Abstract

We analyze the properties of Ince–Gaussian beams propagating in turbulent atmosphere. Due to analytic difficulties, this analysis is done with the aid of a random phase screen setup. Intensity profile, beam size, and the kurtosis parameter are evaluated against the changes in beam orders, propagation distance, and turbulence levels. It is found that when propagating in turbulence, Ince–Gaussian beams will no longer keep their beam profile invariant like in free space but will experience beam profile changes. These changes will cause additional beam spreading, as well as an increase in beam size and the kurtosis parameter.

© 2014 Optical Society of America

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    [CrossRef]
  9. X. Chu, C. Qiao, and X. Feng, “Moments of intensity distribution of super-Gauss beam in turbulent atmosphere,” Appl. Phys. B 105, 909–914 (2011).
    [CrossRef]
  10. G. Zhou, “The beam propagation factors and the kurtosis parameters of a Lorentz beam,” Opt. Laser Technol. 41, 953–955 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013 (2)

X. Li and X. Ji, “Propagation of higher-order intensity moments through an optical system in atmospheric turbulence,” Opt. Commun. 298–299, 1–7 (2013).
[CrossRef]

Y. Ni, X. Wang, and G. Zhou, “Propagation of a Hermite–Laguerre–Gaussian beam in a turbulent atmosphere,” Appl. Phys. B 111, 131–140 (2013).
[CrossRef]

2011 (4)

X. Chu, “Moment and kurtosis parameter of partially coherent cosh-Gaussian beam in turbulent atmosphere,” Appl. Phys. B 103, 1013–1019 (2011).
[CrossRef]

X. Chu, “Arbitrary moments of elliptical Gaussian–Schell beam in turbulent atmosphere,” J. Opt. Soc. Am. A 28, 917–923 (2011).
[CrossRef]

X. Chu, C. Qiao, and X. Feng, “Moments of intensity distribution of super-Gauss beam in turbulent atmosphere,” Appl. Phys. B 105, 909–914 (2011).
[CrossRef]

X. Liu and J. Pu, “Investigation on the scintillation reduction of elliptical vortex beams propagating in atmospheric turbulence,” Opt. Express 19, 26444–26450 (2011).
[CrossRef]

2010 (2)

Y. Gu and G. Gbur, “Scintillation of pseudo-Bessel correlated beams in atmospheric turbulence,” J. Opt. Soc. Am. A 27, 2621–2629 (2010).
[CrossRef]

X. M. Qian, W. Y. Zhu, A. T. Wang, C. Gu, and R. Z. Rao, “Numerical simulation for coherent and partially coherent beam propagation through atmospheric turbulence,” Chin. Phys. Lett. 27, 044214 (2010).
[CrossRef]

2009 (5)

2008 (2)

2006 (4)

H. T. Eyyuboğlu, Y. Baykal, and E. Sermutlu, “Convergence of general beams into Gaussian intensity profiles after propagation in turbulent atmosphere,” Opt. Commun. 265, 399–405 (2006).
[CrossRef]

T. Xu and S. Wang, “Propagation of Ince–Gaussian beams in a thermal lens medium,” Opt. Commun. 265, 1–5 (2006).
[CrossRef]

J. B. Bantley, J. A. Davis, M. A. Bandres, and J. C. Gutierrez-Vega, “Generation of helical Ince–Gaussian beams with a liquid-crystal display,” Opt. Lett. 31, 649–651 (2006).
[CrossRef]

X. Xiao and D. Voelz, “Wave optics simulation approach for partial spatially coherent beams,” Opt. Express 14, 6986–6992 (2006).
[CrossRef]

2005 (1)

2004 (4)

2000 (1)

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005), Chap. 5.

Bandres, M. A.

Bantley, J. B.

Baykal, Y.

H. T. Eyyuboğlu, Y. Baykal, and E. Sermutlu, “Convergence of general beams into Gaussian intensity profiles after propagation in turbulent atmosphere,” Opt. Commun. 265, 399–405 (2006).
[CrossRef]

Belmonte, A.

Cheng, W.

Chu, X.

X. Chu, “Arbitrary moments of elliptical Gaussian–Schell beam in turbulent atmosphere,” J. Opt. Soc. Am. A 28, 917–923 (2011).
[CrossRef]

X. Chu, “Moment and kurtosis parameter of partially coherent cosh-Gaussian beam in turbulent atmosphere,” Appl. Phys. B 103, 1013–1019 (2011).
[CrossRef]

X. Chu, C. Qiao, and X. Feng, “Moments of intensity distribution of super-Gauss beam in turbulent atmosphere,” Appl. Phys. B 105, 909–914 (2011).
[CrossRef]

Davis, J. A.

Eyyuboglu, H. T.

H. T. Eyyuboğlu, Y. Baykal, and E. Sermutlu, “Convergence of general beams into Gaussian intensity profiles after propagation in turbulent atmosphere,” Opt. Commun. 265, 399–405 (2006).
[CrossRef]

Feng, X.

