Abstract

The effects of oceanic turbulence on the off-axis optical transmittance and beam spread are examined when a partially coherent flat-topped beam wave propagates in an underwater medium. To observe the oceanic turbulence effect, the power spectrum of homogeneous and isotropic oceanic water combining the effects of salinity and temperature is used. Employing the extended Huygens–Fresnel integral and Carter’s definition for the general beam formulation that is applied to a partially coherent flat-topped beam, the effects of the parameters of power spectrum, the link on the off-axis average transmittance, and beam spread are analyzed. The results obtained with the help of the MATLAB program indicate that if the flatness of the optical beam increases, the average transmittance increases, and the beam spread decreases. Partial coherence is found to be inversely proportional to the average transmittance and directly proportional to beam spread. Increase in the source size is found to increase the average transmittance and to reduce the beam spread. Loss of the kinetic energy of fluid causes less turbulence. The rate of dissipation of kinetic energy per unit mass of fluid is directly proportional to the average transmittance, while it is inversely proportional to the beam spread. The rate of dissipation of the mean square temperature is inversely proportional to the average transmittance and directly proportional to the beam spread. When the temperature-induced optical turbulence is dominant, the average transmittance almost never decreases. However, the salinity-induced optical turbulence sharply reduces the average transmittance and increases the beam spread of the partially coherent flat-topped beam in underwater turbulence. When the off-axis parameter becomes larger, average transmittance decreases.

© 2019 Optical Society of America

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References

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2018 (9)

Y. Ata and Y. Baykal, “Anisotropy effect on multi-Gaussian beam propagation in turbulent ocean,” Chin. Opt. Lett. 16, 080102 (2018).
[Crossref]

Y. Baykal, “Effect of anisotropy on intensity fluctuations in oceanic turbulence,” J. Mod. Opt. 65, 825–829 (2018).
[Crossref]

M. C. Gökçe and Y. Baykal, “Aperture averaging and BER for Gaussian beam in underwater oceanic turbulence,” Opt. Commun. 410, 830–835 (2018).
[Crossref]

Y. Baykal, “Bit error rate of pulse position modulated optical wireless communication links in oceanic turbulence,” J. Opt. Soc. Am. A 35, 1627–1632 (2018).
[Crossref]

Y. Ata and Y. Baykal, “Effect of anisotropy on bit-error-rate for an asymmetrical Gaussian beam in a turbulent ocean,” Appl. Opt. 57, 2258–2262 (2018).
[Crossref]

D. Liu and Y. Wang, “Average intensity of partially coherent Lorentz beams in oceanic turbulence,” Prog. Electromagn. Res. M 68, 181–191 (2018).
[Crossref]

D. Liu, Y. Wang, and H. Zhong, “Average intensity of radial phase-locked partially coherent standard Hermite-Gaussian beam in oceanic turbulence,” Opt. Laser Technol. 106, 495–505 (2018).
[Crossref]

T. Wu, X. Ji, X. Li, H. Wang, Y. Deng, and Z. Ding, “Characteristic parameters of optical wave and short-term beam spreading in oceanic turbulence,” Acta Phys. Sin. 67, 224206 (2018).

M. C. Gökçe and Y. Baykal, “Effets of liver tissue turbulence on propagation of annular beam,” Optik 171, 313–318 (2018).
[Crossref]

2017 (4)

M. Yousefi, F. D. Kashani, S. Golmohammady, and A. Mashal, “Scintillation and bit error rate analysis of a phase-locked partially coherent flat-topped array laser beam in oceanic turbulence,” J. Opt. Soc. Am. A 34, 2126–2137 (2017).
[Crossref]

L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, and C. Fan, “Beam wander of laser beam propagating through oceanic turbulence,” Opt. Eng. 56, 104107 (2017).

Y. Baykal, “BER of asymmetrical optical beams in oceanic and marine atmospheric media,” Opt. Commun. 393, 29–33 (2017).
[Crossref]

Y. Baykal, “Higher order mode laser beam intensity fluctuations in strong oceanic turbulence,” Opt. Commun. 390, 72–75 (2017).
[Crossref]

2016 (10)

Y. Baykal, “Scintillations of LED sources in underwater medium,” Appl. Opt. 55, 8860–8863 (2016).
[Crossref]

Y. Baykal, “Scintillation index in strong oceanic turbulence,” Opt. Commun. 375, 15–18 (2016).
[Crossref]

M. C. Gökçe and Y. Baykal, “Scintillation analysis of multiple-input single output underwater optical links,” Appl. Opt. 55, 6130–6136 (2016).
[Crossref]

S. A. Arpali, Y. Baykal, and Ç. Arpali, “BER evaluations for multimode beams in underwater turbulence,” J. Mod. Opt. 63, 1297–1300 (2016).
[Crossref]

D. Liu, L. Chen, Y. Wang, G. Wang, and H. Yin, “Average intensity properties of flat-topped vortex hollow beam propagating through oceanic turbulence,” Optik 127, 6961–6969 (2016).
[Crossref]

F. D. Kashani and M. Yousefi, “Analyzing the propagation behavior of coherence and polarization degrees of a phase-locked partially coherent radial flat-topped array laser beam in underwater turbulence,” Appl. Opt. 55, 6311–6320 (2016).
[Crossref]

