「文献阅读」基于双刻蚀和锥形耦合器的超紧凑硅基偏振分离旋转器

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

结构图

 Schematic of the proposed PSR. (a) 3D view. (b) Cross view.

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

 Schematic of the proposed PSR. (a) 3D view. (b) Cross view.

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.

在这里作者先固定了h1W1的值分别为220 nm和0.63 μm,上一篇文章也提到了,SOI晶圆中上表层是厚度为220 nm的硅。当然,这里由于制作工艺的限制,h2可以选择150 nm或70 nm。由于WG1在耦合区是锥形刻蚀的,其中传输的模式的有效折射率随着截面形状的不同而发生变化。故作者计算了一下模式偏振率(mode polarization ratio)以保证在波导中没有模式的转化。

假设光束沿x方向传输,那么模式偏振率$\gamma$y定义为:$$\gamma _y=\dfrac{\int |E_y|^2dydz}{\int (|E_y|^2+|E_z|^2)dydz}$$这里EyEz分别为波导中导模的电场在yz方向的分量。现在还没有确定的材料只有包层了,作者针对空气包层和二氧化硅包层作了仿真。

这里需要做一个说明。

在戴道锌老师的这篇论文中,mode polarization ratio这一概念首次被提出,它主要是为了表征模式的偏振纯度的,换句话说,是为了表征模式杂化的程度的。

 Cross section for an SOI nanowire with angled sidewalls (the angle is θ>0).

上图是一个典型的波导结构,作者在θ=8°的情况下计算了各个模式的色散曲线,发现在绿圈标注的地方出现了与θ=0°完全不同的情况。

在θ=0°时,各个模式的色散曲线彼此交叉,但在θ=8°时,原本要交叉的两条曲线发生了反向操作且区县之间有了微小的gap。比如,在芯层宽度wco从0.628μm开始增大时,左边的TM0模式不再是TM0模,将逐渐演化为TE1模,这就是典型的利用模式杂化实现模式转换的基本原理。其产生的原因便是波导在垂直方向上不再对称,打破了原有的色散规律。

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

当光束沿$z$轴传输时,模式偏振率如上式。对于一个典型的TE模式而言,Ex要比Ey大得多,故Ey可以近似取为0,$\gamma$x几乎等于100%。相反,对于典型的TM模式而言,$\gamma$x几乎等于0%。而在中间的$\gamma$x值,也即代表TE和TM的混合模式,简称杂化模式。

形象一点的话,如下图所示,如果计算波导宽度在0.628μm处mode#2和mode#4的模场分布图,可以看到计算得到的$\gamma$x都接近于50%,这说明此时的模场是TE和TM的混合情况。

  Field profiles (E<sub>x</sub> and E<sub>y</sub>) for modes #2 and #4 of a SOI nanowire with θ = 8°, w<sub>co</sub> =  0.628μm, and ncl = 1.444 (SiO<sub>2</sub>). (a) mode #2; (b) mode #4. The total height of the Si core  layer is h<sub>co</sub> = 220nm.

换句话说,如果制作一个锥形波导,0.628μm在起始宽度w1和最终宽度w2之间,且w1小于w2,则从起始段耦合进TM0模,最终在输出端会耦合出TE1模,而$\gamma$x则会从0%慢慢增长为100%。

在1550 nm下,作者通过改变W2W3得到了WG1波导中模式对应的模式有效折射率和模式偏振率曲线。

 Mode effective index and the polarization ratio in WG1 for different end widths and different waveguide widths. (a) Air top cladding and h2 = 150 nm. (b) Air top cladding and h2 = 70 nm. (c) Air top cladding. (d) SiO2 top cladding and h2 = 150 nm. (e) SiO2 top cladding and h2 = 70 nm. (f ) SiO2 top cladding.

「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。

那么现在,我们需要解决的问题便是:如何让WG1中的TM0模式耦合到WG2中的TE0模式,且还需要保证这个耦合出来的TE0模式输出之后还仍然是TE0模式(后面的这个要求默认已经满足了,因为WG2在垂直方向上对称)。

根据直波导的耦合模理论,PSR的相位匹配条件是在WG1中的TM0模式有效折射率与在WG2中的TE0模式有效折射率相等。一旦这个条件满足,混合的超模的$\gamma$y会接近50%。

一方面,为了实现相位匹配条件,对于包层为空气和二氧化硅而言,W3必须小于0.325μm (这个地方从上图中看不出来,主要原因是颜色识别度太低);另一方面,为了保证TE0模式在WG1中的传输损耗最低,则需要保证其对应的$\gamma$y曲线越接近100%越好(即在WG1中的TE0模要与WG2中的任何模式保持相位失配),从论文的表述应该是W3越大,黄色$\gamma$y越大。故最终,作者选择W3为0.3μm (for air top cladding) 和 0.27μm (for SiO2 top cladding)。

