization management, the polarizer is used to obtain the specific polarization [8,9], especially the most confined fundamental TE mode (named as TE mode for short). Many TE-pass polarizers with different insertion loss (IL) and polarization extinction ratio (PER) performances have been reported based on different principles [10–13]. In Ref. [14], a TE-pass polarizer was proposed by using an asymmetrical directional coupler (ADC), and its bandwidth of PER > 15 dB is only about 80 nm due to the wavelength sensitivity of the ADC. In Ref. [15], a TE-pass polarizer was demonstrated using a series of adiabatically-bent waveguides, but its bandwidth is also limited to about 100 nm due to the wavelength sensitivity of the loss. In Ref. [16], a high PER TE-pass polarizer using a silicon hybrid plasmonic grating was proposed, and the measured PER is larger than 24 dB over 60-nm bandwidth but the IL is a bit large. In Ref. [17], a high-performance TE-pass polarizer with IL < 0.25 dB and PER > 20 dB over 415-nm bandwidth was proposed. However, this structure is based on a vertically asymmetric waveguide geometry and thus requires a specific upper cladding material. Furthermore, this structure needs a two-step etching process, which would also complicate the fabrication.
Recently, the subwavelength grating (SWG) metamaterial has gained increasing research interests due to its robust freedom for index and dispersion engineering [18–21]. Formed by different refractive index materials periodically alternating with a period much smaller than the optical wavelength, the SWG structure can be treated as an equivalent homogeneous but anisotropic material for the propagating optical field, and consequently offers another dimension to manipulate the optical field. So far, many excellent devices assisted by the SWG metamaterials have been proposed and demonstrated [22–24]. In Ref. [25], a wavelength-independent multimode interference (MMI) coupler maintaining low IL, low power imbalance, and low phase deviation with a bandwidth of 450 nm was proposed theoretically. In Ref. [26], an ultra-broadband and ultra-compact polarization beam splitter (PBS) was shown theoretically and experimentally. Assisted by the SWG metamaterials, it shows IL < 1 dB and ER > 20 dB over 200-nm bandwidth with a footprint of just 12.25×1.9 µm2. There are also some works about polarizers assisted by the SWG metamaterials. In Ref. [27], a low loss TE-pass polarizer was proposed and demonstrated by using the SWG structure to make the fundamental TM mode (named as TM mode for short) cut-off. However, this structure is also based on a vertically asymmetric waveguide geometry, and thus requires a specific upper cladding material. In Ref. [28], an anisotropic metamaterial-assisted TE-pass polarizer with IL <1 dB and PER > 20 dB over 415-nm bandwidth was demonstrated, which was the first TE-pass polarizer covering all optical communication bands.
In this paper, we propose a high-performance silicon TE-pass polarizer covering all optical communication bands with low IL and high PER. This polarizer mainly consists of the middle-SWG (mSWG) and two side-SWGs (sSWGs), which give different refractive indices for the TE mode and TM mode. Therefore, for the TE mode, the refractive index of the mSWG is larger than that of the sSWGs, and consequently makes the TE mode maintain as a guided mode with low loss. As for the TM mode, the refractive index of the mSWG is smaller than that of the sSWGs, and consequently makes the TM mode leaky with high loss. Furthermore, due to the principle of the effective medium theory (EMT), our proposed TE-pass polarizer is suited for any upper cladding material (e.g. air and SiO2) just with minor adjustment of some parameters. The numerical results show that our proposed polarizer has a remarkable performance with IL < 0.34 dB over 420 nm (PER > 23.5 dB) or 380 nm (PER > 30 dB) for the air cladding, and IL < 0.3 dB over 420 nm (PER > 25 dB) or 320 nm (PER > 30 dB) for the SiO2 cladding. The fabricated TE-pass polarizer shows IL < 0.8 dB and PER > 23 dB for the bandwidths of 1.26-1.36 µm and 1.52-1.58 µm, where other bandwidths were not measured due to the limited measurement instruments in our lab but the most important O-band and C-band are covered.
2. Design and principle
Figure 1(a) shows the schematic configuration of the proposed TE-pass polarizer, which is based on the 220-nm-thick SOI platform. This TE-pass polarizer mainly consists of the mSWG and sSWGs. The input and output of the mSWG change gradually to connect with the standard input and output strip waveguides. Besides, the sSWGs with N silicon sub-wavelength waveguides each side change by a step length of lstep to reduce the loss and reflection. Figure 1(b) shows the zoom-in top view and some key parameters of the proposed TE-pass polarizer.