Y. Wu, Y. Zhang, and Y. Zhu, “Average intensity and directionality of partially coherent model beams propagating in turbulent ocean,” J. Opt. Soc. Am. A 33, 1451–1458 (2016).
[Crossref]

M. C. Gökçe, Y. Baykal, and M. Uysal, “Aperture averaging in multiple input single-output free space optical systems using partially coherent radial array beams,” J. Opt. Soc. Am. A 33, 1041–1048 (2016).
[Crossref]

M. C. Gökçe, Y. Baykal, and M. Uysal, “Performance analysis of multiple-input multiple-output free-space optical systems with partially coherent Gaussian beams and finite-sized detectors,” Opt. Eng. 55, 111607 (2016).
[Crossref]

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

2015 (3)

2014 (5)

2013 (2)

M. Tang and D. Zhao, “Propagation of radially polarized beams in the oceanic turbulence,” Appl. Phys. B 111, 665–670 (2013).
[Crossref]

Y. Ata and Y. Baykal, “Average transmittance in non-Kolmogorov turbulence,” Opt. Commun. 305, 126–130 (2013).
[Crossref]

2012 (2)

H. Gerçekcioğlu and Y. Baykal, “Intensity fluctuations of flat-topped beam in non-Kolmogorov weak turbulence,” J. Opt. Soc. Am. A 29, 169–173 (2012).
[Crossref]

N. Farwell and O. Korotkova, “Intensity and coherence properties of light in oceanic turbulence,” Opt. Commun. 285, 872–875 (2012).
[Crossref]

2011 (2)

X. Chu, C. Qiao, and X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1150–1154 (2011).
[Crossref]

Y. Ata and Y. Baykal, “Turbulence effect on transmittance of atmospheric optics telecommunication system using dense wavelength division multiplexing,” J. Mod. Opt. 58, 1644–1650 (2011).
[Crossref]

2010 (1)

Y. Baykal, H. T. Eyyuboğlu, and Y. Cai, “Partially coherent off-axis Gaussian beam scintillations,” J. Mod. Opt. 57, 1221–1227 (2010).
[Crossref]

2009 (1)

2008 (1)

M. Alavinejad and B. Ghafary, “Turbulence-induced degradation properties of partially coherent flat-topped beams,” Opt. Laser Eng. 46, 1795–1797 (2008).
[Crossref]

2007 (1)

2006 (1)

2005 (1)

Y. Baykal and H. T. Eyyuboğlu, “Scintillation index of flat-topped Gaussian beams,” J. Opt. Soc. Am. A 45, 3793–3797 (2005).
[Crossref]

2000 (1)

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent fluctuation of the sea water refractive index,” Int. J. Fluid Mech. Res. 27, 82–98 (2000).
[Crossref]

1985 (1)

1983 (1)

Alavinejad, M.

M. Alavinejad and B. Ghafary, “Turbulence-induced degradation properties of partially coherent flat-topped beams,” Opt. Laser Eng. 46, 1795–1797 (2008).
[Crossref]

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

L. C. Andrews, Field Guide to Atmospheric Optics (SPIE, 2004).

Arpali, Ç.

S. A. Arpali, Y. Baykal, and Ç. Arpali, “BER evaluations for multimode beams in underwater turbulence,” J. Mod. Opt. 63, 1297–1300 (2016).
[Crossref]

Arpali, S. A.

S. A. Arpali, Y. Baykal, and Ç. Arpali, “BER evaluations for multimode beams in underwater turbulence,” J. Mod. Opt. 63, 1297–1300 (2016).
[Crossref]

Ata, Y.

Y. Ata and Y. Baykal, “Anisotropy effect on multi-Gaussian beam propagation in turbulent ocean,” Chin. Opt. Lett. 16, 080102 (2018).
[Crossref]

Y. Ata and Y. Baykal, “Effect of anisotropy on bit-error-rate for an asymmetrical Gaussian beam in a turbulent ocean,” Appl. Opt. 57, 2258–2262 (2018).
[Crossref]

Y. Ata and Y. Baykal, “Transmittance of multi Gaussian optical beams for uplink applications in atmospheric turbulence,” IEEE J. Sel. Areas Commun. 33, 1996–2001 (2015).
[Crossref]

A. Keskin, Y. Baykal, and Y. Ata, “Optical transmittance in turbulent underwater medium,” Proc. Çankaya Univ., Eng. Tech. Symp. 7, 137–141 (2014).

Y. Ata and Y. Baykal, “Structure functions for optical wave propagation in underwater medium,” Wave Random Complex 24, 164–173 (2014).
[Crossref]

Y. Ata and Y. Baykal, “Scintillations of optical plane and spherical waves in underwater turbulence,” J. Opt. Soc. Am. A 31, 1552–1556 (2014).
[Crossref]

Y. Ata and Y. Baykal, “Average transmittance in non-Kolmogorov turbulence,” Opt. Commun. 305, 126–130 (2013).
[Crossref]

Y. Ata and Y. Baykal, “Turbulence effect on transmittance of atmospheric optics telecommunication system using dense wavelength division multiplexing,” J. Mod. Opt. 58, 1644–1650 (2011).
[Crossref]

Baykal, Y.

