Abstract

The variation of polarization distribution of reflected beam at specular interface and far field caused by spin separation has been studied. Due to the diffraction effect, we find a distinct difference of light polarization at the two regions. The variation of polarization distribution of reflected light provides a new method to measure the spin separation displacement caused by Spin Hall Effect of light.

© 2012 OSA

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References

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  1. M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
    [CrossRef] [PubMed]
  2. K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
    [CrossRef] [PubMed]
  3. K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(6), 066609 (2007).
    [CrossRef] [PubMed]
  4. O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
    [CrossRef] [PubMed]
  5. Y. Qin, Y. Li, H. Y. He, and Q. H. Gong, “Measurement of spin Hall effect of reflected light,” Opt. Lett. 34(17), 2551–2553 (2009).
    [CrossRef] [PubMed]
  6. Y. Qin, Y. Li, X. B. Feng, Y. F. Xiao, H. Yang, and Q. H. Gong, “Observation of the in-plane spin separation of light,” Opt. Express 19(10), 9636–9645 (2011).
    [CrossRef] [PubMed]
  7. A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008).
    [CrossRef] [PubMed]

2011

2009

2008

A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008).
[CrossRef] [PubMed]

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[CrossRef] [PubMed]

2007

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(6), 066609 (2007).
[CrossRef] [PubMed]

2006

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[CrossRef] [PubMed]

2004

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[CrossRef] [PubMed]

Aiello, A.

Bliokh, K. Y.

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(6), 066609 (2007).
[CrossRef] [PubMed]

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[CrossRef] [PubMed]

Bliokh, Y. P.

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(6), 066609 (2007).
[CrossRef] [PubMed]

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[CrossRef] [PubMed]

Feng, X. B.

Gong, Q. H.

He, H. Y.

Hosten, O.

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[CrossRef] [PubMed]

Kwiat, P.

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[CrossRef] [PubMed]

Li, Y.

Murakami, S.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[CrossRef] [PubMed]

Nagaosa, N.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[CrossRef] [PubMed]

Onoda, M.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[CrossRef] [PubMed]

Qin, Y.

Woerdman, J. P.

Xiao, Y. F.

Yang, H.

Opt. Express

Opt. Lett.

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(6), 066609 (2007).
[CrossRef] [PubMed]

Phys. Rev. Lett.

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[CrossRef] [PubMed]

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[CrossRef] [PubMed]

Science

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Experimental setup and coordinate systems for studying the polarization distribution. The He-Ne laser generates a fundamental Gaussian beam with the wavelength of 632.8nm.HWP, half-wave plate for adjusting the intensity after P1. L1 and L2, lenses with 100mm and 150mm focal lengths, respectively. P1 and P2, Glan polarizers. In our experiment we set the reflect interface at the back focal plane of L1 and at the front focal plane of L2. Our observation plane (CCD) is chosen at the back focal plane of L2. The refractive index of glass prism is 1.49.

Fig. 2
Fig. 2

The results of theoretical calculation of the polarization properties at interface (a), (c) and at far field (b), (d). (a) and (b) are schematics to show the polarization property. (c) shows the calculation value of χ (rad) at the interface and (d) shows the calculation value of γ (rad) after 10m propagation for the reflected beam. Note that the incident beam is horizontally polarized and beam waist at the interface is 10 μm.

Fig. 3
Fig. 3

Variation of polarization distribution during the propagation with horizontally polarized incident beam. Since the trend is similar, the figure only shows the polarization property at a certain position: xR = 0, y = radius of beam waist at distance zR. In our calculation, w0 = 10μm and incident angle = 45°.

Fig. 4
Fig. 4

Intensity profiles of reflected beam at the back focal plane of lens L2. (a), (b) and (c) show the theoretical results. (d), (e) and (f) are the experimental results.

Fig. 5
Fig. 5

Relation between Δy (the distance dark fringe move along y-axis) and Δθ (the angle rotate away from vertical direction) for horizontally polarized incident beam. The circles, triangles and dots are experimental data at three incident angles: 30, 45 and 66°. The solid lines are theoretical results. The displacements of SHEL, δ H , are calculated of 89.5, 231.5 and −213.3nm at three incident angles 30, 45 and 66°, respectively.

Equations (11)

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| H( k (I) ) r p θ I (| H( k (R) ) + k x R Δ H | H( k (R) ) + k y δ H | V( k (R) ) ,
| V( k (I) ) r s θ I (| V( k (R) ) + k x R Δ V | V( k (R) ) k y δ V | H( k (R) ) ,
δ H =cot θ I (1 r s θ I / r p θ I )/ k I , δ V =cot θ I (1 r p θ I / r s θ I )/ k I , Δ H =1( r p / r p θ I 1 )/ k x I , Δ V =1( r s / r s θ I 1)/ k x I .
| ϕ final ( k x R , k y ) = r p θ I ϕ initial ( k x R , k y )(|H+ k x R Δ H |H+ k y δ H |V),
| ψ final (x,y) = r p θ I 2 ψ initial (xi Δ H ,y δ H )|+ + r p θ I 2 ψ initial (xi Δ H ,y+ δ H )| = r p θ I 2 [ ψ initial (xi Δ H ,y δ H )+ ψ initial (xi Δ H ,y+ δ H )]|H + r p θ I i 2 [ ψ initial (xi Δ H ,y δ H ) ψ initial (xi Δ H ,y+ δ H )]|V,
tan(2γ)= 2Re( E H E V * ) | E H | 2 | E V | 2 , tan(2χ)= 2Im( E H E V * ) ( | E H | 2 | E V | 2 ) 2 + ( 2Re( E H E V * ) ) 2 .
ψ( x R ,y, z R )= e i k R z R iλ z R e i k R x R 2 + y 2 2 z R F{ ψ final (x,y)}= e i k I z R iλ z R e i k I x R 2 + y 2 2 z R ϕ final ( k I x R z R , k I y z R ).
ψ( x R ,y, z R ) r p θ I k I w 0 2 e k I ( x R 2 + y 2 ) k I w 0 2 +2i z R ( k I w 0 2 +2i z R ) 2 { [ k I ( w 0 2 2i Δ H x R )+2i z R ]|H2i δ H k I y|V },
tanθ= k I y f δ H /(1+ k I x R f Δ H ).
Δθ= k I Δy f δ H or Δy= Δθ δ H k I f.
I( x R ,y,f)| e w 2 ( k I 2 x R 2 + k I 2 y 2 )/(4 f 2 ) [ δ H k I ycos(Δθ)/f+(1+ Δ H k I x R /f)sin(Δθ)] | 2 .

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