Skip to main content
Top
Published in: Optical and Quantum Electronics 4/2024

01-04-2024

Propagation properties of higher-order cosine-hyperbolic-Gaussian beams in a chiral medium

Authors: Faroq Saad, Zoubir Hricha, Abdelmajid Belafhal

Published in: Optical and Quantum Electronics | Issue 4/2024

Log in

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

search-config
loading …

Abstract

The paraxial propagation of a higher-order cosine-hyperbolic-Gaussian beam (HOChGB) in a chiral medium is investigated theoretically. Analytical expression of the HOChGB passing through a chiral medium is derived based on the Huygens-Fresnel Integral and the ABCD transfer matrix. From the obtained formula, the propagation properties of this beam in a chiral medium are analyzed with numerical illustrative examples. The obtained results show that the evolution of the intensity pattern of HOChGB depends strongly on the chiral factor, the beam order, and the decentered parameter.

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!

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!

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!

Literature
go back to reference Baimuratov, A.S., Gun’ko, Y.K., Shalkovskiy, A.G., Baranov, A.V., Fedorov, A.V., Rukhlenko, I.D.: Optical activity of chiral nanoscrolls. Adv. Opt. Mater. 5, 1600982–1600987 (2017) Baimuratov, A.S., Gun’ko, Y.K., Shalkovskiy, A.G., Baranov, A.V., Fedorov, A.V., Rukhlenko, I.D.: Optical activity of chiral nanoscrolls. Adv. Opt. Mater. 5, 1600982–1600987 (2017)
go back to reference Beaulieu, S., Comby, A., Descamps, D., Fabre, B., Garcia, G.A., Géneaux, R., Harvey, A.G., Légaré, F., Mašín, Z., Nahon, L., Nahon, L., Ordonez, A.F., Petit, S., Pons, B., Mairesse, Y., Smirnova, O., Blanchet, V.: Photoexcitation circular dichroism in chiral molecules. Nat. Phys. 14, 484–489 (2018) Beaulieu, S., Comby, A., Descamps, D., Fabre, B., Garcia, G.A., Géneaux, R., Harvey, A.G., Légaré, F., Mašín, Z., Nahon, L., Nahon, L., Ordonez, A.F., Petit, S., Pons, B., Mairesse, Y., Smirnova, O., Blanchet, V.: Photoexcitation circular dichroism in chiral molecules. Nat. Phys. 14, 484–489 (2018)
go back to reference Belafhal, A., Hricha, Z., Dalil-Essakali, L., Usman, T.: A note on some integrals involving Hermite polynomials and their applications. Adv. Math. Mod. and Appl. 5(3), 313–319 (2020) Belafhal, A., Hricha, Z., Dalil-Essakali, L., Usman, T.: A note on some integrals involving Hermite polynomials and their applications. Adv. Math. Mod. and Appl. 5(3), 313–319 (2020)
go back to reference Casperson, L.W., Hall, D.G., Tovar, A.A.: Sinusoidal-Gaussian beams in complex optical systems. J. Opt. Soc. Am. A 14, 3341–3348 (1997)ADSMathSciNet Casperson, L.W., Hall, D.G., Tovar, A.A.: Sinusoidal-Gaussian beams in complex optical systems. J. Opt. Soc. Am. A 14, 3341–3348 (1997)ADSMathSciNet
go back to reference Chen, R.P., Dai, C.Q.: The effect of Kerr nonlinearity on a cosh-gaussian beam. Lasers Eng. 19(3), 255–264 (2009) Chen, R.P., Dai, C.Q.: The effect of Kerr nonlinearity on a cosh-gaussian beam. Lasers Eng. 19(3), 255–264 (2009)
go back to reference Chen, S., Zhang, T., Feng, X.: Propagation properties of cosh-squared-Gaussian beam through fractional Fourier transform systems. Opt. Comm. 282, 1083–1087 (2009)ADS Chen, S., Zhang, T., Feng, X.: Propagation properties of cosh-squared-Gaussian beam through fractional Fourier transform systems. Opt. Comm. 282, 1083–1087 (2009)ADS
go back to reference Chern, R.L., Chang, P.H.: Negative refractive and backward wave in chiral mediums: illustrations of Gaussian beams. J. Appl. Phys. 113(15), 153504–153509 (2013)ADS Chern, R.L., Chang, P.H.: Negative refractive and backward wave in chiral mediums: illustrations of Gaussian beams. J. Appl. Phys. 113(15), 153504–153509 (2013)ADS
