Near-field propagation of vortex beams: Models and computation algorithms
Tóm tắt
Từ khóa
Tài liệu tham khảo
Wang, Z., Zhang, N., and Yuan, X.-C., High-volume optical vortex multiplexing and de-multiplexing for free-space optical communication, Optics Express, 2011, vol. 19, no. 2, pp. 482–492.
Wang, J., Yang, J.-Y., Fazal, I. M., Ahmed, N., Yan, Y., Huang, H., Ren, Y., Yue, Y., Dolinar, S., Tur, M., and Willner, A.E., Terabit free-space data transmission employing orbital angular momentum multiplexing, Nature Photonics, June 2012.
Torres, J. P., Multiplexing twisted light, Nature Photonics, June 2012.
Bozinovic, N., Yue, Y., Ren, Y., Tur, M., Kristensen, P., Huang, H., Willner, A.E., and Ramachandran, S., Terabit-scale orbital angular momentum mode division multiplexing in fibers, Science, 2013, vol. 340, no. 6140, pp. 1545–1548.
Khonina, S.N., Kazanskiy, N.L., and Soifer, V.A., Optical vortices in a fiber: mode division multiplexing and multimode self-imaging, in Recent Progress in Optical Fiber Research, Yasin, M.S., Harun, W., and Arof, H., Eds., Croatia: INTECH Publisher, 2012.
Martinez-Herrero, R., Mejias, P.M., Bosch, S., and Carnicer, A., Vectorial structure of nonparaxial electromagnetic beams, J. Opt. Soc. Am. A, 2001, vol. 18, pp. 1678–1680.
Ciattoni, A., Crosignani, B., and Porto, P.D., Vectorial analytical description of propagation of a highly non-paraxial beam, Opt. Commun., 2002, vol. 202, pp. 17–20.
Guha, Sh. and Gillen, G.D., Description of light propagation through a circular aperture using nonparaxial vector diffraction theory, Optics Express, 2005, vol. 13, no. 5, pp. 1424–1447.
Guo, H., Chen, J., and Zhuang, S., Vector plane wave spectrum of an arbitrary polarized electromagnetic wave, Optics Express, 2006, vol. 14, no. 6, pp. 2095–2100.
Deng, D. and Guo, Q., Analytical vectorial structure of radially polarized light beams, Optics Letters, 2007, vol. 32, no. 18, pp. 2711–2713.
Anokhov, S.P., Plane wave diffraction by a perfectly transparent half-plane, J. Opt. Soc. Am. A, 2007, vol. 24, no. 9, pp. 2493–2498.
Kovalev, A.A. and Kotlyar, V.V., Nonparaxial vectorial diffraction of the Gaussian beam by a spiral phase plate, Computer Optics, 2007, vol. 31, no. 4, pp. 19–22 [in Russian].
Wu, G., Lou, Q., and Zhou, J., Analytical vectorial structure of hollow Gaussian beams in the far eld, Optics Express, 2008, vol. 16, no. 9, pp. 6417–6424.
Zhou, G., The analytical vectorial structure of a nonparaxial Gaussian beam close to the source, Optics Express, 2008, vol. 16, no. 6, pp. 3504–3514.
Delen, N. and Hooker, B., Verification and comparison of a fast Fourier transform-based full diffraction method for tilted and offset planes, Applied Optics, 2001, vol. 40, no. 21, pp. 3525–3531.
Cooper, I.J., Sheppard, C.J.R., and Sharma, M., Numerical integration of diffraction integrals for a circular aperture, Optik, 2002, vol. 113, no. 7, pp. 293–298.
Duan, K. and Lu, B., A comparison of the vectorial nonparaxial approach with Fresnel and Fraunhofer approximations, Optik, 2004, vol. 115, no. 5, pp. 218–222.
Cooper, I.J., Sheppard, C.J.R., and Roy, M., The numerical integration of fundamental diraction integrals for converging polarized spherical waves using a two-dimensional form of Simpson’s 1/3 Rule, Journal of Modern Optics, 2005, vol. 52, no. 8, pp. 1123–1134.
Veerman, J.A.C., Rusch, J.J., and Paul Urbach, H., Calculation of the Rayleigh-Sommerfeld diffraction integral by exact integration of the fast oscillating factor, J. Opt. Soc. Am. A, 2005, vol. 22, no. 4, pp. 636–646.
Zhao, Z., Duan, K., and Lu, B., Focusing and diffraction by an optical lens and a small circular aperture, Optik, 2006, vol. 117, pp. 253–258.
