Research Article
BibTex RIS Cite

Arbitrary Phase Optimization Through Adaptively-Scheduled Nanophotonic Inverse Design

Year 2023, Volume: 7 Issue: 2, 142 - 159, 20.12.2023

Emir Salih Mağden

https://doi.org/10.38088/jise.1346005

Abstract

Design of integrated photonic devices continues to drive innovation in electro-optical systems for many applications ranging from communications to sensing and computing. Traditional design methods for integrated photonics involve using fundamental physical principles of guided-wave behavior to engineer optical functionalities for specific application requirements. While these traditional approaches may be sufficient for basic functionalities, the set of physically realizable optical capabilities these methods remains limited. Instead, photonic design can be formulated as an inverse problem where the target device functionality is specified, and a numerical optimizer creates the device with appropriate geometrical features within specified constraints. However, even with inverse design methods, achieving arbitrarily-specified phase offsets on-chip remains an important problem to solve for the reliability of interferometry-based nanophotonic applications. In order to address difficulties in achieving simultaneous phase and power optimization in inverse nanophotonic design, in this paper, we develop a set of optimization approaches that can enable user-specified phase differences in single-wavelength and multi-wavelength nanophotonic devices. By specifying phase offset targets for each output, we prevent convergence failures resulting from the changes in the figure of merit and gradient throughout the iterative optimization process. Additionally, by introducing phase-dependent figure of merit terms through an adaptive scheduling approach during the optimization, we accelerate device convergence up to a factor of 4.4 times. Our results outline a clear path towards the optimization of nanophotonic components with arbitrary phase-handling capabilities, with potential applications in a wide variety of integrated photonic systems and platforms.