go back to reference Chu, X.: Propagation of a cosh-Gaussian beam through an optical system in turbulent atmosphere. Opt. Express 15(26), 17613–17618 (2007)ADSPubMed Chu, X.: Propagation of a cosh-Gaussian beam through an optical system in turbulent atmosphere. Opt. Express 15(26), 17613–17618 (2007)ADSPubMed
go back to reference Collins, S.A.: Lens-system diffraction integral written in terms of matrix optics. J. Opt. Soc. Am. 60, 1168–1177 (1970)ADS Collins, S.A.: Lens-system diffraction integral written in terms of matrix optics. J. Opt. Soc. Am. 60, 1168–1177 (1970)ADS
go back to reference Deng, F., Yu, W., Huang, J., Zhao, R., Lin, J., Deng, D.: Propagation of Airy-Gaussian beams in a chiral medium. Eur. Phys. J. D 70(4), 1–6 (2016) Deng, F., Yu, W., Huang, J., Zhao, R., Lin, J., Deng, D.: Propagation of Airy-Gaussian beams in a chiral medium. Eur. Phys. J. D 70(4), 1–6 (2016)
go back to reference Eyyuboglu, H.T., Baykal, Y.: Analysis of reciprocity of cos-Gaussian and cosh-Gaussian laser beams in turbulent atmosphere. Opt. Express 12(20), 4659–4674 (2004)ADSPubMed Eyyuboglu, H.T., Baykal, Y.: Analysis of reciprocity of cos-Gaussian and cosh-Gaussian laser beams in turbulent atmosphere. Opt. Express 12(20), 4659–4674 (2004)ADSPubMed
go back to reference Gill, J.S.: Self-focusing of Cosh-Gaussian laser beam in a Kerr medium with linear absorption. Advanced Photonics & Renewable Energy, OSA Technical Digest (CD) (Optical Society of America, 2010), paper NTuC58 Gill, J.S.: Self-focusing of Cosh-Gaussian laser beam in a Kerr medium with linear absorption. Advanced Photonics & Renewable Energy, OSA Technical Digest (CD) (Optical Society of America, 2010), paper NTuC58
go back to reference Gradshteyn, I.S., Ryzhik, I.M.: Tables of Integrals Series, and Products, 5th edn. Academic Press, New York (1994) Gradshteyn, I.S., Ryzhik, I.M.: Tables of Integrals Series, and Products, 5th edn. Academic Press, New York (1994)
go back to reference Hricha, Z., Belafhal, A.: Focusing properties and focal shift of hyperbolic-cosine-Gaussian beams. Opt. Commun. 253, 242–249 (2005)ADS Hricha, Z., Belafhal, A.: Focusing properties and focal shift of hyperbolic-cosine-Gaussian beams. Opt. Commun. 253, 242–249 (2005)ADS
go back to reference Hricha, Z., Lazrek, M., Belafhal, A.: Paraxial propagation of cosine-hyperbolic-Gaussian beams in a chiral medium. J. Mod. Opt. 69(12), 1–11 (2022) Hricha, Z., Lazrek, M., Belafhal, A.: Paraxial propagation of cosine-hyperbolic-Gaussian beams in a chiral medium. J. Mod. Opt. 69(12), 1–11 (2022)
go back to reference Hricha, Z., Yaalou, M., Belafhal, A.: Paraxial propagation and focusing of higher-order cosh-Gaussian beams. J. Mod. Op. 68, 742–752 (2021)ADSMathSciNet Hricha, Z., Yaalou, M., Belafhal, A.: Paraxial propagation and focusing of higher-order cosh-Gaussian beams. J. Mod. Op. 68, 742–752 (2021)ADSMathSciNet
go back to reference Hua, S., Liu, Y.W., Zhang, H.J., Tang, L.Z., Feng, Y.C.: Propagation of an Airy-Gaussian-vortex beam in a chiral medium. Opt. Commun. 388, 29–37 (2017)ADS Hua, S., Liu, Y.W., Zhang, H.J., Tang, L.Z., Feng, Y.C.: Propagation of an Airy-Gaussian-vortex beam in a chiral medium. Opt. Commun. 388, 29–37 (2017)ADS
go back to reference Hui, Y., Cui, Z., Li, Y., Zhao, W., Han, Y.: Propagation and dynamical characteristics of a Bessel Gaussian beam in a chiral medium. J. Opt. Soc. Am. A 35(8), 1299–1305 (2018)ADS Hui, Y., Cui, Z., Li, Y., Zhao, W., Han, Y.: Propagation and dynamical characteristics of a Bessel Gaussian beam in a chiral medium. J. Opt. Soc. Am. A 35(8), 1299–1305 (2018)ADS
