#### For citation:

Morozov Y. A., Balakin M. I., Kochkurov L. A., Morozov M. I. Difference-Frequency Generator and Optical Parametric Oscillator Pumped by a Semiconductor Disk Laser: Comparative Study with a Time Delay Model. *Izvestiya of Saratov University. Physics *, 2019, vol. 19, iss. 1, pp. 34-42. DOI: 10.18500/1817-3020-2019-19-1-34-42

# Difference-Frequency Generator and Optical Parametric Oscillator Pumped by a Semiconductor Disk Laser: Comparative Study with a Time Delay Model

Background and Objectives: High-resolution spectroscopy is known to need sources of coherent radiation in the mid- and farinfrared spectral bands. Sources based on optical nonlinear interaction (a difference-frequency generator and an optical parametric oscillator) are known to be almost ideally suitable for an application. Intracavity realizations of the devices with a nonlinear crystal located in the cavity, can likely be made simple, compact and easy to use. Both a difference-frequency generator and an optical parametric oscillator may be thought of as a time delay dynamical system. The study of dynamical system stability and its transient dynamics that follows the primary pump turning on, is thus of importance. Such an analysis is among the main objectives of the manuscript. Materials and Methods: The mathematical model based on the differential rate equations with time delay has been proposed and numerically simulated. The linear stability of the steady state operation has been studied using the DDEBIFTOOL package. The transient dynamics of the dynamical system is analyzed with the Fortran codes. Results: The steady state operation point of the ICSRO is stable in a limited area the parameters, while that of the ICDFG keeps the stability for all values of the device parameters. The steady state operation takes on the order of 1000 carrier lifetimes to be settled. Conclusion: The findings obtained are of importance and have to be taken into account as the ICSRO and ICDFG to be applied in the high-resolution spectroscopy.

1. Tittel F. K., Richter D., Fried A. Mid-infrared laser applications in spectros copy. Ed. by I. T. Sorokina, K. L. Vodopyanov. Berlin, Heidelberg, Springer-Verlag, 2003, pp. 445–516.

2. Stothard D. J. M., Ebrahimzadeh M., Dunn M. H. Lowpump-threshold ontinuous-wave singly resonant optical parametric oscillator. Optics Letters, 1998, vol. 23, pp. 1895–1897.

3. Stothard D. J. M., Hopkins J.-M., Burns D., Dunn M. H. Stable, continuous-wave, intracav ity, optical parametric oscillator pumped by a semiconductor disk laser (VECSEL). Optics Express, 2009, vol. 17, pp. 10648–10658.

4. Scheller M., Yarborough J. M., Moloney J. V., Fallahi M., Koch M., Koch S. W. Room temperature continuous wave milliwatt terahertz sousce. Optics Express, 2010, vol. 18, pp. 27112–27117.

5. Lukowski M., Hessenius C., Bedford R., Fallahi M. Tunable type II intracavity difference frequency generation at 5.4 μm in a two chip vertical external cavity surface emitting laser. Optics Letters, 2015, vol. 40, pp. 4174–4177.

6. Morozov Yu. A., Morozov M. Yu., Kozlovsky V. I., Okhotnikov O. G. 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. of Selected Topics in Quantum Electron, 2015, vol. 21, pp. 1603105 (5 p).

7. Hessenius C., Lukowski M., Fallahi M. High-power tunable two-wavelength generation in a two chip co-linear T-cavity vertical external-cavity surface-emitting laser. Appl. Phys. Lett., 2012, vol. 101, pp. 121110.

8. Fan L., Fallahi M., Hader J., Zakharian A. R., Moloney J. V., Stolz W., Koch S. W., Bedford R., Murray J. T. Linearly polarized dual-wavelength vertical-externalcavity surface-emitting laser. Appl. Phys. Lett., 2007, vol. 90, pp. 181124.

9. Leinonen T., Morozov Yu. A., Härkönen A., Pessa M. Vertical external-cavity surface-emitting laser for dualwavelength generation. IEEE Phot. Techn. Lett., 2005, vol. 17, pp. 2508–2510.

10. Morozov Y. A. Multi-mode dynamics of optical oscillators based on intracavity nonlinear frequency downconversion. Appl. Phys. B, 2018, vol. 124, pp. 12 (7 p).

11. Calvez S., Burns D., Dawson M. D. Optimization of an optically pumped 1.3-μm GaInNAs vertical-cavity surface-emitting laser. IEEE Phot. Techn. Lett., 2002, vol. 14, pp. 131–133.

12. Levi O., Pinquet T., Skauli T., Eyres L., Parameswaran K., Harris J., Fejer M., Kulp T., Bisson S., Gerard B., Lallier E., Becouarn L. Difference frequency generation of 8-μm radiation in orientation-patterned GaAs. Opt. Lett., 2002, vol. 27, pp. 2091‒2093.

13. Park J.-D., Seo D.-S., McInerney J. Self-pulsations in strongly coupled asymmetric external cavity semiconductor lasers. IEEE J. Quantum Electron, 1990, vol. 26, pp.1353–1362.

14. Hui R.-Q., Tao S.-P. Improved rate equations for external cavity semiconductor lasers. IEEE J. Quantum Electron, 1989, vol. 25, pp. 1580–1584.

15. Tartwijk G. H. M. van, Lenstra D. Semiconductor laser with optical injection and feedback. Quantum Semiclass. Opt., 1995, vol. 7, pp. 87–143.

16. Morozov Yu. A., Leinonen T., Härkönen A., Pessa M. Simultaneous dual-wavelength emission from vertical external-cavity surface-emitting laser: A numerical modeling. IEEE J. Quantum Electron., 2006, vol. 42, pp. 1055–1061.

17. Lang R., Kobayashi K. External optical feedback effects on semiconductor injection laser properties. IEEE J. Quantum Electron., 1980, vol. 16, pp. 347–355.

18. Quantum-well lasers. Ed. by P. S. Zory. San Diego, Acad. Press, 1983. 504 p.

19. Rattunde M., Schmitz J., Mermelstein C., Kiefer R., Wagner J. III-Sb-based type-I QW diode lasers. Ed. by A. Krier. London, Springer, 2006, pp. 131–158 (Springer Series in Optical Sciences).

20. Engelborghs K., Luzyanina T., Samaey G. DDEBIFTOOL v.2.00 user manual: a Matlab package for bifurcation analysis of delay differential equations: Rep.: TW 330. Katholieke Universiteit Leuven. Leuven, Belgium, 2001.

21. Yanchuk S., Giacomelli G. Spatio-temporal phenomena in complex systems with time delays. J. Phys. A: Math. Theor., 2017, vol. 50, pp. 103001 (56 p).

- 1428 reads