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SCIENCE CHINA Information Sciences, Volume 63, Issue 6: 160409(2020) https://doi.org/10.1007/s11432-020-2888-2

A design method for high fabrication tolerance integrated optical mode multiplexer

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  • ReceivedFeb 1, 2020
  • AcceptedApr 23, 2020
  • PublishedMay 11, 2020

Abstract

The tapered asymmetric directional coupler has the potential to realize high fabrication tolerance and high transmission efficiency on-chip mode multiplexer. However, the geometry parameter selection of tapered structure remains empirical. In this paper, we propose a design method for the tapered structure based on genetic algorithm. Combined with the adjusted coupling equations and interpolation method, low-time-cost optimization can be realized. Three mode multiplexers ($\mathrm{TE}_{0}\&~\mathrm{TE}_{1}$, $\mathrm{TE}_{0}\&~\mathrm{TE}_{2}$ and $\mathrm{TE}_{0}\&~\mathrm{TE}_{5}$) are designed by our method. According to simulation results, the insertion loss of the designed devices is lower than 1.8 dB and the crosstalk is lower than $-15$ dB when the fabrication error is within required range ($\pm$10 nm for $\mathrm{TE}_{0}\&~\mathrm{TE}_{2}$ and $\mathrm{TE}_{0}\&~\mathrm{TE}_{5}$, and $\pm$20 nm for $\mathrm{TE}_{0}\&~\mathrm{TE}_{1}$) in the bandwidth of 1.5–1.6 $\mu$m. In addition, the entire optimization process takes only 2 h for each device, which is around the time cost of a single 3D simulation.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61635001, 61535002), Major International Cooperation and Exchange Program of the National Natural Science Foundation of China (Grant No. 61120106012), and Beijing Municipal Science $\&$ Technology Commission (Grant No. Z19110004819006).


Supplement

Appendix

The derivation of the adjusted coupling equation

According to CMT, the field of the whole tapered structure could be written as the sum of egien-modes in different waveguides: \begin{equation}\left\{\begin{array}{l} \tilde{E}=A(z) \tilde{E}_{1}+B(z) \tilde{E}_{2}, \\ \tilde{H}=A(z) \tilde{H}_{1}+B(z) H_{2}. \end{array}\right. \tag{11}\end{equation}

Combining (A1) with Maxwell's equations, we can get \begin{equation}\begin{aligned} \frac{{\rm d} A}{{\rm d} z} &+\frac{{\rm d} B}{{\rm d} z} \frac{\int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty} u_{z} \cdot\left(\tilde{E}_{1}^{*} \times \widetilde{H}_{2}+\tilde{E}_{2} \times \tilde{H}_{1}^{*}\right) {\rm d} x {\rm d} y}{\int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty} u_{z} \cdot\left(\tilde{E}_{1}^{*} \times \tilde{H}_{1}+\tilde{E}_{1} \times \tilde{H}_{1}^{*}\right) {\rm d} x {\rm d} y} \\ &+{\rm j} A \frac{\omega \varepsilon_{0} \int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty}\left(N^{2}-N_{1}^{2}\right) \tilde{E}_{1}^{*} \cdot \tilde{E}_{1} {\rm d} z {\rm d} y}{\int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty} u_{z} \cdot\left(\tilde{E}_{1}^{*} \times \widetilde{H}_{1}+\tilde{E}_{1} \times \tilde{H}_{1}^{*}\right) {\rm d} x {\rm d} y} \\ &+{\rm j} A \frac{\omega \varepsilon_{0} \int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty}\left(N^{2}-N_{2}^{2}\right) \tilde{E}_{1}^{*} \cdot \tilde{E}_{2} {\rm d} x {\rm d} y}{\int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty} u_{z} \cdot\left(\tilde{E}_{1}^{*} \times \widetilde{H}_{1}+\tilde{E}_{1} \times \widetilde{H}_{1}^{*}\right) {\rm d} x {\rm d} y}=0, \end{aligned} \tag{12}\end{equation}

