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Numerical simulation of propagation of laser beams formed by multielement apertures in a turbulent atmosphere under thermal blooming

  • Optical Waves Propagation
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Abstract

An algorithm for simulating laser beam propagation in a turbulent atmosphere under conditions of thermal blooming for the case where the beam is formed by a multielement aperture is presented. Coherent and incoherent combining of elementary fields of the multielement aperture is considered. Based on numerical simulation, properties of a combined beam are analyzed in comparison with an equivalent Gaussian beam. A complex diffraction pattern is shown to appear upon coherent combinig as a result of superposition of fields formed by individual elements of the initial aperture. Average values of maximum intensity, both of the Gaussian beam and the combined laser beam, little differ from each other when the nonlinearity parameter N c > 1. Under conditions of strong turbulence and strong nonlinearity, integral radiation characteristics of combined beams are close to characteristics of the Gaussian beam, the effective size of which is determined by sizes of the combined beam. The intensity of combined laser beams in a turbulent atmosphere fluctuates upon incoherent combining of fields to a lesser extent as compared to coherent combining.

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References

  1. S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Introduction to Statistical Radiophysics. Random Fields (Nauka, Moscow, 1978) [in Russian].

    Google Scholar 

  2. V. I. Tatarskii, Wave Propagation in a Turbulent Atmosphere (Nauka, Moscow, 1967) [in Russian].

    Google Scholar 

  3. A. S. Gurvich, A. I. Kon, V. L. Mironov, and S. S. Khmelevtsov, Laser Radiation in a Turbulent Atmosphere (Nauka, Moscow, 1976) [in Russian].

    Google Scholar 

  4. V. A. Banakh and V. L. Mironov, Ranging Propagation of Laser Radiation in a Turbulent Atmosphere (Nauka, Novosibirsk, 1986) [in Russian].

    Google Scholar 

  5. V. E. Zuev, V. A. Banakh, and V. V. Pokasov, Optics of Turbulent Atmosphere (Gidrometeoizdat, Leningrad, 1988) [in Russian].

    Google Scholar 

  6. V. P. Aksenov, V. A. Banakh, V. V. Valuev, V. E. Zuev, V. V. Morozov, I. N. Smalikho, and R. Sh. Tsvyk, Powerful Laser Beams in Randomly Inhomogeneous Atmosphere, Ed. by V.A. Banakha (Izd-vo SO RAN, Novosibirsk, 1998) [in Russian].

  7. L. S. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE Press, Bellingham, Washington, 2005).

    Book  Google Scholar 

  8. V. P. Kandidov, “Monte Carlo Method in Nonlinear Statistical Optics,” Phys.-Uspekhi 39(12), 1243–1272 (1996).

    Article  ADS  Google Scholar 

  9. F. G. Gebhardt, “Twenty-Five of Thermal Blooming. An Overview,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, Proc. SPIE 1221, 2–25 (1990).

    Article  ADS  Google Scholar 

  10. Wm. A. Coles, J. P. Filice, and R. G. Frehlich, “Simulation of Wave Propagation in Three-Dimensional Random Media,” Appl. Opt. 34(12), 2089–2100 (1995).

    Article  ADS  Google Scholar 

  11. V. P. Lukin and B. V. Fortes, Adaptive Formation of Beams and Images in the Atmosphere (Publishing House of SB RAS, Novosibirsk, 1999) [in Russian].

    Google Scholar 

  12. J. M. Martin and S. M. Flatte, “Intensity Images and Statistics from Numerical Simulation of Wave Propagation in 3-D Random Media,” J. Opt. Soc. Amer. 27(11), 2111–2125 (2000).

    Google Scholar 

  13. V. A. Banakh, I. N. Smalikho, and C. Werner, “Numerical Simulation of the Effect Refractive Turbulence on Coherent Lidar Return Statistics in the Atmosphere,” Appl. Opt. 39(30), 5403–5414 (2000).

    Article  ADS  Google Scholar 

  14. J. A. Rubio, A. Belmonte, and A. Comeron, “Numerical Simulation of Long-Path Spherical Wave Propagation in Three-Dimensional Random Media,” Opt. Eng. 38(9), 1462–1469 (1999).

    Article  ADS  Google Scholar 

  15. G. Gbur and R. K. Tyson, “Vortex Beam Propagation through Atmospheric Turbulence and Topological Charge Conservation,” J. Opt. Soc. Amer., A 25(1), 225–230 (2008).

    Article  ADS  Google Scholar 

  16. F. Yu. Kanev and V. P. Lukin, Adaptive Optics. Numerical and Experimental Researches (Publishing House of IAO SB RAS, Tomsk, 2005) [in Russian].

    Google Scholar 

  17. R. Frehlich, “Simulation of Laser Propagation in a Turbulent Atmosphere,” Appl. Opt. 39(3), 393–397 (2000).

    Article  ADS  Google Scholar 

  18. V. A. Banakh, I. N. Smalikho, and A. V. Falits, “Effectiveness of the Subharmonic Method in Problems of Computer Simulation of Laser Beam Propagation in a Turbulent Atmosphere,” Atmos. Ocean. Opt. 25(2), 106–109 (2012).

