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

For citation:

Morozov Y. A. Intracavity optical parametric oscillator: Model of dynamic system with different values of time delay for pump and signal radiation. Izvestiya VUZ. Applied Nonlinear Dynamics, 2021, vol. 29, iss. 5, pp. 727-738. DOI: 10.18500/0869-6632-2021-29-5-727-738

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 274)
Article type: 
535.015; 535.14; 535.530; 537.86

Intracavity optical parametric oscillator: Model of dynamic system with different values of time delay for pump and signal radiation

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

 Most of intracavity pumped optical parametric oscillators (OPO) are made nowaday according to a scheme with a single-resonance OPO located in the cavity of a pump laser. Usually the cavities of the pump and OPO (signal) emission have different values of round-trip time (delay). Aim of the study is therefore to build up the mathematical model of intracavity optical parametric oscillator (ICOPO) considered as a time-delay dynamic system with two values of delay in both cavities (the pump and signal). Methods. The model allows to analyze the steady state (equilibrium point) of the dynamic system and its stability with the help of characteristic equation’s solution. Results. Countless set of the characteristic equation roots is shown to consist of complex-conjugate pairs with imaginary parts which are nearly multiples of intermode beat frequencies in the pump and signal cavities. The diagram of stability depending on the position of nonlinear crystal in the resonator was built on the parameter plane. Features of the plane partition into the areas of stability/instabilty vs behavior of the characteristic equation roots are examined. Discussion. The results of the study allow to consider an ICOPO as the time-delay dynamic system thus adding to the physical picture of intracavity parametric oscillators.

This work was carried out within the framework of the state task of Kotelnikov IREE of RAS
  1. Faist J, Capasso F, Sivco DL, Sirtori C, Hutchinson AL, Cho AY. Quantum cascade laser. Science. 1994;264(5158):553–556. DOI: 10.1126/science.264.5158.553.
  2. Tittel FK, Richter D, Fried A. Mid-Infrared Laser Applications in Spectroscopy. In: Sorokina IT, Vodopyanov KL, editors. Solid-State Mid-Infrared Laser Sources. Vol. 89 of Topics in Applied Physics. Berlin, Heidelberg: Springer-Verlag; 2003. P. 458–529. DOI: 10.1007/3-540-36491-9_11.
  3. Dmitriev VG, Tarasov LV. Applied Nonlinear Optics. Moscow: FIZMATLIT; 2004. 512 p. (in Russian).
  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 Quantum Electronics. 2019; 51(3):70. DOI: 10.1007/s11082-019-1782-3.
  5. Wang K, Gao M, Yu S, Ning J, Xie Z, Lv X, Zhao G, Zhu S. A compact and high efficiency intracavity OPO based on periodically poled lithium niobate. Sci. Rep. 2021;11(1):5079. DOI: 10.1038/s41598-021-84721-9.
  6. Wu RF, Phua PB, Lai KS, Lim YL, Lau E, Chng A, Bonnin C, Lupinski D. Compact 21-w 2-µm intracavity optical parametric oscillator. Opt. Lett. 2000;25(19):1460–1462. DOI: 10.1364/OL.25.001460.
  7. Liu Y, Xie X, Ning J, Lv X, Zhao G, Xie Z, Zhu S. A high-power continuous-wave mid-infrared optical parametric oscillator module. Appl. Sci. 2018;8(1):1–5. DOI: 10.3390/app8010001.
  8. Morozov YA, Morozov MY, Kozlovsky VI, Okhotnikov OG. Compact intracavity singly-resonant optical parametric oscillator pumped by GaSb-based vertical external cavity surface-emitting laser: Concept and the main operational characteristics. IEEE J. Sel. Top. Quantum Electron. 2015;21(1):1603105. DOI: 10.1109/JSTQE.2014.2385310.
  9. Henderson AJ, Padgett MJ, Colville FG, Zhang J, Dunn MH. Doubly-resonant optical parametric oscillators: tuning behaviour and stability requirements. Opt. Commun. 1995;119(1–2):256–264. DOI: 10.1016/0030-4018(95)00278-G.
  10. Colville FG, Dunn MH, Ebrahimzadeh M. Continuous-wave, singly resonant, intracavity parametric oscillator. Opt. Lett. 1997;22(2):75–77. DOI: 10.1364/ol.22.000075.
  11. Stothard DJM, Ebrahimzadeh M, Dunn MH. Low-pump-threshold continuous-wave singly resonant optical parametric oscillator. Opt. Lett. 1998;23(24):1895–1897. DOI: 10.1364/OL.23.001895.
  12. Stothard DJM, Hopkins JM, Burns D, Dunn MH. Stable, continuous-wave, intracavity, optical parametric oscillator pumped by a semiconductor disk laser (VECSEL). Opt. Express. 2009;17(13): 10648–10658. DOI: 10.1364/OE.17.010648.
  13. Turnbull GA, Dunn MH, Ebrahimzadeh M. Continuous-wave, intracavity optical parametric oscillators: an analysis of power characteristics. Appl. Phys. B. 1998;66(6):701–710. DOI: 10.1007/s003400050456.
  14. Debuisschert T, Raffy J, Pocholle JP, Papuchon M. Intracavity optical parametric oscillator: study of the dynamics in pulsed regime. J. Opt. Soc. Am. B. 1996;13(7):1569–1587. DOI: 10.1364/JOSAB.13.001569.
  15. Morozov YA. Transient power characteristics of a compact singly resonant intracavity optical parametric oscillator pumped by a semiconductor disk laser. J. Opt. Soc. Am. B. 2016;33(7): 1470–1475. DOI: 10.1364/JOSAB.33.001470.
  16. Morozov YA. Multi-mode dynamics of optical oscillators based on intracavity nonlinear frequency down-conversion. Appl. Phys. B. 2018;124(1):12. DOI: 10.1007/s00340-017-6881-x.
  17. Hempler N, Robertson G, Hamilton C, Maker GT, Malcolm GPA. Advances in narrow-linewidth continuous wave semiconductor disk laser pumped optical parametric oscillators. Proc. SPIE. 2012;8242:82420J. DOI: 10.1117/12.905889.
  18. Morozov YA, Morozov MY, Balakin MI, Kochkurov LA, Konyukhov AI. Time-delay model of nonlinear frequency down-conversion in the cavity of a semiconductor disk laser. Physical Review Applied. 2019;11(4):044027. DOI: 10.1103/PhysRevApplied.11.044027.
  19. Morozov YA. Analysis of steady-state stability for intracavity optical parametric oscillator: Method of small-parameter expansion. Izvestiya VUZ. Applied Nonlinear Dynamics. 2020;28(4): 348–360 (in Russian). DOI: 10.18500/0869-6632-2020-28-4-348-360.
  20. Engelborghs K, Luzyanina T, Roose D. Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL. ACM Transactions on Mathematical Software. 2002;28(1): 1–21. DOI: 10.1145/513001.513002.