Wang, X., Fan, Z., and Tang, T., Numerical calculation of a converging vector electromagnetic wave diffracted by an aperture by using Borgnis potentials. I. General theory, J. Opt. Soc. Am. A, 2006, vol. 23, no. 4, pp. 872–877.
Shen, F. and Wang, A., Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula, Applied Optics, 2006, vol. 45, no. 6, pp. 1102–1110.
Kotlyar, V.V., Kovalev, A.A., and Stafeev, S.S., Sharp focus area of radially-polarized Gaussian beam by propagation through an axicon, Prog. in Electr. Res. C, 2008, vol. 5, pp. 35–43.
Nascov, V. and Logof tu, P.C., Fast computation algorithm for the Rayleigh-Sommerfeld diffraction formula using a type of scaled convolution, Applied Optics, 2009, vol. 48, no. 22, pp. 4310–4319.
Matsushima, K. and Shimobaba, T., Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields, Optics Express, 2009, vol. 17, no. 22, pp. 19662–19673.
Ustinov, A.V., The fast way for calculation of first class Rayleigh-Sommerfeld integral, Computer Optics, 2009, vol. 33, no. 4, pp. 412–419 [in Russian].
Osterberg, H. and Smith, L.W., Closed solutions of Rayleigh’s diffraction integral for axial points, J. Opt. Soc. Am., 1961, vol. 51, pp. 1050–1054.
Wolf, E. and Marchand, E.W., Comparison of the Kirchhoff and the Rayleigh-Sommerfeld theories of diffraction at an aperture, J. Opt. Soc. Am., 1964, vol. 54, no. 5, pp. 587–594.
Gravelsaeter, T. and Stamnes, J.J., Diffraction by circular apertures. 1: Method of linear phase and amplitude approximation, Applied Optics, 1982, vol. 21, no. 20, pp. 3644–3651.
Sheppard, C.J.R. and Hrynevych, M., Diffraction by a circular aperture: a generalization of Fresnel diffraction theory, J. Opt. Soc. Am. A, 1992, vol. 9, no. 2, pp. 274–281.
Mielenz, K.D., Optical diffraction in close proximity to plane apertures. I. Boundary-value solutions for circular apertures and slits, J. Res. Natl. Inst. Stand. Technol., 2002, vol. 107, pp. 355–362.
Romero, J.A. and Hernández, L., Vectorial approach to Huygens’s principle for plane waves: circular aperture and zone plates, J. Opt. Soc. Am. A, 2006, vol. 23, no. 5, pp. 1141–1145.
Romero, J.A. and Hernández, L., Diffraction by a circular aperture: an application of the vectorial theory of Huygens’s principle in the near eld, J. Opt. Soc. Am. A, 2008, vol. 25, no. 8, pp. 2040–2043.
Li, J., Zhu, S., and Lu, B., The rigorous electromagnetic theory of the diffraction of vector beams by a circular aperture, Opt. Commun., 2009, vol. 282, pp. 4475–4480.
Born, M. and Wolf, E., Principles of Optics, 6th ed., Oxford: Pergamon, 1980, Chap. 8.3.
Andrews, C.L., Diffraction pattern in a circular aperture measured in the microwave region, J. Appl. Phys., 1950, vol. 21. pp. 761–767.
Silver, S., Microwave aperture antennas and diffraction theory, J. Opt. Soc. Am., 1962, vol. 52, pp. 131–139.
Totzeck, M., Validity of the scalar Kirchhoff and Rayleigh-Sommerfeld diffraction theories in the near field of small phase objects, J. Opt. Soc. Am. A, 1991, vol. 8, no. 1, pp. 27–32.
Tsoy, V.I. Melnikov, L.A., The use of Kirchho approach for the calculation of the near eld amplitudes of electromagnetic eld, Optics Communications, 2005, vol. 256, pp. 1–9.
Luneburg, R.K., Mathematical Theory of Optics, Berkeley, California: University of California Press, 1966.
Carter, W.H., Electromagnetic field of a Gaussian beam with an elliptical cross section, J. Opt. Soc. Am. A, 1972, vol. 62, no. 10, pp. 1195–1201.
Agrawal, G.P. and Pattanayak, D.N. Gaussian beam propagation beyond the paraxial approximation, J. Opt. Soc. Am. A, 1979, vol. 69, no. 4, pp. 575–578.
Marathay, A.S. and McCalmont, J.F., On the usual approximation used in the Rayleigh-Sommerfeld diffraction theory, J. Opt. Soc. Am. A, 2004, vol. 21, pp. 510–516.
Khonina, S.N., Ustinov, A.V., Volotovsky, S.G., and Ananin, M.A., Fast calculation algorithms for diffraction of radially-vortical laser fields on the microaperture, Izvest. SNC RAS, 2010, vol. 12, no. 3, pp. 15–25 [in Russian].