Y. Baykal, “Effect of anisotropy on intensity fluctuations in oceanic turbulence,” J. Mod. Opt. 65, 825–829 (2018).
[Crossref]

Y. Ata and Y. Baykal, “Anisotropy effect on multi-Gaussian beam propagation in turbulent ocean,” Chin. Opt. Lett. 16, 080102 (2018).
[Crossref]

Y. Ata and Y. Baykal, “Effect of anisotropy on bit-error-rate for an asymmetrical Gaussian beam in a turbulent ocean,” Appl. Opt. 57, 2258–2262 (2018).
[Crossref]

M. C. Gökçe and Y. Baykal, “Aperture averaging and BER for Gaussian beam in underwater oceanic turbulence,” Opt. Commun. 410, 830–835 (2018).
[Crossref]

Y. Baykal, “Bit error rate of pulse position modulated optical wireless communication links in oceanic turbulence,” J. Opt. Soc. Am. A 35, 1627–1632 (2018).
[Crossref]

M. C. Gökçe and Y. Baykal, “Effets of liver tissue turbulence on propagation of annular beam,” Optik 171, 313–318 (2018).
[Crossref]

Y. Baykal, “BER of asymmetrical optical beams in oceanic and marine atmospheric media,” Opt. Commun. 393, 29–33 (2017).
[Crossref]

Y. Baykal, “Higher order mode laser beam intensity fluctuations in strong oceanic turbulence,” Opt. Commun. 390, 72–75 (2017).
[Crossref]

Y. Baykal, “Scintillations of LED sources in underwater medium,” Appl. Opt. 55, 8860–8863 (2016).
[Crossref]

Y. Baykal, “Scintillation index in strong oceanic turbulence,” Opt. Commun. 375, 15–18 (2016).
[Crossref]

M. C. Gökçe and Y. Baykal, “Scintillation analysis of multiple-input single output underwater optical links,” Appl. Opt. 55, 6130–6136 (2016).
[Crossref]

S. A. Arpali, Y. Baykal, and Ç. Arpali, “BER evaluations for multimode beams in underwater turbulence,” J. Mod. Opt. 63, 1297–1300 (2016).
[Crossref]

M. C. Gökçe, Y. Baykal, and M. Uysal, “Performance analysis of multiple-input multiple-output free-space optical systems with partially coherent Gaussian beams and finite-sized detectors,” Opt. Eng. 55, 111607 (2016).
[Crossref]

M. C. Gökçe, Y. Baykal, and M. Uysal, “Aperture averaging in multiple input single-output free space optical systems using partially coherent radial array beams,” J. Opt. Soc. Am. A 33, 1041–1048 (2016).
[Crossref]

Y. Ata and Y. Baykal, “Transmittance of multi Gaussian optical beams for uplink applications in atmospheric turbulence,” IEEE J. Sel. Areas Commun. 33, 1996–2001 (2015).
[Crossref]

A. Keskin, Y. Baykal, and Y. Ata, “Optical transmittance in turbulent underwater medium,” Proc. Çankaya Univ., Eng. Tech. Symp. 7, 137–141 (2014).

Y. Ata and Y. Baykal, “Structure functions for optical wave propagation in underwater medium,” Wave Random Complex 24, 164–173 (2014).
[Crossref]

Y. Baykal, “Scintillations of higher-order laser beams in non-Kolmogorov medium,” Opt. Lett. 39, 2160–2163 (2014).
[Crossref]

Y. Ata and Y. Baykal, “Scintillations of optical plane and spherical waves in underwater turbulence,” J. Opt. Soc. Am. A 31, 1552–1556 (2014).
[Crossref]

Y. Ata and Y. Baykal, “Average transmittance in non-Kolmogorov turbulence,” Opt. Commun. 305, 126–130 (2013).
[Crossref]

H. Gerçekcioğlu and Y. Baykal, “Intensity fluctuations of flat-topped beam in non-Kolmogorov weak turbulence,” J. Opt. Soc. Am. A 29, 169–173 (2012).
[Crossref]

Y. Ata and Y. Baykal, “Turbulence effect on transmittance of atmospheric optics telecommunication system using dense wavelength division multiplexing,” J. Mod. Opt. 58, 1644–1650 (2011).
[Crossref]

Y. Baykal, H. T. Eyyuboğlu, and Y. Cai, “Partially coherent off-axis Gaussian beam scintillations,” J. Mod. Opt. 57, 1221–1227 (2010).
[Crossref]

Y. Baykal, H. T. Eyyuboğlu, and Y. Cai, “Scintillations of partially coherent multiple Gaussian beams in turbulence,” Appl. Opt. 48, 1943–1954 (2009).
[Crossref]

H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Complex degree of coherence for partially coherent beams,” J. Opt. Soc. Am. A 24, 2891–2901 (2007).
[Crossref]

Y. Baykal, “Formulation of correlations for general-type beams in atmospheric turbulence,” J. Opt. Soc. Am. A 23, 889–893 (2006).
[Crossref]

Y. Baykal and H. T. Eyyuboğlu, “Scintillation index of flat-topped Gaussian beams,” J. Opt. Soc. Am. A 45, 3793–3797 (2005).
[Crossref]

Y. Baykal and M. A. Plonus, “Intensity fluctuations due to a spatially partially coherent source in atmospheric turbulence as predicted by Rytov’s method,” J. Opt. Soc. Am. A 2, 2124–2132 (1985).
[Crossref]

S. J. Wang, Y. Baykal, and M. A. Plonus, “Receiver-aperture averaging effects for the intensity fluctuation of a beam wave in the turbulent atmosphere,” J. Opt. Soc. Am. 73, 831–837 (1983).
[Crossref]

Brundage, H.