Fig. 1. (a) Schematic configuration of the proposed TE-pass polarizer. (b) Zoom-in top view of the TE-pass polarizer. (c) Relation curves of the equivalent refractive indices and the duty cycle of silicon. (d) Structure with different equivalent refractive indices for the TE mode. (e) Structure with different equivalent refractive indices for the TM mode.
According to Rytov’s formulas, the equivalent refractive indices for the electric field polarization parallel and perpendicular to the periodic interfaces of the SWG can be written as
Figure 1(c) shows the relation curves of the equivalent refractive indices and the duty cycle of silicon based on the Eqs. (1) and (2). For the mSWG with the duty cycle η1, both the TE mode and TM mode have the same refractive index n$\shortparallel$mid. However, for the sSWGs with the duty cycle η2, the TE mode and TM mode would possess different refractive indices of n⊥side and n$\shortparallel$side. Therefore, one interesting phenomenon appears. If we let η2 > η1 (for a certain region), we can find that n⊥side < n$\shortparallel$mid but n$\shortparallel$side > n$\shortparallel$mid would be achieved, which is shown clearly in Fig. 1(c). Figure 1(d) and 1(e) show the structures with different equivalent refractive indices for the TE and TM modes. We can see that the TE mode can still be a guided mode due to n⊥side < n$\shortparallel$mid. However, the TM mode would become leaky with high loss due to n$\shortparallel$side > n$\shortparallel$mid. Consequently, a TE-pass polarizer can be achieved based on this mechanism.
For the proposed TE-pass polarizer, the key performance parameters are the IL of the TE mode and the PER of the TM mode. They are defined as
where, TTE and TTM are the transmissions of the TE mode and TM mode respectively. And the input powers of the TE mode and TM mode are normalized to 1.3. Simulation and analysis
3.1 TE-pass polarizer with the air cladding
According to the principle illustrated in Section 2, we carry out the numerical simulations to investigate the effect of different parameters and the best performance that can be reached. The numerical simulations are based on the three-dimensional finite-difference time-domain (3D FDTD) method using Lumerical commercial software. One should notice that the material dispersion should be considered for the large simulation bandwidth (e.g. 415-nm bandwidth in our work), which can be realized by doing material fit in Material Explorer in Lumerical FDTD solutions. We first simulate the TE-pass polarizer with the air cladding.
Some key parameters are first selected according to the transmission of the optical field or the existing fabrication techniques. The width of the input and output waveguides is chosen as wwg = 0.43 µm to satisfy the single-mode condition over all optical communication bands. The length and end width of the taper are set as ltaper = 4 µm and wend = 100 nm to ensure that the TE mode evolves from the input waveguide to the mSWG (or from the mSWG to the output waveguide) with low loss. The periods of the mSWG and the sSWGs are chosen to be Λ1 = Λ2 = 200 nm, which ensures that the SWGs work in the deep-subwavelength region. The duty cycles of the mSWG and the sSWGs are selected as η1 = 0.4 and η2 = 0.6, which ensures that not only the TE-pass polarizer can work based on the principle illustrated in Section 2 but also the 80-nm minimum feature size can be fabricated with the existing nanometer-scale fabrication techniques. The length of the N-th silicon sub-wavelength waveguide of the sSWGs is fixed at lN = 200 nm. Therefore, the parameters that remained to be optimized are lmid (the length of the mSWG), N (the number of the silicon sub-wavelength waveguides in the sSWGs on each side), and lstep (the step length of the sSWGs).
Then, the effect of different parameters is investigated. Figure 2(a) and 2(b) show the simulated IL and PER of the TE-pass polarizer with the air cladding for different lmid of 0.8 µm, 1.0 µm, and 1.2 µm at N = 23 and lstep = 0.3 µm. A larger lmid would cause a smaller IL but a worse PER, which means that there exists a tradeoff between the IL and PER for lmid. The reason for this tradeoff is that the confinement of the TE mode would become strong but the leaky strength of the TM mode would decrease as lmid increases. Figure 2(c) and 2(d) show the simulated IL and PER of the TE-pass polarizer with the air cladding for different N of 19, 23, and 27 at lmid = 1.0 µm and lstep = 0.3 µm. As N increases, the IL would decrease a bit and the overall PER would also become better. But we also note that there exists some deterioration of the PER at λ ≈ 1.26 µm. Figure 2(e) and 2(f) show the simulated IL and PER of the TE-pass polarizer with the air cladding for different lstep of 0.3 µm, 0.35 µm, and 0.4 µm at lmid = 1.0 µm and N = 23. We can find that the IL would increase as lstep decreases but the overall PER would become better.
