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Modulation Instability in Driven VCSELs Above Threshold

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Abstract

Transverse dynamics of a broad-area semiconductor surface-emitting laser with a vertical resonator (VCSEL) with еxternal optical injection was investigated above threshold. It is obtained that two types of instabilities can develop in system: Turing and Hopf instabilities. Turing instability in turn can be subdivided into plane-wave instability (PWI) and modulation instability (MI). We found some sets of system parameters where the steady-state curve of the homogeneous solution can be bistable or monostable. Modulation instability can lead to the development of spatial patterns, which was obtained.

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REFERENCES

  1. Kumar, S., Suppression and control of modulation instability, Thesis for the Doctor’s degree of Philosophy in Physical Science, Spain, 2017.

  2. Rimoldi, C., Eslami, M., Prati, F., and Tissoni, G., Extreme events in a broad-area semiconductor laser with coherent injection, Phys. Rev. A, 2022, vol. 105, no. 2, pp. 023525-1-9.

    Article  Google Scholar 

  3. Malendevich, R., Jankovic, L., Stegeman, G., and Aitchisonet, J., Spatial modulation instability in a Kerr slab waveguide, Opt Lett., 2001, vol. 26, no. 23, pp. 1879–1881.

    Article  Google Scholar 

  4. Staliunas, K., Ctor, V., and Sá Nchez-Morcillo J., Spatial-localized structures in degenerate optical parametric oscillators, Phys. Rev. A, 1998, vol. 57, no. 2, pp. 1454–1457.

    Article  Google Scholar 

  5. Bespalov, V.I. and Talanov, V.I., Filamentary structure of light beams in nonlinear liquids, ZhETF Pis`ma, 1966, vol. 3, no. 11, pp. 471–476.

    Google Scholar 

  6. Zakharov, V.E. and Ostrovsky, L.A., Modulation instability: The beginning, Physica D, 2009, vol. 238, no. 5, pp. 540–548.

    Article  MathSciNet  MATH  Google Scholar 

  7. Tissoni, G., Lugiato, L.A., Protsenko, I., Kheradmand, R., and Brambilla, M., Cavity solitons in driven VCSELs above threshold, in Proc. of SPIE Conference: Quantum Electronics Conference-2005, 2005, vol. 5452, p. 133.

  8. Bergé, L., Wave collapse in physics: Principles and applications to light and plasma waves, Phys. Rep., 1998, vol. 303, no. 5, pp. 259–370.

    Article  MathSciNet  Google Scholar 

  9. Staliunas, K. and Sánchez-Morcillo, V., Transverse patterns in nonlinear optical resonators, Springer Tracts Mod. Phys., 2004, vol. 183.

    Google Scholar 

  10. Prati, F. and Columbo, L., Long-wavelength instability in broad-area semiconductor lasers, Phys. Rev. A, 2007, vol. 75, no. 5, pp. 053811-1-6.

    Article  Google Scholar 

  11. Ahmed, W.W., Kumar, S., Herrero, R., Botey, M., Radziunas, M., and Staliunaset, K., Stabilization of flat-mirror vertical-external-cavity surface-emitting lasers by spatiotemporal modulation of the pump profile, Phys. Rev. A, 2015, vol. 92, no. 4, pp. 043829-1-8.

    Article  Google Scholar 

  12. Ahmed, W.W., Kumar, S., Herrero, R., Botey, M., Radziunas, M., and Staliunaset, K., Suppression of modulation instability in pump modulated flat-mirror VECSELs, in Proc. of SPIE Nonlinear Optics and its Applications IV, Belgium, 2016, vol. 9894, pp. 27–33.

  13. Chih-Hsien Cheng, Wei-Chi Lo, Borching Su, Chao-Hsin Wu, and Gong-Ru Lin, Review of VCSELs for complex data-format transmission beyond 100-Gbit/s, IEEE Photonics J., 2021, vol. 13, no. 5. pp. 1–13.

    Article  Google Scholar 

  14. Hao-Tien, Cheng,Yun-Cheng, Yang,Te-Hua Liu, and Chao-Hsin Wu, Recent advances in 850 nm VCSELs for high-speed interconnects, Photonics, 2022. vol. 9, no. 2, p. 107.

    Article  Google Scholar 

  15. Anjin, Liu, Wolf, P., Bimberg, D., and Liu, A. Vertical-cavity surface-emitting lasers for data communication and sensing, Photonics Res., 2019, vol. 7, no. 2, pp. 121–136.

    Article  Google Scholar 

  16. Pakhomov, A.A., Molevich, N.E., Krents, A.A., and Anchikov, D.A., Intrinsic performance-limiting instabilities in two-level class-B broad-area lasers, Opt. Commun., 2016, vol. 372. pp. 14–21.

    Article  Google Scholar 

  17. Leyva, I. and Guerra, J.M., Time-resolved pattern evolution in a large-aperture class A laser, Phys. Rev. A, 2002, vol. 66, no. 2, p. 23820.

