## Observation of the in-plane spin separation of light |

Optics Express, Vol. 19, Issue 10, pp. 9636-9645 (2011)

http://dx.doi.org/10.1364/OE.19.009636

Acrobat PDF (1351 KB)

### Abstract

We report on the observation of the spin separation of light in the plane of incidence when a linearly polarized beam is reflected or refracted at a planar dielectric interface. Remarkably, the in-plane spin separation reaches hundreds of nanometers, comparable with the transverse spin separation induced by the well-known spin Hall effect of light. The observation is properly explained by considering the in-plane spread of wave-vectors. This study thus offers new insights on the spinoptics and may provide a potential method to control light in optical nanodevices.

© 2011 OSA

## 1. Introduction

1. M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics **3**(6), 337–340 (2009). [CrossRef]

4. K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos-Hanchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. **34**(3), 389–391 (2009). [CrossRef] [PubMed]

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

11. H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A **80**(4), 043810 (2009). [CrossRef]

12. A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A **45**(11), 8204–8208 (1992). [CrossRef] [PubMed]

13. A. Bérard and H. Mohrbach, “Spin Hall effect and Berry phase of spinning particles,” Phys. Lett. A **352**(3), 190–195 (2006). [CrossRef]

14. A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin Hall effect of light,” Phys. Rev. Lett. **103**(10), 100401 (2009). [CrossRef] [PubMed]

18. D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. **102**(12), 123903 (2009). [CrossRef] [PubMed]

19. J. M. Menard, A. E. Mattacchione, M. Betz, and H. M. van Driel, “Imaging the spin Hall effect of light inside semiconductors via absorption,” Opt. Lett. **34**(15), 2312–2314 (2009). [CrossRef] [PubMed]

20. J. M. Ménard, A. E. Mattacchione, H. M. van Driel, C. Hautmann, and M. Betz, “Ultrafast optical imaging of the spin Hall effect of light in semiconductors,” Phys. Rev. B **82**(4), 045303 (2010). [CrossRef]

## 2. Experimental setup

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

10. Y. Qin, Y. Li, X. B. Feng, Z. P. Liu, H. Y. He, Y. F. Xiao, and Q. H. Gong, “Spin Hall effect of reflected light at the air-uniaxial crystal interface,” Opt. Express **18**(16), 16832–16839 (2010). [CrossRef] [PubMed]

_{a}, y, z

_{a}), where a=I, R, T denotes incident, reflected, transmitted beams, respectively. The z

_{a}axis attaches to the direction of the central wave vector.

*γ*(the angle between

_{I}*x*

_{I}and the central electric-field-vector). The reflected or refracted beam splits into its two spin components: the component parallel (σ=+1, right-circularly polarized, denoted by

*s*and

*p*plane waves at the incident angle of

7. 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]

10. Y. Qin, Y. Li, X. B. Feng, Z. P. Liu, H. Y. He, Y. F. Xiao, and Q. H. Gong, “Spin Hall effect of reflected light at the air-uniaxial crystal interface,” Opt. Express **18**(16), 16832–16839 (2010). [CrossRef] [PubMed]

## 3. Results

_{R}-direction,

*θ*= 70°, however, the y-displacement monotonously decreases from 136 nm to 50.2 nm toward –y direction. The difference results from the sign of

_{I}_{R}-displacement is always in +x

_{R}direction and reaches maximum at

*x*

_{I}direction of the wave-vector.

## 4. Theoretical analysis

### 4.1 Calculation of the transverse and in-plane spin separations at an interface

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

9. 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]

_{I}axis and

*λ*being the wavelength of the light in the incident medium. For the reflected beam:

*θ*.

_{I}*κ*:

*p*and

*s*plane waves about the central wave vector (corresponding to

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

7. 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]

7. 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]

10. Y. Qin, Y. Li, X. B. Feng, Z. P. Liu, H. Y. He, Y. F. Xiao, and Q. H. Gong, “Spin Hall effect of reflected light at the air-uniaxial crystal interface,” Opt. Express **18**(16), 16832–16839 (2010). [CrossRef] [PubMed]

1. M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics **3**(6), 337–340 (2009). [CrossRef]

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

4. K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos-Hanchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. **34**(3), 389–391 (2009). [CrossRef] [PubMed]

21. K. Artmann, “Berechnung der seitenversetzung des totalreflektierten strahles,” Ann. Phys. **437**(1-2), 87–102 (1948). [CrossRef]

**75**(6), 066609 (2007). [CrossRef] [PubMed]

9. 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]

_{I}=0°) and vertical polarization (along y, γ

_{I}=90°), respectively. After reflection, using the Eqs. (1)-(6), the beam state

*σ*=+1 or −1) spin component, induced by SHEL and IPSSL, respectively. Equations (8) and (4) represent the interplay of the spin-orbit interaction (involving

*φ*

_{P2}presents the rotation of the polarizer P2 from y in order to be crossed with the polarization direction of the central wave vector of the reflected light.

