This article was last updated on 2022-08-18 17:08:83

## 文献概述

AbstractContent
TitleUltracompact silicon polarization splitter-rotator using a dual-etched and tapered coupler
Published2020-9-21
PlatformSilicon
FunctionTM&TE—> TE&TE
Footprinta total length of ~24μm
ResultThe minimum extinction ratio is greater than 30, 20, or 15 dB within the bandwidth of 33, 100, or 150 nm, respectively, while the maximum polarization conversion loss is less than 0.4, 0.9, or 1 dB.
PDFhere

## 笔记

### 1. Why PSR?

The Photonics integrated circuits (PICs) are usually characterized with a compact footprint due to the ultrahigh index contrast. However, the high birefringence (双折射) usually leads to high polarization dependence of the structure and brings random polarization state change over an optical link. To overcome this problem, typically, an Si photonic device is designed for polarization splitting or polarization conversion. The polarization processing device mainly includes polarization beam splitters (PBSs) and polarization rotators (PRs). The polarization splitter-rotators (PSRs) combine the functions of both PBS and PR, which can separate two orthogonal polarization states and rotate one of them by 90°.

Due to the polarization dependence of many devices, a purer polarization state means less subsequent processing (后续处理) and additional loss, such that the complexity of subsequent optical processing could be greatly reduced. Thus, the PSR is an essential device for polarization multiplexing and polarization diversity systems in a few applications such as telecom, Datacom, and quantum circuits.

### 2. Principle and Design

The device consists of a dual-etched taper waveguide (WG1) and a silicon nanowire waveguide (WG2). In the coupling region, the WG1 is taper-etched to satisfy the phase-matching condition (for the coupling between the quasi-TM mode in through-port and the quasi-TE mode in the cross port) with a length of Lc . An S-bend is introduced after the coupling region, to make the two waveguides decoupled. This S-bend is partially etched with a width of We . In order to make the residual TM0 mode completely leak into the substrate, the dual-level etching is used after the S-bend section, and only the TE0 mode can be guided in this output port.

$$\gamma _x=\dfrac{\int |E_x|^2dxdy}{\int (|E_x|^2+|E_y|^2)dxdy}$$

「Obviously, the modes in WG1 and WG2 are relatively pure, and no mode conversion occurs throughout the employment of this double-etched PSR. 」这句话说的也是一个道理。只不过如作者所说，这里的TE0和TM0模式都相对纯净，只通过颜色看的话，两条色散曲线的$\gamma$y分别位于50%的两边，用肉眼可以看到曲线颜色与中间50%处对应的颜色差别还是挺大的。所以，当我们的W2W1=0.63μm开始逐渐减小到0μm的过程中，在单个波导中没有发生模式转换。即：如果TE0模式从WG1波导中输入，那么当它从WG1输出端口耦合输出时依然是TE0模式，如果TM0模式从WG1波导中输入（此时没有WG2），那么当它从WG1输出端口耦合输出时也依然是TM0模式，这个考虑对于现在这个结构来说很有必要，因为垂直不对称了。作者想要表达的应该是：我现在证明了在WG1中传输的TE/TM模不会因为垂直方向的不对称而发生偏振模式的改变。

「Theoretically, the coupling efficiency is not proportional(正比) to the coupling length but fluctuates periodically as the coupling length increases.」耦合周期为Lπ，可以使用超模理论进行求解。

Figure 5 shows the mode profiles of three supermodes in the coupling region at 1550 nm. It can be seen that the TE0 mode is well confined in WG1 without coupling into WG2, while the TE1 and TM0 modes are well guided in the coupling region. Due to the interference among supermodes with different propagation constants, the TM0 mode will be coupled to another waveguide at the effective beat length Lπ , which can be calculated by$$L_\pi =\dfrac{\pi}{\beta_{TE_1}-\beta_{TM_0}}=\dfrac{\lambda }{2(n_{TE_1}-n_{TM_0})}$$

Theoretically, the smaller the gap between the waveguides, the shorter the length required for 100% coupling. To facilitate the fabrication procedures, the gap between two waveguides is set as 100 and 150 nm. According to the parameters shown in Table 1, we can obtain Lπ = 6.8 µm or Lπ = 7.75 µm, respectively.

## 想法

Author     : Hao Zhang (张豪)
Link         : https://nuts-sugar.gitee.io/blogs/a48d.html
Copyright: Based on CC BY-SA 4.0 protocol , please indicate them when reprinting!