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Abstract
We propose and experimentally demonstrate a novel ultracompact silicon polarization rotator based on equivalent asymmetric waveguide cross section in only single-step etching procedure for densely integrated on-chip mode-division multiplexing system. In the conventional mode hybridization scheme, the asymmetric waveguide cross section is employed to excite the hybridized modes to realize high performance polarization rotator with compact footprint and high polarization extinction ratio. However, the fabrication complexity severely restricts the potential application of asymmetric waveguide cross section. We use inverse-designed photonic-crystal-like subwavelength structure to realize an equivalent asymmetric waveguide cross section, which can be fabricated in only single-step etching process. Besides, a theory-assisted inverse design method based on a manually-set initial pattern is employed to optimize the device to improve design efficiency and device perform. The fabricated device exhibited high performance with a compact footprint of only 1.2 × 7.2 µm2, high extinction ratio (> 19 dB) and low insertion loss (< 0.7 dB) from 1530 to 1590 nm.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over the past decades, mode-division multiplexing (MDM) on a silicon-on-insulator (SOI) platform has drawn tremendous attention for enhancing the transmission capacity of an on-chip optical interconnect, as a more attractive and promising solution [1]. To realize an on-chip MDM system, various multimode silicon photonic devices have been investigated, including mode (de)multiplexers ((De) MUX) [2–6], mode bent waveguides [7–9] and mode waveguide crossings [10–12]. All these silicon photonic devices are usually strongly polarization-sensitive due to the large birefringence of SOI waveguide. The polarization diversity circuit, as the potential effective approach, is employed to handle the polarization dependence by polarization splitter–rotator or polarization rotator [13]. However, the high performance and compact polarization rotator, as an essential component for flexibly manipulating mode polarization in densely integrated polarization diversity circuit, is still an urgent problem to overcome. Various polarization rotation schemes have been widely investigated, such as mode coupling, mode evolution and mode hybridization. For mode coupling schemes, the fundamental transverse electric mode (TE0) is first converted to high order mode and then transformed to the orthogonal polarization fundamental transverse magnetic mode (TM0) due to the same mode effective refractive indices [14,15]. In the mode evolution scheme, specially designed tapers with large scale and different thicknesses are introduced to enable gradual mode conversion between orthogonal polarization states for satisfying adiabatic evolution [16,17]. Therefore, both schemes suffer from large device scale and design complexity, which are not suitable in a densely integrated MDM system. In mode hybridization schemes, the asymmetric waveguide cross section is introduced to excited two hybridized modes and transfer optical power periodically between two orthogonal polarization states [18–20], which usually exhibit high performance with compact footprints. However, two or more step-etching processes are usually inevitable to fabricate the asymmetric waveguide cross section. The fabrication complexity severely restricts the potential application of the asymmetric waveguide cross section.
In this work, we propose a novel ultracompact polarization rotator based on the photonic-crystal-like (PhC-like) subwavelength structures in the asymmetric waveguide cross section, optimize it using the theory-assisted inverse design method and fabricate in only single-step etching procedure. By making full use of the lag effect, the PhC-like subwavelength (SW) structure could be fabricated in one single-step etching procedure and also be CMOS-compatible [21]. As a result, to release the fabrication complexity and improve the fabrication robustness greatly, we use the PhC-like SW structure to realize an equivalent asymmetric waveguide cross section. The equivalent asymmetric waveguide is employed to excite the two hybridized modes to realize polarization rotation. Besides, benefitting from the capability of flexible refractive index engineering at the nanoscale, inverse design methods offer an effective route to optimize and design nanophotonic devices, which enable us to realize ultracompact and multifunctional devices simultaneously [22–26]. Here, the inverse design method using a manually-set initial pattern is employed to optimize the device to improve design efficiency and device performance. Our simulation results show that the performance of the optimized device based on manually-set initial pattern is significantly improved compared with ones based on random initial patterns. The optimized device was fabricated and experimentally demonstrated in only single-step etching procedure. The fabricated device occupied an ultracompact footprint of only 1.2 × 7.2 µm2. The measured insertion loss was less than 0.7 dB and polarization extinction ratio was larger than 19 dB over the observable 60 nm wavelength range.
