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Frontiers of Optoelectronics

ISSN 2095-2759

ISSN 2095-2767(Online)

CN 10-1029/TN

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Front Optoelec Chin    2009, Vol. 2 Issue (4) : 397-402    https://doi.org/10.1007/s12200-009-0074-0
RESEARCH ARTICLE
Propagation properties of beams generated by Gaussian mirror resonator in fractional Fourier transform plane
Bin TANG()
School of Mathematics and Physics, Jiangsu Polytechnic University, Changzhou 213164, China
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Abstract

Based on the definition of the fractional Fourier transform (FRFT) and irradiance moments in the cylindrical coordinate system, the propagation expressions and kurtosis parameter of beams generated by Gaussian mirror resonator passing through the ideal fractional Fourier transformation systems are obtained. The propagation properties and kurtosis parametric characteristic of the beams in the FRFT plane are analyzed in detail. Some numerical examples are given to illustrate the analytical results. The influences of the fractional order on the intensity distribution and the kurtosis parameter of the beams are also investigated. The results show that the intensity distribution and the kurtosis parameter of the beams in the FRFT plane are closely related to the fractional order and beam parameters.
Keywords Gaussian mirror resonator      fractional Fourier transform (FRFT)      propagation property      kurtosis parameter     
Corresponding Author(s): TANG Bin,Email:csu_tangbin@163.com   
Issue Date: 05 December 2009
 Cite this article:   
Bin TANG. Propagation properties of beams generated by Gaussian mirror resonator in fractional Fourier transform plane[J]. Front Optoelec Chin, 2009, 2(4): 397-402.
 URL:  
https://academic.hep.com.cn/foe/EN/10.1007/s12200-009-0074-0
https://academic.hep.com.cn/foe/EN/Y2009/V2/I4/397
Fig.1  Optical system for performing FRFT. (a) One-lens system; (b) two-lens system
Fig.2  Intensity distribution of beams generated by Gaussian mirror resonator in fractional plane after going through FRFT systems with a different fractional order p. (a) =0.1; (b) =0.7; (c) =1; (d) =1.1; (e) =1.3; (f) =1.9
Fig.3  Normalized on-axis intensity with different beam waists and focal lengths in fractional plane with varying fractional order (=0.7, =1.5). (a) =1.5 mm; (b) =200 mm
Fig.4  Variations of kurtosis parameter for different beams () generated by Gaussian mirror resonator versus fractional orders passage through ideal FRFT systems (=1.5 mm, =200 mm). (a) =1.0; (b) =0.7
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