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Photonic spin Hall effect (SHE) is an interesting transport phenomenon, and has attracted growing attention. The spin-dependent splitting of photonic SHE as a weak effect is just tens of nanometers so that it can usually be detected indirectly with the weak measurement techniques. To detect it directly and use it properly, many efforts have been devoted to enhancing the photonic SHE. Recently, the surface plasmon resonance (SPR) excited by a pure nanometal structure is used to enhance the photonic SHE. However, the pure metal permittivities are limited, therefore the regulation of the photonic SHE is also restricted. It is worth mentioning that the alloy made from the pure metal with different composition proportions can achieve the artificial control of permittivity. More importantly, the alloy can also be used to manipulate the SPR. In this paper, we systematically investigate the photonic SHE in a nanoalloy structure composed of BK7 glass, alloy film and air in order to realize the enhancement of photonic SHE. First of all, the resonant angle of SPR varying with the permittivity of alloy is studied by using the angular spectrum theory of beam. It is found that the resonant angle of the SPR is mainly influenced by the real part of the permittivity of alloy, while the imaginary part has little influence on it. The resonant angle of SPR will increase with the increase of the real part of the permittivity. Secondly, the spin-dependent splitting is studied by changing the alloy permittivity when the incident angle is set to be a resonant angle. We find that the distribution of the larger spin-dependent splitting at the resonant angle is zonal. The optimal permittivity of alloy film is ε2=-2.8 + 1.6i, and the alloy can be composed of Ag and Ni according to the Bruggerman theory. Under the condition of the optimal permittivity, the spin-dependent splitting reaches about 1.2×105 nm at a resonant angle of 51.5°, which is about 40 times larger than the previous result in a pure nanometal structure. Finally, when the incident angle is fixed at 44.1°, it is revealed that the spin-dependent splitting varying with the permittivity is axially symmetric and spherical radiation is centered at a maximum value. The farther away from the center, the smaller the corresponding beam shift is. The alloy permittivity in the spherical radiation center is ε2=-10.6 + 1.2i, which can be composed of Au and Ag. The value of spin-dependent splitting reaches about 8000 nm, which is greatly improved when compared with the previous maximum value 3000 nm in a pure nanometal structure. These findings can effectively enhance the photonic SHE and provide theoretical basis for the research and development of nanophotonic devices such as the SPR-based sensor.
[1] Onoda M, Murakami S, Nagaosa N 2004 Phys. Rev. Lett. 93 083901
[2] Bliokh K Y, Bliokh Y P 2006 Phys. Rev. Lett. 96 073903
[3] Hermosa N, Nugrowati A M, Aiello A, Woerdman J P 2011 Opt. Lett. 36 3200
[4] Gorodetski Y, Bliokh K Y, Stein B, Genet C, Shitrit N, Kleiner V, Hasman E, Ebbesen T W 2012 Phys. Rev. Lett. 109 013901
[5] Ling X H, Zhou X X, Huang K, Liu Y C, Qiu C W, Luo H L, Wen S C 2017 Rep. Prog. Phys. 80 066401
[6] Gosselin P, Bérard A, Mohrbach H 2007 Phys. Rev. D 75 084035
[7] Dartora C A, Cabrera G G, Nobrega K Z, Montagner V F, Matielli M H K, de Campos F K R, Filho H T S 2011 Phys. Rev. A 83 012110
[8] Ménard J M, Mattacchione A E, van Driel H M, Hautmann C, Betz M 2010 Phys. Rev. B 82 045303
[9] Alizadeh M H, Reinhard B M 2016 Opt. Express 24 8471
[10] Lee Y U, Wu J W 2015 Sci. Rep. 5 13900
[11] Yi X N, Li Y, Liu Y C, Ling X H, Zhang Z Y, Luo H L 2014 Acta Phys. Sin. 63 094203 (in Chinese) [易煦农, 李瑛, 刘亚超, 凌晓辉, 张志友, 罗海陆 2014 物理学报 63 094203]
[12] Chen M, Luo Z M, Wan T, Liu J 2017 Acta Opt. Sin. 37 0226002 (in Chinese) [陈敏, 罗朝明, 万婷, 刘靖 2017 光学学报 37 0226002]
[13] Liu Y C, Ke Y G, Luo H L, Wen S C 2017 Nanophotonics 6 51
[14] Luo Z M, Chen S Z, Ling X H, Zhang J, Luo H L 2014 Acta Phys. Sin. 63 154203 (in Chinese) [罗朝明, 陈世祯, 凌晓辉, 张进, 罗海陆 2014 物理学报 63 154203]