H. Brundage, “Designing a wireless underwater optical communication system,” M.Sc. thesis (Massachusetts Institute of Technology, 2010).

Cai, Y.

Chen, L.

D. Liu, L. Chen, Y. Wang, G. Wang, and H. Yin, “Average intensity properties of flat-topped vortex hollow beam propagating through oceanic turbulence,” Optik 127, 6961–6969 (2016).
[Crossref]

Chu, X.

X. Chu, C. Qiao, and X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1150–1154 (2011).
[Crossref]

Deng, Y.

T. Wu, X. Ji, X. Li, H. Wang, Y. Deng, and Z. Ding, “Characteristic parameters of optical wave and short-term beam spreading in oceanic turbulence,” Acta Phys. Sin. 67, 224206 (2018).

Ding, Z.

T. Wu, X. Ji, X. Li, H. Wang, Y. Deng, and Z. Ding, “Characteristic parameters of optical wave and short-term beam spreading in oceanic turbulence,” Acta Phys. Sin. 67, 224206 (2018).

Eyyuboglu, H. T.

Y. Baykal, H. T. Eyyuboğlu, and Y. Cai, “Partially coherent off-axis Gaussian beam scintillations,” J. Mod. Opt. 57, 1221–1227 (2010).
[Crossref]

Y. Baykal, H. T. Eyyuboğlu, and Y. Cai, “Scintillations of partially coherent multiple Gaussian beams in turbulence,” Appl. Opt. 48, 1943–1954 (2009).
[Crossref]

H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Complex degree of coherence for partially coherent beams,” J. Opt. Soc. Am. A 24, 2891–2901 (2007).
[Crossref]

Y. Baykal and H. T. Eyyuboğlu, “Scintillation index of flat-topped Gaussian beams,” J. Opt. Soc. Am. A 45, 3793–3797 (2005).
[Crossref]

Fan, C.

L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, and C. Fan, “Beam wander of laser beam propagating through oceanic turbulence,” Opt. Eng. 56, 104107 (2017).

Farwell, N.

N. Farwell and O. Korotkova, “Intensity and coherence properties of light in oceanic turbulence,” Opt. Commun. 285, 872–875 (2012).
[Crossref]

Feng, X.

X. Chu, C. Qiao, and X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1150–1154 (2011).
[Crossref]

Gerçekcioglu, H.

Ghafary, B.

M. Alavinejad and B. Ghafary, “Turbulence-induced degradation properties of partially coherent flat-topped beams,” Opt. Laser Eng. 46, 1795–1797 (2008).
[Crossref]

Gökçe, M. C.

M. C. Gökçe and Y. Baykal, “Effets of liver tissue turbulence on propagation of annular beam,” Optik 171, 313–318 (2018).
[Crossref]

M. C. Gökçe and Y. Baykal, “Aperture averaging and BER for Gaussian beam in underwater oceanic turbulence,” Opt. Commun. 410, 830–835 (2018).
[Crossref]

M. C. Gökçe and Y. Baykal, “Scintillation analysis of multiple-input single output underwater optical links,” Appl. Opt. 55, 6130–6136 (2016).
[Crossref]

M. C. Gökçe, Y. Baykal, and M. Uysal, “Aperture averaging in multiple input single-output free space optical systems using partially coherent radial array beams,” J. Opt. Soc. Am. A 33, 1041–1048 (2016).
[Crossref]

M. C. Gökçe, Y. Baykal, and M. Uysal, “Performance analysis of multiple-input multiple-output free-space optical systems with partially coherent Gaussian beams and finite-sized detectors,” Opt. Eng. 55, 111607 (2016).
[Crossref]

M. C. Gökçe, “Beam shaping effects on MIMO free-space optical communication systems,” Ph.D. dissertation (Çankaya University, 2016).

M. C. Gökçe, “Scintillation analysis and evaluation of super Lorentz-Gaussian laser beams for optical wireless,” M.Sc. thesis (Ankara University, 2012).

Golmohammady, S.

Gradshteyn, I. S.

I. S. Gradshteyn and M. I. Ryzhik, Table of Integrals, Series, and Products (Academic, 2007).

Hu, Z.

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

Ji, X.

T. Wu, X. Ji, X. Li, H. Wang, Y. Deng, and Z. Ding, “Characteristic parameters of optical wave and short-term beam spreading in oceanic turbulence,” Acta Phys. Sin. 67, 224206 (2018).

L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, and C. Fan, “Beam wander of laser beam propagating through oceanic turbulence,” Opt. Eng. 56, 104107 (2017).

Kashani, F. D.

Keskin, A.

A. Keskin, Y. Baykal, and Y. Ata, “Optical transmittance in turbulent underwater medium,” Proc. Çankaya Univ., Eng. Tech. Symp. 7, 137–141 (2014).

A. Keskin, “Wireless optical wave propagation in underwater medium,” M.Sc. thesis (Çankaya University, 2013).

Korotkova, O.

