Gain saturation effects in THz quantum cascade lasers
https://doi.org/10.29235/1561-2430-2022-58-2-237-244
Abstract
The effect of gain saturation in quantum-cascade structures with 2–4 quantum wells per period is herein analyzed on the basis of a system of balance equations. It is shown that the nonlinearity parameter decreases with an increase in the relaxation rate of laser levels, but the total current through the structure also increases. The use of the proposed multiphoton designs leads to a decrease in the non-linearity parameter without increasing the operating current. For example, in a two-photon scheme of laser transitions with the same transition probabilities and differential gains, two times slower saturation of the gain with an increase in the photon density is achieved, which leads to a high generation efficiency than in single-photon schemes.
About the Authors
D. V. UshakovBelarus
Dmitrii V. Ushakov – Ph. D. (Physics and Mathematics), Associate Professor, Dean of the Faculty of Radiophysics and Computer Technologies
4, Nezavisimosti Ave., 220030, Minsk
A. A. Afonenko
Belarus
Alexander A. Afonenko – Dr. Sc. (Physics and Mathematics), Associate Professor, Head of the Department of Quantum Radiophysics and Optoelectronics
4, Nezavisimosti Ave., 220030, Minsk
R. A. Khabibullin
Russian Federation
Rustam A. Khabibullin – Ph. D. (Physics and Mathematics), Senior Researcher
7, building 5, Nagorny proezd, 117105, Moscow
V. K. Kononenko
Belarus
Valerii K. Kononenko – Dr. Sc. (Physics and Mathematics), Professor, Professor of the Department of Quantum Radiophysics and Optoelectronics
4, Nezavisimosti Ave., 220030, Minsk
I. S. Manak
Belarus
Ivan S. Manak – Ph. D. (Physics and Mathematics), Associate Professor, Associate Professor of the Department of Quantum Radiophysics and Optoelectronics
4, Nezavisimosti Ave., 220030, Minsk
References
1. Ananiev Yu. A., Gribkovsky V. P., Mak A. A., Stepanov B. I. Optical properties of a four-level quantum generator. Doklady Akademii nauk SSSR = Proceedings of the USSR Academy of Sciences, 1963, vol. 150, no. 3, pp. 507–510 (in Russian).
2. Methods for Calculating Optical Quantum Generators. Ed. B. I. Stepanov. Minsk, Nauka i tekhnika Publ., 1968, vol. 1. 483 p. (in Russian).
3. Schulz-Dubois E. O. Pulse Sharpening and Gain Saturation in Traveling-Wave Masers. Bell System Technical Journal, 1964, vol. 43, no. 2, pp. 625–658. https://doi.org/10.1002/j.1538-7305.1964.tb00999.x
4. Rigrod W. W. Saturation Effects in High Gain Lasers. Journal of Applied Physics, 1965, vol. 36, no. 8, pp. 2487–2490. https://doi.org/10.1063/1.1714517
5. Kononenko V. K., Gribkovskii V. P. Effect of saturation in semiconductor light amplifiers and filters. Optika i spektroskopiya = Optics and Spectroscopy, 1970, vol. 29, no. 5. pp. 975–984 (in Russian).
6. Gribkovskii V. P. Theory of Absorption and Emission of Light in Semiconductors. Minsk, Nauka i tekhnika Publ., 1975. 464 p. (in Russian).
7. Gribkovsky V. P. Semiconductor Lasers. Minsk, Universitetskoe Publ., 1988. 304 p. (in Russian).
8. Kononenko V. K. Absorption saturation in the region of the tails of the state density. Journal of Applied Spectroscopy, 1984, vol. 41, no. 1, pp. 820–823. https://doi.org/10.1007/BF00657701
9. Gaponenko S. V., Zimin L. G., Nikeenko N. K. Saturation of absorption in zinc selenide. Journal of Applied Spectroscopy, 1984, vol. 40, no. 2, pp. 198–201. https://doi.org/10.1007/BF00660261
10. Göbel E. O., Höger R., Kuhl J., Polland H. J., Ploog K. Homogeneous gain saturation in GaAs/AlGaAs quantum well lasers. Journal of Applied Physics, 1985, vol. 47, no. 8, pp. 781–783. https://doi.org/10.1063/1.96036
11. Kononenko V. K. Nonlinear Absorption in Quantum-Size Heterostructures. Physica Status Solidi B, 1988, vol. 150, no. 2, pp. 695–698. https://doi.org/10.1002/pssb.2221500256
12. Kononenko V. K., Manak I. S., Furunzhiev É. R. Gain saturation in quantum-well heterostructures. Journal of Applied Spectroscopy, 1997, vol. 64, no. 6, pp. 813–817. https://doi.org/10.1007/BF02678866
13. Hasnain G., Chang-Hasnain C. J., Döhler G. H., Miller J. N., Johnson N. M., Whinnery J. R., Dienes A. Tunable absorption and electroluminescence in GaAs doping superlattices. Superlattices & Microstructures, 1987, vol. 3, no. 3, pp. 277– 282. https://doi.org/10.1016/0749-6036(87)90072-3
14. Renn M., Metzner C., Döhler G. H. Effect of random impurity distribution on the luminescence of n-i-p-i doping superlattices. Physical Review B, 1993, vol. 48, no. 15, pp. 11220–11227. https://doi.org/10.1103/PhysRevB.48.11220
15. Metzner C., Schrüfer K., Wieser U. [et al.]. Disorder effects on luminescence in δ-doped n-i-p-i superlattices. Physical Review B, 1995, vol. 51, no. 8, pp. 5106–5115. https://doi.org/10.1103/PhysRevB.51.5106
16. Ushakov D. V., Kononenko V. K., Manak I. S. Nonlinear optical properties in semiconductor doping superlattices. Journal of Applied Spectroscopy, 2001, vol. 68, no. 4, pp. 656–662. https://doi.org/10.1023/A:1012586425501
17. Ushakov D. V., Kononenko V. K., Manak I. S. Saturation of absorption in n-i-p-i crystals. SPIE Proceedings, 2001, vol. 4358, pp. 171–174. https://doi.org/10.1117/12.418850
18. Kononenko V. K., Smirnov A. G., Ushakov D. V. Influence of gain saturation on output power characteristics of the photonic crystal type heterostructures. Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya = Bulletin of the Russian Academy of Sciences: Physics, 2004, vol. 68, no. 1, pp. 127–130 (in Russian).
