Vol. 140

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Degree of Depolarization of Quantization Hermite-Gaussian Beam in a Turbulent Atmosphere

By Licheng Zhang, Yixin Zhang, and Yun Zhu
Progress In Electromagnetics Research, Vol. 140, 471-490, 2013


Based on quantum Stokes operators and non-Kolmogorov spectrum model of index-of-refraction fluctuation, the analytical formulas for the quantum degree of depolarization of quantization Hermite-Gaussian (QHG) beams propagating in a turbulent atmosphere slant channel are derived. The nonclassical polarization properties of QHG beams propagating in turbulent atmosphere are studied numerically. It is found that the polarization fluctuations of QHG beams are dependent of the turbulence factors such as spectrum powerlaw exponent, refractive index structure parameter at the ground and zenith angle. The degree of depolarization of QHG beams has a saltation and reaches the minimum value at spectrum power-law exponent α = 11/3, the refractive index structure parameter at the ground of the turbulent atmosphere slightly affects the polarization degree of QHG beams which have travelled a long distance, and the change of polarization degree decreases with the increasing zenith angle. Furthermore, the numerical simulations show that QHG beams with higher photonnumber level, lower beam order, shorter wavelength are less affected by the turbulence. These results indicate that One can choose low-order QHG beams with wavelength λ = 690 nm as optical carrier, increase photon number, set the size of transmitting aperture ω0 as about 0.1 m, and detect communication signals at the central region of beams to improve the performance of a polarization-encoded free-space quantum communication system.


Licheng Zhang, Yixin Zhang, and Yun Zhu, "Degree of Depolarization of Quantization Hermite-Gaussian Beam in a Turbulent Atmosphere," Progress In Electromagnetics Research, Vol. 140, 471-490, 2013.


    1. Villoresi, P., T. Jennewein, F. Tamburini, M. Aspelmeyer, C. Bonato, R. Ursin, C. Pernechele, V. Luceri, G. Bianco, A. Zeilinger, and C. Barbieri, "Experimental verification of the feasibility of a quantum channel between space and Earth," New J. Phys., Vol. 10, No. 3, 033038, 2008.

    2. Bonato, C., A. Tomaello, V. D. Deppo, G. Naletto, and P. Villoresi, "Feasibility of satellite quantum key distribution," New J. Phys., Vol. 11, No. 4, 045017, 2009.

    3. Hughes, R. J., J. E. Nordholt, D. Derkacs, and C. G. Peterson, "Practical free-space quantum key distribution over 10km in daylight and at night," New J. Phys., Vol. 4, No. 3, 43, 2002.

    4. Rarity, J. G., P. R. Tapster, P. M. Gorman, and P. Knight, "Ground to satellite secure key exchange using quantum cryptography," New J. Phys., Vol. 4, No. 2, 82, 2002.

    5. Resch, K. J., M. Lindenthal, B. Blauensteiner, H. R. Böhm, A. C. Fedrizzi, A. Poppe, T. Schmitt-Manderbach, M. Taraba, R. Ursin, P. Walther, K. H. Weier, H. Weinfurter, and A. Zeilinger, "Distributing entanglement and single photons through an intracity, free-space quantum channel," Opt. Express, Vol. 13, No. 1, 202-209, 2005.

    6. Rarity, J. G., P. R. Tapster, and P. M. Gorman, "Secure free-space key exchange to 1.9km and beyond," J. Mod. Opt., Vol. 48, No. 13, 1887-1901, 2001.

    7. Kurtsiefer, C., P. Zarda, M. Halder, H.Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, "Quantum cryptography: A step towards global key distribution," Nature, Vol. 419, 450, 2002.

    8. Aspelmeyer, M., H. R. Böhm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science, Vol. 301, No. 5633, 621-623, 2003.

    9. Heim, B., D. Elser, T. Bartley, M. Sabuncu, C. Wittmann, D. Sych, C. Marquardt, and G. Leuchs, "Atmospheric channel characteristics for quantum communication with continuous polarization variables," Appl. Phys. B, Vol. 98, 635-640, 2010.

    10. Elser, D., T. Bartley, B. Heim, C. Wittmann, D. Sych, and G. Leuchs, "Feasibility of free space quantum key distribution with coherent polarization states," New J. Phys., Vol. 11, 045014, 2009.

    11. Semenov, A. A. and W. Vogel, "Entanglement transfer through the turbulent atmosphere," Phys. Rev. A, Vol. 81, 023835, 2010.

    12. Erven, C., C. Couteau, R. Laflamme, and G. Weihs, "Entangled quantum key distribution over two free-space optical links," Opt. Express, Vol. 16, No. 21, 16840-16853, 2008.

    13. Peng, C., T. Yang, X. Bao, J. Zhang, X. Jin, F. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B. Tian, and J. Pan, "Experimental free-space distribution of entangled photon pairs over 13 km: Towards satellite-based global quantum communication," Phys. Rev. Lett., Vol. 4, No. 15, 150501, 2005.

    14. Peloso, M. P., I. Gerhardt, C. H. A. Lamas-Linare, and C. Kurtsiefer, "Daylight operation of a free space, entanglement-based quantum key distribution system," New J. Phys., Vol. 11, 045007, 2009.

    15. Aspelmeyer, M., T. Jennewein, and A. Zeilinger, "Long-distance quantum communication with entangled photons using satellites," IEEE J. Select. Top. Quantu. Electro., Vol. 9, No. 6, 1541-1551, 2003.