N. Farwell and O. Korotkova, “Intensity and coherence properties of light in oceanic turbulence,” Opt. Commun. 285, 872–875 (2012).
[Crossref]

Li, X.

T. Wu, X. Ji, X. Li, H. Wang, Y. Deng, and Z. Ding, “Characteristic parameters of optical wave and short-term beam spreading in oceanic turbulence,” Acta Phys. Sin. 67, 224206 (2018).

Li, Y.

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

Liu, D.

D. Liu, Y. Wang, and H. Zhong, “Average intensity of radial phase-locked partially coherent standard Hermite-Gaussian beam in oceanic turbulence,” Opt. Laser Technol. 106, 495–505 (2018).
[Crossref]

D. Liu and Y. Wang, “Average intensity of partially coherent Lorentz beams in oceanic turbulence,” Prog. Electromagn. Res. M 68, 181–191 (2018).
[Crossref]

D. Liu, L. Chen, Y. Wang, G. Wang, and H. Yin, “Average intensity properties of flat-topped vortex hollow beam propagating through oceanic turbulence,” Optik 127, 6961–6969 (2016).
[Crossref]

D. Liu, Y. Wang, and H. Yin, “Evolution properties of partially coherent flat-topped vortex hollow beam in oceanic turbulence,” Appl. Opt. 54, 10510–10516 (2015).
[Crossref]

D. Liu and Y. Wang, “Evolution behavior of Gaussian Schell-model vortex beams propagating through oceanic turbulence,” Opt. Express 22, 17723–17734 (2014).
[Crossref]

Lu, L.

L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, and C. Fan, “Beam wander of laser beam propagating through oceanic turbulence,” Opt. Eng. 56, 104107 (2017).

Mashal, A.

Nikishov, V. I.

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent fluctuation of the sea water refractive index,” Int. J. Fluid Mech. Res. 27, 82–98 (2000).
[Crossref]

Nikishov, V. V.

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent fluctuation of the sea water refractive index,” Int. J. Fluid Mech. Res. 27, 82–98 (2000).
[Crossref]

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

Plonus, M. A.

Qiao, C.

X. Chu, C. Qiao, and X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1150–1154 (2011).
[Crossref]

Ryzhik, M. I.

I. S. Gradshteyn and M. I. Ryzhik, Table of Integrals, Series, and Products (Academic, 2007).

Simpson, J.

J. Simpson, “A 1Mbps underwater communication system using LEDs and photodiodes with signal processing capability,” M.Sc. thesis (North California State University, 2008).

Tang, M.

M. Tang and D. Zhao, “Propagation of radially polarized beams in the oceanic turbulence,” Appl. Phys. B 111, 665–670 (2013).
[Crossref]

Uysal, M.

M. C. Gökçe, Y. Baykal, and M. Uysal, “Aperture averaging in multiple input single-output free space optical systems using partially coherent radial array beams,” J. Opt. Soc. Am. A 33, 1041–1048 (2016).
[Crossref]

M. C. Gökçe, Y. Baykal, and M. Uysal, “Performance analysis of multiple-input multiple-output free-space optical systems with partially coherent Gaussian beams and finite-sized detectors,” Opt. Eng. 55, 111607 (2016).
[Crossref]

Wang, G.

D. Liu, L. Chen, Y. Wang, G. Wang, and H. Yin, “Average intensity properties of flat-topped vortex hollow beam propagating through oceanic turbulence,” Optik 127, 6961–6969 (2016).
[Crossref]

Wang, H.

T. Wu, X. Ji, X. Li, H. Wang, Y. Deng, and Z. Ding, “Characteristic parameters of optical wave and short-term beam spreading in oceanic turbulence,” Acta Phys. Sin. 67, 224206 (2018).

Wang, S. J.

Wang, Y.

D. Liu, Y. Wang, and H. Zhong, “Average intensity of radial phase-locked partially coherent standard Hermite-Gaussian beam in oceanic turbulence,” Opt. Laser Technol. 106, 495–505 (2018).
[Crossref]

D. Liu and Y. Wang, “Average intensity of partially coherent Lorentz beams in oceanic turbulence,” Prog. Electromagn. Res. M 68, 181–191 (2018).
[Crossref]

D. Liu, L. Chen, Y. Wang, G. Wang, and H. Yin, “Average intensity properties of flat-topped vortex hollow beam propagating through oceanic turbulence,” Optik 127, 6961–6969 (2016).
[Crossref]

D. Liu, Y. Wang, and H. Yin, “Evolution properties of partially coherent flat-topped vortex hollow beam in oceanic turbulence,” Appl. Opt. 54, 10510–10516 (2015).
[Crossref]

D. Liu and Y. Wang, “Evolution behavior of Gaussian Schell-model vortex beams propagating through oceanic turbulence,” Opt. Express 22, 17723–17734 (2014).
[Crossref]

Wang, Z.

L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, and C. Fan, “Beam wander of laser beam propagating through oceanic turbulence,” Opt. Eng. 56, 104107 (2017).

Wu, T.

T. Wu, X. Ji, X. Li, H. Wang, Y. Deng, and Z. Ding, “Characteristic parameters of optical wave and short-term beam spreading in oceanic turbulence,” Acta Phys. Sin. 67, 224206 (2018).

Wu, Y.

