Research of degree of polarization of PCELG beam propagating through a circular aperture

WANG Bing; FEI Jin-cheng; CUI Zhi-feng; WANG Jia-si; QU Jun

doi:10.7510/jgjs.issn.1001-3806.2013.05.024

Volume 37 Issue 5

Jul. 2013

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Research of degree of polarization of PCELG beam propagating through a circular aperture

1.
College of Physics and Electronic Information, Anhui Normal University, Wuhu 241000, China

Corresponding author: QU Jun, qujun70@mail.ahnu.edu.cn
Received Date: 2012-11-28
Accepted Date: 2012-12-21

Abstract

To study the degree of polarization of partially coherent elegant Laguerre-Gaussian (PCELG) beam propagating through a circular aperture in turbulent atmosphere, based on extended Huygens-Fresnel principle, the formulas for the degree of polarization of PCELG beam were derived via theoretical calculation and the corresponding numerical calculation was carried out. The results indicate that the aperture diffraction effect will result in increasing oscillations of the polarization of PCELG beam. In turbulent atmosphere or in free space, the transverse degree of polarization near to the axis has a dramatic oscillation while the degree of polarization far from the axis approaches to 1. The further the propagation distance is, the larger the off-axis distance is. After propagating for a sufficiently long distance through the circular aperture in free space, the degree of polarization of PCELG beam approaches a value different from the initial one. However, it tends to the initial value in turbulent atmosphere. The results are useful for beam propagation and applications in atmosphere.