Keywords

Nanophotonic Design Inverse Design Silicon Photonics

Project Number

119E195

References

  • Thomson, D., Zilkie, A., Bowers, J. E., Komljenovic, T., Reed, G. T., Vivien, L., Marris-Morini, D., Cassan, E., Virot, L., and Fédéli, J.-M. (2016). Roadmap on silicon photonics. Journal of Optics, 18(7), 073003.
  • Liu, A., Liao, L., Chetrit, Y., Basak, J., Nguyen, H., Rubin, D., and Paniccia, M. (2009). Wavelength division multiplexing based photonic integrated circuits on silicon-on-insulator platform. IEEE Journal of Selected Topics in Quantum Electronics, 16(1), 23-32.
  • Dong, P. (2016). Silicon photonic integrated circuits for wavelength-division multiplexing applications. IEEE Journal of Selected Topics in Quantum Electronics, 22(6), 370-378.
  • Heck, M. J., Bauters, J. F., Davenport, M. L., Spencer, D. T. and Bowers, J. E. (2014). Ultra‐low loss waveguide platform and its integration with silicon photonics. Laser & Photonics Reviews, 8(5), 667-686.
  • Lu, Z., Yun, H., Wang, Y., Chen, Z., Zhang, F., Jaeger, N. A., and Chrostowski, L. (2015). Broadband silicon photonic directional coupler using asymmetric-waveguide based phase control. Optics express, 23(3), 3795-3808.
  • Witzens, J. (2018). High-speed silicon photonics modulators. Proceedings of the IEEE, 106(12), 2158-2182.
  • Piels, M. and Bowers, J. E. (2023). Photodetectors for silicon photonic integrated circuits. Photodetectors, 419-436.
  • Bogaerts, W. and Chrostowski, L. (2018). Silicon photonics circuit design: methods, tools and challenges. Laser & Photonics Reviews, 12(4), 1700237.
  • Molesky, S., Lin, Z., Piggott, A. Y., Jin, W., Vucković, J., and Rodriguez, A. W. (2018). Inverse design in nanophotonics. Nature Photonics, 12(11), 659-670.
  • So, S., Badloe, T., Noh, J., Bravo-Abad, J. and Rho, J. (2020). Deep learning enabled inverse design in nanophotonics. Nanophotonics, 9(5), 1041-1057.
  • Jensen, J. S. and Sigmund, O. (2011). Topology optimization for nano‐photonics. Laser & Photonics Reviews, 5(2), 308-321.
  • Wiecha, P. R., Arbouet, A., Girard, C. and Muskens, O. L. (2021). Deep learning in nano-photonics: inverse design and beyond. Photonics Research, 9(5), B182-B200.
  • Piggott, A. Y., Petykiewicz, J., Su, L. and Vučković, J. (2017). Fabrication-constrained nanophotonic inverse design. Scientific reports, 7(1), 1786.
  • Tahersima, M. H., Kojima, K., Koike-Akino, T., Jha, D., Wang, B., Lin, C., and Parsons, K. (2019). Deep neural network inverse design of integrated photonic power splitters. Scientific reports, 9(1), 1368.
  • Jia, H., Zhou, T., Fu, X., Ding, J. and Yang, L. (2018). Inverse-design and demonstration of ultracompact silicon meta-structure mode exchange device. Acs Photonics, 5(5), 1833-1838.
  • Piggott, A. Y., Ma, E. Y., Su, L., Ahn, G. H., Sapra, N. V., Vercruysse, D., Netherton, A. M., Khope, A. S., Bowers, J. E., and Vuckovic, J. (2020). Inverse-designed photonics for semiconductor foundries. ACS Photonics, 7(3), 569-575.
  • Hammond, A. M., Slaby, J. B., Probst, M. J. and Ralph, S. E. (2022). Phase-Injected Topology Optimization for Scalable and Interferometrically Robust Photonic Integrated Circuits. ACS Photonics, 10(4), 808-814.
  • Guan, H., Ma, Y., Shi, R., Zhu, X., Younce, R., Chen, Y., Roman, J., Ophir, N., Liu, Y., and Ding, R. (2017). Compact and low loss 90° optical hybrid on a silicon-on-insulator platform. Optics Express, 25(23), 28957-28968.
  • Schenk, O. and Gärtner, K. (2004). Solving unsymmetric sparse systems of linear equations with PARDISO. Future Generation Computer Systems, 20(3), 475-487.
  • Zeng, Z., Venuthurumilli, P. K. and Xu, X. (2021). Inverse design of plasmonic structures with FDTD. ACS Photonics, 8(5), 1489-1496.
  • Hammond, A. M., Oskooi, A., Johnson, S. G. and Ralph, S. E. (2021). Photonic topology optimization with semiconductor-foundry design-rule constraints. Optics Express, 29(15), 23916-23938.
  • Li, Z., Pestourie, R., Park, J.-S., Huang, Y.-W., Johnson, S. G., and Capasso, F. (2022). Inverse design enables large-scale high-performance meta-optics reshaping virtual reality. Nature communications, 13(1), 2409.
  • Hammond, A. M., Oskooi, A., Chen, M., Lin, Z., Johnson, S. G., and Ralph, S. E. (2022). High-performance hybrid time/frequency-domain topology optimization for large-scale photonics inverse design. Optics Express, 30(3), 4467-4491.
  • Piggott, A. Y., Lu, J., Lagoudakis, K. G., Petykiewicz, J., Babinec, T. M., and Vučković, J. (2015). Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics, 9(6), 374-377.
  • Hughes, T. W., Minkov, M., Williamson, I. A. and Fan, S. (2018). Adjoint method and inverse design for nonlinear nanophotonic devices. ACS Photonics, 5(12), 4781-4787.
  • Minkov, M., Williamson, I. A., Andreani, L. C., Gerace, D., Lou, B., Song, A. Y., Hughes, T. W., and Fan, S. (2020). Inverse design of photonic crystals through automatic differentiation. Acs Photonics, 7(7), 1729-1741.
  • Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., and Lerer, A. (2017). Automatic differentiation in pytorch.
  • Yuan, Y.-x. (1991). A modified BFGS algorithm for unconstrained optimization. IMA Journal of Numerical Analysis, 11(3), 325-332.
  • Chang, W., Ren, X., Ao, Y., Lu, L., Cheng, M., Deng, L., Liu, D., and Zhang, M. (2018). Inverse design and demonstration of an ultracompact broadband dual-mode 3 dB power splitter. Optics Express, 26(18), 24135-24144.
  • Xu, J., Liu, Y., Guo, X., Song, Q. and Xu, K. (2022). Inverse design of a dual-mode 3-dB optical power splitter with a 445 nm bandwidth. Optics Express, 30(15), 26266-26274.
  • Li, R., Zhang, C., Xie, W., Gong, Y., Ding, F., Dai, H., Chen, Z., Yin, F., and Zhang, Z. (2023). Deep reinforcement learning empowers automated inverse design and optimization of photonic crystals for nanoscale laser cavities. Nanophotonics, 12(2), 319-334.
  • Xu, K., Liu, L., Wen, X., Sun, W., Zhang, N., Yi, N., Sun, S., Xiao, S., and Song, Q. (2017). Integrated photonic power divider with arbitrary power ratios. Optics letters, 42(4), 855-858.
  • Hughes, T. W., Williamson, I. A., Minkov, M. and Fan, S. (2019). Forward-mode differentiation of Maxwell’s equations. ACS Photonics, 6(11), 3010-3016.

