近年來，雲端計算和社交網路的應用成長快速，已然超越摩爾定律，加大了更多頻寬的需求。在所有可能的解決方法中，積體光路 (Photonic Integrated Circuits) 作為一種前景大好的技術脫穎而出。積體光路過光子傳輸數據，而且如同積體電路，提供了另一種「以每個潛在低成本的元件，實現大量和高製造良率」的途徑。然而，隨著高速通訊系統不斷發展，人們對具有更高容量、靈活性和效率的積體光路的需求不斷增加。
為了滿足這些需求，一種「積體光路上的光可以在程式控制下重新決定走向」的想法，使可程式化的積體光路出現了。其中，作為可程式化積體光路單元的 2×2 馬赫-曾德爾干涉儀 (Mach-Zehnder Interferometers) ，已經成為了在古典領域和量子領域中，對輸入光的向量實施么正轉換的流行選擇。
然而在實踐中，我們必須校正積體光路中的移相器 (Phase Shifters) 以補償由於製程引起的相位誤差 (Phase Errors)。雖然利用網格內部和外部的光偵測器進行校正的方法已經被展示，但還沒有利用紅外線相機 (Infrared Cameras) 進行校正的方法出現。在這裡我們提出了一種「利用紅外線相機觀察光柵耦合器 (Grating Couplers) 以校正矩形網格（Rectangular Meshes）中的單一個馬赫-曾德爾干涉儀」的演算法，並進行實驗以評估其可行性。接著我們說明了我們在矩形網格中設計的幾個特定情況，並期望該方法能夠被廣泛應用於光向前傳播的網路。

The rapid growth of cloud computing and social networking applications in recent years has increased the need for greater bandwidth beyond Moore's Law. Among all possible solutions, photonic integrated circuits (PICs) stand out as a promising technology that transmits data by photons and offers another route, like electronic integrated circuits, towards large volume and high manufacturing yield at a potentially low cost per device. Nonetheless, as the high-speed communications systems continue to develop, the demand for PICs with higher capacity, flexibility, and efficiency has escalated.
To solve those issues, programmable PICs emerged based on the idea that light on the PICs can be spatially rerouted under software control. Among them, 2×2 Mach-Zehnder Interferometers (MZIs) as the building blocks of programmable PICs have become a popular choice for implementing unitary transformations on input light vectors in both the classical and quantum domains.
However, in practice, the phase-shifters in a PIC must be calibrated to compensate for phase errors due to fabrication imperfections. Calibration using photodetectors internal and external to the mesh both have been demonstrated, but not using IR cameras. Here, we propose an algorithm for calibrating single MZIs in a rectangular mesh using an IR camera to observe the grating couplers and experiment to evaluate its feasibility. We illustrate specific cases we devised in a rectangular mesh and expect the approach to be generally applied to networks where the light only propagates forward.

[1] S. Bernabé et al., "Silicon photonics for terabit/s communication in data centers and exascale computers," Solid-State Electronics, vol. 179, p. 107928, 2021/05/01/ 2021, doi: https://doi.org/10.1016/j.sse.2020.107928.
[2] R. Sabella, "Silicon Photonics for 5G and Future Networks," IEEE Journal of Selected Topics in Quantum Electronics, vol. 26, no. 2, pp. 1-11, 2020, doi: 10.1109/JSTQE.2019.2948501.
[3] N. Thomas-peter et al., "Integrated photonic sensing," New Journal of Physics, vol. 13, p. 055024, 2011.
[4] D. Pérez, I. Gasulla, and J. Capmany, "Toward Programmable Microwave Photonics Processors," Journal of Lightwave Technology, vol. 36, no. 2, pp. 519-532, 2018, doi: 10.1109/JLT.2017.2778741.
[5] N. C. Harris et al., "Large-scale quantum photonic circuits in silicon," (in English), Nanophotonics, Review vol. 5, no. 3, pp. 456-468, Aug 2016, doi: 10.1515/nanoph-2015-0146.
[6] D. Pérez-López, A. M. Gutierrez, E. Sánchez, P. DasMahapatra, and J. Capmany, "Integrated photonic tunable basic units using dual-drive directional couplers," Opt. Express, vol. 27, no. 26, pp. 38071-38086, 2019/12/23 2019, doi: 10.1364/OE.27.038071.
[7] D. Pérez-López, E. Sánchez, and J. Capmany, "Programmable True Time Delay Lines Using Integrated Waveguide Meshes," Journal of Lightwave Technology, vol. 36, no. 19, pp. 4591-4601, 2018, doi: 10.1109/JLT.2018.2831008.