Mansuripur, M., Certain computational aspects of vector diffraction problems, J. Opt. Soc. Am. A, 1989, vol. 6, no. 5, pp. 786–805.
Lin, Y., Hu, J., and Wu, K., Vector fuzzy control iterative algorithm for the design of sub-wavelength diffractive optical elements for beam shaping, Optics Communications, 2009, vol. 282, pp. 3210–3215.
Desyatnikov, A.S., Torner, L., and Kivshar, Y.S., Optical vortices and vortex solitons, Progress in Optics, 2005, vol. 10, p. 47.
Soifer, V.A., Kotlyar, V.V., and Khonina, S.N., Optical microparticle manipulation: advances and new possibilities created by diffractive optics, Physics of Particles and Nuclei, 2004, vol. 35, no. 6, pp. 733–766.
Dienerowitz, M., Mazilu, M., Reece, P.J., Krauss, T.F., and Dholakia, K., Optical vortex trap for resonant confinement of metal nanoparticles, Opt. Express, 2008, vol. 16, no. 7, pp. 4991–4999.
Tychinskii, V.P., Super-resolution and singularities in phase images, Uspekhi Fizicheskikh Nauk, 2008, vol. 178, no. 11, pp. 1205–1214.
Wang, W., Ishii, N., Hanson, S.G., Miyamoto, Y., and Takeda, M., Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement, Opt. Commun., 2005, vol. 248, pp. 59–68.
Wang, W., Yokozeki, T., Ishijima, R., Wada, A., Miyamoto, Y., and Takeda, M., Optical vortex metrology for nanometric speckle displacement measurement, Opt. Express, 2006, vol. 14, no. 1, pp. 120–127.
Singh, R.K., Senthilkumaran, P., and Singh, K., Structure of a tightly focused vortex beam in the presence of primary coma, Optics Communications, 2009, vol. 282, pp. 1501–1510.
Kotlyar, V.V., Kovalev, A.A., Khonina, S.N., Skidanov, R.V., Soifer, V.A., Elfstrom, H., Tossavainen, N., and Turunen, J., Diffraction of conic and Gaussian beams by a spiral phase plate, Appl. Opt., 2006, vol. 45, no. 12, pp. 2656–2665.
Kotlyar, V.V., Kovalev, A.A., Skidanov, R.V., Moiseev, O.Yu., and Soifer, V.A., Diffraction of a finite-radius plane wave and a Gaussian beam by a helical axicon and a spiral phase plate, J. Opt. Soc. Am. A, 2007, vol. 24, no. 7, pp. 1955–1964.
Mei, Z. and Zhao, D., Nonparaxial analysis of vectorial Laguerre-Bessel-Gaussian beams, Opt. Express, 2007, vol. 15, pp. 11942–11951.
Kovalev, A.A. and Kotlyar, V.V., Nonparaxial vectorial diffraction of the Gaussian beam by a spiral phase plate, Computer Optics, 2007, vol. 31, no. 4, pp. 19–22 [in Russian].
Kotlyar, V. and Kovalev, A., Nonparaxial propagation of a Gaussian optical vortex with initial radial polarization, J. Opt. Soc. Am. A, 2010, vol. 27, no. 3, pp. 372–380.
Kotlyar, V.V., Almazov, A.A., Khonina, S.N., Soifer, V.A., Elfstrom, H., and Turunen, J., Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate, J. Opt. Soc. Am. A, 2005, vol. 22, no. 5, pp. 849–861.
Goodman, J.W., Introduction to Fourier Optics, McGraw-Hill, 1968, Chap. 3.
Vinogradova, M.B., Rudenko, O.V., and Sukhorukov, A.P., Wave Theory, 2nd ed., Moscow: “Nauka” Publisher, 1979 [in Russian].
Balalayev, S.A. and Khonina, S.N., Realisation of fast algorithm of Kirchhoff’s diffraction integral on an example of Bessel modes, Computer Optics, 2006, vol. 30, pp. 69–73 [in Russian].
Gradshteyn, S. and Ryzhik, I.M., Table of Integrals, Series, and Products, Elsevier, 2007.
Zhang, Y., Wang, L., and Zheng, C., Vector propagation of radially polarized Gaussian beams diffracted by an axicon, J. Opt. Soc. Am. A, 2005, vol. 22, no. 11, pp. 2542–2542.
Prudnikov, A.P., Brychkov, Yu.A., and Marychev, O.I., Integrals and Series. Special Functions, Moscow: “Nauka” Puiblishers, 1983 [in Russian].