References

[1]	ZHU Zh W,XU J C,CANG J. Propagation properties of J0-correlated partially coherent flat-topped beams in a turbulent atmosphere[J]. Laser Technology,2010,34(4): 565-568(in Chinese).
[2]	FEI J Ch,CUI Zh F,WANG J S,et al. Propagation characteristics of elegant Laguerre-Gaussian beam passing through a circular aperture in turbulent atmosphere[J]. Laser Technology,2011,35(6): 849-853(in Chinese).
[3]	YANG A L,ZHANG E T,JI X L,et al. Angular spread of partially coherent Hermite-cosh-Gaussian beams propagating through atmospheric turbulence[J]. Optics Express,2008,16(12): 8366-8380.
[4]	SHIRAI T,DOGARIU A,WOLF E. Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence[J]. Journal of the Optical Society of America,2003,A20(6): 1094-1102.
[5]	MOHAMED S,OLGA K,ARISTIDE D,et al. Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere[J]. Waves in Random Media,2004,14(4):513-523.
[6]	OLGA K,MOHAMED S,WOLF E. The far-zone behavior of the degree of polarization of partially coherent beams propagating through atmospheric turbulence[J]. Optics Communications,2004,233(4/6): 225-230.
[7]	ROYCHOWDHURY H,PONOMARENKO S A,WOLF E. Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere[J]. Journal of Modern Optics,2005,52(11): 1611-1618.
[8]	GAO W R. Changes of polarization of light beams on propagation through tissue[J]. Optics Communications,2006,260(2): 749-754.
[9]	ZHAO D M,DU X Y. Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere[J]. Optics Express,2009,17(6): 4257-4262.
[10]	JI X L,CHEN S H,LI X Q. Polarization properties of partially coherent electromagnetic Hermite-Gaussian beams in atmospheric turbulence[J]. Chinese Journal of Lasers,2008,35(1): 67-72 (in Chinese).
[11]	ZHONG Y L,CUI Zh F,QU J,et al. Polarization properties of partially coherent electromagnetic elegant Laguerre-Gaussian beams in turbulent atmosphere[J]. Applied Physics,2011,B102(4): 937-944.
[12]	CAI Y J,HE S L. Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere[J]. Applied Physics Letters,2006,89(4): 041117.
[13]	CAI Y J,LIN Q,EYYUBOGLU H T,et al. Average irradiance and polarization properties of a radially or azimuthally polarized beam in a turbulent atmosphere[J].Optics Express,2008,16(11): 7665-7673.
[14]	EYYUBOGLU H T,BAYKAL Y,CAI Y J. Degree of polarization for partially coherent general beams in turbulent atmosphere[J]. Applied Physics,2007,B89(1): 91-97.
[15]	JI X L,ZHANG E T,LV B D. Changes in the spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atmosphere[J].Optics Communications,2007,275(2): 292-300.
[16]	KASHANI F D,ALAVINEJAD M,GHAFARY B. Polarization characteristics of aberrated partially coherent flat-topped beam propagating through turbulent atmosphere[J]. Optics Communications,2009,282(20): 4029-4034.
[17]	YANG A L,ZHANG E T,JI X L,et al. Propagation properties of partially coherent Hermite-cosh-Gaussian beams through atmospheric turbulence[J].Optics Laser Technology,2009,41(6): 714-722.
[18]	JI X L,CHEN X W. Changes in the polarization,the coherence and spectrum of partially coherent electromagnetic Hermite-Gaussian beams in turbulence[J].Optics Laser Technology,2009,41(2): 165-171.
[19]	PU J X. Invariance of spectrum and polarization of electromagnetic Gaussian Schell-model beams propagating in free space[J]. Chinese Optics Letters,2006,4(4): 196-198.
[20]	GOVIND P A,WOLF E. Propagation-induced polarization changes in partially coherent optical beams[J]. Journal of the Optical Society of America,2000,A17(11): 2019-2023.
[21]	JAMES D F V. Change of polarization of light beams on propagation in free space[J]. Journal of the Optical Society of America,1994,A11(5): 1641-1643.
[22]	DU X Y,ZHAO D M,KOROTKOVA O. Changes in the statistical properties of stochastic anisotropic electromagnetic beams on propagation in the turbulent atmosphere[J]. Optics Express,2007,15(25): 16909-16915.
[23]	PAN L Zh. Far-field behavior of partially polarized Gaussian Schell-model beams diffracted through an aperture[J]. Acta Optica Sinica,2006,26(8): 1250-1255(in Chinese).
[24]	WANG H Y,LI X Y. Spectral properties of stochastic electromagnetic twist anisotropic Gaussian-Schell model beam truncated by a slit aperture propagating in turbulent atmosphere[J]. Optics Laser Technology,2010,42(7): 1066-1076.
[25]	JI X L,PU Z C. Effects of atmospheric turbulence on the polarization of apertured electronmagnetic Gaussian Schell-model beams[J]. Journal of Optics,2009,A11(4): 45701-45707.
[26]	ZHAO T J. Effect of the aperture on the on-axis polarization properties of partially coherent light[J]. Laser Technology,2008,32(4): 424-433(in Chinese).
[27]	SHU J H,CHEN Z Y,PU J X. Changes in the degree of polarization of partially coherent lights diffracted by multiple circular apertures[J].Chinese Journal of Lasers,2008,35(6): 849-854(in Chinese).
[28]	WEN J J,BREAZEALE M A. A diffraction beam field expressed as the superposition of Gaussian beams[J]. Journal of the Acoustical Society of America,1988,83(5): 1752-1756.
[29]	TAKENAKA T,YOKOTA M,FUKUMITSU O. Propagation of light beams beyond the paraxial approximation[J]. Journal of the Optical Society of America,1985,A2(6): 826-829.
[30]	SAGHAFI S,SHEPPARD C J R. Near field and far field of elegant Hermite-Gaussian and Laguerre-Gaussian modes[J]. Journal of Modern Optics,1998,45(10): 1999-2009.
[31]	CAI Y J. Propagation of various flat-topped beams in a turbulent atmosphere[J]. Journal of Optics,2006,A8(6): 537-545.
[32]	KIMEL I,ELIAS L R. Relations between Hermite and Laguerre Gaussian modes[J]. IEEE Journal of Quantum Electronics,1993,29(9): 2562-2567.
[33]	WOLF E. Unified theory of coherence and polarization of random electromagnetic beams[J]. Physics Letters,2003,A312(5/6): 263-267.
[34]	WANG F,CAI Y J,EYYUBOGLU H T,et al. Average intensity and spreading of partially coherent standard and elegant Hermite-Gaussian beams in turbulent atmosphere[J]. Progress in Electromagnetics Research,2010,103: 33-56.
[35]	ZHANG G W,PU J X,SAHIN S,et al. The spectral degree of cross-polarization of stochastic electromagnetic beams[J]. Acta Photonica Sinica,2009,38(8): 2093-2098 (in Chinese).
[36]	DAN Y Q,ZHANG B,PAN P P. Propagation of partially coherent flat-topped beams through a turbulent atmosphere[J]. Journal of the Optical Society of America,2008,A25(9): 2223-2231.
[37]	CHENG F L,CAI Y J. Propagation factor of a truncated partially coherent flat-topped beam in turbulent atmosphere[J]. Optics Communications,2011,284(1): 30-37.
[38]	FAN T Y. Laser beam combining for high-power,high-radiance sources[J]. IEEE Journal of Selected Topics in Quantum Electronics,2005,11(3): 567-577.
[39]	CAI Y J,CHEN Y,EYYUBOGLU H T,et al. Propagation of laser array beams in a turbulent atmosphere[J].Applied Physics,2007,B88(3): 467-475.
[40]	WANG H,LIU D,ZHOU Z. The propagation of radially polarized partially coherent beam through an optical system in turbulent atmosphere[J]. Applied Physics,2010,B101(1/2): 361-369.
[41]	JIN Y M. Practical integral table[M]. Hefei: University of Science and Technology of China Press,2006: 237(in Chinese).