[15] Qin Y, Li Y, He H Y, Gong Q H 2009 Opt. Lett. 34 2551
[16] Neugebauer M, Grosche S, Rothau S, Leuchs G, Banzer P 2016 Opt. Lett. 41 3499
[17] Hosten O, Kwiat P 2008 Science 319 787
[18] Luo H L, Zhou X X, Shu W X, Wen S C, Fan D Y 2011 Phys. Rev. A 84 043806
[19] Qiu X D, Zhang Z Y, Xie L G, Qiu J D, Gao F H, Du J L 2015 Opt. Lett. 40 1018
[20] Luo H L, Ling X H, Zhou X X, Shu W X, Wen S C, Fan D Y 2011 Phys. Rev. A 84 033801
[21] Wang B, Li Y, Pan M M, Ren J L, Xiao Y F, Yang H, Gong Q H 2013 Phys. Rev. A 88 043842
[22] Tang T T, Li C Y, Luo L 2016 Sci. Rep. 6 30762
[23] Ling X H, Zhou X X, Yi X N, Shu W X, Liu Y C, Chen S Z, Luo H L, Wen S C, Fan D Y 2015 Light Sci. Appl. 4 e290
[24] Zhou X X, Xiao Z C, Luo H L, Wen S C 2012 Phys. Rev. A 85 043809
[25] Zhou X X, Ling X H 2016 IEEE Photon. J. 8 4801108
[26] Yang G, Fu X J, Zhou J 2013 J. Opt. Soc. Am. B 30 282
[27] Zhang Z, Liu Q, Qi Z M 2013 Acta Phys. Sin. 62 060703 (in Chinese) [张喆, 柳倩, 祁志美 2013 物理学报 62 060703]
[28] Born M, Wolf E 1999 Principles of Optics (Cambridge:Cambridge University Press) pp38-44
[29] Salasnich L 2012 Phys. Rev. A 86 055801
[30] Berthault A, Rousselle D, Zerah G 1992 J. Magn. Magn. Mater. 112 477
[31] Jiang J J, Li D, Geng D Y, An J, He J, Liu W, Zhang Z D 2014 Nanoscale 6 3967
[32] Bliokh K Y, Niv A, Kleiner V, Hasman E 2008 Nat. Photon. 2 748
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[1] Onoda M, Murakami S, Nagaosa N 2004 Phys. Rev. Lett. 93 083901
[2] Bliokh K Y, Bliokh Y P 2006 Phys. Rev. Lett. 96 073903
[3] Hermosa N, Nugrowati A M, Aiello A, Woerdman J P 2011 Opt. Lett. 36 3200
[4] Gorodetski Y, Bliokh K Y, Stein B, Genet C, Shitrit N, Kleiner V, Hasman E, Ebbesen T W 2012 Phys. Rev. Lett. 109 013901
[5] Ling X H, Zhou X X, Huang K, Liu Y C, Qiu C W, Luo H L, Wen S C 2017 Rep. Prog. Phys. 80 066401
[6] Gosselin P, Bérard A, Mohrbach H 2007 Phys. Rev. D 75 084035
[7] Dartora C A, Cabrera G G, Nobrega K Z, Montagner V F, Matielli M H K, de Campos F K R, Filho H T S 2011 Phys. Rev. A 83 012110
[8] Ménard J M, Mattacchione A E, van Driel H M, Hautmann C, Betz M 2010 Phys. Rev. B 82 045303
[9] Alizadeh M H, Reinhard B M 2016 Opt. Express 24 8471
[10] Lee Y U, Wu J W 2015 Sci. Rep. 5 13900
[11] Yi X N, Li Y, Liu Y C, Ling X H, Zhang Z Y, Luo H L 2014 Acta Phys. Sin. 63 094203 (in Chinese) [易煦农, 李瑛, 刘亚超, 凌晓辉, 张志友, 罗海陆 2014 物理学报 63 094203]
[12] Chen M, Luo Z M, Wan T, Liu J 2017 Acta Opt. Sin. 37 0226002 (in Chinese) [陈敏, 罗朝明, 万婷, 刘靖 2017 光学学报 37 0226002]
[13] Liu Y C, Ke Y G, Luo H L, Wen S C 2017 Nanophotonics 6 51
[14] Luo Z M, Chen S Z, Ling X H, Zhang J, Luo H L 2014 Acta Phys. Sin. 63 154203 (in Chinese) [罗朝明, 陈世祯, 凌晓辉, 张进, 罗海陆 2014 物理学报 63 154203]
[15] Qin Y, Li Y, He H Y, Gong Q H 2009 Opt. Lett. 34 2551
[16] Neugebauer M, Grosche S, Rothau S, Leuchs G, Banzer P 2016 Opt. Lett. 41 3499
[17] Hosten O, Kwiat P 2008 Science 319 787
[18] Luo H L, Zhou X X, Shu W X, Wen S C, Fan D Y 2011 Phys. Rev. A 84 043806
[19] Qiu X D, Zhang Z Y, Xie L G, Qiu J D, Gao F H, Du J L 2015 Opt. Lett. 40 1018
[20] Luo H L, Ling X H, Zhou X X, Shu W X, Wen S C, Fan D Y 2011 Phys. Rev. A 84 033801
[21] Wang B, Li Y, Pan M M, Ren J L, Xiao Y F, Yang H, Gong Q H 2013 Phys. Rev. A 88 043842
[22] Tang T T, Li C Y, Luo L 2016 Sci. Rep. 6 30762
[23] Ling X H, Zhou X X, Yi X N, Shu W X, Liu Y C, Chen S Z, Luo H L, Wen S C, Fan D Y 2015 Light Sci. Appl. 4 e290
[24] Zhou X X, Xiao Z C, Luo H L, Wen S C 2012 Phys. Rev. A 85 043809
[25] Zhou X X, Ling X H 2016 IEEE Photon. J. 8 4801108
[26] Yang G, Fu X J, Zhou J 2013 J. Opt. Soc. Am. B 30 282
[27] Zhang Z, Liu Q, Qi Z M 2013 Acta Phys. Sin. 62 060703 (in Chinese) [张喆, 柳倩, 祁志美 2013 物理学报 62 060703]
[28] Born M, Wolf E 1999 Principles of Optics (Cambridge:Cambridge University Press) pp38-44
[29] Salasnich L 2012 Phys. Rev. A 86 055801
[30] Berthault A, Rousselle D, Zerah G 1992 J. Magn. Magn. Mater. 112 477
[31] Jiang J J, Li D, Geng D Y, An J, He J, Liu W, Zhang Z D 2014 Nanoscale 6 3967
[32] Bliokh K Y, Niv A, Kleiner V, Hasman E 2008 Nat. Photon. 2 748
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