go back to reference Kang, X., Li, C., He, Z., Zhao, L.: The far properties of non-paraxial cosine-squared Gaussian beams. App. Meca. Mater. 738–739, 440–443 (2015) Kang, X., Li, C., He, Z., Zhao, L.: The far properties of non-paraxial cosine-squared Gaussian beams. App. Meca. Mater. 738–739, 440–443 (2015)
go back to reference Kaur, S., Kaur, M., Kaur, R., Gill, T.S.: Propagation characteristics of Hermite-cosh-Gaussian laser beams in a rippled density plasma. Laser Part. Beam 35(1), 100–107 (2017)ADS Kaur, S., Kaur, M., Kaur, R., Gill, T.S.: Propagation characteristics of Hermite-cosh-Gaussian laser beams in a rippled density plasma. Laser Part. Beam 35(1), 100–107 (2017)ADS
go back to reference Konar, S., Mishra, M., Jana, S.: Nonlinear evolution of cosh-Gaussian laser beams and generation of flat-top spatial solitons in cubic quantic nonlinear media”. Phys. Lett. A 362, 505–510 (2007)ADS Konar, S., Mishra, M., Jana, S.: Nonlinear evolution of cosh-Gaussian laser beams and generation of flat-top spatial solitons in cubic quantic nonlinear media”. Phys. Lett. A 362, 505–510 (2007)ADS
go back to reference Kwon, D.H., Werner, P.L., Werner, D.H.: Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation. Opt. Express 16, 11802–11807 (2008)ADSPubMed Kwon, D.H., Werner, P.L., Werner, D.H.: Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation. Opt. Express 16, 11802–11807 (2008)ADSPubMed
go back to reference Lee, S., Wang, Z., Feng, C., Jiao, J., Khan, A., Li, L.: Circular dichroism in planar extrinsic chirality metamaterial at oblique incident beam. Opt. Commun. 309, 201–204 (2013)ADS Lee, S., Wang, Z., Feng, C., Jiao, J., Khan, A., Li, L.: Circular dichroism in planar extrinsic chirality metamaterial at oblique incident beam. Opt. Commun. 309, 201–204 (2013)ADS
go back to reference Li, J., Chen, Y., Xin, Y., Xu, S.: Propagation of higher-order cosh-Gaussian beams in uniaxial crystals orthogonal to the optical axis. Eur. Phys. J. D 57(3), 419–425 (2010a)ADS Li, J., Chen, Y., Xin, Y., Xu, S.: Propagation of higher-order cosh-Gaussian beams in uniaxial crystals orthogonal to the optical axis. Eur. Phys. J. D 57(3), 419–425 (2010a)ADS
go back to reference Li, J., Chen, Y., Xu, S., Wang, Y., Zhou, M., Zhao, Q., Xin, Y., Chen, F.: Far-field vectorial structure of a higher-order cosh-Gaussian beam. J. Mod. Opt. 57(20), 2039–2047 (2010b)ADS Li, J., Chen, Y., Xu, S., Wang, Y., Zhou, M., Zhao, Q., Xin, Y., Chen, F.: Far-field vectorial structure of a higher-order cosh-Gaussian beam. J. Mod. Opt. 57(20), 2039–2047 (2010b)ADS
go back to reference Li, J., Zhuang, S., Xie, Y., Huang, C.: Gradient force pattern of truncated hyperbolic-cosine Gaussian beam through phase plate focusing system. Opt. Lasers Eng. 46(12), 124201–124207 (2007)ADS Li, J., Zhuang, S., Xie, Y., Huang, C.: Gradient force pattern of truncated hyperbolic-cosine Gaussian beam through phase plate focusing system. Opt. Lasers Eng. 46(12), 124201–124207 (2007)ADS
go back to reference Liu, X.Y., Zhao, D.M.: Propagation of vortex Airy beam in chiral medium. Opt. Commun. 321, 6–10 (2014)ADS Liu, X.Y., Zhao, D.M.: Propagation of vortex Airy beam in chiral medium. Opt. Commun. 321, 6–10 (2014)ADS
go back to reference Lü, B., Ma, H., Zhang, B.: Propagation properties of cosh-Gaussian beams. Opt. Commun. 164, 165–170 (1999)ADS Lü, B., Ma, H., Zhang, B.: Propagation properties of cosh-Gaussian beams. Opt. Commun. 164, 165–170 (1999)ADS