    16. Zhang, S. and L. Yi, "Two-dimensional Hermite-Gaussian solutions in strongly nonlocal nonlinear medium with rectangular boundaries," Opt. Commun., Vol. 282, No. 8, 1654-1658, 2009.

    17. Walborn, S., S. Padua, and C. Monken, "Conservation and entanglement of Hermite-Gaussian modes in parametric down-conversion," Phys. Rev. A, Vol. 71, 053812, 2005.

    18. Meyrath, T., F. Schreck, and J. Hanssen, "A high frequency optical trap for atoms using Hermite-Gaussian beams," Opt. Express, Vol. 13, No. 8, 2843-2851, 2005.

    19. Young, C. Y., Y. V. Gilchrest, and B. R. Macon, "Turbulence-induced beam spreading of higher-order mode optical waves," Opt. Eng., Vol. 41, No. 5, 1097-1103, 2002.

    20. Yu, S. and W. Gu, "Generation of elegant Hermite-Gaussian beams using the graded-phase mirror," J. Opt. A: Pure Appl. Opt., Vol. 5, No. 5, 460, 2003.

    21. Chen, Y., T. Huang, C. Kao, C. Wang, and S. Wang, "Generation of Hermite-Gaussian modes in fiber-coupled laser-diode end-pumped lasers," IEEE J. Quantum Electron, Vol. 33, No. 6, 1025-1031, 1997.

    22. Cai, Y. and C. Chen, "Paraxial propagation of a partially coherent Hermite-Gaussian beam through aligned and misaligned ABCD optical systems," J. Opt. Soc. Am. A, Vol. 24, No. 8, 2394-2401, 2007.

    23. Qiu, Y., H. Guo, and Z. Chen, "Paraxial propagation of partially coherent Hermite-Gauss beams," Opt. Commun., Vol. 245, No. 1, 21-26, 2005.

    24. Ji, X., X. Chen, and B. Lv, "Spreading and directionality of partially coherent Hermite-Gaussian beams propagating through atmospheric turbulence," J. Opt. Soc. Am. A, Vol. 25, No. 1, 21-28, 2008.

    25. Chu, X., "Evolution of beam quality and shape of Hermite-Gaussian beam in non-Kolmogorov turbulence," Progress In Electromagnetics Research, Vol. 153, 339-353, 2011.

    26. Lv, B., H. Ma, and B. Zhang, "Propagation properties of cosh-Gaussian beams," Opt. Commun., Vol. 164, No. 4-6, 165-170, 1999.

    27. Jana, S. and S. Konar, "Tunable spectral switching in the far field with a chirped cosh-Gaussian pulse," Opt. Commun., Vol. 267, No. 1, 24-31, 2006.

    28. Konar, S., M. Mishra, and S. Jana, "Nonlinear evolution of cosh-Gaussian laser beams and generation of flat top spatial solitons in cubic quintic nonlinear media," Phys. Lett. A, Vol. 362, No. 5-6, 505-510, 2007.

    29. Li, Y., Z. Wu, and L. Wang, "Polarization characteristics of a partially coherent Gaussian Schell-mode beam in slant atmospheric turbulence," Progress In Electromagnetics Research, Vol. 121, 453-468, 2011.

    30. Tao, R., L. Si, Y. Ma, P. Zhou, and Z. Liu, "Relay propagation of partially coherent Cosh-Gaussian beams in non-Kolmogorov turbulence," Progress In Electromagnetics Research, Vol. 131, 495-515, 2012.

    31. Wu, Z., H. Wei, R. Yang, and L. Guo, "Study on scintillation considering inner-and outer-scales for laser beam propagation on the slant path through the atmospheric turbulence," Progress In Electromagnetics Research, Vol. 80, 277-293, 2008.

    32. Wei, H., Z.Wu, and Q. Ma, "Log-amplitude variance of laser beam propagation on the slant path through the turbulent atmosphere," Progress In Electromagnetics Research, Vol. 108, 277-291, 2010.

    33. Alodzhants, A. P., S. M. Arakelyan, and A. S. Chirkin, "Polarization quantum states of light in nonlinear distributed feedback systems: Quantum nondemolition measurements of the Stokes parameters of light and atomic angular momentum," Appl. Phys. B, Vol. 66, No. 1, 53-65, 1998.

    34. Wang, Y., Y. Zhang, J. Wang, and J. Jia, "Degree of polarization for single-photon beam in a turbulent atmosphere," Opt. Commun., Vol. 284, No. 13, 3221-3226, 2011.

    35. Perina, J., V. Perinova, M. C. Teich, and P. Diament, "Two descriptions for the photocounting detection of radiation passed through a random medium: A comparison for the turbulent atmosphere," Phys. Rev. A, Vol. 7, No. 5, 1732-1737, 1973.

    36. Perinova, V. and A. Luks, "Quantization of Hermite-Gaussian and Laguerre-Gaussian beams and their spatial transformations," J. Mod. Opt., Vol. 53, No. 5-6, 659-675, 2008.

    37. Wang, S. C. H. and M. A. Plonus, "Optical beam propagation for a partially coherent source in the turbulent atmosphere," J. Opt. Soc. Am., Vol. 69, No. 9, 1297-1304, 1979.

    38. Yura, H. T., "Mutual coherence function of a finite cross section: Optical beam propagating in turbulent medium," Appl. Opt., Vol. 11, No. 6, 1399-1406, 1972.

    39. Stribling, B. E., B. M. Welsh, and M. C. Roggemann, "Optical propagation in non-Kolmogorov atmospheric turbulence," Proc. SPIE, Vol. 2471, 181, 1995.

    40. Gradysteyn, I. S. and I. M. Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York, 1980.