High-speed calibration method for cascaded phase shifters in integrated quantum photonic chips

Abstract

Integrated photonics has the advantages of miniaturization, low cost, stability and easy manipulation in comparison with bulk optics. However, as the scale and complexity of the chip increase, the calibration of cascaded phase shifters on-chip will be almost impossible. The time needed to calibrate the cascaded phase shifters with using conventional method increases exponentially with the number of cascades, and the maximum number of cascades achieved so far is only 5. In this paper, we propose a high-speed calibration method by which the calibration time increases only linearly with the number of cascades increasing, achieving an exponential acceleration. For <i>N</i>-cascaded phase shifters, the number of points scanned by each shifter is m, our method only needs to scan <inline-formula><tex-math id="M1">\begin{document}$ ({m}^{2}+m+1)N-1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M1.png"/></alternatives></inline-formula> points instead of <inline-formula><tex-math id="M2">\begin{document}$ {m}^{n} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M2.png"/></alternatives></inline-formula> with using the proposed method. The main idea of this method is that we can calibrate phase shifters one by one via two-dimensional (2D) scanning. For example, for <i>N</i>-cascaded phase shifter, the calibration of phase shifter <i>N</i> can be realized by calibrating the 2D scanning phase shifter <inline-formula><tex-math id="M3">\begin{document}$ N-1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M3.png"/></alternatives></inline-formula> and the 2D scanning phase shifter <i>N</i>, and the calibration of phase shifter <inline-formula><tex-math id="M4">\begin{document}$ N-1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M4.png"/></alternatives></inline-formula> can be achieved by calibrating the 2D scanning phase shifter <inline-formula><tex-math id="M5">\begin{document}$ N-2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M5.png"/></alternatives></inline-formula> and the 2D scanning phase shifter <inline-formula><tex-math id="M6">\begin{document}$ N-1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M6.png"/></alternatives></inline-formula>, and so on. The 2D scanning phase shifter <inline-formula><tex-math id="M7">\begin{document}$ N-1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M7.png"/></alternatives></inline-formula> and the 2D scanning phase shifter <i>N</i> scan the phase shifter <i>N</i> by m points and then the current of phase shifter <inline-formula><tex-math id="M8">\begin{document}$ N-1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M8.png"/></alternatives></inline-formula> is changed to scan the phase shifter <i>N</i>. Whenever changing the current of phase shifter <inline-formula><tex-math id="M9">\begin{document}$ N-1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M9.png"/></alternatives></inline-formula> once, we can plot a curve of current-transmission. The lowest point of the curve changes with the change of the current phase shifter <inline-formula><tex-math id="M10">\begin{document}$ N-1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M10.png"/></alternatives></inline-formula>. When the lowest point of the curve takes a maximum value, that point is the 0 or π phase of phase shifter <i>N</i>. Similarly, when the lowest point of the curve takes a maximum value, that point is the <inline-formula><tex-math id="M11">\begin{document}$ -0.5{\rm{\pi }} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M11.png"/></alternatives></inline-formula> or <inline-formula><tex-math id="M12">\begin{document}$ 0.5{\rm{\pi }} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M12.png"/></alternatives></inline-formula> phase of phase shifter <inline-formula><tex-math id="M13">\begin{document}$ N-1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M13.png"/></alternatives></inline-formula>. Then we can calibrate all phase shifters by using this method, but each phase shifter has two possibilities. Then we can set a specific current of all phase shifters to finish the calibration. The different parameters are verified to see their effect on fidelity. It is found that small experimental error has little effect on fidelity. When <inline-formula><tex-math id="M14">\begin{document}$ m > 20 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210401_M14.png"/></alternatives></inline-formula>, the fidelity becomes approximately a constant. For every 1760 increase in <i>N</i>, the fidelity decreases by about 0.01%. The fidelity of 20-cascaded phase shifters is 99.8%. The splitting ratio of MMI may is not 50∶50 as designed because of chip processing errors. So, different splitting ratios are simulated and it is found that the splitting ratio affects the fidelity more seriously than other parameters. But our method works still well even when the splitting ratio is 45∶55, whose fidelity is 99.95% if we know the splitting ratio. The method will greatly expand the application scope of integrated quantum photonics.