Fig. 2. Simulated (a) IL and (b) PER of the TE-pass polarizer with the air cladding for different lmid at N = 23 and lstep = 0.3 µm. Simulated (c) IL and (d) PER of the TE-pass polarizer with the air cladding for different N at lmid = 1.0 µm and lstep = 0.3 µm. Simulated (e) IL and (f) PER of the TE-pass polarizer with the air cladding for different lstep at lmid = 1.0 µm and N = 23.
Considering the tradeoff between the IL of the TE mode and the PER of the TM mode, the three parameters are chosen as lmid = 1.0 µm, N = 23, and lstep = 0.3 µm. Figure 3(a) and 3(b) show the simulated IL and PER of the proposed TE-pass polarizer with the air cladding at these chosen parameters. We can see that the proposed polarizer with the air cladding has a remarkable performance with IL < 0.34 dB and PER > 23.5 dB over 420-nm bandwidth (1.26-1.68 µm), which covers all communication bands. Besides, it has a performance with PER > 30 dB over 380-nm bandwidth (1.26-1.64 µm). Figure 3(c)–3(e) show the propagation of the Ey component of the TE mode at λ = 1.26 µm, λ = 1.55 µm, and λ = 1.68 µm respectively. We can see that the TE mode is tightly confined at the mSWG as a guided mode. The negligible Ey component at the sSWGs and the gradual evolution of the Ey component between the mSWG and the input or output waveguide indicate the low loss of the TE mode. As for the TM mode, it will leak from the mSWG to the sSWGs due to the higher equivalent refractive index of the sSWGs, as shown by Fig. 3(f)–3(h). It seems that the TM mode is not completely diffracted into the free space as shown by Fig. 3(g)–3(h), but the backward scattering and return loss are minor, which is confirmed in our simulation. Table 1 summarizes the key parameters of the proposed TE-pass polarizer with the air cladding.
Fig. 3. Simulated (a) IL and (b) PER of the proposed TE-pass polarizer with the air cladding at lmid = 1.0 µm, N = 23, and lstep = 0.3 µm. Propagation of the Ey component of the TE mode at (c) λ = 1.26 µm, (d) λ = 1.55 µm, and (e) λ = 1.68 µm. Propagation of the Ez component of the TM mode at (f) λ = 1.26 µm, (g) λ = 1.55 µm, and (h) λ = 1.68 µm. (i) is the colorbar of (c) to (h).
Table 1. Key parameters of the proposed TE-pass polarizer with the air cladding.
3.2 TE-pass polarizer with the SiO2 cladding
In Section 3.1, we demonstrate a high-performance TE-pass polarizer with the air cladding. For the same waveguide structure, the TE mode is confined more tightly and the TM mode is confined less tightly with the air cladding compared to other upper cladding materials with higher refractive indices. Therefore, a high-performance TE-pass polarizer usually can be achieved more easily with the air cladding, as shown in Ref. [17] and Ref. [28]. However, the actual upper cladding (not the air cladding) is more desired to protect the optical circuit and pattern the electrode. Based on the principle illustrated in Section 2, our proposed TE-pass polarizer is insensitive to the upper cladding material, which means that it can work well at different upper cladding materials just with minor adjustments of some parameters. Here we take the SiO2 cladding as an example to further illustrate the advantage of our proposed TE-pass polarizer. One should note that the upper cladding material can also be changed to other materials, such as SU8 and PMMA. The effect of the three parameters lmid, N, and lstep is similar to what is illustrated in Section 3.1. Therefore, we will not repeat it here.
