Top

Optical and Quantum Electronics

Published in:

01-11-2023

Propagation analysis of Whittaker–Gaussian laser beam in a gradient-index medium

Authors: N. Nossir, L. Dalil-Essakali, A. Belafhal

Published in: Optical and Quantum Electronics | Issue 11/2023

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this paper, the propagation of Whittaker–Gaussian beam passing through a gradient-index (GRIN) medium is studied. Based on the extended Huygens–Fresnel diffraction integral, the analytical expression of the intensity distribution for the resulting beam called Humbert beam is derived and discussed through numerical examples. The obtained results indicate that the diffracted beam evolves periodically versus the propagation distance in GRIN and its behavior depends interestingly on the beam initial parameters and the gradient-index parameter. Our results can be useful for some applications such as in multi-dimensional optical manipulation, remote sensing domain and imaging.

previous article Study the optoelectronic properties of reduced graphene oxide doped on the porous silicon for photodetector

next article Fabrication, structure, physical properties and FTIR spectroscopy of zirconate doped-borophosphate bioglasses

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Arlt, J., Garcés-Chávez, V., Sibbett, W., Dholakia, K.: Optical micromanipulation using a Bessel light beam. Opt. Commun. 197, 239–245 (2001)ADS

Augustyniak, I., Lamperska, W., Masajada, J., Płociniczak, L., Popiołek-Masajada, A.: Off-axis vortex beam propagation through classical optical system in terms of Kummer confluent hypergeometric function. Photonics 7, 1–21 (2020)

Bai, Z.Y., Deng, D.M., Guo, Q.: Elegant Ince Gaussian beams in a quadratic-index medium. Chin. Phys. B 20, 1–3 (2011)

Belafhal, A., Dalil-Essakali, L.: Collins formula and propagation of Bessel-modulated Gaussian light beams through an ABCD optical system. Opt. Commun. 177, 181–188 (2000)ADS

Benzehoua, H., Belafhal, A.: Analyzing the spectral characteristics of a pulsed Laguerre higher-order cosh-Gaussian beam propagating through a paraxial ABCD optical system. Opt. Quant. Electron. 55, 7–18 (2023)

Boufalah, F., Dalil-Essakali, L., Belafhal, A.: Transformation of a generalized Bessel Laguerre–Gaussian beam by a paraxial ABCD optical system. Opt. Quant. Electron. 51, 274–288 (2019)

Buchholz, H.: The Confluent Hypergeometric Function with Special Emphasis on its Applications. Springer, New York (1969)MATH

Cao, Z., Zhai, C., Xu, S., Chen, Y.: Propagation of on-axis and off-axis Bessel beams in a gradient-index medium. JOSA A 35, 230–235 (2018)ADS

Chib, S., Dalil-Essakali, L., Belafhal, A.: Propagation properties of a novel generalized flattened Hermite-cosh-Gaussian light beam. Opt. Quant. Electron. 52, 1–14 (2020)

Collins, S.A.: Lens-system diffraction integral written in terms of matrix optics. J. Opt. Soc. Am. 60, 1168–1177 (1970)ADS

Deng, D.: of elegant Hermite cosine Gaussian laser beams. Opt. Commun. 259, 409–414 (2006)ADS

Deng, D.M.: Propagation of Airy–Gaussian beams in a quadratic index medium. Eur. Phys. J. D 65, 553–556 (2011)ADS

Dickson, L.D.: Characteristics of a propagating Gaussian beam. Appl. Opt. 9, 1854–1861 (1970)ADS

Ebrahim, A.A.A., Yahya, N.A., Swillam, M.A., Belafhal, A.: Introduction and propagation properties of circular Lorentz–Bessel–Gaussian beams. Opt. Quant. Electron. 54, 1–13 (2022)

El Halba, E.M., Boustimi, M., Ez-zariy, L., Hennani, S., Belafhal, A.: Propagation characteristics of Bessel like beams through ABCD optical system. Opt. Quantum Electron. 49, 269–279 (2017)

Erdelyi, A., Magnus, W., Ober Hettinger, F.: Tables of Integral Transforms. McGraw-Hill, New York (1954)

Feit, M.D., Fleck, J.A.: Light propagation in graded index optical fiber. Appl. Opt. 17, 3990–3998 (1987)ADS

Feng, L., Zhang, J., Pang, Z., Wang, L., Zhong, T., Yang, X., Deng, D.: Propagation properties of the chirped Airy beams through the gradient-index medium. Opt. Commun. 402, 60–65 (2017)ADS

Gao, Y.Q., Zhu, B.Q., Liu, D.Z., Lin, Z.Q.: Propagation of flat-topped multi-Gaussian beams through an apertured ABCD optical system. J. Opt. Soc. Am. A 26, 2139–2146 (2009)ADS

Gomez-Reino, C., Perez, M.V., Bao, C.: Gradient-Index Optics: Fundamentals and Applications (2002).