2. Operation principle and simulation results
The schematic of the polarization rotator based on the equivalent asymmetric waveguide cross section is shown in Fig. 1(a). The device is designed on a SOI wafer with a 220 nm-thick top silicon layer. The proposed device was composed of three sections, including the polarization rotation section and the input/output coupling sections. In the polarization rotation section, the equivalent asymmetric waveguide cross section is introduced to excite two hybridized modes to achieve polarization rotation. We use polarization conversion efficiency (PCE) to evaluate the performance of the device. PCE and the optical axis rotation angle θ are defined as [18]:
Fig. 1. (a)−(b) Schematics of the polarization rotator based on the equivalent asymmetric waveguide cross section and PhC-like subwavelength asymmetric waveguide cross section, respectively. (c) The cross section of equivalent asymmetric waveguide.
To release the fabrication complexity of the asymmetric waveguide cross section, the PhC-like subwavelength structure is utilized to replace the cut-corner region for realizing polarization rotation, as illustrated in Fig. 1(b). The PhC-like structures is composed of discrete pixels in the shape of a silicon square (120 nm × 120 nm) with a central circular air hole. The radius and etching depth of circular air hole are 45 nm and 140 nm, respectively. According to the effective medium theory [27], the effective material index of the PhC-like subwavelength structure is 2.38. By making the full use of the lag effect in the etching procedure, the etching depth of the subwavelength structures is approximate 140 nm by setting proper etching time while the depth of waveguide is fully etched up to 220 nm. In this way, the PhC-like structures enable us to realize the asymmetric waveguide in only single-step etching process.
Moreover, free-form PhC-like SW structures could also manipulate the phase profiles of the excited hybridized modes in inverse design region with a full design space at the nanoscale [21], which is used to further increase the PCE and minimize the coupling insertion loss between input/output waveguide sections and polarization rotation section. In this way, an ultra-compact and highly functional polarization rotator could be achieved simultaneously.
The theory-assisted inverse design method using a manually-set initial pattern is used to promote the design efficiency and device performance [8]. Notably, the conventional inverse design method is usually sensitive to the initial patterns. Generally, an extensive random initial pattern may be used to obtain varying random optimized patterns and a better pattern is selected as the device optimized pattern, which extremely decreases design efficiency. To overcome this issue, the manually-set initial pattern based on a theoretical model is replaced by a random initial pattern to achieve the better device perform and high design efficiency. As described in previous discussion, the inverse design region should be composed of the polarization rotation section and input/output coupling sections. The length of the polarization rotation section should be half-beat length Lπ. Figure 2(a) shows the polarization rotation angle θ as a function of Wetch and Hetch of the asymmetric waveguide cross section. Considering the fabrication process and feature scale of the PhC-like subwavelength structure, the optimized Wetch and Hetch of the cut-corner section is set to be 720 nm and 140 nm, respectively to achieve a high PCE. The calculated electric filed profiles for HP1 and HP2 in the polarization rotation section are shown in Figs. 2(b) and 2(c), respectively. As a result, the corresponding calculated half-beat length Lπ and rotation angle θ are 6 µm and 42°, respectively. The input/output coupling sections are also set to decrease the insertion loss. As a result, a compact footprint of our proposed device is pre-designed as 1.2 × 7.2 μm2. The inverse design region composed of 10 × 60 discrete pixels. Each pixel has only two state: ‘0’ represents the air hole is etched up to 140 nm while ‘1’ represents the hole is not etched. To realize high polarization rotation, the corresponding 6 lines of holes within the polarization rotation section should be set to be ‘0’. Therefore, the manually-set initial pattern based on the equivalent asymmetric waveguide is set as shown in Fig. 3. The goal of the optimized design is to obtain the optimized circular holes’ combinations in the inverse design region to realize the high PCE and polarization extinction ratio.
To verify the viability and reasonability of our equivalent model, three random initial patterns are also designed for comparison and analysis, as presented in Figs. 3(b)–3(d). The simulation results indicate the optimized device based on the manually-set initial pattern usually exhibits a better performance than those with random initial patterns. The figure-of-merit (FOM), PCE, polarization extinction ratio (PER) and insertion loss (IL) in our inverse design process are defined as:
Fig. 2. (a) The polarization rotation angle θ as a function of Wetch and Hetch of the asymmetric waveguide cross section at the wavelength of 1550 nm. (b)−(c) The calculated electric field profiles for HP1 and HP2, respectively. The corresponding mode effective indices are 1.69 and 1.56, respectively.
