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We study shifts of the beam centroid of linearly polarized paraxial Laguerre-Gaussian beams reflected and refracted at an interface of isotropic dielectric in the cylindrical coordinate system. According to the Fresnel approximation and the Taylor series expansion, we derive analytical expressions for transverse and longitudinal shifts and their general relationship with topological charge in the cases of partial and total reflection, respectively. It is shown that in the partial reflection regime, transverse shifts of both reflected and refracted beams are in proportion to the topological charge of beams and their directions are determined by the sign of the topological charge, while only the value of longitudinal shift is related to the topological charge. In the regime of total reflection, the shift of reflected beam centroid is independent of topological charge. To verify our analytical results, we perform numerical simulations of the shifts of reflected and refracted beams directly and indicate the applicable condition of the analytical expressions. The shifts of the beam centroid can be applied to the measurement of the topological charge and radial node number of Laguerre-Gaussian beams, which is of significance for information encoding and communication.
[1] Horowitz B R, Tamir T 1971 J. Opt. Soc. Am. 61 586
[2] Chan C C, Tamir T 1987 J. Opt. Soc. Am. A 4 655
[3] Bliokh K Y, Bliokh Y P 2007 Phys. Rev. E 75 066609
[4] Aiello A, Woerdman J P 2008 Opt. Lett. 33 1437
[5] Merano M, Aiello A, van Exter M P, Woerdman J P 2009 Nat. Photonics 3 337
[6] Goos F, Hänchen H 1947 Ann. Phys 1 333
[7] Fedorov F I 1955 Dokl. Akad. Nauk SSSR 105 465
[8] Imbert C 1972 Phys. Rev. D 5 787
[9] Bliokh K Y, Bliokh Y P 2006 Phys. Rev. Lett. 96 073903
[10] Hosten O, Kwiat P 2008 Science 319 787
[11] Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185
[12] Allen L, Padgett M J, Babiker M, Wolf E 1999 "The Orbital Angular Momentum of Light" in Prog. Optics 39 291
[13] Maleev I D, Swartzlander J G A 2003 J. Opt. Soc. Am. B 20 1169
[14] He H, Friese M E J, Heckenberg N R, Rubinsztein-Dunlop H 1995 Phys. Rev. Lett. 75 826
[15] Mair A, Vaziri A, Weihs G, Zeilinger A 2001 Nature 412 313
[16] Wu J Z, Li Y J 2007 Chin. Phys. 16 1334
[17] Fedoseyev V G 2001 Opt. Commun. 193 9
[18] Okuda H, Sasada H 2006 Opt. Express 14 8393
[19] Okuda H, Sasada H 2008 J. Opt. Soc. Am. A 25 881
[20] Fedoseyev V G 2008 Phys. Lett. A 372 2527
[21] Aiello A, Merano M, Woerdman J P 2009 Phys. Rev. A: At. Mol. Opt. Phys. 80 061801
[22] Aiello A, Woerdman H 2007 ArXiv 0710 1643v2
[23] Allen L, Lembessis V E, Babiker M 1996 Phys. Rev. A 53 R2937
[24] Goodman J W 1996 Introduction to Fourier optics 2nd(New York: McGraw-Hill)
[25] Jeffrey A, Zwillinger D 2000 Table of Integrals, Series, and Products 6th(New York: Academic Press)
[26] Antar Y M, Boerner W M 1974 Can. J. Phys. 52 962
[27] Bliokh K Y, Shadrivov I V, Kivshar Y S 2009 Opt. Lett. 34 389
[28] Li F, Jiang Y S, Tang H, Wang H Y 2009 Acta Phy.Sin. 58 6202 (in Chinese) [黎 芳、江月松、唐 华、王海洋 2009 58 6202]
[29] Li F, Tang H, Jiang Y S, Ou J 2011 Acta Phy. Sin. 60 014204 (in Chinese) [黎 芳、唐 华、江月松、欧 军 2011 60 014204]
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[1] Horowitz B R, Tamir T 1971 J. Opt. Soc. Am. 61 586
[2] Chan C C, Tamir T 1987 J. Opt. Soc. Am. A 4 655
[3] Bliokh K Y, Bliokh Y P 2007 Phys. Rev. E 75 066609
[4] Aiello A, Woerdman J P 2008 Opt. Lett. 33 1437
[5] Merano M, Aiello A, van Exter M P, Woerdman J P 2009 Nat. Photonics 3 337
[6] Goos F, Hänchen H 1947 Ann. Phys 1 333
[7] Fedorov F I 1955 Dokl. Akad. Nauk SSSR 105 465
[8] Imbert C 1972 Phys. Rev. D 5 787
[9] Bliokh K Y, Bliokh Y P 2006 Phys. Rev. Lett. 96 073903
[10] Hosten O, Kwiat P 2008 Science 319 787
[11] Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185
[12] Allen L, Padgett M J, Babiker M, Wolf E 1999 "The Orbital Angular Momentum of Light" in Prog. Optics 39 291
[13] Maleev I D, Swartzlander J G A 2003 J. Opt. Soc. Am. B 20 1169
[14] He H, Friese M E J, Heckenberg N R, Rubinsztein-Dunlop H 1995 Phys. Rev. Lett. 75 826
[15] Mair A, Vaziri A, Weihs G, Zeilinger A 2001 Nature 412 313
[16] Wu J Z, Li Y J 2007 Chin. Phys. 16 1334
[17] Fedoseyev V G 2001 Opt. Commun. 193 9
[18] Okuda H, Sasada H 2006 Opt. Express 14 8393
[19] Okuda H, Sasada H 2008 J. Opt. Soc. Am. A 25 881
[20] Fedoseyev V G 2008 Phys. Lett. A 372 2527
[21] Aiello A, Merano M, Woerdman J P 2009 Phys. Rev. A: At. Mol. Opt. Phys. 80 061801
[22] Aiello A, Woerdman H 2007 ArXiv 0710 1643v2
[23] Allen L, Lembessis V E, Babiker M 1996 Phys. Rev. A 53 R2937
[24] Goodman J W 1996 Introduction to Fourier optics 2nd(New York: McGraw-Hill)
[25] Jeffrey A, Zwillinger D 2000 Table of Integrals, Series, and Products 6th(New York: Academic Press)
[26] Antar Y M, Boerner W M 1974 Can. J. Phys. 52 962
[27] Bliokh K Y, Shadrivov I V, Kivshar Y S 2009 Opt. Lett. 34 389
[28] Li F, Jiang Y S, Tang H, Wang H Y 2009 Acta Phy.Sin. 58 6202 (in Chinese) [黎 芳、江月松、唐 华、王海洋 2009 58 6202]
[29] Li F, Tang H, Jiang Y S, Ou J 2011 Acta Phy. Sin. 60 014204 (in Chinese) [黎 芳、唐 华、江月松、欧 军 2011 60 014204]
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