19. Kononenko V. K., Smirnov A. G., Ushakov D. V., Nefedov I. S. Photon Heterostructures on Semiconductor Doping Superlattices. Vestnik fonda fundamental’nykh issledovanii = Bulletin of the Foundation of Fundamental Research, 2005, vol. 34, no. 4, pp. 54–75 (in Russian).
20. Ushakov D. V., Kononenko V. K., Marciniak M. Nonlinearities in the reflection and transmission spectra of the photonic bandgap heterostructures with n-i-p-i crystals. Optical and Quantum Electronics, 2007, vol. 39, no. 4–6, pp. 431– 439. https://doi.org/10.1007/s11082-007-9083-7
21. Chanin D. J. Effect of gain saturation on injection laser switching. Journal of Applied Physics, 1979, vol. 50, no. 6, pp. 3858–3860. https://doi.org/10.1063/1.326510
22. Schatz R. Dynamics of Spatial Hole Burning Effects in DFB Lasers. IEEE Journal of Quantum Electronics, 1995, vol. 31, no. 11, pp. 1981–1993. https://doi.org/10.1109/3.469279
23. Huang J., Casperson L.W. Gain and saturation in semiconductor lasers. Optical and Quantum Electronics, 1993, vol. 25, no. 6, pp. 369–390. https://doi.org/10.1007/BF00420579
24. Agrawal G. P. Gain nonlinearities in semiconductor lasers: Theory and application to distributed feedback lasers. IEEE Journal of Quantum Electronics, 1987, vol. 23, no. 6, pp. 860–868. https://doi.org/10.1109/jqe.1987.1073406
25. Agrawal G. P. Spectral hole burning and gain saturation in semiconductor lasers: Strong signal theory. Journal of Applied Physics, 1988, vol. 63, no. 4, pp. 1232–1235. https://doi.org/10.1063/1.339990
26. Unterrainer K., Colombelli R., Gmachl C., Capasso F., Hwang H., Sergent A., Sivco D., and Cho A. Quantum cascade lasers with double metal-semiconductor waveguide resonators. Applied Physics Letters, 2002, vol. 80, no. 17, pp. 3060–3062. https://doi.org/10.1063/1.1469657
27. Fathololoumi S., Dupont E., Chan C. W. I., Wasilewski Z. R., Laframboise S. R., Ban D., Mátyás A., Jirauschek C., Hu Q., and Liu H. C. Terahertz quantum cascade lasers operating up to 200 K with optimized oscillator strength and improved injection tunneling. Optics Express, 2012, vol. 20, no. 4, pp. 3866–3876. https://doi.org/10.1364/OE.20.003866
28. Kumar S., Hu Q., Reno J. L. 186 K operation of terahertz quantum-cascade lasers based on a diagonal design. Applied Physics Letters, 2009, vol. 94, no. 13, pp. 131105. https://doi.org/10.1063/1.3114418
29. Bosco L., Franckié M., Scalari G., Beck M., Wacker A., Faist J. Thermoelectrically cooled THz quantum cascade laser operating up to 210 K. Applied Physics Letters, 2019, vol. 115, no. 1, pp. 010601. https://doi.org/10.1063/1.5110305
30. Ushakov D. V., Manak I. S. Two-period model for calculation of level populations in subbands of multi-period quantum-cascade superlattice structures. Journal of Applied Spectroscopy, 2007, vol. 74, no. 6, pp. 892–896. https://doi.org/10.1007/s10812-007-0138-0
31. Ushakov D. V., Afonenko A. A., Dubinov A. A., Gavrilenko V. I., Volkov O. Yu., Shchavruk N. V., Ponomarev D. S., Khabibullin R. A. Balance-equation method for simulating terahertz quantum-cascade lasers using a wave-function basis with reduced dipole moments of tunnel-coupled states. Quantum Electronics, 2019, vol. 49, no. 10, pp. 913–918. https://doi.org/10.1070/QEL17068
32. Ushakov D., Afonenko A., Khabibullin R., Ponomarev D., Aleshkin V., Morozov S., Dubinov A. HgCdTe-based quantum cascade lasers operating in the GaAs phonon Reststrahlen band predicted by the balance equation method. Optics Express, 2020, vol. 28, no. 17, pp. 25371–25382. https://doi.org/10.1364/OE.398552