\begin{equation}\begin{aligned} \frac{{\rm d} B}{{\rm d} z} &+\frac{{\rm d} A}{{\rm d} z} \frac{\int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty} u_{z} \cdot\left(\tilde{E}_{2}^{*} \times \tilde{H}_{2}+\tilde{E}_{2} \times \tilde{H}_{1}^{*}\right) {\rm d} x {\rm d} y}{\int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty} u_{z} \cdot\left(\tilde{E}_{1}^{*} \times \tilde{H}_{1}+\tilde{E}_{1} \times \tilde{H}_{1}^{*}\right) {\rm d} x {\rm d} y} \\ &+{\rm j} A \frac{\omega \varepsilon_{0} \int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty}\left(N^{2}-N_{1}^{2}\right) \tilde{E}_{1}^{*} \cdot \tilde{E}_{1} {\rm d} x {\rm d} y}{\int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty} u_{z} \cdot\left(\tilde{E}_{1}^{*} \times \widetilde{H}_{1}+\tilde{E}_{1} \times \widetilde{H}_{1}^{*}\right) {\rm d} x {\rm d} y} \\ &+{\rm j} A \frac{\omega \varepsilon_{0} \int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty}\left(N^{2}-N_{2}^{2}\right) E_{1}^{*} \cdot \tilde{E}_{2} {\rm d} x {\rm d} y}{\int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty} u_{z} \cdot\left(\tilde{E}_{1}^{*} \times \widetilde{H}_{1}+\tilde{E}_{1} \times \widetilde{H}_{1}^{*}\right) {\rm d} x {\rm d} y}=0. \end{aligned} \tag{13}\end{equation}

For a tapered ADC structure, the eigen modes in the two waveguide are given by \begin{equation}\left\{\begin{array}{l} \displaystyle\tilde{E}_{p}=E_{p}(z) \exp \left[-{\rm j} \int \beta_{p}({z}) \mathrm{d} {z}\right], \\ \displaystyle\widetilde{H}_{p}=H_{p}(z) \exp \left[-{\rm j} \int \beta_{p}({z}) \mathrm{d} {z}\right]. \end{array}\right. \tag{14}\end{equation}

Substituting (A4) into (A2) and (A3), the coupling equations can be expressed as \begin{equation}\begin{aligned} \frac{{\rm d} A}{{\rm d} z}&+ c_{12}(z) \frac{{\rm d} B}{{\rm d} z} \exp \left[-{\rm j} \int\left(\beta_{2}(z)-\beta_{1}(z)\right) {\rm d} z\right]+{\rm j} \chi_{1}(z) A \\ &+{\rm j} \kappa_{12}(z) B \exp \left[-{\rm j} \int\left(\beta_{2}(z)-\beta_{1}(z)\right) {\rm d} z\right]=0, \end{aligned} \tag{15}\end{equation} \begin{equation}\begin{aligned} \frac{{\rm d} B}{{\rm d} z}&+ c_{21}(z) \frac{{\rm d} A}{{\rm d} z} \exp \left[+{\rm j} \int\left(\beta_{2}(z)-\beta_{1}(z)\right) {\rm d} z\right]+{\rm j} \chi_{2}(z) B \\ &+{\rm j} \kappa_{21}(z) A \exp \left[+{\rm j} \int\left(\beta_{2}(z)-\beta_{1}(z)\right) {\rm d} z\right]=0. \end{aligned} \tag{16}\end{equation}

Ignoring $c_{p~q}$ and $\chi_{p}$, we can get the simplified coupling equations: \begin{equation}\begin{array}{l} \displaystyle\frac{{\rm d} A}{{\rm d} z}=-{\rm j} \kappa_{12}(z) B\operatorname{exp}\left[-{\rm j} \int\left(\beta_{2}(z)-\beta_{1}(z)\right) {\rm d} z\right], \\ \displaystyle\frac{{\rm d} B}{{\rm d} z}=-{\rm j} \kappa_{21}(z) A\operatorname{exp}\left[+{\rm j} \int\left(\beta_{2}(z)-\beta_{1}(z)\right) {\rm d} z\right]. \end{array} \tag{17}\end{equation}


References

[1] Pavesi L, Lockwood D J. Silicon Photonics III. Berlin: Springer, 2016. 1--5. Google Scholar

[2] Fang Q, Liow T Y, Song J F. WDM multi-channel silicon photonic receiver with 320 Gbps data transmission capability.. Opt Express, 2010, 18: 5106-5113 CrossRef PubMed Google Scholar

[3] Errando-Herranz C, Das S, Gylfason K B. Suspended polarization beam splitter on silicon-on-insulator.. Opt Express, 2018, 26: 2675-2681 CrossRef PubMed Google Scholar

[4] Chen Yuan, Jincheng Dai, Hao Jia, et al. Design of a C-band polarization rotator-splitter based on a mode-evolution structure and an asymmetric directional couple. Journal of Semiconductors, 2018, 39(12): 105-111. Google Scholar

[5] Shi Y, Chen J, Xu H. Silicon-based on-chip diplexing/triplexing technologies and devices. Sci China Inf Sci, 2018, 61: 080402 CrossRef Google Scholar