go back to reference Mahajan, R., Gill, T.S., Kaur, R., Agrawal, M.: Stable Gaussian dynamics of a cosh-Gaussian laser beam in relativistic thermal quantum plasma. Laser Part. Beams 36(3), 341–352 (2018)ADS Mahajan, R., Gill, T.S., Kaur, R., Agrawal, M.: Stable Gaussian dynamics of a cosh-Gaussian laser beam in relativistic thermal quantum plasma. Laser Part. Beams 36(3), 341–352 (2018)ADS
go back to reference Ohtsuka, K.: Preparation and Properties of Two-Dimensional Microporous Pillared Interlayered Solids. JOSA B 37(11), 3379–3385 (2020) Ohtsuka, K.: Preparation and Properties of Two-Dimensional Microporous Pillared Interlayered Solids. JOSA B 37(11), 3379–3385 (2020)
go back to reference Patil, S.D., Navarre, S.T., Takale, M.V., Dongare, M.B.: Self-focusing of cosh-Gaussian laser beams in a parabolic medium with linear absorption. Opt. Lasers Eng. 47, 604–606 (2009) Patil, S.D., Navarre, S.T., Takale, M.V., Dongare, M.B.: Self-focusing of cosh-Gaussian laser beams in a parabolic medium with linear absorption. Opt. Lasers Eng. 47, 604–606 (2009)
go back to reference Patil, S.D., Takale, M.V., Navarre, S.T., Fulari, V.J., Dongare, M.B.: Relativistic self-focusing of cosh-Gaussian laser beams in a plasma. Opt. Laser Tech. 44(2), 314–317 (2012)ADS Patil, S.D., Takale, M.V., Navarre, S.T., Fulari, V.J., Dongare, M.B.: Relativistic self-focusing of cosh-Gaussian laser beams in a plasma. Opt. Laser Tech. 44(2), 314–317 (2012)ADS
go back to reference Pendry, J.B.: A chiral route to negative refraction. Science 306, 1353–1355 (2004)ADSPubMed Pendry, J.B.: A chiral route to negative refraction. Science 306, 1353–1355 (2004)ADSPubMed
go back to reference Ren, Y., Zhou, T., Jiang, C., Tang, B.: Thermally switching between perfect absorber and asymmetric transmission in vanadium dioxide-assisted metamaterials. Opt. Express 29(5), 7666–7679 (2021)ADSPubMed Ren, Y., Zhou, T., Jiang, C., Tang, B.: Thermally switching between perfect absorber and asymmetric transmission in vanadium dioxide-assisted metamaterials. Opt. Express 29(5), 7666–7679 (2021)ADSPubMed
go back to reference Sersic, I., Van de Haar, M.A., Arango, F.B., Koenderink, A.F.: Ubiquity of optical activity in planar metamaterial scatterers. Phys. Rev. Lett. 108, 428–437 (2012) Sersic, I., Van de Haar, M.A., Arango, F.B., Koenderink, A.F.: Ubiquity of optical activity in planar metamaterial scatterers. Phys. Rev. Lett. 108, 428–437 (2012)
go back to reference Tang, B., Li, Z., Palacios, E., Liu, Z., Butun, S., Aydin, K.: Chiral-selective plasmonic metasurface absorbers operating at visible frequencies. IEEE Photon. Technol. Lett. 29(3), 295–298 (2017)ADS Tang, B., Li, Z., Palacios, E., Liu, Z., Butun, S., Aydin, K.: Chiral-selective plasmonic metasurface absorbers operating at visible frequencies. IEEE Photon. Technol. Lett. 29(3), 295–298 (2017)ADS
go back to reference Wani, M.A., Kant, N.: Self-Focusing of Hermite-cosh-Gaussian laser beams in Plasma under density transition. Adv. Opt. 2014, 942750–942754 (2014) Wani, M.A., Kant, N.: Self-Focusing of Hermite-cosh-Gaussian laser beams in Plasma under density transition. Adv. Opt. 2014, 942750–942754 (2014)
go back to reference Xie, J.T., Zhang, J.B., Ye, J.R., Liu, H., Liang, Z., Long, S., Zhou, K., Deng, D.: Paraxial propagation of the first order chirped Airy-vortex beams in the chiral medium. Opt. Express 26(5), 5845–5856 (2018)ADSPubMed Xie, J.T., Zhang, J.B., Ye, J.R., Liu, H., Liang, Z., Long, S., Zhou, K., Deng, D.: Paraxial propagation of the first order chirped Airy-vortex beams in the chiral medium. Opt. Express 26(5), 5845–5856 (2018)ADSPubMed
go back to reference Yaalou, M., Hricha, Z., Belafhal, A.: Paraxial propagation of Hermite cosine-hyperbolic-Gaussian beams in a chiral medium. Opt. Quant. Elec. 55, 1–12 (2023) Yaalou, M., Hricha, Z., Belafhal, A.: Paraxial propagation of Hermite cosine-hyperbolic-Gaussian beams in a chiral medium. Opt. Quant. Elec. 55, 1–12 (2023)
