ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Morozov Y. A. Analysis of steady-state stability for intracavity optical parametric oscillator: Method of small-parameter expansion. Izvestiya VUZ. Applied Nonlinear Dynamics, 2020, vol. 28, iss. 4, pp. 348-360. DOI: 10.18500/0869-6632-2020-28-4-348-360

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535.015; 535.14; 535.530; 537.86

Analysis of steady-state stability for intracavity optical parametric oscillator: Method of small-parameter expansion

Morozov Y. A., Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences

The aim of the study is to analytically determine the linear stability of a steady-state operation point for an optical parametric oscillator (OPO) intracavity pumped by a semiconductor disk laser (SDL). Methods. In order to build the analytic approximation to the characteristic equation roots, the method of small-parameter expansion is used. The results of analytic and numerical methods are compared with each other. Results. As the primary pump intensity does not exceed the threshold value of parametric generation σOPO, the steady-state operation point is shown to be stable, like that of an ordinary SDL does. Small deviations relax to the steady state in the form of a pulse sequence with a period that equals one round-trip time. Relations defining the attenuation decrement and the carrier frequency of the pulse sequence are presented. The relative changes in these deviations during one cavity round-trip are independent of this round-trip time. It is shown that in the above-threshold regime there is such a pump intensity σAH > σOPO at which the steady state loses stability as a result of the Andronov–Hopf bifurcation. Discussion. The results of the study could be applied for making and analysis of new optical devices based on nonlinear-optical interaction.


1. Faist J., Capasso F., Sivco D.L., Sirtori C., Hutchinson A.L., and Cho A.Y. Quantum cascade laser // Science. 1994. Vol. 264. P. 553–556.

2. Tittel F.K., Richter D., and Fried A. Mid-Infrared Laser Applications in Spectroscopy. Berlin, Heidelberg: Springer-Verlag, 2003. 516 p.

3. He Y., Xu D., Yao J., Wang Y., Guo Y., Zhu X., Yan C., Tang L., Li J., Zhong K., Wu Y., and Yao J. Intracavity-pumped, mid-infrared tandem optical parametric oscillator based on BaGa4Se7 crystal // IEEE Phot. Journal. 2019. Vol. 11. 1300109 (10 pp).

4. Das S. Optical parametric oscillator: Status of tunable radiation in mid-IR to IR spectral range based on ZnGeP2 crystal pumped by solid state lasers // Optical and Quant. Electronics. 2019. Vol. 51. 70 (47 pp).

5. Deng C. Modeling of self-pumped singly resonant optical parametric oscillator // IEEE Phot. Journal. 2018. Vol. 10. 1502212 (13 pp).

6. Ebrahim-Zadeh M., Kumar S.C., Esteban-Martin A., and Samanta G.K. Breakthroughs in photonics 2012: Breakthroughs in optical parametric oscillators // IEEE Phot. Journal. 2013. Vol. 5. 0700105 (5 pp).

7. Stothard D.J.M., Hopkins J.-M., Burns D., and Dunn M.H. Stable, continuous-wave, intracavity, optical parametric oscillator pumped by a semiconductor disk laser (VECSEL) // Optics Express. 2009. Vol. 17. P. 10648–10658.

8. Morozov Y.A., Morozov M.Y., Kozlovsky V.I., and Okhotnikov O.G. Compact intracavity singlyresonant optical parametric oscillator pumped by GaSb-based vertical external cavity surfaceemitting laser: Concept and the main operational characteristics // IEEE J. of Selected Topics in Quantum Electron. 2015. Vol. 21. 1603105 (5 pp).

9. Turnbull G.A., Dunn M.H., and Ebrahimzadeh M. Continuous-wave, intracavity optical parametric oscillators: An analysis of power characteristics // Appl. Phys B. 1998. Vol. 66. P. 701–710.

10. Debuisschert T., Raffy J., Pocholle J.P., and Papuchon M. Intracavity optical parametric oscillator: Study of the dynamics in pulsed regime // JOSA B. 1996. Vol. 13. P. 1569–1587.

11. Morozov Y.A. Transient power characteristics of a compact singly resonant intracavity optical parametric oscillator pumped by a semiconductor disk laser // JOSA B. 2016. Vol. 33. P. 1470–1475.

12. Morozov Y.A., Morozov M.Y., Balakin M., Kochkurov L.A., and Konyukhov A.I. Time-delay model of nonlinear frequency down-conversion in the cavity of a semiconductor disk laser // Phys. Rev. Applied. 2019. Vol. 11. 044027 (8 pp).

13. Lang R. and Kobayashi K. External optical feedback effects on semiconductor injection laser properties // IEEE J. Quantum Electron. 1980. Vol. 16. P. 347–355.

14. Engelborghs K., Luzyanina T., and Roose D. Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL // ACM Transactions on Mathematical Software. 2002. Vol. 28. P. 1–21.

15. Naifeh A. Introduction to Perturbation Techniques. New York: John Wiley and Sons, 1981, 535 p.

16. Morozov M.Y., Morozov Y.A., and Krasnikova I.V. Dynamic regimes of the dual-wavelength vertical external cavity surface-emitting laser. Journ. of Commun. Technology and Electronics, 2010, vol. 55, pp. 1162–1168.

17. Tredicce J.R., Arecchi F.T., Lippi G.L., and Puccioni G.P. Instabilities in lasers with an injected signal // JOSA B. 1985. Vol. 2. P. 173–183.