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通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

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Research of degree of polarization of PCELG beam propagating through a circular aperture

Corresponding author: QU Jun, qujun70@mail.ahnu.edu.cn

1. College of Physics and Electronic Information, Anhui Normal University, Wuhu 241000, China

Received Date: 2012-11-28

Accepted Date: 2012-12-21

Available Online: 2013-09-25

Abstract: To study the degree of polarization of partially coherent elegant Laguerre-Gaussian (PCELG) beam propagating through a circular aperture in turbulent atmosphere, based on extended Huygens-Fresnel principle, the formulas for the degree of polarization of PCELG beam were derived via theoretical calculation and the corresponding numerical calculation was carried out. The results indicate that the aperture diffraction effect will result in increasing oscillations of the polarization of PCELG beam. In turbulent atmosphere or in free space, the transverse degree of polarization near to the axis has a dramatic oscillation while the degree of polarization far from the axis approaches to 1. The further the propagation distance is, the larger the off-axis distance is. After propagating for a sufficiently long distance through the circular aperture in free space, the degree of polarization of PCELG beam approaches a value different from the initial one. However, it tends to the initial value in turbulent atmosphere. The results are useful for beam propagation and applications in atmosphere.

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Reference (41)

[1]	ZHU Zh W,XU J C,CANG J. Propagation properties of J0-correlated partially coherent flat-topped beams in a turbulent atmosphere[J]. Laser Technology,2010,34(4): 565-568(in Chinese).
[2]	FEI J Ch,CUI Zh F,WANG J S,et al. Propagation characteristics of elegant Laguerre-Gaussian beam passing through a circular aperture in turbulent atmosphere[J]. Laser Technology,2011,35(6): 849-853(in Chinese).
[3]	YANG A L,ZHANG E T,JI X L,et al. Angular spread of partially coherent Hermite-cosh-Gaussian beams propagating through atmospheric turbulence[J]. Optics Express,2008,16(12): 8366-8380.
[4]	SHIRAI T,DOGARIU A,WOLF E. Mode analysis of spreading of partially coherent beams propagating through atmospheric turbulence[J]. Journal of the Optical Society of America,2003,A20(6): 1094-1102.
[5]	MOHAMED S,OLGA K,ARISTIDE D,et al. Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere[J]. Waves in Random Media,2004,14(4):513-523.
[6]	OLGA K,MOHAMED S,WOLF E. The far-zone behavior of the degree of polarization of partially coherent beams propagating through atmospheric turbulence[J]. Optics Communications,2004,233(4/6): 225-230.
[7]	ROYCHOWDHURY H,PONOMARENKO S A,WOLF E. Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere[J]. Journal of Modern Optics,2005,52(11): 1611-1618.
[8]	GAO W R. Changes of polarization of light beams on propagation through tissue[J]. Optics Communications,2006,260(2): 749-754.
[9]	ZHAO D M,DU X Y. Polarization modulation of stochastic electromagnetic beams on propagation through the turbulent atmosphere[J]. Optics Express,2009,17(6): 4257-4262.
[10]	JI X L,CHEN S H,LI X Q. Polarization properties of partially coherent electromagnetic Hermite-Gaussian beams in atmospheric turbulence[J]. Chinese Journal of Lasers,2008,35(1): 67-72 (in Chinese).
[11]	ZHONG Y L,CUI Zh F,QU J,et al. Polarization properties of partially coherent electromagnetic elegant Laguerre-Gaussian beams in turbulent atmosphere[J]. Applied Physics,2011,B102(4): 937-944.
[12]	CAI Y J,HE S L. Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere[J]. Applied Physics Letters,2006,89(4): 041117.
[13]	CAI Y J,LIN Q,EYYUBOGLU H T,et al. Average irradiance and polarization properties of a radially or azimuthally polarized beam in a turbulent atmosphere[J].Optics Express,2008,16(11): 7665-7673.
[14]	EYYUBOGLU H T,BAYKAL Y,CAI Y J. Degree of polarization for partially coherent general beams in turbulent atmosphere[J]. Applied Physics,2007,B89(1): 91-97.
[15]	JI X L,ZHANG E T,LV B D. Changes in the spectrum and polarization of polychromatic partially coherent electromagnetic beams in the turbulent atmosphere[J].Optics Communications,2007,275(2): 292-300.
[16]	KASHANI F D,ALAVINEJAD M,GHAFARY B. Polarization characteristics of aberrated partially coherent flat-topped beam propagating through turbulent atmosphere[J]. Optics Communications,2009,282(20): 4029-4034.