go back to reference Yaalou, M., Hricha, Z., Belafhal, A.: Transformation of higher-order cosh-Gaussian beams into an Airy-related beams by an optical airy transform system. Opt. Quant. Elect. 52, 461–471 (2020) Yaalou, M., Hricha, Z., Belafhal, A.: Transformation of higher-order cosh-Gaussian beams into an Airy-related beams by an optical airy transform system. Opt. Quant. Elect. 52, 461–471 (2020)
go back to reference Yang, X., Z., Wu, Qu, T.: Paraxial propagation of the cosh-Airy vortex beams in a chiral medium. Chin. Phys. B 29(3), 034201–034217 (2020). Yang, X., Z., Wu, Qu, T.: Paraxial propagation of the cosh-Airy vortex beams in a chiral medium. Chin. Phys. B 29(3), 034201–034217 (2020).
go back to reference Zeng, Z., Deng, D.: Paraxial propagation of Pearcey Gaussian beams with the astigmatic phase in the chiral medium. J. Opt. Soc. Am. B 37(1), 30–37 (2020)ADS Zeng, Z., Deng, D.: Paraxial propagation of Pearcey Gaussian beams with the astigmatic phase in the chiral medium. J. Opt. Soc. Am. B 37(1), 30–37 (2020)ADS
go back to reference Zhang, S., Park, Y.S., Li, J., Lu, X., Zhang, W., Zhang, X.: Negative refractive index in chiral metamaterials. Phys. Rev. Lett. 102, 023901–023904 (2009) Zhang, S., Park, Y.S., Li, J., Lu, X., Zhang, W., Zhang, X.: Negative refractive index in chiral metamaterials. Phys. Rev. Lett. 102, 023901–023904 (2009)
go back to reference Zhang, Y.Y., Wang, L., Zhang, Z.Y.: Circular dichroism in planar achiral plasmonic L-shaped nanostructure arrays. IEEE Photon. J. 9, 4800407–4800413 (2017) Zhang, Y.Y., Wang, L., Zhang, Z.Y.: Circular dichroism in planar achiral plasmonic L-shaped nanostructure arrays. IEEE Photon. J. 9, 4800407–4800413 (2017)
go back to reference Zhou, G.: Fractional Fourier transform of a higher-order cosh-Gaussian beam. J. Mod. Opt. 56(7), 886–892 (2009)ADS Zhou, G.: Fractional Fourier transform of a higher-order cosh-Gaussian beam. J. Mod. Opt. 56(7), 886–892 (2009)ADS
go back to reference Zhou, G.: Propagation of a higher-order cosh-Gaussian beam in turbulent atmosphere. Opt. Exp. 19, 3945–3951 (2011) Zhou, G.: Propagation of a higher-order cosh-Gaussian beam in turbulent atmosphere. Opt. Exp. 19, 3945–3951 (2011)
go back to reference Zhou, G., Zheng, J.: Beam propagation of a higher-order cosh-Gaussian beams. Opt. Laser Technol. 41(2), 202–208 (2009)ADS Zhou, G., Zheng, J.: Beam propagation of a higher-order cosh-Gaussian beams. Opt. Laser Technol. 41(2), 202–208 (2009)ADS
go back to reference Zhuang, F., Du, X., Zhao, D.: Polarization modulation for a stochastic electromagnetic beam passing through a chiral medium. Opt. Lett. 36(14), 2683–2685 (2011)ADSPubMed Zhuang, F., Du, X., Zhao, D.: Polarization modulation for a stochastic electromagnetic beam passing through a chiral medium. Opt. Lett. 36(14), 2683–2685 (2011)ADSPubMed
go back to reference Zhuang, F., Du, X., Ye, Y., Zhao, D.: Evolution of Airy beams in a chiral medium. Opt. Lett. 37(11), 1871–1873 (2012)ADSPubMed Zhuang, F., Du, X., Ye, Y., Zhao, D.: Evolution of Airy beams in a chiral medium. Opt. Lett. 37(11), 1871–1873 (2012)ADSPubMed
Metadata
Title
Propagation properties of higher-order cosine-hyperbolic-Gaussian beams in a chiral medium
Authors
Faroq Saad
Zoubir Hricha
Abdelmajid Belafhal
Publication date
01-04-2024
Publisher
Springer US
Published in
Optical and Quantum Electronics / Issue 4/2024
Print ISSN: 0306-8919
Electronic ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-024-06349-z

Other articles of this Issue 4/2024

Optical and Quantum Electronics 4/2024 Go to the issue