Solving a spectral problem for large-area photonic crystal surface-emitting lasers
Abstract
We present algorithms for constructing and resolving spectral problems for novel photonic crystal surface-emitting lasers with large emission areas, given by first-order PDEs with two spatial dimensions. These algorithms include methods to overcome computer-arithmetic-related challenges when dealing with huge and small numbers. We show that the finite difference schemes constructed using relatively coarse numerical meshes enable accurate estimation of several major optical modes, which are essential in practical applications.
Keyword : modeling, finite difference, spectral problem, Green’s function, exponential growth, simulations, semiconductor laser, photonic crystal
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
M.J. Bergmann and H.C. Casey. Optical-field calculations for lossy multiple-layer AlxGa1−xN/InxGa1−xN laser diodes. Journal of Applied Physics, 84(3):1196– 1203, 1998. https://doi.org/10.1063/1.368185
J. Bezanson, A. Edelman, S. Karpinski and V.B. Shah. Julia: A fresh approach to numerical computing. SIAM review, 59(1):65–98, 2017. https://doi.org/10.1137/141000671
J. Chilwell and I. Hodgkinson. Thin-films field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides. Journal of the Optical Society of America A, 1(7):742–753, 1984. https://doi.org/10.1364/JOSAA.1.000742
M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata and G. Sasaki. Coherent two-dimensional lasing action in surface-emitting laser with triangularlattice photonic crystal structure. Applied Physics Letters, 75(3):316–318, 1999. https://doi.org/10.1063/1.124361
T. Inoue, R. Morita, M. Yoshida, M. De Zoysa, Y. Tanaka and S. Noda. Comprehensive analysis of photonic-crystal surface-emitting lasers via time-dependent three-dimensional coupled-wave theory. Physical Review B, 99(3):035308, 2019. https://doi.org/10.1103/PhysRevB.99.035308
Y. Liang, C. Peng, K. Sakai, S. Iwahashi and S. Noda. Three-dimensional coupled-wave analysis for square-lattice photonic crystal surface emitting lasers with transverse-electric polarization: finite-size effects. Optics Express, 20(14):15945–15961, 2012. https://doi.org/10.1364/OE.20.015945
C. Peng, Y. Liang, K. Sakai, S. Iwahashi and S. Noda. Coupledwave analysis for photonic-crystal surface-emitting lasers on air holes with arbitrary sidewalls. Optics Express, 19(24):24672–24686, 2011. https://doi.org/10.1364/OE.19.024672
M. Radziunas and R. Čiegis. Effective numerical algorithm for simulations of beam stabilization in broad area semiconductor lasers and amplifiers. Mathematical Modelling and Analysis, 19(5):627–646, 2014. https://doi.org/10.3846/13926292.2014.979453
M. Radziunas and H.-J. Wu¨nsche. Multisection lasers: Longitudinal modes and their dynamics. In J. Piprek(Ed.), Optoelectronic Devices - Advanced Simulation and Analysis, chapter 5, pp. 121–150. Springer, New York, 2005. https://doi.org/10.1007/0-387-27256-9_5
M. Yoshida, S. Katsuno, T. Inoue, J. Gelleta, K. Izumi, M. De Zoysa, K. Ishizaki and S. Noda. High-brightness scalable continuouswave single-mode photonic-crystal laser. Nature, 618(7966):727––732, 2023. https://doi.org/10.1038/s41586-023-06059-8
A. Zeghuzi, M. Radziunas, H.-J. Wünsche, J.-P. Koester, H. Wenzel, U. Bandelow and A. Knigge. Traveling wave analysis of non-thermal far-field blooming in high-power broad-area lasers. IEEE Journal of Quantum Electronics, 55(2):2000207, 2019. https://doi.org/10.1109/JQE.2019.2893352
A. Zeghuzi, H.-J. Wünsche, H. Wenzel, M. Radziunas, J. Fuhrmann, A. Klehr, U. Bandelow and A. Knigge. Time-dependent simulation of thermal lensing in high-power broad-area semiconductor lasers. IEEE Journal of Selected Topics in Quantum Electronics, 25(6):1502310, 2019. https://doi.org/10.1109/JSTQE.2019.2925926