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

Y. Wu, Y. Zhang, and Y. Zhu, “Average intensity and directionality of partially coherent model beams propagating in turbulent ocean,” J. Opt. Soc. Am. A 33, 1451–1458 (2016).
[Crossref]

Yin, H.

D. Liu, L. Chen, Y. Wang, G. Wang, and H. Yin, “Average intensity properties of flat-topped vortex hollow beam propagating through oceanic turbulence,” Optik 127, 6961–6969 (2016).
[Crossref]

D. Liu, Y. Wang, and H. Yin, “Evolution properties of partially coherent flat-topped vortex hollow beam in oceanic turbulence,” Appl. Opt. 54, 10510–10516 (2015).
[Crossref]

Yousefi, M.

Zhang, J.

L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, and C. Fan, “Beam wander of laser beam propagating through oceanic turbulence,” Opt. Eng. 56, 104107 (2017).

Zhang, P.

L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, and C. Fan, “Beam wander of laser beam propagating through oceanic turbulence,” Opt. Eng. 56, 104107 (2017).

Zhang, Y.

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

Y. Wu, Y. Zhang, and Y. Zhu, “Average intensity and directionality of partially coherent model beams propagating in turbulent ocean,” J. Opt. Soc. Am. A 33, 1451–1458 (2016).
[Crossref]

Zhao, D.

M. Tang and D. Zhao, “Propagation of radially polarized beams in the oceanic turbulence,” Appl. Phys. B 111, 665–670 (2013).
[Crossref]

Zhong, H.

D. Liu, Y. Wang, and H. Zhong, “Average intensity of radial phase-locked partially coherent standard Hermite-Gaussian beam in oceanic turbulence,” Opt. Laser Technol. 106, 495–505 (2018).
[Crossref]

Zhu, Y.

Acta Phys. Sin. (1)

T. Wu, X. Ji, X. Li, H. Wang, Y. Deng, and Z. Ding, “Characteristic parameters of optical wave and short-term beam spreading in oceanic turbulence,” Acta Phys. Sin. 67, 224206 (2018).

Appl. Opt. (6)

Appl. Phys. B (1)

M. Tang and D. Zhao, “Propagation of radially polarized beams in the oceanic turbulence,” Appl. Phys. B 111, 665–670 (2013).
[Crossref]

Chin. Opt. Lett. (1)

IEEE J. Sel. Areas Commun. (1)

Y. Ata and Y. Baykal, “Transmittance of multi Gaussian optical beams for uplink applications in atmospheric turbulence,” IEEE J. Sel. Areas Commun. 33, 1996–2001 (2015).
[Crossref]

Int. J. Fluid Mech. Res. (1)

V. V. Nikishov and V. I. Nikishov, “Spectrum of turbulent fluctuation of the sea water refractive index,” Int. J. Fluid Mech. Res. 27, 82–98 (2000).
[Crossref]

J. Mod. Opt. (4)

Y. Ata and Y. Baykal, “Turbulence effect on transmittance of atmospheric optics telecommunication system using dense wavelength division multiplexing,” J. Mod. Opt. 58, 1644–1650 (2011).
[Crossref]

Y. Baykal, “Effect of anisotropy on intensity fluctuations in oceanic turbulence,” J. Mod. Opt. 65, 825–829 (2018).
[Crossref]

S. A. Arpali, Y. Baykal, and Ç. Arpali, “BER evaluations for multimode beams in underwater turbulence,” J. Mod. Opt. 63, 1297–1300 (2016).
[Crossref]

Y. Baykal, H. T. Eyyuboğlu, and Y. Cai, “Partially coherent off-axis Gaussian beam scintillations,” J. Mod. Opt. 57, 1221–1227 (2010).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (11)

Y. Baykal, “Formulation of correlations for general-type beams in atmospheric turbulence,” J. Opt. Soc. Am. A 23, 889–893 (2006).
[Crossref]

H. Gerçekcioğlu and Y. Baykal, “Intensity fluctuations of flat-topped beam in non-Kolmogorov weak turbulence,” J. Opt. Soc. Am. A 29, 169–173 (2012).
[Crossref]

Y. Baykal and H. T. Eyyuboğlu, “Scintillation index of flat-topped Gaussian beams,” J. Opt. Soc. Am. A 45, 3793–3797 (2005).
[Crossref]

M. Yousefi, F. D. Kashani, S. Golmohammady, and A. Mashal, “Scintillation and bit error rate analysis of a phase-locked partially coherent flat-topped array laser beam in oceanic turbulence,” J. Opt. Soc. Am. A 34, 2126–2137 (2017).
[Crossref]

M. Yousefi, S. Golmohammady, A. Mashal, and F. D. Kashani, “Analyzing the propagation behavior of scintillation index and bit error rate of partially coherent flat-topped laser beam in oceanic turbulence,” J. Opt. Soc. Am. A 32, 1982–1992 (2015).
[Crossref]

Y. Ata and Y. Baykal, “Scintillations of optical plane and spherical waves in underwater turbulence,” J. Opt. Soc. Am. A 31, 1552–1556 (2014).
[Crossref]

Y. Wu, Y. Zhang, and Y. Zhu, “Average intensity and directionality of partially coherent model beams propagating in turbulent ocean,” J. Opt. Soc. Am. A 33, 1451–1458 (2016).
[Crossref]