Year 2023, Volume: 7 Issue: 2, 142 - 159, 20.12.2023

Emir Salih Mağden

https://doi.org/10.38088/jise.1346005

Abstract

Supporting Institution

Türkiye Bilimsel ve Teknolojik Araştırma Kurumu - TÜBİTAK

Project Number

119E195

References

  • Thomson, D., Zilkie, A., Bowers, J. E., Komljenovic, T., Reed, G. T., Vivien, L., Marris-Morini, D., Cassan, E., Virot, L., and Fédéli, J.-M. (2016). Roadmap on silicon photonics. Journal of Optics, 18(7), 073003.
  • Liu, A., Liao, L., Chetrit, Y., Basak, J., Nguyen, H., Rubin, D., and Paniccia, M. (2009). Wavelength division multiplexing based photonic integrated circuits on silicon-on-insulator platform. IEEE Journal of Selected Topics in Quantum Electronics, 16(1), 23-32.
  • Dong, P. (2016). Silicon photonic integrated circuits for wavelength-division multiplexing applications. IEEE Journal of Selected Topics in Quantum Electronics, 22(6), 370-378.
  • Heck, M. J., Bauters, J. F., Davenport, M. L., Spencer, D. T. and Bowers, J. E. (2014). Ultra‐low loss waveguide platform and its integration with silicon photonics. Laser & Photonics Reviews, 8(5), 667-686.
  • Lu, Z., Yun, H., Wang, Y., Chen, Z., Zhang, F., Jaeger, N. A., and Chrostowski, L. (2015). Broadband silicon photonic directional coupler using asymmetric-waveguide based phase control. Optics express, 23(3), 3795-3808.
  • Witzens, J. (2018). High-speed silicon photonics modulators. Proceedings of the IEEE, 106(12), 2158-2182.
  • Piels, M. and Bowers, J. E. (2023). Photodetectors for silicon photonic integrated circuits. Photodetectors, 419-436.
  • Bogaerts, W. and Chrostowski, L. (2018). Silicon photonics circuit design: methods, tools and challenges. Laser & Photonics Reviews, 12(4), 1700237.
  • Molesky, S., Lin, Z., Piggott, A. Y., Jin, W., Vucković, J., and Rodriguez, A. W. (2018). Inverse design in nanophotonics. Nature Photonics, 12(11), 659-670.
  • So, S., Badloe, T., Noh, J., Bravo-Abad, J. and Rho, J. (2020). Deep learning enabled inverse design in nanophotonics. Nanophotonics, 9(5), 1041-1057.
  • Jensen, J. S. and Sigmund, O. (2011). Topology optimization for nano‐photonics. Laser & Photonics Reviews, 5(2), 308-321.
  • Wiecha, P. R., Arbouet, A., Girard, C. and Muskens, O. L. (2021). Deep learning in nano-photonics: inverse design and beyond. Photonics Research, 9(5), B182-B200.
  • Piggott, A. Y., Petykiewicz, J., Su, L. and Vučković, J. (2017). Fabrication-constrained nanophotonic inverse design. Scientific reports, 7(1), 1786.
  • Tahersima, M. H., Kojima, K., Koike-Akino, T., Jha, D., Wang, B., Lin, C., and Parsons, K. (2019). Deep neural network inverse design of integrated photonic power splitters. Scientific reports, 9(1), 1368.
  • Jia, H., Zhou, T., Fu, X., Ding, J. and Yang, L. (2018). Inverse-design and demonstration of ultracompact silicon meta-structure mode exchange device. Acs Photonics, 5(5), 1833-1838.
  • Piggott, A. Y., Ma, E. Y., Su, L., Ahn, G. H., Sapra, N. V., Vercruysse, D., Netherton, A. M., Khope, A. S., Bowers, J. E., and Vuckovic, J. (2020). Inverse-designed photonics for semiconductor foundries. ACS Photonics, 7(3), 569-575.