    Article  Google Scholar 

  19. P. A. Konyaev, E. A. Tartakovskii, and G. A. Filimonov, “Computer Simulation of Optical Wave Propagation with the Use of Parallel Programming,” Atmos. Ocean. Opt. 24(5), 425–431 (2011).

    Article  Google Scholar 

  20. V. A. Banakh and A. V. Falits, “Turbulent Statistics of Laser Beam Intensity on Ground-to-Satellite Optical Link,” Proc. SPIE 4678, 132–143 (2001).

    Article  ADS  Google Scholar 

  21. S. L. Lachinova and M. A. Vorontsov, “Laser Beam Projection with Adaptive Array of Fiber Collimators. I. Basic Considerations for Analysis,” J. Opt. Soc. Amer., A 25(8), 1949–1959 (2008).

    Article  ADS  Google Scholar 

  22. S. L. Lachinova and M. A. Vorontsov, “Laser Beam Projection with Adaptive Array of Fiber Collimators. II. Analysis of Atmospheric Compensation Efficiency,” J. Opt. Soc. Amer., A 25(8), 1960–1973 (2008).

    Article  ADS  Google Scholar 

  23. T. Weyrauch, M. A. Vorontsov, G. W. Carhart, L. A. Beresnev, A. P. Rostov, E. E. Polnau, and J. J. Liu, “Experimental Demonstration of Coherent Beam Combining over a 7 km Propagation Path,” Opt. Lett. 36(22), 4455–4457 (2011).

    Article  ADS  Google Scholar 

  24. P. Sprangle, A. Ting, J. Pefiano, R. Fischer, and B. Hafizi, “Incoherent Combining and Atmospheric Propagation of High-Power Fiber Lasers for Directed-Energy Applications,” IEEE, J. Quant. Electron. 45(2), 138–148 (2009).

    Article  ADS  Google Scholar 

  25. H. T. Eyyuboglu, Y. Baykal, and V. Falits, “Scintillation Behavior of Laguerre Gaussian Beams in Strong Turbulence,” Appl. Phys., B 104(4), 1001–1006 (2011).

    Article  ADS  Google Scholar 

  26. C. Arpali, S. A. Arpali, Y. Baykal, and H. T. Eyyuboglu, “Intensity Fluctuations of Partially Coherent Laser Beam Arrays in Weak Atmospheric Turbulence,” Appl. Phys., B 103(1), 237–244 (2011).

    Article  ADS  Google Scholar 

  27. V. V. Vorob’ev, Thermal Blooming of Laser Radiation in the Atmosphere. Theory and Model Experiment (Nauka, Moscow, 1987) [in Russian].

    Google Scholar 

  28. V. A. Banakh, Kh. Verner, and I. N. Smalikho, “Effect of Turbulent Fluctuations of Refractive Index on the Time Spectrum of Wind Velocity Measured by Doppler lidar,” Atmos. Ocean. Opt. 13(9), 741–746 (2000).

    Google Scholar 

  29. V. V. Dudorov, V. V. Kolosov, and G. A. Filimonov, “Algorithm for Formation of an Infinite Random Turbulent Screen,” Proc. SPIE 6160, 61600 (2006).

    Article  Google Scholar 

  30. I. N. Smalikho, “Calculation of the Backscatter Amplification Coefficient of Laser Radiation Propagating in a Turbulent Atmosphere Using Numerical Simulation,” Atmos. Ocean. Opt. 26(2), 135–139 (2013).

    Article  Google Scholar 

  31. V. A. Banakh, V. V. Zhmylevskii, A. B. Ignat’ev, V. V. Morozov, and I. N. Smalikho, “Partially Coherent Laser Beam Pointing by Atmosphere Backscatter,” Atmos. Ocean. Opt. 24(2), 156–164 (2011).

    Article  Google Scholar 

  32. V. L. Mironov, Laser Beam Propagation in a Turbulent Atmosphere (Nauka, Novosibirsk, 1981) [in Russian].

    Google Scholar 

  33. V. A. Banakh, V. M. Buldakov, and V. L. Mironov, “Intensity Fluctuations of Partly Coherent Light Beam in a Turbulent Atmosphere,” Opt. Spektrosk. 54(6), 1054–1059 (1983).

    Google Scholar 

  34. V. A. Banakh and V. M. Buldakov, “Influence of Initial Degree of Light Beam Spatial Coherence on Intensity Fluctuations in a Turbulent Atmosphere,” Opt. Spektrosk. 55(4), 707–712 (1983).

    Google Scholar 

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Authors and Affiliations

  1. V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, pl. Akademika Zueva 1, Tomsk, 634021, Russia

    V. A. Banakh & A. V. Falits

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  1. V. A. Banakh
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  2. A. V. Falits
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Original Russian Text © V.A. Banakh, A. V. Falits, 2013, published in Optica Atmosfery i Okeana.

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Banakh, V.A., Falits, A.V. Numerical simulation of propagation of laser beams formed by multielement apertures in a turbulent atmosphere under thermal blooming. Atmos Ocean Opt 26, 455–465 (2013). https://doi.org/10.1134/S102485601306002X

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  • DOI: https://doi.org/10.1134/S102485601306002X

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