在理想情况下,第一级刻蚀的梯形WG1应在中心宽度处实现相位匹配。由上图还可以得出,WG1中TE模的有效折射率远大于TM模的有效折射率,又因为WG2-TEWG1-TM & WG2-TEWG2-TM,因此,WG1中TE模有效折射率大于WG2中TM有效折射率。如果W2很小的话,很有可能WG2中的TM模式与WG1中的TM模式相位匹配,这样会出现一小部分WG1中的TM0模式直接耦合进WG2中(cross-coupled & not convert to the TE mode)。因此,需要对W2进行优化。

 Mode conversion efficiencies for different end widths of the first-level taper W<sub>2</sub>. (a) TM<sub>0</sub>−TE<sub>0</sub> and (b) TM<sub>0</sub>−TM<sub>0</sub> conversion with SiO<sub>2</sub> top cladding. (c) TM<sub>0</sub>−TE<sub>0</sub> and (d) TM<sub>0</sub>−TM<sub>0</sub> conversion with air top cladding. The taper length is 3 µm, the X span and Y span of the S-bend are 8 and 2 µm, respectively.

上图是在耦合长度Lc为8μm、g为100nm情况下不同的W2对应的模式转换效率。我们的目标是尽量使WG1和WG2中的TM-TM耦合效率低,WG1-WG2的TM-TE高,因此通过上图也可以明显地看出,最好是选择空气作为上包层、W2选为0.36μm。文章中也提到:「 It can be seen that the mode conversion efficiency in Fig. 3(a) is much lower than that in Fig. 3(c), and part of the TM0 mode is coupled to the WG2 without mode conversion. This means that the PSR use SiO2 top cladding, which requires a longer coupling length than air top cladding. 」表述的没问题。此时的(WG1)TM-(WG2)TE耦合效率为80%。因此,还有部分TM模式留在了WG1中。

为了提高消光比,在S-bend结构之后加入了第二级锥形刻蚀波导,目的是让残留的TM模式泄漏到衬底中,使其仅支持单模(TE0)。因此,作者求解了此时在h2分别为70nm和150nm时的TM模式和TE0模式的传输损耗。

 TM<sub>0</sub> mode profile at the through-port with (a) h<sub>2</sub> = 70 nm, (b) h<sub>2</sub> = 150 nm. The transmission loss of TM-attenuating taper for the TE<sub>0</sub> mode with (c) h<sub>2</sub> = 70 nm, (d) h<sub>2</sub> = 150 nm.

从(a)和(b)可以看出,此时TM模式都泄漏到衬底中去了,对比(c)和(d)图,可以看到当h2为150nm时,TE0模式的传输损耗较低,故选择h2为150nm。

 Mode conversion efficiencies for different end widths of the first-level taper W<sub>2</sub>. (a) TM<sub>0</sub>−TE<sub>0</sub> and (b) TM<sub>0</sub>−TM<sub>0</sub> conversion with SiO<sub>2</sub> top cladding. (c) TM<sub>0</sub>−TE<sub>0</sub> and (d) TM<sub>0</sub>−TM<sub>0</sub> conversion with air top cladding. The taper length is 3 µm, the X span and Y span of the S-bend are 8 and 2 µm, respectively.

在上图中,作者未对耦合长度Lc进行优化,故现在对其优化以实现更高的模式转换效率。

「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$$L_\pi =\dfrac{\pi}{\beta_{TE_1}-\beta_{TM_0}}=\dfrac{\lambda }{2(n_{TE_1}-n_{TM_0})}$$

 y- and z-component mode profiles of three supermodes: (a) even TE mode; (b) odd TE mode; (c) even TM mode.

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.

最终优化了Lc,结果如下:

 Output powers from the through- and cross ports vary with the length of L<sub>c</sub> . (a) g = 100 nm, (b) g = 150 nm.

优化的部分不再赘述,最终得到第一级锥形刻蚀区Lc为6.25μm。而后,S-bend with an X-span of 8.25μm,此时模式转换效率高达95% @ 1550nm。最终的光场传输如下图所示:

 Light propagation in PSR when (a) TE<sub>0</sub> mode and (b) TM<sub>0</sub> mode launched, respectively.

最后,作者对器件进行了制作,还分析了fabrication tolerance。

3. Results

这里的公式解决了我上一篇文章中的困惑,nice~

最后,作者对输出频谱进行了测试,结果如下,很棒的效果。

想法

这篇论文和上一篇论文的结果大致一样,但我感觉这篇讲的要更详细。尤其是在设计部分,其实涉及到很多知识,包括耦合模理论、超模理论、模式杂化等,且作者在优化问题上的表述也非常全面。读完这一篇,再回去看上一篇,会舒服很多。

如果让我来设计,可能只会一味地多参数扫描,但需要知道的是,这个结构的未知参数太多了,暴力求解绝对不是可行的办法。需要学习一下作者的设计思路,这对于今后写论文也有很大的参考价值。