A study of propagation of cosh-squared-Gaussian beam through fractional Fourier transform systems

• Autorzy: Hashemi S. S. , Ghavami S. S. , Soltanolkotabi M. , Branch F.
• Języki publikacji: PL

Abstrakty

EN

In this paper, we consider properties of cosh-squared-Gaussian beam passing through ideal and apertured fractional Fourier transforms (FRFT) systems. We use Collins integral formula and the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions. These studies indicate that the normalized intensity distributions with FRFT order are periodic. The variation period is 2 and is independent of the impact of aperture.

Słowa kluczowe

EN

cosh-squared-Gaussian; fractional Fourier transforms (FRFT)

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Optica Applicata
• Rocznik: 2011
• Tom: Vol. 41, nr 4
• Strony: 897--909
• Opis fizyczny: Bibliogr. 36 poz.

Twórcy

autor

Hashemi S. S.

autor

Ghavami S. S.

autor

Soltanolkotabi M.

autor

Branch F.

• Islamic Azad University, Isfahan, Iran

Bibliografia

• [1] NAMIAS V., The fractional order Fourier transform and its application in quantum mechanics, Journal of Applied Mathematics 25(3), 1980, pp. 241–265.
• [2] MCBRIDE A.C., KERR F.H., On namias’s fractional Fourier transforms, Journal of Applied Mathematics 39(2), 1987, pp. 159–175.
• [3] MENDLOVIC D., OZAKTAS H.M., Fractional Fourier transforms and their optical implementation: I, Journal of the Optical Society of America A 10(9),1993, pp. 1875–1881.
• [4] OZAKTAS H.M., MENDLOVIC D., Fractional Fourier transforms and their optical implementation: II, Journal of the Optical Society of America A 10(12), 1993, pp. 2522–2531.
• [5] LOHMANN A.W., Image rotation, Wigner rotation, and the fractional Fourier transform, Journal of the Optical Society of America A 10(10), 1993, pp. 2181–2187.
• [6] WANG X., ZHAO D., Image encryption based on anamorphic fractional Fourier transform and three-step phase-shifting interferometry, Optics Communications 268(2), 2006, pp. 240–244.
• [7] JIN W., MA L., YAN C., Real color fractional Fourier transform holograms, Optics Communications 259(2), 2006, pp. 513–516.
• [8] WANG X., ZHOU J., Scaled fractional Fourier transform and optical systems, Optics Communications 147(4–6), 1998, pp. 341–348.
• [9] SAHIN A., OZAKTAS H.M., MENDLOVIC D., Optical implementation of the two-dimensional fractional Fourier transform with different orders in the two dimensions, Optics Communications 120(3–4), 1995, pp. 134–138.
• [10] LÜ B., KONG F., ZHANG B., Optical systems expressed in terms of fractional Fourier transforms, Optics Communications 137(1–3), 1997, pp. 13–16.
• [11] CAI L.Z., YANG X.L., Observation of fractional Fourier transforms of continuously variable orders with a scale invariant input, Optics Communications 201(4–6), 2002, pp. 319–323.
• [12] DU X., ZHAO D., Elliptical cosh-Gaussian beams, Optics Communications 265(2), 2006, pp. 418–424.
• [13] CAI Y., LIN Q., Fractional Fourier transform for elliptical Gaussian beams, Optics Communications 217(1–6), 2003, pp. 7–13.
• [14] WANG F., CAI Y., Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics, Journal of the Optical Society of America A 24(7), 2007,pp. 1937–1944
• [15] ZHENG C., Fractional Fourier transform for partially coherent off-axis Gaussian Schell-model beam,Journal of the Optical Society of America A 23(9), 2006, pp.2161–2165.
• [16] MEI Z., ZHAO D., Propagation of Laguerre–Gaussian and elegant Laguerre–Gaussian beams in apertured fractional Hankel transform systems, Journal of the Optical Society of America A 21(12),2004, pp. 2375–2381.