[17]	YANG A L,ZHANG E T,JI X L,et al. Propagation properties of partially coherent Hermite-cosh-Gaussian beams through atmospheric turbulence[J].Optics Laser Technology,2009,41(6): 714-722.
[18]	JI X L,CHEN X W. Changes in the polarization,the coherence and spectrum of partially coherent electromagnetic Hermite-Gaussian beams in turbulence[J].Optics Laser Technology,2009,41(2): 165-171.
[19]	PU J X. Invariance of spectrum and polarization of electromagnetic Gaussian Schell-model beams propagating in free space[J]. Chinese Optics Letters,2006,4(4): 196-198.
[20]	GOVIND P A,WOLF E. Propagation-induced polarization changes in partially coherent optical beams[J]. Journal of the Optical Society of America,2000,A17(11): 2019-2023.
[21]	JAMES D F V. Change of polarization of light beams on propagation in free space[J]. Journal of the Optical Society of America,1994,A11(5): 1641-1643.
[22]	DU X Y,ZHAO D M,KOROTKOVA O. Changes in the statistical properties of stochastic anisotropic electromagnetic beams on propagation in the turbulent atmosphere[J]. Optics Express,2007,15(25): 16909-16915.
[23]	PAN L Zh. Far-field behavior of partially polarized Gaussian Schell-model beams diffracted through an aperture[J]. Acta Optica Sinica,2006,26(8): 1250-1255(in Chinese).
[24]	WANG H Y,LI X Y. Spectral properties of stochastic electromagnetic twist anisotropic Gaussian-Schell model beam truncated by a slit aperture propagating in turbulent atmosphere[J]. Optics Laser Technology,2010,42(7): 1066-1076.
[25]	JI X L,PU Z C. Effects of atmospheric turbulence on the polarization of apertured electronmagnetic Gaussian Schell-model beams[J]. Journal of Optics,2009,A11(4): 45701-45707.
[26]	ZHAO T J. Effect of the aperture on the on-axis polarization properties of partially coherent light[J]. Laser Technology,2008,32(4): 424-433(in Chinese).
[27]	SHU J H,CHEN Z Y,PU J X. Changes in the degree of polarization of partially coherent lights diffracted by multiple circular apertures[J].Chinese Journal of Lasers,2008,35(6): 849-854(in Chinese).
[28]	WEN J J,BREAZEALE M A. A diffraction beam field expressed as the superposition of Gaussian beams[J]. Journal of the Acoustical Society of America,1988,83(5): 1752-1756.
[29]	TAKENAKA T,YOKOTA M,FUKUMITSU O. Propagation of light beams beyond the paraxial approximation[J]. Journal of the Optical Society of America,1985,A2(6): 826-829.
[30]	SAGHAFI S,SHEPPARD C J R. Near field and far field of elegant Hermite-Gaussian and Laguerre-Gaussian modes[J]. Journal of Modern Optics,1998,45(10): 1999-2009.
[31]	CAI Y J. Propagation of various flat-topped beams in a turbulent atmosphere[J]. Journal of Optics,2006,A8(6): 537-545.
[32]	KIMEL I,ELIAS L R. Relations between Hermite and Laguerre Gaussian modes[J]. IEEE Journal of Quantum Electronics,1993,29(9): 2562-2567.
[33]	WOLF E. Unified theory of coherence and polarization of random electromagnetic beams[J]. Physics Letters,2003,A312(5/6): 263-267.
[34]	WANG F,CAI Y J,EYYUBOGLU H T,et al. Average intensity and spreading of partially coherent standard and elegant Hermite-Gaussian beams in turbulent atmosphere[J]. Progress in Electromagnetics Research,2010,103: 33-56.
[35]	ZHANG G W,PU J X,SAHIN S,et al. The spectral degree of cross-polarization of stochastic electromagnetic beams[J]. Acta Photonica Sinica,2009,38(8): 2093-2098 (in Chinese).
[36]	DAN Y Q,ZHANG B,PAN P P. Propagation of partially coherent flat-topped beams through a turbulent atmosphere[J]. Journal of the Optical Society of America,2008,A25(9): 2223-2231.
[37]	CHENG F L,CAI Y J. Propagation factor of a truncated partially coherent flat-topped beam in turbulent atmosphere[J]. Optics Communications,2011,284(1): 30-37.
[38]	FAN T Y. Laser beam combining for high-power,high-radiance sources[J]. IEEE Journal of Selected Topics in Quantum Electronics,2005,11(3): 567-577.
[39]	CAI Y J,CHEN Y,EYYUBOGLU H T,et al. Propagation of laser array beams in a turbulent atmosphere[J].Applied Physics,2007,B88(3): 467-475.
[40]	WANG H,LIU D,ZHOU Z. The propagation of radially polarized partially coherent beam through an optical system in turbulent atmosphere[J]. Applied Physics,2010,B101(1/2): 361-369.
[41]	JIN Y M. Practical integral table[M]. Hefei: University of Science and Technology of China Press,2006: 237(in Chinese).

Research of degree of polarization of PCELG beam propagating through a circular aperture

Abstract

References

Proportional views

通讯作者: 陈斌, bchen63@163.com

Proportional views