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Propagation and localization of cylindrical wave in a two-dimensional isotropic and homogeneous random medium is studied. By expanding the random permittivity fluctuation in the form of a Wiener integral equation in the frequency domain, and representing the wave fields by a linear combination of outgoing and incoming waves, the scalar Helmholtz equation is solved by means of stochastic functional approach to obtain the analytical expression of cylindrical wave. The spatial wave energy distribution is derived to demonstrate the localization phenomenon, and the localization length is also calculated. Compared with the waves in non-random medium, the wave transfer equation between plane wave and cylindrical wave in random medium shows an additional exponential factor to indicate the modulation effects due to the medium randomness in both the amplitude and the phase. Numerical simulations are presented to illustrate the functional dependence of the localization phenomenon.
[1] ［1］Anderson P W 1958 Phys. Rev. 109 1492
[2] ［2］Genack A Z, Garcia N 1991 Phys. Rev. Lett. 66 2064
[3] ［3］Berry M V, Klein S 1997 Eur. J. Phys. 18 222
[4] ［4］Wiersma D S, Bartolini P, Lagendijk A, Roghini R 1997 Nature 390 671
[5] ［5］Chabanov A A, Stoytchev M, Genack A Z 2000 Nature 404 850
[6] ［6］Storze M, Gross P, Aegerter C M, Maret G 2006 Phys. Rev. Lett. 96 063904
[7] ［7］Hu H, Strybulevych A, Page J H, Skipetrov S E, Tiggelen B A 2008 Nat. Phys. 4 945
[8] ［8］Chabé J, Lemarié G, Grémaud B, Delande D, Szriftgiser P, Garreau J C 2008 Phys. Rev. Lett. 101 255702
[9] ［9］Cao Y J, Yang X 2008 Acta Phys. Sin. 57 3620 (in Chinese) ［曹永军、杨旭 2008 57 3620］
[10] ］Wang H Q, Liu Z D, Wang B 2008 Acta Phys. Sin. 57 5550 (in Chinese) ［王慧琴、刘正东、王冰 2008 57 5550］
[11] ］Abrahams E, Anderson P W, Licciardello D C, Ramakrishnan T V 1979 Phys. Rev. Lett. 42 673
[12] ］Sheng P, White B, Zhang Z Q, Papanicolaou G 1986 Phys. Rev. B 34 4757
[13] ］Soukoulis C M, Jiang X, Xu J Y, Cao H 2002 Phys. Rev. B 65 041103
[14] ］Zhuang F, Shen J Q, Ye J 2007 Acta Phys. Sin. 56 541 (in Chinese) ［庄飞、沈建其、叶军 2007 56 541］
[15] ］Gao X, Yang Z Q, Hou J, Qi L M, Lan F, Shi Z J, Li D Z, Liang Z 2009 Acta Phys. Sin. 58 1105 (in Chinese) ［高喜、杨梓强、侯钧、亓丽梅、兰峰、史宗君、李大治、梁正 2009 58 1105］
[16] ］Ye Z, Li S, Sun X 2002 Phys. Rev. E 66 045602
[17] ］Sigalas M M, Soukoulis C M, Chan C T, Turner D 1996 Phys. Rev. B 53 8340
[18] ］Asatryan A A, Robinson P A, McPhedran R C, Botten L C, Sterke M, Langtry T L, Nicorovici N A 2003 Phys. Rev. E 67 036605
[19] ］Rusek M, Orlowski A, Mostowski J 1997 Phys. Rev. E 56 4892
[20] ］Ziegler K 2003 J. Quant. Spectrosc. Radiat. Transfer 79 1189