[6] Shu, H., Shen, B., Wang, X, et al. A Design Guideline for Mode (DE) Multiplexer Based on Integrated Tapered Asymmetric Directional Coupler. IEEE Photonics Journal, 2019, 11(5):1-12. Google Scholar

[7] Shu H, Deng Q, Wang X. A Polarization Multiplexing Optical Circuit for Efficient Phase Tuning. IEEE Photon Technol Lett, 2019, 31: 1549-1552 CrossRef Google Scholar

[8] Li C, Wu H, Tan Y. Silicon-based on-chip hybrid (de)multiplexers. Sci China Inf Sci, 2018, 61: 080407 CrossRef Google Scholar

[9] Han L, Liang S, Zhu H. Two-mode de/multiplexer based on multimode interference couplers with a tilted joint as phase shifter.. Opt Lett, 2015, 40: 518-521 CrossRef PubMed Google Scholar

[10] Uematsu T, Ishizaka Y, Kawaguchi Y. Design of a Compact Two-Mode Multi/Demultiplexer Consisting of Multimode Interference Waveguides and a Wavelength-Insensitive Phase Shifter for Mode-Division Multiplexing Transmission. J Lightwave Technol, 2012, 30: 2421-2426 CrossRef Google Scholar

[11] Guo D, Chu T. Silicon mode (de)multiplexers with parameters optimized using shortcuts to adiabaticity.. Opt Express, 2017, 25: 9160-9170 CrossRef PubMed Google Scholar

[12] Chang W, Lu L, Ren X. Ultra-compact mode (de) multiplexer based on subwavelength asymmetric Y-junction.. Opt Express, 2018, 26: 8162-8170 CrossRef PubMed Google Scholar

[13] Wang J, Chen P, Chen S. Improved 8-channel silicon mode demultiplexer with grating polarizers.. Opt Express, 2014, 22: 12799-12807 CrossRef PubMed Google Scholar

[14] Liu L, Ding Y, Yvind K. Efficient and compact TE-TM polarization converter built on silicon-on-insulator platform with a simple fabrication process.. Opt Lett, 2011, 36: 1059-1061 CrossRef PubMed Google Scholar

[15] Stern B, Zhu X, Chen C P. On-chip mode-division multiplexing switch. Optica, 2015, 2: 530-535 CrossRef Google Scholar

[16] Dorin B A, Ye W N. Two-mode division multiplexing in a silicon-on-insulator ring resonator.. Opt Express, 2014, 22: 4547-4558 CrossRef PubMed Google Scholar

[17] Pan C, Rahman B M A. Accurate Analysis of the Mode (de)multiplexer Using Asymmetric Directional Coupler. J Lightwave Technol, 2016, 34: 2288-2296 CrossRef Google Scholar

[18] Ding Y, Xu J, Da Ros F. On-chip two-mode division multiplexing using tapered directional coupler-based mode multiplexer and demultiplexer.. Opt Express, 2013, 21: 10376-10382 CrossRef PubMed Google Scholar

[19] Sun Y, Xiong Y, Ye W N. Experimental demonstration of a two-mode (de)multiplexer based on a taper-etched directional coupler.. Opt Lett, 2016, 41: 3743-3746 CrossRef PubMed Google Scholar

[20] Zhao W K, Chen K X, Wu J Y. Broadband Mode Multiplexer Formed With Non-Planar Tapered Directional Couplers. IEEE Photon Technol Lett, 2019, 31: 169-172 CrossRef Google Scholar

[21] Yariv A. Coupled-mode theory for guided-wave optics. IEEE J Quantum Electron, 1973, 9: 919-933 CrossRef Google Scholar

[22] Mulugeta T, Rasras M. Silicon hybrid (de)multiplexer enabling simultaneous mode and wavelength-division multiplexing.. Opt Express, 2015, 23: 943-949 CrossRef PubMed Google Scholar

[23] Chambers L D. The Practical Handbook of Genetic Algorithms: Applications. 2nd ed. Boca Raton: CRC Press, 2000. Google Scholar

  • Figure 1

    (Color online) (a) Schematic of the ADC based mode multiplexer; (b) detailed geometry parameters of the coupling region in a non-tapered ADC; (c) detailed geometry parameters of the coupling region in a tapered ADC.

  • Table 1  

    Table 1The geometric parameters of designed devices

    $W_{bs}$ (nm) $W_{be}$ (nm) $L_{c}$ ($\mu$m)
    $\mathrm{{\rm~TE}_{0}\&{\rm~TE}_{1}}$ 761 879 54.08
    $\mathrm{{\rm~TE}_{0}\&{\rm~TE}_{2}}$ 1222 1318 51.54
    $\mathrm{{\rm~TE}_{0}\&{\rm~TE}_{5}}$ 2208 2428 58.23

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