X. Chu, C. Qiao, and X. Feng, “Moments of intensity distribution of super-Gauss beam in turbulent atmosphere,” Appl. Phys. B 105, 909–914 (2011).
[CrossRef]

Gbur, G.

Gu, C.

X. M. Qian, W. Y. Zhu, A. T. Wang, C. Gu, and R. Z. Rao, “Numerical simulation for coherent and partially coherent beam propagation through atmospheric turbulence,” Chin. Phys. Lett. 27, 044214 (2010).
[CrossRef]

Gu, Y.

Gutierrez-Vega, J. C.

Haus, J. H.

Ji, X.

X. Li and X. Ji, “Propagation of higher-order intensity moments through an optical system in atmospheric turbulence,” Opt. Commun. 298–299, 1–7 (2013).
[CrossRef]

Li, X.

X. Li and X. Ji, “Propagation of higher-order intensity moments through an optical system in atmospheric turbulence,” Opt. Commun. 298–299, 1–7 (2013).
[CrossRef]

Liu, X.

Ni, Y.

Y. Ni, X. Wang, and G. Zhou, “Propagation of a Hermite–Laguerre–Gaussian beam in a turbulent atmosphere,” Appl. Phys. B 111, 131–140 (2013).
[CrossRef]

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005), Chap. 5.

Pu, J.

Qian, X.

Qian, X. M.

X. M. Qian, W. Y. Zhu, A. T. Wang, C. Gu, and R. Z. Rao, “Numerical simulation for coherent and partially coherent beam propagation through atmospheric turbulence,” Chin. Phys. Lett. 27, 044214 (2010).
[CrossRef]

Qiao, C.

X. Chu, C. Qiao, and X. Feng, “Moments of intensity distribution of super-Gauss beam in turbulent atmosphere,” Appl. Phys. B 105, 909–914 (2011).
[CrossRef]

Rao, R.

Rao, R. Z.

X. M. Qian, W. Y. Zhu, A. T. Wang, C. Gu, and R. Z. Rao, “Numerical simulation for coherent and partially coherent beam propagation through atmospheric turbulence,” Chin. Phys. Lett. 27, 044214 (2010).
[CrossRef]

Schmidt, J. D.

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in MATLAB (SPIE, 2010).

Schwarz, U. T.

Sermutlu, E.

H. T. Eyyuboğlu, Y. Baykal, and E. Sermutlu, “Convergence of general beams into Gaussian intensity profiles after propagation in turbulent atmosphere,” Opt. Commun. 265, 399–405 (2006).
[CrossRef]

Voelz, D.

Wang, A. T.

X. M. Qian, W. Y. Zhu, A. T. Wang, C. Gu, and R. Z. Rao, “Numerical simulation for coherent and partially coherent beam propagation through atmospheric turbulence,” Chin. Phys. Lett. 27, 044214 (2010).
[CrossRef]

Wang, S.

T. Xu and S. Wang, “Propagation of Ince–Gaussian beams in a thermal lens medium,” Opt. Commun. 265, 1–5 (2006).
[CrossRef]

Wang, X.

Y. Ni, X. Wang, and G. Zhou, “Propagation of a Hermite–Laguerre–Gaussian beam in a turbulent atmosphere,” Appl. Phys. B 111, 131–140 (2013).
[CrossRef]

Xiao, X.

Xu, T.

T. Xu and S. Wang, “Propagation of Ince–Gaussian beams in a thermal lens medium,” Opt. Commun. 265, 1–5 (2006).
[CrossRef]

Zhan, Q.

Zhou, G.

Y. Ni, X. Wang, and G. Zhou, “Propagation of a Hermite–Laguerre–Gaussian beam in a turbulent atmosphere,” Appl. Phys. B 111, 131–140 (2013).
[CrossRef]

G. Zhou, “The beam propagation factors and the kurtosis parameters of a Lorentz beam,” Opt. Laser Technol. 41, 953–955 (2009).
[CrossRef]

G. Zhou, “Fractional Fourier transform of Ince–Gaussian beams,” J. Opt. Soc. Am. A 26, 2586–2591 (2009).
[CrossRef]

Zhu, W.

Zhu, W. Y.

X. M. Qian, W. Y. Zhu, A. T. Wang, C. Gu, and R. Z. Rao, “Numerical simulation for coherent and partially coherent beam propagation through atmospheric turbulence,” Chin. Phys. Lett. 27, 044214 (2010).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. B (3)

X. Chu, C. Qiao, and X. Feng, “Moments of intensity distribution of super-Gauss beam in turbulent atmosphere,” Appl. Phys. B 105, 909–914 (2011).
[CrossRef]

Y. Ni, X. Wang, and G. Zhou, “Propagation of a Hermite–Laguerre–Gaussian beam in a turbulent atmosphere,” Appl. Phys. B 111, 131–140 (2013).
[CrossRef]

X. Chu, “Moment and kurtosis parameter of partially coherent cosh-Gaussian beam in turbulent atmosphere,” Appl. Phys. B 103, 1013–1019 (2011).
[CrossRef]

Chin. Phys. Lett. (1)