    Article  Google Scholar 

  18. Cabrera, E., Melle, S., Calderón, O., and Guerra, J., Dynamic transition from modelike patterns to turbulentlike patterns in a broad-area Nd:YAG laser, Opt. Lett., 2006, vol. 31, no. 8. pp. 1067–1069.

    Article  Google Scholar 

  19. Yarunova, E.A., Krents, A.A., and Molevich, N.E., Spatiotemporal dynamics of broad-area lasers with the pump modulation and injection of external optical radiation, Radiophys. Quantum Electron., 2021, vol. 64, no. 4, pp. 290–299.

    Article  Google Scholar 

  20. Wieczorek, S., Krauskopf, B., Simpson, T.B., and Lenstra, D., The dynamical complexity of optically injected semiconductor lasers, Phys. Rep., 2005. vol. 416, no. 1–2, pp. 1–128.

    Article  Google Scholar 

  21. Koch, T.L. and Bowers, J.E., Nature of wavelength chirping in directly modulated semiconductor lasers, Electron. Lett., 1984, vol. 20, no. 25, pp. 1038–1040.

    Article  Google Scholar 

  22. O’Brien, D., Hegarty, S.P., Huyet, G., and Uskov, A.V., Sensitivity of quantum-dot semiconductor lasers to optical feedback, Opt. Lett., 2004, vol. 29, no. 10, pp. 1072–1074.

    Article  Google Scholar 

  23. Li, H., Ye, J., and McInerney, J.G., Detailed analysis of coherence collapse in semiconductor lasers, IEEE J. Quantum Electron., 1993, vol. 29, no. 9, pp. 2421–2432.

    Article  Google Scholar 

  24. Tao Zhang, Ning Hua Zhu, Bang Hong Zhang, and Xin Zhang, Measurement of chirp parameter and modulation index of a semiconductor laser based on optical spectrum analysis, IEEE Photonics Technol. Lett., 2007, vol. 19, no. 4, pp. 227–229.

    Article  Google Scholar 

  25. Spinelli, L., Tissoni, G., Brambilla, M., Prati, F., and Lugiato, L.A., Spatial solitons in semiconductor microcavities, Phys. Rev. A, 1998, vol. 58, no. 3, pp. 2542–2559.

    Article  Google Scholar 

  26. Lugiato, L., Spinelli, L., Tissoni, G., and Brambilla, M., Modulational instabilities and cavity solitons in semiconductor microcavities, J. Opt. B, 1999, vol. 1, pp. 43–51.

    Article  Google Scholar 

  27. Brambilla, M., Lugiato, L.A., Prati, F., Spinelli, L., and Firthet, W.J., Spatial soliton pixels in semiconductor devices, Phys. Rev. Lett., 1997, vol. 79, no. 11, pp. 2042–2045.

    Article  Google Scholar 

  28. Tissoni, G., Spinelli, L., Brambilla, M., Maggipinto, T., Perrini, I., and Lugiato L., Cavity solitons in passive bulk semiconductor microcavities. I. Microscopic model and modulational instabilities, J. Opt. Soc. Am. B, 1999, vol. 16, no. 11, pp. 2083–2093.

    Article  Google Scholar 

  29. Eremin, Y.A. and Lopushenko, V.V., Numerical analysis of the functional properties of the 3d resonator of a plasmon nanolaser with regard to nonlocality and prism presence via the discrete sources method, Comput. Opt., 2021, vol. 45, no. 3, pp. 331–339.

    Article  Google Scholar 

  30. Golovashkin, D.L., Morunov, N.D., and Yablokova, L.V., Block algorithms to solve zheng/chen/zhang’s finite-difference equations, Comput. Opt., 2021, vol. 45, no. 3, pp. 461–468.

    Article  Google Scholar 

  31. Kalitkin N.N., Numerical Methods, Chief Editorial Board for Physical and Mathematical Literature, Moscow: Nauka, 1978.

    Google Scholar 

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Funding

This work was supported by the Ministry of Science and Higher Education of the Russian Federation within the framework of the state assignment (project no. 0023–2019–0003, FSSS–2023–0009).

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Authors and Affiliations

  1. Samara National Research University, 443086, Samara, Russia

    E. A. Yarunova, A. A. Krents & N. E. Molevich

  2. Lebedev Physical Institute, FIAN branch in Samara, 443110, Samara, Russia

    E. A. Yarunova, A. A. Krents & N. E. Molevich

Authors
  1. E. A. Yarunova
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  2. A. A. Krents
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  3. N. E. Molevich
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Correspondence to E. A. Yarunova.

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Yarunova, E.A., Krents, A.A. & Molevich, N.E. Modulation Instability in Driven VCSELs Above Threshold. Opt. Mem. Neural Networks 32 (Suppl 1), S46–S53 (2023). https://doi.org/10.3103/S1060992X2305020X

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  • DOI: https://doi.org/10.3103/S1060992X2305020X

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