Gradshteyn, I.S., Ryzhik, I.M.: Tables of Integrals, Series and Products, 5th edn. Academic Press, New York (1994)MATH

Gu, J., Yang, P., Zhang, Y.: The intensity distribution of Hermite–Gaussian beam through an annular aperture. Optik 124, 5858–5862 (2013)ADS

Gutierrez-Vega, J.C., Bandres, M.A.: Ince-Gaussian beams in a quadratic-index medium. J. Opt. Soc. Am. A 22, 306–309 (2005)MathSciNetADS

Kotlyar, V.V., Kovalev, A.A., Nalimov, A.G.: Propagation of hypergeometric laser beams in a medium with a parabolic refractive index. J. Opt. 15, 1–10 (2013)

Lazrek, M., Hricha, Z., Belafhal, A.: Propagation of vortex Hermite-cosh-Gaussian beams in a gradient-index medium. Opt. Quant. Electron. 54, 1–11 (2022)

Levy, U., Nezhad, M., Kim, H.C., Tsai, C.H., Pang, L., Fainman, Y.: Implementation of a graded-index medium by use of subwavelength structures with graded fill facto. J. Opt. Soc. Am. A 22, 724–733 (2005)ADS

Lopez-Mago, D., Bandres, M.A., Gutiérrez-Vega, J.C.: Propagation of Whittaker–Gaussian beams. Laser Beam Shaping X 7430, 286–293 (2009)

McMullin, J.N.: The ABCD matrix in arbitrarily tapered quadratic-index waveguides. Appl. Opt. 25, 2184–2187 (1986)ADS

Mei, Z., Zhao, D., Wei, X., Jing, F., Zhu, Q.: Propagation of Bessel-modulated Gaussian beams through a paraxial ABCD optical system with an annular aperture. Optik 116, 521–526 (2005)ADS

Monin, E.O., Ustinov, A.V.: The transformation of Hermite–Gauss beams with embedded optical vortex by lens system. J. Phys. Conf. Ser. 1038, 012039–012045 (2018)

Moore, D.T.: Gradient-index optics: a review. Appl. Opt. 19, 1035–1038 (1980)ADS

Newstein, M., Rudman, B.: Laguerre–Gaussian periodically focusing beams in a quadratic index medium. IEEE J. Quant. Elect. 23, 481–482 (1987)ADS

Nossir, N., Essakali, L.D., Belafhal, A.: Propagation analysis of some doughnut lasers beams through a paraxial ABCD optical system. Opt. Quant. Electron. 52, 1–16 (2020)

Nossir, N., Dalil-Essakali, L., Belafhal, A.: Diffraction of generalized Humbert–Gaussian beams by a Helical axicon. Opt. Quant. Electron. 53, 1–13 (2021)

Poon, T.C., Kim, T.: Engineering Optics with MATLAB. World Scientific, Singapore (2006)

Renninger, W.H., Wise, F.W.: Optical solitons in graded-index multimode fibers. Nat. Commun. 4, 1–6 (2013)

Saad, F., Belafhal, A.: Conical diffraction of dark and antidark beams modulated by a Gaussian profile in biaxial crystals. Optik 154, 344–353 (2018)ADS

Saad, F., Belafhal, A.: Propagation properties of hollow higher-order cosh-Gaussian beams in quadratic index medium and fractional Fourier transform. Opt. Quant. Electron. 53, 1–16 (2021)

Song, S.H., Park, S., Oh, C.H., Kim, P.S., Cho, M.H., Kim, Y.S.: Gradient-index planar optics for optical interconnections. Opt. Lett. 23, 1025–1027 (1998)ADS

Srivastava, H.M., Manocha, H.L.: A Treatise on Generating Functions. Halsted Press, New York (1984)MATH

Tomlinson, W.J.: Applications of GRIN-rod lenses. Opt. Fiber Commun. Syst. 19, 1127–1138 (1980)

Tovar, A.A.: Propagation of Laguerre–Bessel–Gaussian beams. J. Opt. Soc. Am. A 17, 2010–2018 (2000)MathSciNetADS

Yaalou, M., Hricha, Z., Belafhal, A.: Transformation of vortex cosine-hyperbolic-Gaussian beam by an airy transform. Opt. Quant. Electron. 8, 1–19 (2023)

Yang, S., Wang, J., Guo, M., Qin, Z., Li, J.: Propagation properties of Gaussian vortex beams through the gradient-index medium. Opt. Commun. 465, 1–18 (2020)

Yangjian, C., Sailing, H.: Propagation of hollow Gaussian beams through apertured paraxial optical systems. J. Opt. Soc. 23, 1410–1418 (2006)

Zou, D., Li, X., Pang, X., Zheng, H., Ge, Y.: Propagation properties of hollow sinh-Gaussian beams in quadratic-index medium. Opt. Commun. 401, 54–58 (2017)ADS

Title: Propagation analysis of Whittaker–Gaussian laser beam in a gradient-index medium
Authors: N. Nossir
L. Dalil-Essakali
A. Belafhal
Publication date: 01-11-2023
Publisher: Springer US
Published in: Optical and Quantum Electronics / Issue 11/2023
Print ISSN: 0306-8919
Electronic ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-023-05317-3

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 11/2023

Radiated power and directivity analysis of a nano-dot photoconductive antenna

Investigation of travelling wave solutions for the (3 + 1)-dimensional hyperbolic nonlinear Schrödinger equation using Riccati equation and F-expansion techniques

Importance of satisfying thermodynamic consistency in optoelectronic device simulations for high carrier densities

Numerically efficient full-vectorial rational Chebyshev pseudo-spectral modal analysis for optical Waveguides

ZEONEX based hollow rectangular core photonic crystal fiber (PCF) sensor design and numerical investigation for alcohol detection of variant classes

Centrosymmetric structure of novel barium (II)-dibenzo-15-crown-5-ether-zinc (II)-tetra-thiocyanate single crystal for nonlinear optical application