Y. Baykal, “Bit error rate of pulse position modulated optical wireless communication links in oceanic turbulence,” J. Opt. Soc. Am. A 35, 1627–1632 (2018).
[Crossref]

Y. Baykal and M. A. Plonus, “Intensity fluctuations due to a spatially partially coherent source in atmospheric turbulence as predicted by Rytov’s method,” J. Opt. Soc. Am. A 2, 2124–2132 (1985).
[Crossref]

H. T. Eyyuboğlu, Y. Baykal, and Y. Cai, “Complex degree of coherence for partially coherent beams,” J. Opt. Soc. Am. A 24, 2891–2901 (2007).
[Crossref]

M. C. Gökçe, Y. Baykal, and M. Uysal, “Aperture averaging in multiple input single-output free space optical systems using partially coherent radial array beams,” J. Opt. Soc. Am. A 33, 1041–1048 (2016).
[Crossref]

Opt. Commun. (7)

Y. Baykal, “Higher order mode laser beam intensity fluctuations in strong oceanic turbulence,” Opt. Commun. 390, 72–75 (2017).
[Crossref]

Y. Baykal, “Scintillation index in strong oceanic turbulence,” Opt. Commun. 375, 15–18 (2016).
[Crossref]

Y. Baykal, “BER of asymmetrical optical beams in oceanic and marine atmospheric media,” Opt. Commun. 393, 29–33 (2017).
[Crossref]

M. C. Gökçe and Y. Baykal, “Aperture averaging and BER for Gaussian beam in underwater oceanic turbulence,” Opt. Commun. 410, 830–835 (2018).
[Crossref]

Y. Ata and Y. Baykal, “Average transmittance in non-Kolmogorov turbulence,” Opt. Commun. 305, 126–130 (2013).
[Crossref]

N. Farwell and O. Korotkova, “Intensity and coherence properties of light in oceanic turbulence,” Opt. Commun. 285, 872–875 (2012).
[Crossref]

Y. Wu, Y. Zhang, Y. Li, and Z. Hu, “Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence,” Opt. Commun. 371, 59–66 (2016).
[Crossref]

Opt. Eng. (2)

M. C. Gökçe, Y. Baykal, and M. Uysal, “Performance analysis of multiple-input multiple-output free-space optical systems with partially coherent Gaussian beams and finite-sized detectors,” Opt. Eng. 55, 111607 (2016).
[Crossref]

L. Lu, Z. Wang, P. Zhang, J. Zhang, X. Ji, and C. Fan, “Beam wander of laser beam propagating through oceanic turbulence,” Opt. Eng. 56, 104107 (2017).

Opt. Express (1)

Opt. Laser Eng. (1)

M. Alavinejad and B. Ghafary, “Turbulence-induced degradation properties of partially coherent flat-topped beams,” Opt. Laser Eng. 46, 1795–1797 (2008).
[Crossref]

Opt. Laser Technol. (2)

D. Liu, Y. Wang, and H. Zhong, “Average intensity of radial phase-locked partially coherent standard Hermite-Gaussian beam in oceanic turbulence,” Opt. Laser Technol. 106, 495–505 (2018).
[Crossref]

X. Chu, C. Qiao, and X. Feng, “Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence,” Opt. Laser Technol. 43, 1150–1154 (2011).
[Crossref]

Opt. Lett. (1)

Optik (2)

D. Liu, L. Chen, Y. Wang, G. Wang, and H. Yin, “Average intensity properties of flat-topped vortex hollow beam propagating through oceanic turbulence,” Optik 127, 6961–6969 (2016).
[Crossref]

M. C. Gökçe and Y. Baykal, “Effets of liver tissue turbulence on propagation of annular beam,” Optik 171, 313–318 (2018).
[Crossref]

Proc. Çankaya Univ., Eng. Tech. Symp. (1)

A. Keskin, Y. Baykal, and Y. Ata, “Optical transmittance in turbulent underwater medium,” Proc. Çankaya Univ., Eng. Tech. Symp. 7, 137–141 (2014).

Prog. Electromagn. Res. M (1)

D. Liu and Y. Wang, “Average intensity of partially coherent Lorentz beams in oceanic turbulence,” Prog. Electromagn. Res. M 68, 181–191 (2018).
[Crossref]

Wave Random Complex (1)

Y. Ata and Y. Baykal, “Structure functions for optical wave propagation in underwater medium,” Wave Random Complex 24, 164–173 (2014).
[Crossref]

Other (8)

A. Keskin, “Wireless optical wave propagation in underwater medium,” M.Sc. thesis (Çankaya University, 2013).

H. Brundage, “Designing a wireless underwater optical communication system,” M.Sc. thesis (Massachusetts Institute of Technology, 2010).

J. Simpson, “A 1Mbps underwater communication system using LEDs and photodiodes with signal processing capability,” M.Sc. thesis (North California State University, 2008).

M. C. Gökçe, “Beam shaping effects on MIMO free-space optical communication systems,” Ph.D. dissertation (Çankaya University, 2016).

I. S. Gradshteyn and M. I. Ryzhik, Table of Integrals, Series, and Products (Academic, 2007).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

L. C. Andrews, Field Guide to Atmospheric Optics (SPIE, 2004).

M. C. Gökçe, “Scintillation analysis and evaluation of super Lorentz-Gaussian laser beams for optical wireless,” M.Sc. thesis (Ankara University, 2012).