X. M. Qian, W. Y. Zhu, A. T. Wang, C. Gu, and R. Z. Rao, “Numerical simulation for coherent and partially coherent beam propagation through atmospheric turbulence,” Chin. Phys. Lett. 27, 044214 (2010).
[CrossRef]

J. Opt. Soc. Am. A (5)

Opt. Commun. (3)

T. Xu and S. Wang, “Propagation of Ince–Gaussian beams in a thermal lens medium,” Opt. Commun. 265, 1–5 (2006).
[CrossRef]

X. Li and X. Ji, “Propagation of higher-order intensity moments through an optical system in atmospheric turbulence,” Opt. Commun. 298–299, 1–7 (2013).
[CrossRef]

H. T. Eyyuboğlu, Y. Baykal, and E. Sermutlu, “Convergence of general beams into Gaussian intensity profiles after propagation in turbulent atmosphere,” Opt. Commun. 265, 399–405 (2006).
[CrossRef]

Opt. Express (5)

Opt. Laser Technol. (1)

G. Zhou, “The beam propagation factors and the kurtosis parameters of a Lorentz beam,” Opt. Laser Technol. 41, 953–955 (2009).
[CrossRef]

Opt. Lett. (4)

Other (2)

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in MATLAB (SPIE, 2010).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005), Chap. 5.

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Figures (9)

Fig. 1.
Fig. 1.

Source plane intensities for selected orders of IG beams.

Fig. 2.
Fig. 2.

Variation of the intensity profile of the IG beam I21c(rx=0,ry) along the propagation axis.

Fig. 3.
Fig. 3.

Variation of the intensity profile of the IG beam I31c(rx=ry) along the propagation axis.

Fig. 4.
Fig. 4.

Variation of the beam size of selected IG beams along rx against the propagation distance.

Fig. 5.
Fig. 5.

Variation of the beam size of selected IG beams along ry with the propagation distance.

Fig. 6.
Fig. 6.

Variation of the kurtosis parameter, Kx, against the propagation distance.

Fig. 7.
Fig. 7.

Variation of the kurtosis parameter, Ky, against the propagation distance.

Fig. 8.
Fig. 8.

Variation of the beam size of selected IG beams along ry with the structure constant.

Fig. 9.
Fig. 9.

Variation of the kurtosis parameter, Ky, against the structure constant.

Tables (2)

Tables Icon

Table 1. List of Random Phase Screen Parameters for the End Points of Figs. 47a

Tables Icon

Table 2. List of Random Phase Screen Parameters for the End Points of Figs. 8 and 9a

Equations (12)

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

E(sx,sy)=S(θ)H(p)G(sx,sy),
θ=0.5cos1[sx2+sy2(sx2+sy2+ds2)24sx2ds2ds2],p=0.5cosh1[sx2+sy2+(sx2+sy2+ds2)24sx2ds2ds2],
d2S(θ)dθ2+2ds2αs2sin(2θ)dS(θ)dθ+[a2nds2αs2cos(2θ)]S(θ)=0,d2H(p)dp22ds2αs2sinh(2p)dH(p)dp[a2nds2αs2cosh(2p)]H(p)=0,
G(sx,sy)=exp(sx2+sy2αs2).
Snmc(θ)=i=0n/2Cicos(2iθ),neven,Snmc(θ)=i=0(n1)/2Cicos[(2i+1)θ],nodd,Snms(θ)=i=1n/2Cisin(2iθ),neven,Snms(θ)=i=0(n1)/2Cisin[(2i+1)θ],nodd.
Enmc,s(sx,sy)=Snmc,s(θ)Snmc,s(jp)exp(sx2+sy2αs2).
Inmc,s(sx,sy)=Enmc,s(sx,sy)[Enmc,s(sx,sy)]*,
Enmc,s(rx,ry)=αsαrSnmc,s(φ)Snmc,s(jq)exp(rx2+ry2αr2)×exp[jk(Lrx2+ry22F)j(n+1)λLπαs2],
αr=(π2αs4+λ2L2π2αs2)0.5,
Inmc,s(rx,ry)=Enmc,s(rx,ry)[Enmc,s(rx,ry)]*.
Kx=Kx4Kx0y0Kx2,Ky=Ky4Kx0y0Ky2,K=Kx4+2Kx2y2+Ky4Kx2+2Kx2Ky2+Ky2Kx0y0,Kx4=rx4Inmc,s(rx,ry)drxdry,Ky4=ry4Inmc,s(rx,ry)drxdry,Kx2=rx2Inmc,s(rx,ry)drxdry,Ky2=ry2Inmc,s(rx,ry)drxdry,Kx2y2=rx2ry2Inmc,s(rx,ry)drxdry,Kx0y0=Inmc,s(rx,ry)drxdry.
Beam size alongrxaxisαnmc,s=(2Kx2Kx0y0)0.5=[2rx2Inmc,s(rx,ry)drxdryInmc,s(rx,ry)drxdry]0.5.Beam size alongryaxisαnmc,s=(2Ky2Kx0y0)0.5=[2ry2Inmc,s(rx,ry)drxdryInmc,s(rx,ry)drxdry]0.5.

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