Fig. 3. (a)−(d) The manually-set and random initial patterns. (e)−(h) The optimized patterns for the manually-set and random initial patterns. (i) The calculated FOMs after every iteration for the manual and random initial patterns. (j)−(k) The transmission spectra for TM0 and TE0 of the four optimized devices with different initial patterns at the output waveguide, respectively.
The nonlinear direct-binary-search (DBS) optimization algorithm is employed to achieve the optimized pattern of circular holes’ combinations [22]. A 3D finite-difference time-domain (FDTD) method is utilized to calculate the FOM by a commercial software (Lumerical FDTD Solutions) [28]. When the FOM exhibits no great improvement (< 1% for our case) after one iteration, the whole optimization process will end up. It takes about 36 hours to get the optimized nanopattern after 5 rounds of iteration on a computer with an 8-core central processing unit (Intel Xeon E5-2637).
As shown in Figs. 3(e)–3(f), the optimized patterns based on the manually-set and the random initial pattern are achieved under the same optimization process, respectively. The calculated FOMs after every iteration for the manual and random initial patterns are illustrated in Fig. 3(i). The corresponding transmission spectra for TM0 and TE0 at the output ports with different initial patterns are shown in Figs. 3(j) and 3(k), respectively. The FOMs and ILs for the manually-set initial pattern are usually better than those for the random ones. As expected, our simulation results indicate that the inverse design method using a manually-set initial pattern based on a theoretical model may improve design efficiency and device performance greatly, which enables the widespread use of the inverse design method to design ultracompact and highly functional nanophotonic devices for on-chip optical interconnect.
The manually-set initial and optimized patterns are present in Figs. 4(a) and 4(b), respectively. Figures 4(c) and 4(d) show the optical field distributions of Hz and Hy, respectively. As expected, the optimized polarization rotator converges to our proposed equivalent model based on asymmetric waveguide cross section. The optical field evolution of the optimized device can be also divided into three parts. In the I and III parts, these sections works as adiabatic evolution tapers to reduce insertion loss between the input/output waveguide and polarization rotation section. In the II part, the equivalent asymmetric waveguide cross section is formed to realize polarization rotation. The calculated IL is less than 0.7 dB and the polarization extinction ratio is larger than 25 dB over the wavelength from 1530 to 1590 nm, as shown in Fig. 4(e).
Fig. 4. (a)−(b) The manually-set initial and corresponding optimized patterns of polarization rotator, respectively. (c)−(d) The magnetic field profile evolution of Hz and Hy, respectively. (e) The calculated transmittance spectra for the inversely-designed polarization rotator.
3. Experiment results
To evaluate device performance, we fabricated and experimentally demonstrated the proposed ultracompact polarization rotator based on the PhC-like SW structure asymmetric waveguide cross section. First, the electron-beam lithography system (Vistec EBPG 5000 Plus) was utilized to form the optimized pattern on a 220 nm-thick top silicon layer. The inductively coupled plasma (ICP) etcher (Plasma lab System100) was used to transfer the mask to the silicon device layer. By making full use of the lag effect, we can actually ensure the nanopattern to be approximately etched up to 140 nm by setting the proper etching time while the waveguide can be fully etched to 220 nm [21]. In this way, the ultracompact polarization rotator based on the PhC-like SW structure asymmetric waveguide cross section was fabricated in only single-step etching process, which enables the application potential for chip-scale densely integrated MDM system.
Figures 5(a)−5(d) show the top-view scanning electron micrograph (SEM) images for the two mirrored polarization rotators and single polarization rotator, respectively. Only TE-type grating couplers were used to couple the light into/out from the waveguides. A broad amplified spontaneous emission (ASE) light source and an optical spectrum analyzer (Yokogawa AQ6370C-20) were utilized to measure the spectral transmission. The two cascaded mirrored polarization rotators were fabricated to evaluate IL. TE polarization light is coupled into the input waveguide by a TE-type grating coupler, transferred to the TM0 mode by the polarization rotator and converted back to TE0 again by the mirrored polarization rotator. As a result, we can calculate the IL of per polarization rotator. Besides, a single polarization rotator was also fabricated to evaluate polarization extinction ratio. The normalized measured transmission spectra of the fabricated polarization rotator are shown in Fig. 5(e). The measured IL was less than 0.7 dB and PER was larger than 19 dB over a wavelength span of 60 nm from 1530 nm to 1590 nm, which has a good agreement with our simulation results. To our best knowledge, it is the first experimental demonstration of ultracompact polarization rotator based on the asymmetric waveguide cross section in a single-step etching procedure. Besides, our polarization rotator only occupied a footprint of 1.2 × 7.2 μm2, which would show great potential in densely integrated MDM system for on-chip optical interconnect.
