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Based on the propagation law of partially coherent beams and Fourier transform, the analytical expressions for the spectral intensity and spectral degree of coherence of focused spatially and spectrally partially coherent Hermite-Gaussian (H-G) pulsed beams are derived and used to study the spatial correlation properties in the focal region. It is shown that the spectral degree of coherence depends on the spatial correlation length, temporal coherence length and beam order. As the temporal coherence length decreases, the spectral degree of coherence decreases, whereas the temporal coherence length does not contribute to the spatial distribution of the spectral degree of coherence. An increase of the beam order results in an oscillatory behavior of the spectral degree of coherence, which becomes more prominent with the increase of beam order or the decrease of spatial correlation length.
[1] Christov I P 1986 Opt. Acta 33 63
[2] Pääkkönen P, Turunen J, Vahimaa P, Friberg A T, Wyrowski F 2002 Opt. Commun. 204 53
[3] Lajunen H, Tervo J, Turunen J, Vahimaa P, Wyrowski F 2003 Opt. Express. 11 1894
[4] Lajunen H, Vahimaa P, Tervo J 2005 J. Opt. Soc. Am. A 22 1536
[5] Lin Q, Wang L G, Zhu S Y 2003 Opt. Commun. 219 65
[6] Wang L G, Lin Q, Chen H, Zhu S Y 2003 Phys. Rev. E 67 056613
[7] Fischer D G, Visser T D 2004 J. Opt. Soc. Am. A 21 2097
[8] Roychowdhury H, Agrawal G P, Wolf E 2006 J. Opt. Soc. Am. A 23 940
[9] Rao L, Pu J 2007 J. Opt. Soc. Am. A 24 2242
[10] Ji X, Chen X, Chen S, Li X, L B 2007 J. Opt. Soc. Am. A 24 3554
[11] Ji X, Ji G 2008 Appl. Phys. B 92 111
[12] Eyyuboglu H T, Baykal Y, Cai Y 2007 J. Opt. Soc. Am. A 24 2891
[13] Chen X W, Tang M Y, Ji X L 2008 Acta Phys. Sin. 57 2607 (in Chinese) [陈晓文, 汤明玥, 季小玲 2008 57 2607 ]
[14] Cheng K, Zhang H R, L B D 2010 Acta Phys. Sin. 59 246 (in Chinese) [程科, 张洪润, 吕百达 2010 59 246 ]
[15] Mandel L, Wolf E 1995 Optical Coherence and Quantum Optics (Cambridge: Cambridge U. Press)
[16] Li C J, L B D 2009 Acta Phys. Sin. 58 6192 (in Chinese) [黎昌金, 吕百达 2009 58 6192 ]
[17] Collins S A 1970 J. Opt. Soc. Am. 60 1168
[18] Wu J, Boardman A D 1991 J. Mod. Opt. 38 1355
[19] Torres-Company V, Mínguez-Vega G, Lancis J, Friberg A T 2007 Opt. Lett. 32 1608
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[1] Christov I P 1986 Opt. Acta 33 63
[2] Pääkkönen P, Turunen J, Vahimaa P, Friberg A T, Wyrowski F 2002 Opt. Commun. 204 53
[3] Lajunen H, Tervo J, Turunen J, Vahimaa P, Wyrowski F 2003 Opt. Express. 11 1894
[4] Lajunen H, Vahimaa P, Tervo J 2005 J. Opt. Soc. Am. A 22 1536
[5] Lin Q, Wang L G, Zhu S Y 2003 Opt. Commun. 219 65
[6] Wang L G, Lin Q, Chen H, Zhu S Y 2003 Phys. Rev. E 67 056613
[7] Fischer D G, Visser T D 2004 J. Opt. Soc. Am. A 21 2097
[8] Roychowdhury H, Agrawal G P, Wolf E 2006 J. Opt. Soc. Am. A 23 940
[9] Rao L, Pu J 2007 J. Opt. Soc. Am. A 24 2242
[10] Ji X, Chen X, Chen S, Li X, L B 2007 J. Opt. Soc. Am. A 24 3554
[11] Ji X, Ji G 2008 Appl. Phys. B 92 111
[12] Eyyuboglu H T, Baykal Y, Cai Y 2007 J. Opt. Soc. Am. A 24 2891
[13] Chen X W, Tang M Y, Ji X L 2008 Acta Phys. Sin. 57 2607 (in Chinese) [陈晓文, 汤明玥, 季小玲 2008 57 2607 ]
[14] Cheng K, Zhang H R, L B D 2010 Acta Phys. Sin. 59 246 (in Chinese) [程科, 张洪润, 吕百达 2010 59 246 ]
[15] Mandel L, Wolf E 1995 Optical Coherence and Quantum Optics (Cambridge: Cambridge U. Press)
[16] Li C J, L B D 2009 Acta Phys. Sin. 58 6192 (in Chinese) [黎昌金, 吕百达 2009 58 6192 ]
[17] Collins S A 1970 J. Opt. Soc. Am. 60 1168
[18] Wu J, Boardman A D 1991 J. Mod. Opt. 38 1355
[19] Torres-Company V, Mínguez-Vega G, Lancis J, Friberg A T 2007 Opt. Lett. 32 1608
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