Vol. 34, issue 10, article # 11

Abstract:

The process of second harmonic generation (SHG) of laser radiation in a BBO crystal is theoretically studied with the aim of determining optimal values of focusing and wave detuning parameters providing maximal SHG efficiency. This optimization problem is solved under an additional condition, that is, the maximal radiation power density should not exceed an a priori specified value. No restrictions are posed on the radiation power. The study consists of two parts. In the first part (this work), the influence of this additional condition on the process and results of solution of the optimization problem is studied with the use of the preset field approximation. Due to the additional condition, optimal focusing and wave detuning parameters become dependent on the radiation power, but the algorithm of solution of the problem becomes noticeably simpler, which allows the computation time to be significantly reduced, by about an order of magnitude.

Keywords:

second harmonic generation, solution to a set of nonlinear equations, preset field approximation, optimization of focusing and wave detuning parameter

References:

1. Dmitriev V.G., Tarasov L.V. Prikladnaya nelinejnaya optika. Izdanie 2-oe. M.: Fizmatlit, 2004. 512 p.
2. Boyd G.D., Kleinman D.A. Parametric interaction of focused Gaussian light beams // J. Appl. Phys. 1968. V. 39, N 8. P. 3597–3639.
3. Kolosov V.V., Troitskij V.O. Optimal'naya fokusirovka puchka pri generatsii vtoroj garmoniki v odnoosnom kristalle. Priblizhenie zadannogo polya // Optika atmosf. i okeana. 2007. V. 20, N 2. P. 106–112.
4. Troitskij V.O. Osobennosti generatsii vtoroj garmoniki lazernogo izlucheniya pri uglah sinhronizma, blizkih k 90° // Optika atmosf. i okeana. 2010. V. 23, N 7. P. 601–607; Troitskii V.O. Generation peculiarities of the second harmonics laser radiation at synchronism angles close to 90 // Atmos. Ocean. Opt. 2011. V. 24, N 1. P. 102–108.
5. Troitskij V.O. Nekotorye voprosy optimal'noj fokusirovki pri generatsii vtoroj garmoniki v nelinejnyh kristallah. Part 2. Rezul'taty chislennyh raschetov // Optika atmosf. i okeana. 2015. V. 28, N 10. P. 941–949; Troitskii V.O. Some problems of optimum focusing in the process of second harmonic generation in nonlinear crystals. Part 2. Results of numerical calculations // Atmos. Ocean. Opt. 2016. V. 29, N 2. P. 199–207.
6. Troitskij V.O. Optimizatsiya volnovoj rasstrojki pri effektivnoj generatsii vtoroj garmoniki // Optika atmosf. i okeana. 2020. V. 33, N 1. P. 25–31; Troitskii V.O. Optimization of wave detuning during effective second harmonic generation // Atmos. Ocean. Opt. 2020. V. 33, N 3. P. 238–244. DOI: 10.15372/AOO20200103.
7. Gulamov A.A., Ibragimov E.A., Redkorechev V.I. Preobrazovanie chastoty lazernogo izlucheniya s predel'noj effektivnost'yu. Tashkent: FAN, 1990. 248 p.
8. Kolosov V.V., Troitskij V.O. Paraksial'noe priblizhenie dlya zadachi rasprostraneniya puchkov v ploskosloistoj srede // Optika atmosf. i okeana. 2005. V. 18, N 9. P. 754–759.
9. Kato K. Second harmonic generation to 2048 A in b-BaB₂O₄ // IEEE J. Quant. Electron. 1986. V. QE-22, N 7. P. 1013–1014.
10.  Troitskij V.O. Generatsiya vtoroj garmoniki lazernogo izlucheniya v odnoosnyh kristallah. Varianty resheniya zadachi v priblizhenii zadannogo polya // Optika atmosf. i okeana. 2010. V. 23, N 4. P. 281–286; Troitskii V.O. Second harmonic generation of laser radiation in uniaxial crystals. Alternate problem solutions in the assumed field approximation // Atmos. Ocean. Opt. 2010. V. 23, N 4. P. 278–283.
11. Born M., Vol'f E. Osnovy optiki. M.: Nauka, 1973. 719 p.
12. Troitskij V.O. Generatsiya vtoroj garmoniki pri fokusirovke puchka v odnoosnyj kristall skreshchennymi tsilindricheskimi linzami. Priblizhenie zadannogo polya // Optika atmosf. i okeana. 2006. V. 19, N 8. P. 741–747.
13. Kolosov V.V., Troitskij V.O. Priblizhennaya metodika resheniya zadachi o generatsii vtoroj garmoniki v nelinejnyh kristallah. Part 2 // Optika atmosf. i okeana. 2019. V. 32, N 12. P. 1012–1019; Kolosov V.V., Troitskii V.O. Approximate technique for solving the problem of second harmonic generation in nonlinear crystals: Part 2 // Atmos. Ocean. Opt. 2020. V. 33, N 3. P. 312–319.
14. Kolosov V.V., Troitskij V.O. Priblizhennaya metodika resheniya zadachi o generatsii vtoroj garmoniki v nelinejnyh kristallah. Part 1 // Optika atmosf. i okeana. 2019. V. 32, N 12. P. 1001–1011; Kolosov V.V., Troitskii V.O. Approximate technique for solution of the problem of second harmonic generation in nonlinear crystals: Part 1 // Atmos. Ocean. Opt. 2020. V. 33, N 3. P. 302–311.