Fig. 5. (a)−(d) Scanning electron micrograph (SEM) images for two mirrored polarization rotators and single polarization rotator, respectively. (e) Normalized measured transmission spectra for the fabricated polarization rotator.
4. Discussion
To investigate the fabrication tolerance, we also simulated the performance of a series of polarization rotators with different etching radii and etching depth of etching holes. Firstly, we study the influence of fabrication error of holes’ radii on the device performance. Figures 6(a) and 6(b) demonstrate the simulated insertion losses and crosstalks for the polarization rotators with the radii varied from 43 nm to 47 nm at a step of 1 nm, respectively, where the etch depth is set as 140 nm. We can find that the smaller hole radii will show better fabrication tolerance than the larger ones. Specifically, as the radii decreases by 2 nm, the insertion loss and the crosstalk will increase about 0.3 dB and 10 dB, respectively. However, when the radii of the nanoholes increase, device performance can be significantly degraded. Subsequently, we also evaluate the impact of etching depth varied from 130 nm to 150 nm when the radius of etching hole is set to 45 nm. The simulation results of the insertion loss and crosstalk are plotted in Figs. 6(c) and 6(d), respectively. The insertion losses increase about 1 dB when the depth changes ±10 nm, and the crosstalk gets worse by 10 dB with the increasing of the etch depth. In general, insertion loss and crosstalk will show obvious degradation when the radius is larger than 45 nm, which probably occurs in an over-etched device.
Fig. 6. (a)−(b) Simulated insertion loss and crosstalk of polarization rotators with different holes radii varying from 43 nm to 47 nm, respectively, and the etch depth is set as 140 nm. (c)−(d) Simulated insertion loss and crosstalk of polarization rotators with different etch depth varying from 130 nm to 150 nm, respectively, where the radius is set as 45 nm.
To improve the fabrication robustness, we can estimate the etching velocity to avoid over-etching by setting an appropriate etching time. By making full use of the lag effect, we can actually ensure the nanopattern to be approximately etched up to 140 nm with the hole radius of 45 nm by setting the proper etching time while the waveguide can be fully etched to 220 nm. Before the device is experimentally fabricated, we will etch a test chip to measure the accurate etching velocity in the ICP process and set an optimized etching time to achieve our target etching radii and etching depths for the waveguide and nanopatterns in the single-step etching process. The typical etching time and the etching velocity are about 22 s and 9 nm/s in our fabrication process, respectively. In this way, an ultracompact and high performance polarization rotator could be fabricated in a single-step etching procedure.
5. Conclusion
In summary, we design and experimentally demonstrate a novel ultracompact polarization rotator based on PhC-like SW structures asymmetric waveguide cross section and optimized it using the improved inverse design method. By making full use of the lag effect, the PhC-like subwavelength structure enables us to fabricate equivalent asymmetric waveguide cross section in one single-step etching procedure, which decreases fabrication complexity and improves fabrication robustness greatly. Besides, due to the capability of flexible refractive index engineering and manipulating the optical field at the nanoscale, the inverse design method is used to improve polarization conversion efficiency and decrease the coupling loss of the device. Besides, the theory-assisted inverse design method based on a manually-set initial pattern, rather than random ones in conventional inverse design method, is employed to optimize the device to improve design efficiency and device performance. The fabricated device exhibited high performance with a compact footprint of only 1.2 × 7.2 µm2, high PER (> 19 dB) and low IL (< 0.7 dB) with a band of 60 nm from 1530 to 1590 nm. The fabricated device will show great potential in practical applications for a chip-scale densely integrated optical interconnect. Moreover, our theory-assisted inverse design method will also enable the widespread use of intelligent computation to design ultracompact and highly functional nanophotonic devices for densely integrated MDM systems.
Funding
National Natural Science Foundation of China (61775069, 61635004); Major Technology Innovation of Hubei Province (2018AAA037); Huazhong University of Science and Technology (2019YGSCXCY041).
Disclosures
The authors declare no conflict of interest.
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