  • Hammond, A. M., Slaby, J. B., Probst, M. J. and Ralph, S. E. (2022). Phase-Injected Topology Optimization for Scalable and Interferometrically Robust Photonic Integrated Circuits. ACS Photonics, 10(4), 808-814.
  • Guan, H., Ma, Y., Shi, R., Zhu, X., Younce, R., Chen, Y., Roman, J., Ophir, N., Liu, Y., and Ding, R. (2017). Compact and low loss 90° optical hybrid on a silicon-on-insulator platform. Optics Express, 25(23), 28957-28968.
  • Schenk, O. and Gärtner, K. (2004). Solving unsymmetric sparse systems of linear equations with PARDISO. Future Generation Computer Systems, 20(3), 475-487.
  • Zeng, Z., Venuthurumilli, P. K. and Xu, X. (2021). Inverse design of plasmonic structures with FDTD. ACS Photonics, 8(5), 1489-1496.
  • Hammond, A. M., Oskooi, A., Johnson, S. G. and Ralph, S. E. (2021). Photonic topology optimization with semiconductor-foundry design-rule constraints. Optics Express, 29(15), 23916-23938.
  • Li, Z., Pestourie, R., Park, J.-S., Huang, Y.-W., Johnson, S. G., and Capasso, F. (2022). Inverse design enables large-scale high-performance meta-optics reshaping virtual reality. Nature communications, 13(1), 2409.
  • Hammond, A. M., Oskooi, A., Chen, M., Lin, Z., Johnson, S. G., and Ralph, S. E. (2022). High-performance hybrid time/frequency-domain topology optimization for large-scale photonics inverse design. Optics Express, 30(3), 4467-4491.
  • Piggott, A. Y., Lu, J., Lagoudakis, K. G., Petykiewicz, J., Babinec, T. M., and Vučković, J. (2015). Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics, 9(6), 374-377.
  • Hughes, T. W., Minkov, M., Williamson, I. A. and Fan, S. (2018). Adjoint method and inverse design for nonlinear nanophotonic devices. ACS Photonics, 5(12), 4781-4787.
  • Minkov, M., Williamson, I. A., Andreani, L. C., Gerace, D., Lou, B., Song, A. Y., Hughes, T. W., and Fan, S. (2020). Inverse design of photonic crystals through automatic differentiation. Acs Photonics, 7(7), 1729-1741.
  • Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., and Lerer, A. (2017). Automatic differentiation in pytorch.
  • Yuan, Y.-x. (1991). A modified BFGS algorithm for unconstrained optimization. IMA Journal of Numerical Analysis, 11(3), 325-332.
  • Chang, W., Ren, X., Ao, Y., Lu, L., Cheng, M., Deng, L., Liu, D., and Zhang, M. (2018). Inverse design and demonstration of an ultracompact broadband dual-mode 3 dB power splitter. Optics Express, 26(18), 24135-24144.
  • Xu, J., Liu, Y., Guo, X., Song, Q. and Xu, K. (2022). Inverse design of a dual-mode 3-dB optical power splitter with a 445 nm bandwidth. Optics Express, 30(15), 26266-26274.
  • Li, R., Zhang, C., Xie, W., Gong, Y., Ding, F., Dai, H., Chen, Z., Yin, F., and Zhang, Z. (2023). Deep reinforcement learning empowers automated inverse design and optimization of photonic crystals for nanoscale laser cavities. Nanophotonics, 12(2), 319-334.
  • Xu, K., Liu, L., Wen, X., Sun, W., Zhang, N., Yi, N., Sun, S., Xiao, S., and Song, Q. (2017). Integrated photonic power divider with arbitrary power ratios. Optics letters, 42(4), 855-858.
  • Hughes, T. W., Williamson, I. A., Minkov, M. and Fan, S. (2019). Forward-mode differentiation of Maxwell’s equations. ACS Photonics, 6(11), 3010-3016.
There are 33 citations in total.