Considering the tradeoff between the IL of the TE mode and the PER of the TM mode, the three parameters are chosen as lmid = 0.9 µm, N = 26, and lstep = 0.3 µm. Figure 4(a) and 4(b) show the simulated IL and PER of the proposed TE-pass polarizer with the SiO2 cladding at these chosen parameters. We can see that the proposed polarizer with the SiO2 cladding also has a remarkable performance with IL < 0.3 dB and PER > 25 dB over 420-nm bandwidth (1.26-1.68 µm), which also covers all communication bands. Besides, it has a performance with PER > 30 dB over 320-nm bandwidth (1.26-1.58 µm). To the best of our knowledge, this is the first TE-pass polarizer covering all communication bands with such high performance with an actual upper cladding material (not the air cladding). Figure 4(c)–4(e) show the propagation of the Ey component of the TE mode at λ = 1.26 µm, λ = 1.55 µm, and λ = 1.68 µm respectively, which is similar to Fig. 3(c)–3(e). We can find that the TE mode is less confined with the SiO2 cladding compared to the air cladding but still possesses very low loss. As for the TM mode, shown by Fig. 4(f)–4(h) and similar to Fig. 3(f)–3(h), it will leak from the mSWG to the sSWGs due to the higher equivalent refractive index of the sSWGs. Table 2 summarizes the key parameters of the proposed TE-pass polarizer with the SiO2 cladding. Comparing Table 1 with Table 2, we can find that the adjustment of the parameters is minor.
Fig. 4. Simulated (a) IL and (b) PER of the proposed TE-pass polarizer with the SiO2 cladding at lmid = 0.9 µm, N = 26, and lstep = 0.3 µm. Propagation of the Ey component of the TE mode at (c) λ = 1.26 µm, (d) λ = 1.55 µm, and (e) λ = 1.68 µm. Propagation of the Ez component of the TM mode at (f) λ = 1.26 µm, (g) λ = 1.55 µm, and (h) λ = 1.68 µm. (i) is the colorbar of (c) to (h).
Table 2. Key parameters of the proposed TE-pass polarizer with the SiO2 cladding.
3.3 Tolerance analysis
Due to the limitation of the actual fabrication, there is always a deviation between the fabricated device and the simulated one. Therefore, tolerance of the designed devices is always a key parameter. Here, we take the tolerance analysis of the proposed TE-pass polarizer with the air cladding as an example. The proposed TE-pass polarizers with other upper cladding materials have a similar trend.
We first assume that the width or thickness of all waveguides changes by Δw or Δh considering the width deviation caused by the fabrication and the thickness deviation of the commercial SOI wafers. Figure 5(a) and 5(b) show the simulated IL and PER of the proposed TE-pass polarizer with the air cladding when Δw are −10 nm, 0 nm, and +10 nm. We can find that the IL shows a bit large when the Δw is −10 nm. And the PER would become better at the shorter wavelength but deteriorate at long wavelength. When the Δw is +10 nm, the IL decreases with IL < 0.2 dB over the total simulation bandwidth. And the PER has some deterioration at the short wavelength but it can still maintain PER > 20 dB over the total simulation bandwidth. Figure 5(c) and 5(d) show the IL and PER of the proposed TE-pass polarizer with the air cladding when Δh are −10 nm, 0 nm, and +10 nm. The effect of Δh is similar to the effect induced by Δw. When Δh is −10 nm, the IL increases a bit and the PER deteriorates at long wavelength. When Δh is +10 nm, there is almost no change of the IL and just some deterioration of the PER at long wavelength compared to the best results (Δh is 0 nm).
Fig. 5. Simulated (a) IL and (b) PER of the proposed TE-pass polarizer with the air cladding when Δw are −10 nm, 0 nm, and +10 nm. Simulated (c) IL and (d) PER of the proposed TE-pass polarizer with the air cladding when Δh are −10 nm, 0 nm, and +10 nm. Simulated (e) IL and (f) PER of the proposed TE-pass polarizer with the air cladding when θ are 90°, 87.5°, and 85°.
Then, we also analyze the effect from the normally existing side-wall tilt angle of the waveguides (expressed as θ) caused by the actual etching process. Figure 5(e) and 5(f) show the IL and PER of the proposed TE-pass polarizer with the air cladding when θ are 90°, 87.5°, and 85°. We can find that the IL decreases a bit and the PER becomes better at long wavelength when θ decreases from 90°. Compared to θ=90°, although the PER for the most simulation bandwidth suffers some deterioration, ER > 20 dB can be guaranteed for the whole simulation bandwidth when θ is 87.5° or 85°.
4. Fabrication and characterization
The proposed TE-pass polarizer with the air cladding was fabricated on the 220-nm SOI platform with 3-µm SiO2 buffer layer. The pattern was first defined through an electron beam lithography (EBL, Raith 150 II) process with the MA-N 2401 photoresist and then was transferred to the silicon top layer by a fully etching process with the inductively coupled plasma (ICP). Another overlay exposure with the PMMA photoresist was performed to fabricate grating couplers at the input and output port for chip-fiber coupling and polarization selectivity.