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Figures (16)

Fig. 1.
Fig. 1. Average transmittance versus the rate of dissipation of kinetic energy per unit mass of fluid ε for various numbers of beams composing the flat-topped beam N.
Fig. 2.
Fig. 2. Average transmittance versus the rate of dissipation of kinetic energy per unit mass of fluid ε for different source size, αs values.
Fig. 3.
Fig. 3. Average transmittance versus the rate of dissipation of mean square temperature χT for various numbers of beams composing the flat-topped beam N and off-axis parameter rx.
Fig. 4.
Fig. 4. Average transmittance versus the rate of dissipation of mean square temperature χT for various degrees of partial coherence ρs.
Fig. 5.
Fig. 5. Average transmittance versus the ratio of temperature and salinity contributions ω for various degrees of partial coherence ρs.
Fig. 6.
Fig. 6. Average transmittance versus the ratio of temperature and salinity contributions ω for different source sizes αs.
Fig. 7.
Fig. 7. Average transmittance versus off-axis parameter rx for various numbers of beams composing the flat-topped beam N.
Fig. 8.
Fig. 8. Beam spread due to oceanic turbulence versus the rate of dissipation of mean square temperature χT for various numbers of beams composing the flat-topped beam N.
Fig. 9.
Fig. 9. Beam spread due to oceanic turbulence versus the rate of dissipation of mean square temperature χT for various degrees of partial coherence ρs.
Fig. 10.
Fig. 10. Beam spread due to oceanic turbulence versus the rate of dissipation of mean square temperature χT for different source size αs values.
Fig. 11.
Fig. 11. Beam spread due to oceanic turbulence versus the rate of dissipation of kinetic energy per unit mass of fluid ε for various degrees of partial coherence ρs.
Fig. 12.
Fig. 12. Beam spread due to oceanic turbulence versus the rate of dissipation of mean square temperature ε for different source size αs values.
Fig. 13.
Fig. 13. Beam spread due to oceanic turbulence versus the ratio of temperature and salinity contributions ω for various degrees of partial coherence ρs.
Fig. 14.
Fig. 14. Beam size in the rx direction at the receiver plane versus the rate of dissipation of kinetic energy per unit mass of fluid ε for various numbers of beams composing the flat-topped beam N.
Fig. 15.
Fig. 15. Beam size in the rx direction at the receiver plane versus the ratio of temperature and salinity contributions ω for various numbers of beams composing the flat-topped beam N.
Fig. 16.
Fig. 16. Beam size in the rx direction at the receiver plane versus the ratio of temperature and salinity contributions ω for different source size αs values.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

I(r,L)=(k2πL)2d2s1d2s2u(s1)u*(s2)×exp(|s1s2|24ρs2)exp{ik2L[|s1r|2|s2r|2]}×exp[ψ(s1,r)+ψ*(s2,r)],
u(s1)=l1=1NAl1exp[0.5(s1x2αsxl12+αyl1s1y2αsyl12)],
Al=(1)l1N(Nl),(Nl)=N!l!(Nl)!,αsl=αs/l,
u(s)=l=1N(1)l1NN!l!(Nl)!exp(|s|22(αs/l)2).
exp[ψ(s1,r)+ψ*(s2,r)]=exp[π2k2L3|s1s2|2κ3ϕn(κ)dκ]=exp(|s1s2|2ρ0_uw2),
ϕn(κ)=0.388×108ε1/3κ11/3[1+2.35(κη)2/3]×XTw2(w2eATδ+eASδ2weATS),
exp(p2x2±qx)dx=exp(q24p2)πp,p>0,
I(r,L)=(πλL)2l1=1Nl2=1NAl1Al2*[14αsl24+k24L2+14αsl22ρs2+1ρ0_uw2αsl22]×exp{k24L2(rx2+ry2)(12αsl12ik2L+1ρ0_uw2+14ρs2)×[14αsl24+14αsl22ρs2+1ρ0_uw2αsl22+14αsl14ik2Lαsl1214αsl24+k24L2+14αsl22ρs2+1ρ0_uw2αsl22]}.
ρ0_uw=[3.603×107k2L(εη)1/3×χT2ω2(0.483ω20.835ω+3.38)]0.5.
τt=I(r,L)I0(r,L),
σxL=2rx2I(rx,ry,L)drxdryI(rx,ry,L)drxdry=AB,
A=2(πλL)2l1=1Nl2=1NAl1Al2*x1drxdryrx2exp[t1(rx2+ry2)],B=(πλL)2l1=1Nl2=1NAl1Al2*1x1drxdryexp(t1rx2)exp(t1ry2),t1=k24L2y1z1x1,x1=[14αsl24+k24L2+14αsl22ρs2+1ρ0_oc2αsl22],y1=14αsl24+14αsl22ρs2+1ρ0_oc2αsl22+14αsl14ik2Lαsl12,z1=12αsl12ik2L+1ρ0_oc2+14ρs2.
x2exp(μx2+2vx)dx=12μπμ(1+2v2μ)exp(v2μ),v=0x2exp(μx2)dx=12μπμ.
σxL=l1=1Nl2=1NAl1Al2*πx1t12,l1=1Nl2=1NAl1Al2*πx1t1.
ΔσxL=σxL_oc(z=L)σxL_fs(z=L),

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