Abstract
In this paper, the effects of turbulent biological tissues (TBT) on the propagation properties of the coherent Laguerre-Gaussian (CLG) beams are studied. Based on the turbulence theory and using the power spectrum refractive-index model, the expression formulae of the average irradiance intensity and spreading properties of a CLG beam propagating in TBT are derived. The influence of propagation distance, beam orders, wavelengths and tissue turbulence parameters are then investigated numerically. It found that, the central dark zone of the circular/elliptical LG beams rises more rapidly as the propagation distance and the structural constant of the refractive index of the biological tissue increase and the beams become eventually more like Gaussian beams in the far-field under the influence of the turbulence biological tissues. Also, the numerical results proved that the effective beam spot radius increases as turbulence, wavelength, and propagation distance are increasing. Ultimately, the beams become circular under the influence of the turbulence of the biological tissue. As found that the effective beam spot radius along the x-axis becomes equal to that of the y-axis in high TBT which explain why an elliptical LG beam is converted into a circular one in higher structural constant of the turbulent tissue. Moreover, our results show that, the influence of the beam order m slightly greater than that of l on the beam spreading.
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References
Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. U.S., Department of Commerce (1970)
Andrews, L.C., Phillips, R.L.: Laser Beam Propagation Through Random Media. SPIE Press, Bellingham (1998)
Andrews, L.C., Phillips, R.L.: Laser Beam Propagation through Random Media. SPIE, Bellingham (2005)
Arpali, S.A., Arpali, Ç., Baykal, Y.: Bit error rate of a Gaussian beam propagating through biological tissue. J. Mod. Opt. 67, 340–345 (2020)
Baykal, Y.: Log-amplitude and phase fluctuations of higher-order annular laser beams in a turbulent medium. J. Opt. Soc. Am. A. 22, 672–679 (2005)
Baykal, Y., Arpali, C., Arpali, S.A.: Scintillation index of optical spherical wave propagating through biological tissue. J. Mod. Opt. 64, 138–142 (2017)
Bekshaev, Y.A., Sviridova, S.V., Popov, A.Y., Tyurin, A.V.: optical vortex generationby volume holographic elements with embedded phase singularity: Effect of misalignments. Opt. Commun. 285, 4005 (2012)
Belafhal A., Hricha Z., Dalil-Essakali L., Usman T.: A note on some integrals involving Hermite polynomials encountered in caustic optics, accepted for publication in Advanced Mathematical Models and Applications (2020)
Boufalah, F., Dalil-Essakali, L., Ez-zariy, L., Belafhal, A.: Introduction of generalized Bessel–Laguerre–Gaussian beams and its central intensity travelling a turbulent atmosphere. Opt. & Quant. Electron. 50, 305–320 (2018)
Chen, M., Yu, L., Zhang, Y.: Signal/noise ratio of orbital angular momentum modes for a partially coherent modified Bessel-correlated beam in a biological tissue. Opt. Soc. Am. A 34, 2046–2051 (2017)
de Boer, J.F., Milner, T.E., van Gemert, M.J.C., Nelson, J.S.: Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography. Opt. Lett. 22, 934–936 (1997)
Dong, Y., Dong, K., Chang, S., Song, Y.: Propagation of rectangular multi-Gaussian Schell-model vortex beams in turbulent atmosphere. Optik 207, 163809–163810 (2019)
Duan, M., Tian, Y., Zhang, Y., Li, J.: Influence of biological tissue and spatial correlation on spectral changes of Gaussian-Schell model vortex beam: Opt. Lasers Eng. 134, 106224–106229 (2020)
Erdelyi A., Magnus W., Oberhettinger F.: Tables of Integral Transforms, McGraw- Hill, (1954)
Ez-zariy, L., Ebrahim, A.A.A., Belafhal, A.: Behavior of the central intensity of a hollow-Gaussian beam against the turbulence. Optik 16, 31091–31099 (2016)
Gao, W.: Changes of polarization of light beams on propagation through tissue. Opt. Commun. 260, 749–754 (2006)
Gao, W., Korotkova, O.: Changes in the state of polarization of a random electro-magnetic beam propagating through tissue. Opt. Commun. 270, 474–478 (2007)
Gbur, G., Tyson, R.K.: Vortex beam propagation through atmospheric turbulence and topological charge conservation. Opt. Soc. Am. A 25, 225–229 (2008)
Gibson, G., Courtial, J., Padgett, M., Vasnetsov, M., Pasko, V., Barnett, S., Franke-Arnold, S.: Free-space information transfer using light beams carrying orbital angular momentum. Opt. Express 12, 5448–5456 (2004)
Gökçe, M.C., Baykal, Y.: Effects of liver tissue turbulence on propagation of annular beam. Optik 171, 313–318 (2018)
Gökçe, M.C., Baykal, Y., Ata, Y.: Laser array beam propagation through liver tissue. J. Visual. 23, 331–338 (2020)