• [17] CAI Y., LIN Q., Properties of a flattened Gaussian beam in the fractional Fourier transform plane,Journal of Optics A: Pure and Applied Optics 5(3), 2003, pp. 272–275.
• [18] CAI Y., LIN Q., Transformation and spectrum properties of partially coherent beams in the fractional Fourier transform plane, Journal of the Optical Society of America A 20(8), 2003, pp. 1528–1536.
• [19] LIN Q., CAI Y., Fractional Fourier transform for partially coherent Gaussian–Schell model beams,Optics Letters 27(19), 2002, pp. 1672–1674.
• [20] CAI Y., GE D., LIN Q., Fractional Fourier transform for partially coherent and partially polarized Gaussian–Schell model beams, Journal of Optics A: Pure and Applied Optics 5(5), 2003, pp. 453–459.
• [21] DU X., ZHAO D., Fractional Fourier transform of off-axial elliptical cosh-Gaussian beams, Optik 119(8), 2008, pp. 379–382.
• [22] COLLINS S.A., Lens-system diffraction integral written in terms of matrix optics, Journal of the Optical Society of America 60(9), 1970, pp. 1168–1177
• [23] MEI Z., ZHAO D., Models for an aperture function and corresponding analytical propagation equations of a flattened Gaussian beam through an annular apertured optical system, Journal of Modern Optics 53(3), 2006, pp. 313–321.
• [24] MAO H., ZHAO D., Different models for a hard-aperture function and corresponding approximate analytical propagation equations of a Gaussian beam through an apertured optical system, Journal of the Optical Society of America A 22(4), 2005, pp. 647–653.
• [25] WEN J.J., BREAZEALE M.A., A diffraction beam field expressed as the superposition of Gaussian beams, Journal of the Acoustical Society of America 83(5), 1988, pp. 1752–1756.
• [26] WEN J.J., BREAZEALE M.A., Computer Optimization of the Gaussian Beam Description of an Ultrasonic Field, Computational Acoustics, Elsevier, Amsterdam, 1990.
• [27] ZHAO D., MAO H., SHEN M., LIU H., JING F., ZHU Q., WEI X., Propagation of flattened Gaussian beams in apertured fractional Fourier transforming systems, Journal of Optics A: Pure and Applied Optics 6(1), 2004, pp. 148–154.
• [28] ZHAO D., MAO H., LIU H., WANG S., JING F., WEI X., Propagation of Hermite–cosh-Gaussian beams in apertured fractional Fourier transforming systems, Optics Communications 236(4–6), 2004, pp. 225–235.
• [29] ZHAO D., MAO H., LIU H., JING F., ZHU Q., WEI X., Propagation of Hermite–Gaussian beams in apertured fractional Fourier transforming systems, Optik 114(11), 2003, pp. 504–508.
• [30] JIANG H., ZHAO D., Propagation characteristics of laser beams with amplitude modulations and phase fluctuations in apertured fractional Fourier transforming system, Optics Communications 264(1), 2006, pp. 18–24.
• [31] DU X., ZHAO D., Fractional Fourier transforms of elliptical Hermite–cosh-Gaussian beams, Physics Letters A 366(3), 2007, pp. 271–275.
• [32] DU X., ZHAO D., Off-axial elliptical Hermite–cosh-Gaussian beams, Optics Communications 268(2), 2006, pp. 282–288.
• [33] CHEN S., ZHANG T., FENG X., Propagation properties of cosh-squared-Gaussian beam through fractional Fourier transform systems, Optics Communications 282(6), 2009, pp. 1083–1087.
• [34] ZHANG E., JI X., LÜ B., Changes in the spectrum of diffracted pulsed cosh-Gaussian beams propagating through atmospheric turbulence, Journal of Optics A: Pure and Applied Optics 9(10), 2007, pp. 951–957.
• [35] DU X., ZHAO D.,Propagation of elliptical cosh-Gaussian beams in misaligned optical system, Optics and Laser Technology 40(1), 2008, pp. 194–200.
• [36] YU S., GUO H., FU X., HU W., Propagation properties of elegant Hermite–cosh-Gaussian laser beams, Optics Communications 204(1–6), 2002, pp. 59–66.