Figure 6(a) shows the system diagram of the experimental measurement. The light from the sources would couple to the device under test (DUT) via the input grating coupler. The output light of the DUT would be collected by another fiber via the output grating coupler and then is sent to the optical spectrum analyzer (OSA). Limited by the bandwidth of the sources and the detection limit of the OSA, we just test the bandwidths of 1.26-1.36 µm and 1.52-1.58µm, which cover the most important O-band and C-band for the optical communication. Figure 6(b) shows the scanning electron microscope (SEM) image of the fabricated polarizer and Fig. 6(c) is its zoom-in view. Figure 6(d) and 6(e) show the measured IL and PER of the fabricated TE-pass polarizer with the air cladding for the bandwidth of 1.26-1.36 µm. Compared to the simulated results, the measured IL increases and the measured PER decreases, but it still maintains IL < 0.8 dB and PER > 23 dB. The deterioration of the performance is mostly due to the imperfect fabrication, including the change of the waveguide width and the side-wall tilt angle of the waveguide (about 85° in our lab). Besides, the PER at the edge of the bandwidth is limited by the detection limit of the OSA, which also would cause some deterioration. Figure 6(f) and 6(g) show the measured IL and PER of the fabricated TE-pass polarizer with the air cladding for the bandwidth of 1.52-1.58 µm. The measured IL and PER also show some deterioration compared to the simulated results, but it still maintains IL < 0.71 dB and PER > 23 dB. Different from the measured PER shown in Fig. 6(e), the deterioration of the PER in Fig. 6(g) is mainly caused by the detection limit of the OSA, which manifests as the decreasing PER with the wavelength away from the center wavelength (λ = 1.55 µm). One should know that the measured ILs in Fig. 6(d) and 6(f) are the averaged results of cascaded ten identical devices, which can reduce the effect of perturbation from the experimental set-ups and make the measurement more reliable.
Fig. 6. (a) System diagram of the experimental measurement. SLD, superluminescent diode; ASE, amplified spontaneous emission; PC, polarization controller; DUT, device under test; OSA, optical spectrum analyzer. (b) SEM image of the fabricated TE-pass polarizer with the air cladding. (c) is the zoom-in view of (b). Measured (d) IL and (e) PER of the fabricated polarizer for the bandwidth of 1.26-1.36 µm. Measured (f) IL and (g) PER of the fabricated polarizer for the bandwidth of 1.52-1.58 µm.
5. Summary
In summary, we have proposed a high-performance silicon TE-pass polarizer covering all optical communication bands with low IL and high PER. This polarizer mainly consists of the mSWG and sSWGs, and thus makes the TE mode maintain as a guided mode with low loss and makes the TM mode leaky with high loss. Furthermore, due to the principle of the EMT, our proposed TE-pass polarizer can work for different upper cladding materials simply after making minor adjustments of some parameters. The numerical results have shown that our proposed polarizer has a remarkable performance with IL < 0.34 dB over 420 nm (PER > 23.5 dB) or 380 nm (PER > 30 dB) for the air cladding, and IL < 0.3 dB over 420 nm (PER > 25 dB) or 320 nm (PER > 30 dB) for the SiO2 cladding. The results of a fabricated TE-pass polarizer with the air cladding have demonstrated an excellent performance of IL < 0.8 dB and PER > 23 dB for the bandwidths of 1.26-1.36 µm and 1.52-1.58 µm, where the limited measurement bandwidth is due to the limited instrument in our research center but it still covers the most important O-band and C-band.
Table 3 gives the performance comparison of several TE-pass polarizers. We can find that our proposed TE-pass polarizer possesses an excellent performance and a very compact footprint. Furthermore, to the best of our knowledge, our proposed TE-pass polarizer is the first TE-pass polarizer that works for all communication bands (with such excellent performance) for any actual upper cladding material (not just the air cladding), which is useful for the actual applications. We believe that our proposed TE-pass polarizer would play an important role in some application areas, including the optical communication and optical sensing.
Table 3. Performance comparison of several TE-pass polarizers.a
Funding
Ningbo Science and Technology Project (2021Z030); Fundamental Research Funds for the Central Universities (2020Z07); Special Development Fund of Shanghai Zhangjiang Science City; National Natural Science Foundation of China (11621101); National Key Research and Development Program of China (No. 2018YFB2200200).
Disclosures
The authors declare that there are no conflicts of interest related to this work.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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