Hitzenberger, C.K., Götzinger, E., Sticker, M., Pircher, M., Fercher, A.F.: Measurement and imaging of birefringence and optic axis orientation by phase resolved polarization sensitive optical coherence tomography. Opt. Express 9, 780–790 (2001)
Hricha, Z., Yaalou, M., Belafha, A.: Intensity characteristics of double-half inverse Gaussian hollow beams through turbulent atmosphere. Opt. & Quant. Electron. 52, 201–208 (2020)
Jin, H., Zheng, W., Ma, H.T., Zhao, Y.: Average intensity and scintillation of light in a turbulent biological tissue. Optik 127, 9813–9820 (2016)
Khandelwal, A.: Incoherent beam combination of low order Laguerre-Gaussian beams propagating in turbulent atmosphere. Results Opt. 1, 100030–100035 (2020)
Khannous, F., Belafhal, A.: A new study of turbulence effects in the marine environment on the intensity distributions of flat-topped Gaussian beams. Optik 127, 8194–8202 (2016)
Kimel, S., Elias, L.R.: Relations between Hermite and Laguerre Gaussian modes. IEEE J. Quantum Electron. 29, 2563–2567 (1993)
Korotkova, O.: Random Light Beams: Theory and Applications. CRC Press, Boca Raton, FL, USA (2014)
Li, N., Chu, X., Zhang, P., Feng, X., Fan, C.Y., Qiao, C.: Compensation for the orbital angular momentum of a vortex beam in turbulent atmosphere by adaptive optics. Opt. Laser Technol. 98, 7–11 (2018a)
Li, Y., Zhang, Y., Zhu, Y.: Probability distribution of the orbital angular momentum mode of the ultrashort Laguerre-Gaussian pulsed beam propagation in oceanic turbulence. Results Phys. 11, 698–705 (2018b)
Li, Y., Wang, L., Gong, L., Wang, Q.: Speckle characteristics of vortex beams scattered from rough targets in turbulent atmosphere. Quant. Spect. Rad. Trans. 257, 107342–107347 (2020)
Lu, X., Zhu, X., Wang, K., Zhao, C., Cai, Y.: Effects of biological tissues on the propagation properties of anomalous hollow beams. Optik 127, 1842–1847 (2016)
Luo, M., Chen, Q., Hua, L., Zhao, D.: Propagation of stochastic electromagnetic vortex beams through the turbulent biological tissues. Phys. Lett. A 378, 308–314 (2014)
Martelli, F., Bianco, S.D., Ismaelli, A., Zaccanti, G.: LLight Propagation Through Biological Tissue and Other Diffusive Dedia: Theory, Solutions, and Software. SPIE Press, Bellingham (2009)
Molina-Terriza, G., Torres, J.P., Torner, L.: Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum. Phys. Rev. Lett. 88, 013601–013604 (2001)
Ni, Y., Zhou, Y., Zhou, G., Chen, R.: Characteristics of partially coherent circular flattened Gaussian vortex beams in turbulent biological tissues. Appl. Sci. 9, 969–982 (2019)
Qu, J., Zhong, Y., Cui, Z., Cai, Y.: Elegant Laguerre-Gaussian beam in a turbulent atmosphere. Optics Commun. 283, 2772–2781 (2010)
Saad, F., Belafhal, A.: A theoretical investigation on the propagation properties of Hollow Gaussian beams passing through turbulent biological tissues. Optik 141, 72–87 (2017)
Schmitt, J., Kumar, G.: Turbulent nature of refractive-index variations in biological tissue. Opt. Lett. 21, 1310–1312 (1996)
Strohaber, J., Scarborough, T.D., Uiterwaal, C.J.G.J.: Ultra short intense-field optical vortices produced with laser-etched mirrors. Appl. Opt. 46, 8583–8590 (2007)
Takenaka, T., Yokota, M., Fukumitsu, O.: Propagation of light beams beyond the paraxial approximation. J. Opt. Soc. Am. A 2, 826–829 (1985)
Tokizane, Y., Oka, K., Morita, R.: Super continuum optical vortex pulse generation without spatial or topological-charge dispersion. Opt. Express 17, 14517–14525 (2009)
Wu Y., Zhang Y., Wang Q., Hu Z.: Average intensity and spreading of partially coherent model beams propagating in a turbulent biological tissue. J. Quant. Spectrosc. Ra. Tr.184, 308–315 (2016)
Yang, X., Gao, M.: Fluctuation characteristics of laser transmissions in atmospheric Turbulence. Optik 202, 163624–163627 (2020)
Yin, J., Gao. W., Zhu. Y. (2003) Generation of dark hollow beams and their applications. In: Wolf, E. (ed.) Progress in Optics. North-Holland, Amsterdam, vol 44, pp. 119–204
Yu, L., Zhang, Y.: Beam spreading and wander of partially coherent Lommel-Gaussian beam in turbulent biological tissue. J. Quant. Spectrosc Radiat Transfer. 217, 315–320 (2018)
Zauderer, E.: Complex argument Hermite-Gaussian and Laguerre-Gaussian beams. J. Opt. Soc. Am. A 3, 465–469 (1986)
Zhong, Y., Cui, Z., Shi, J., Qu, J.: Propagation properties of partially coherent Laguerre-Gaussian beams in turbulent atmosphere. Opt. Laser Technol. 43, 741–747 (2011)
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Ebrahim, A.A.A., Belafhal, A. Effect of the turbulent biological tissues on the propagation properties of Coherent Laguerre-Gaussian beams. Opt Quant Electron 53, 179 (2021). https://doi.org/10.1007/s11082-021-02838-7
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DOI: https://doi.org/10.1007/s11082-021-02838-7