[21] ］Albada M P, Tiggelen B A, Lagendijk A, Tip A 1991 Phys. Rev. Lett. 66 3132
[22] ］Ogura H 1966 J. Phys. Soc. Jpn. 21 1370
[23] ］Spiegel M R 1998 Mathematical Handbook of Formulas and Tables (New York: McGraw-Hill)
[24] ］Ding R, Wang Z L, Ogura H 2008 Radio Sci. 43 2005
[25] ］Ogura H 1975 Phys. Rev. A 11 942
[26] ］Jin Y Q 1994 Electromagnetic Scattering Modeling for Quantitative Remote Sensing (Singapore: World Scientific) p6
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[1] ［1］Anderson P W 1958 Phys. Rev. 109 1492
[2] ［2］Genack A Z, Garcia N 1991 Phys. Rev. Lett. 66 2064
[3] ［3］Berry M V, Klein S 1997 Eur. J. Phys. 18 222
[4] ［4］Wiersma D S, Bartolini P, Lagendijk A, Roghini R 1997 Nature 390 671
[5] ［5］Chabanov A A, Stoytchev M, Genack A Z 2000 Nature 404 850
[6] ［6］Storze M, Gross P, Aegerter C M, Maret G 2006 Phys. Rev. Lett. 96 063904
[7] ［7］Hu H, Strybulevych A, Page J H, Skipetrov S E, Tiggelen B A 2008 Nat. Phys. 4 945
[8] ［8］Chabé J, Lemarié G, Grémaud B, Delande D, Szriftgiser P, Garreau J C 2008 Phys. Rev. Lett. 101 255702
[9] ［9］Cao Y J, Yang X 2008 Acta Phys. Sin. 57 3620 (in Chinese) ［曹永军、杨旭 2008 57 3620］
[10] ］Wang H Q, Liu Z D, Wang B 2008 Acta Phys. Sin. 57 5550 (in Chinese) ［王慧琴、刘正东、王冰 2008 57 5550］
[11] ］Abrahams E, Anderson P W, Licciardello D C, Ramakrishnan T V 1979 Phys. Rev. Lett. 42 673
[12] ］Sheng P, White B, Zhang Z Q, Papanicolaou G 1986 Phys. Rev. B 34 4757
[13] ］Soukoulis C M, Jiang X, Xu J Y, Cao H 2002 Phys. Rev. B 65 041103
[14] ］Zhuang F, Shen J Q, Ye J 2007 Acta Phys. Sin. 56 541 (in Chinese) ［庄飞、沈建其、叶军 2007 56 541］
[15] ］Gao X, Yang Z Q, Hou J, Qi L M, Lan F, Shi Z J, Li D Z, Liang Z 2009 Acta Phys. Sin. 58 1105 (in Chinese) ［高喜、杨梓强、侯钧、亓丽梅、兰峰、史宗君、李大治、梁正 2009 58 1105］
[16] ］Ye Z, Li S, Sun X 2002 Phys. Rev. E 66 045602
[17] ］Sigalas M M, Soukoulis C M, Chan C T, Turner D 1996 Phys. Rev. B 53 8340
[18] ］Asatryan A A, Robinson P A, McPhedran R C, Botten L C, Sterke M, Langtry T L, Nicorovici N A 2003 Phys. Rev. E 67 036605
[19] ］Rusek M, Orlowski A, Mostowski J 1997 Phys. Rev. E 56 4892
[20] ］Ziegler K 2003 J. Quant. Spectrosc. Radiat. Transfer 79 1189
[21] ］Albada M P, Tiggelen B A, Lagendijk A, Tip A 1991 Phys. Rev. Lett. 66 3132
[22] ］Ogura H 1966 J. Phys. Soc. Jpn. 21 1370
[23] ］Spiegel M R 1998 Mathematical Handbook of Formulas and Tables (New York: McGraw-Hill)
[24] ］Ding R, Wang Z L, Ogura H 2008 Radio Sci. 43 2005
[25] ］Ogura H 1975 Phys. Rev. A 11 942
[26] ］Jin Y Q 1994 Electromagnetic Scattering Modeling for Quantitative Remote Sensing (Singapore: World Scientific) p6
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