### 4.2 Calculation of the angular and linear GH/IF shifts

_{R}-dependent parts of the linear shifts,

2. M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A **82**(2), 023817 (2010). [CrossRef]

4. K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos-Hanchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. **34**(3), 389–391 (2009). [CrossRef] [PubMed]

**75**(6), 066609 (2007). [CrossRef] [PubMed]

### 4.3 The intensity profile of the reflected beam after P2

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

**75**(6), 066609 (2007). [CrossRef] [PubMed]

## 5. Conclusion

## Acknowledgements

## References and links

1. | M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics |

2. | M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A |

3. | A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hanchen and Imbert-Fedorov shifts,” Opt. Lett. |

4. | K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos-Hanchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. |

5. | M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. |

6. | 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. |

7. | 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. |

8. | O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science |

9. | Y. Qin, Y. Li, H. Y. He, and Q. H. Gong, “Measurement of spin Hall effect of reflected light,” Opt. Lett. |

10. | Y. Qin, Y. Li, X. B. Feng, Z. P. Liu, H. Y. He, Y. F. Xiao, and Q. H. Gong, “Spin Hall effect of reflected light at the air-uniaxial crystal interface,” Opt. Express |

11. | H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A |

12. | A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A |

13. | A. Bérard and H. Mohrbach, “Spin Hall effect and Berry phase of spinning particles,” Phys. Lett. A |

14. | A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin Hall effect of light,” Phys. Rev. Lett. |

15. | K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics |

16. | K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis effect in optics: unified geometric phase and spin-Hall effect,” Phys. Rev. Lett. |

17. | K. Y. Bliokh and A. S. Desyatnikov, “Spin and orbital Hall effects for diffracting optical beams in gradient-index media,” Phys. Rev. A |

18. | D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. |

19. | J. M. Menard, A. E. Mattacchione, M. Betz, and H. M. van Driel, “Imaging the spin Hall effect of light inside semiconductors via absorption,” Opt. Lett. |

20. | J. M. Ménard, A. E. Mattacchione, H. M. van Driel, C. Hautmann, and M. Betz, “Ultrafast optical imaging of the spin Hall effect of light in semiconductors,” Phys. Rev. B |

21. | K. Artmann, “Berechnung der seitenversetzung des totalreflektierten strahles,” Ann. Phys. |

**OCIS Codes**

(240.0240) Optics at surfaces : Optics at surfaces

(260.5430) Physical optics : Polarization

(240.3695) Optics at surfaces : Linear and nonlinear light scattering from surfaces

**ToC Category:**

Physical Optics

**History**

Original Manuscript: March 9, 2011

Revised Manuscript: April 9, 2011

Manuscript Accepted: April 11, 2011

Published: May 3, 2011

**Citation**

Yi Qin, Yan Li, Xiaobo Feng, Yun-Feng Xiao, Hong Yang, and Qihuang Gong, "Observation of the in-plane spin separation of light," Opt. Express **19**, 9636-9645 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-10-9636

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### References

- M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3(6), 337–340 (2009). [CrossRef]
- M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82(2), 023817 (2010). [CrossRef]
- A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hanchen and Imbert-Fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008). [CrossRef] [PubMed]
- K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos-Hanchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. 34(3), 389–391 (2009). [CrossRef] [PubMed]
- 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]
- 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]
- O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008). [CrossRef] [PubMed]
- 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]
- Y. Qin, Y. Li, X. B. Feng, Z. P. Liu, H. Y. He, Y. F. Xiao, and Q. H. Gong, “Spin Hall effect of reflected light at the air-uniaxial crystal interface,” Opt. Express 18(16), 16832–16839 (2010). [CrossRef] [PubMed]
- H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, “Spin Hall effect of a light beam in left-handed materials,” Phys. Rev. A 80(4), 043810 (2009). [CrossRef]
- A. V. Dooghin, N. D. Kundikova, V. S. Liberman, and B. Y. Zel’dovich, “Optical Magnus effect,” Phys. Rev. A 45(11), 8204–8208 (1992). [CrossRef] [PubMed]
- A. Bérard and H. Mohrbach, “Spin Hall effect and Berry phase of spinning particles,” Phys. Lett. A 352(3), 190–195 (2006). [CrossRef]
- A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin Hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009). [CrossRef] [PubMed]
- K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008). [CrossRef]
- K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis effect in optics: unified geometric phase and spin-Hall effect,” Phys. Rev. Lett. 101(3), 030404 (2008). [CrossRef] [PubMed]
- K. Y. Bliokh and A. S. Desyatnikov, “Spin and orbital Hall effects for diffracting optical beams in gradient-index media,” Phys. Rev. A 79(1), 011807 (2009). [CrossRef]
- D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009). [CrossRef] [PubMed]
- J. M. Menard, A. E. Mattacchione, M. Betz, and H. M. van Driel, “Imaging the spin Hall effect of light inside semiconductors via absorption,” Opt. Lett. 34(15), 2312–2314 (2009). [CrossRef] [PubMed]
- J. M. Ménard, A. E. Mattacchione, H. M. van Driel, C. Hautmann, and M. Betz, “Ultrafast optical imaging of the spin Hall effect of light in semiconductors,” Phys. Rev. B 82(4), 045303 (2010). [CrossRef]
- K. Artmann, “Berechnung der seitenversetzung des totalreflektierten strahles,” Ann. Phys. 437(1-2), 87–102 (1948). [CrossRef]

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