Details

Primary Language English
Subjects Photonics, Optoelectronics and Optical Communications, Photonic and Electro-Optical Devices, Sensors and Systems (Excl. Communications)
Journal Section Research Articles
Authors

Emir Salih Mağden 0000-0001-7680-6818

Project Number 119E195
Early Pub Date November 6, 2023
Publication Date December 20, 2023
Published in Issue Year 2023Volume: 7 Issue: 2

Cite

APA Mağden, E. S. (2023). Arbitrary Phase Optimization Through Adaptively-Scheduled Nanophotonic Inverse Design. Journal of Innovative Science and Engineering, 7(2), 142-159. https://doi.org/10.38088/jise.1346005
AMA Mağden ES. Arbitrary Phase Optimization Through Adaptively-Scheduled Nanophotonic Inverse Design. JISE. December 2023;7(2):142-159. doi:10.38088/jise.1346005
Chicago Mağden, Emir Salih. “Arbitrary Phase Optimization Through Adaptively-Scheduled Nanophotonic Inverse Design”. Journal of Innovative Science and Engineering 7, no. 2 (December 2023): 142-59. https://doi.org/10.38088/jise.1346005.
EndNote Mağden ES (December 1, 2023) Arbitrary Phase Optimization Through Adaptively-Scheduled Nanophotonic Inverse Design. Journal of Innovative Science and Engineering 7 2 142–159.
IEEE E. S. Mağden, “Arbitrary Phase Optimization Through Adaptively-Scheduled Nanophotonic Inverse Design”, JISE, vol. 7, no. 2, pp. 142–159, 2023, doi: 10.38088/jise.1346005.
ISNAD Mağden, Emir Salih. “Arbitrary Phase Optimization Through Adaptively-Scheduled Nanophotonic Inverse Design”. Journal of Innovative Science and Engineering 7/2 (December 2023), 142-159. https://doi.org/10.38088/jise.1346005.
JAMA Mağden ES. Arbitrary Phase Optimization Through Adaptively-Scheduled Nanophotonic Inverse Design. JISE. 2023;7:142–159.
MLA Mağden, Emir Salih. “Arbitrary Phase Optimization Through Adaptively-Scheduled Nanophotonic Inverse Design”. Journal of Innovative Science and Engineering, vol. 7, no. 2, 2023, pp. 142-59, doi:10.38088/jise.1346005.
Vancouver Mağden ES. Arbitrary Phase Optimization Through Adaptively-Scheduled Nanophotonic Inverse Design. JISE. 2023;7(2):142-59.
 Download Cover Image


Creative Commons License

The works published in Journal of Innovative Science and Engineering (JISE) are licensed under a  Creative Commons Attribution-NonCommercial 4.0 International License.