[8] W. Bogaerts et al., "Programmable photonic circuits," Nature, vol. 586, no. 7828, pp. 207-216, 2020/10/01 2020, doi: 10.1038/s41586-020-2764-0.
[9] D. A. Miller, "Self-aligning universal beam coupler," (in eng), Opt Express, vol. 21, no. 5, pp. 6360-70, Mar 11 2013, doi: 10.1364/oe.21.006360.
[10] D. A. B. Miller, "Supplementary document for Analyzing and generating multimode optical fields using self-configuring networks - 4600959.pdf," 2020, doi: 10.6084/m9.figshare.12476123.v2.
[11] F. Shokraneh, M. S. Nezami, and O. Liboiron-Ladouceur, "Theoretical and Experimental Analysis of a 4 × 4 Reconfigurable MZI-Based Linear Optical Processor," Journal of Lightwave Technology, vol. 38, no. 6, pp. 1258-1267, 2020, doi: 10.1109/JLT.2020.2966949.
[12] W. Clements, P. Humphreys, B. Metcalf, W. Kolthammer, and I. Walmsley, "An Optimal Design for Universal Multiport Interferometers," Optica, vol. 3, no. 12, pp. 1460-1465, 2016.
[13] D. A. B. Miller, "Setting up meshes of interferometers – reversed local light interference method," Opt. Express, vol. 25, no. 23, pp. 29233-29248, 2017/11/13 2017, doi: 10.1364/OE.25.029233.
[14] S. Pai et al., "Parallel Programming of an Arbitrary Feedforward Photonic Network," IEEE Journal of Selected Topics in Quantum Electronics, vol. 26, no. 5, pp. 1-13, 2020, doi: 10.1109/JSTQE.2020.2997849.
[15] L. Zhuang, C. G. H. Roeloffzen, M. Hoekman, K.-J. Boller, and A. J. Lowery, "Programmable photonic signal processor chip for radiofrequency applications," Optica, vol. 2, no. 10, pp. 854-859, 2015/10/20 2015, doi: 10.1364/OPTICA.2.000854.
[16] D. Pérez, I. Gasulla, J. Capmany, and R. A. Soref, "Reconfigurable lattice mesh designs for programmable photonic processors and universal couplers," in 2016 18th International Conference on Transparent Optical Networks (ICTON), 10-14 July 2016 2016, pp. 1-4, doi: 10.1109/ICTON.2016.7550584.
[17] A. Lopez, D. Perez, P. DasMahapatra, and J. Capmany, "Auto-routing algorithm for field-programmable photonic gate arrays," (in English), Opt. Express, Article vol. 28, no. 1, pp. 737-752, Jan 2020, doi: 10.1364/oe.382753.
[18] F. Morichetti et al., "Non-Invasive On-Chip Light Observation by Contactless Waveguide Conductivity Monitoring," IEEE Journal of Selected Topics in Quantum Electronics, vol. 20, no. 4, pp. 292-301, 2014, doi: 10.1109/JSTQE.2014.2300046.
[19] D. A. B. Miller, "All linear optical devices are mode converters," (in English), Opt. Express, Article vol. 20, no. 21, pp. 23985-23993, Oct 2012, doi: 10.1364/oe.20.023985.
[20] D. A. B. Miller, "How complicated must an optical component be?," (in English), J. Opt. Soc. Am. A-Opt. Image Sci. Vis., Article vol. 30, no. 2, pp. 238-251, Feb 2013, doi: 10.1364/josaa.30.000238.
[21] M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, "EXPERIMENTAL REALIZATION OF ANY DISCRETE UNITARY OPERATOR," (in English), Phys. Rev. Lett., Article vol. 73, no. 1, pp. 58-61, Jul 1994, doi: 10.1103/PhysRevLett.73.58.
[22] C. Alexiev, J. C. C. Mak, W. D. Sacher, and J. K. S. Poon, "Calibrating rectangular interferometer meshes with external photodetectors," OSA Continuum, vol. 4, no. 11, pp. 2892-2904, 2021/11/15 2021, doi: 10.1364/OSAC.437918.
[23] D. A. B. Miller, "Analyzing and generating multimode optical fields using self -configuring networks," (in English), Optica, Article vol. 7, no. 7, pp. 794-801, Jul 2020, doi: 10.1364/optica.391592.