## Rashba-like spin degeneracy breaking in coupled thermal antenna lattices |

Optics Express, Vol. 19, Issue 23, pp. 23475-23482 (2011)

http://dx.doi.org/10.1364/OE.19.023475

Acrobat PDF (1882 KB)

### Abstract

Observation of a spin degeneracy breaking in thermal radiation emitted from an inhomogeneous anisotropic lattice composed of coupled antennas supporting surface waves is presented. The spin degeneracy removal is manifested by a spin-dependent momentum splitting of the radiative mode which resembles the Rashba effect. The spin split dispersion arises from the inversion asymmetry of the lattice. Our experiment confirms that the spatial rate of the inhomogeneity determines the degree of the spin- dependent momentum redirection. The influence of the inversion asymmetry on the dispersion was studied by comparing the results to those produced by homogeneous lattices and characterizing the behavior of the isolated thermal antennas.

© 2011 OSA

## 1. Introduction

4. G. Dresselhaus, “Spin–orbit coupling effects in zinc blende structures,” Phys. Rev. **100**(2), 580–586 (1955). [CrossRef]

5. R. A. Beth, “Mechanical Detection and Measurement of the Angular Momentum of Light,” Phys. Rev. **50**(2), 115–125 (1936). [CrossRef]

6. 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. Gorodetski, S. Nechayev, V. Kleiner, and E. Hasman, “Plasmonic Aharonov-Bohm effect: Optical spin as the magnetic flux parameter,” Phys. Rev. B **82**(12), 125433 (2010). [CrossRef]

11. Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. **101**(4), 043903 (2008). [CrossRef] [PubMed]

12. N. Dahan, Y. Gorodetski, K. Frischwasser, V. Kleiner, and E. Hasman, “Geometric doppler effect: spin-split dispersion of thermal radiation,” Phys. Rev. Lett. **105**(13), 136402 (2010). [CrossRef] [PubMed]

3. K. Ishizaka, M. S. Bahramy, H. Murakawa, M. Sakano, T. Shimojima, T. Sonobe, K. Koizumi, S. Shin, H. Miyahara, A. Kimura, K. Miyamoto, T. Okuda, H. Namatame, M. Taniguchi, R. Arita, N. Nagaosa, K. Kobayashi, Y. Murakami, R. Kumai, Y. Kaneko, Y. Onose, and Y. Tokura, “Giant Rashba-type spin splitting in bulk BiTeI,” Nat. Mater. **10**(7), 521–526 (2011). [CrossRef] [PubMed]

## 2. Homogeneous isotropic lattice

13. J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature **416**(6876), 61–64 (2002). [CrossRef] [PubMed]

12. N. Dahan, Y. Gorodetski, K. Frischwasser, V. Kleiner, and E. Hasman, “Geometric doppler effect: spin-split dispersion of thermal radiation,” Phys. Rev. Lett. **105**(13), 136402 (2010). [CrossRef] [PubMed]

13. J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature **416**(6876), 61–64 (2002). [CrossRef] [PubMed]

15. J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics **3**(11), 658–661 (2009). [CrossRef]

*homogeneous isotropic lattice*(L1) consisting of a rectangular array of circular voids upon a 6H-SiC substrate (isotropic 'anti-particles') with a diameter

*D*= 4.8

*μm*, depth

*h*= 1

*μm*and periodicity Λ = 11.6

*μm*, was fabricated using standard photolithographic techniques (see Fig. 2 (a) ). Angle-resolved emission spectra were measuredby a Fourier transform infrared spectrometer (Bruker, Vertex 70) at different polar angles,

*θ*, relative to the normal direction and at zero azimuthal angle (Fig. 2(b,c)), while heating the sample to 773 K. The coupling of SPhPs to radiative modes by periodic corrugations is achieved according to the momentum-matching condition,

16. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary Optical Transmission through Sub-Wavelength Hole Arrays,” Nature **391**(6668), 667–669 (1998). [CrossRef]

*k*

_{0}is the wave number of light in free space,

*ε*and

_{s}*ε*are the frequency-dependent relative permittivities of the substrate and the superstrate (in our case

_{a}*ε*= 1 for air);

_{a}*G*and

_{x}*G*are the lattice momenta associated with the periodicity of the array,

_{y}*i, j*) denote the specific radiative modes. The calculated modes, using the momentum-matching condition, depicted in Fig. 2(d), exhibit a good agreement with the measured dispersion.

## 3. Local modes of anisotropic antennas

*1.2μm × 4.8μm*; depth

*h = 1μm*, see Fig. 3 (a) , right inset).

*homogeneous anisotropicantenna lattice*are fundamentally affected by the local modes of each individual antenna. In order to characterize the thermal emission from the individual antenna, we measured the emission spectrum from an array of

*randomly distributed rectangular voids*(L2), thereby eliminating correlation effects due to periodicity. Figure 3(a- I, II) shows two similar spectral cross-sections which were measured at

15. J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics **3**(11), 658–661 (2009). [CrossRef]

18. K. D. Ko and C. K. Toussaint Jr., “A simple GUI for modeling the optical properties of single metal nanoparticles,” J. Quant. Spectrosc. Radiat. Transf. **110**(12), 1037–1043 (2009). [CrossRef]

## 4. Homogeneous anisotropic lattice

*homogeneous anisotropic lattice*(L3) comprised of a periodic rectangular array of anisotropic thermal antennas that were identically oriented at the angle

*x*direction, was then fabricated (see Fig. 3(c)). The measured emission from the structure in the normal direction is shown in Fig. 3(a-III). One can see that in addition to thelocalized modes (Fig. 3(a-II)) the spectrum contains a narrow peak of the collective mode at 830

*cm*, which is also polarized along the short axis of the antenna. By angle-resolved spectroscopy, we found that this spectral peak corresponds to strongly dispersive modes (Fig. 4(a) ) that are similar to the radiative modes of the isotropic antenna array (Fig. 2(c)). A polarization analysis of the dispersion was then performed by measuring the Stokes parameters (

^{−1}*S*

_{0},

*S*

_{1},

*S*

_{2},

*S*

_{3}) [19] to obtain the orientation angle of the polarization ellipse,

*ψ*, and its ellipticity angle,

*ψ*(see Fig. 4(b)) shows that these modes are polarized along the short axis of the antenna,

## 5. Inhomogeneous anisotropic lattice: spin split dispersion

*inhomogeneous anisotropic lattice*(L4) we fabricated arrays of rectangular antennas with a period Λ = 11.6

*μm*whose orientation was sequentially rotated along the

*x*-axis, see Fig. 5(a) . The antennas' angle with respect to the

*x*direction,

*a*is the distance along the

*x*direction for a

*π*rotation. We obtained a spin-projected dispersion (in the

*S*component of the Stokes vectors, which represents the circular polarization portion within the emitted light (Fig. 5(b)). For the normalized parameter

_{3}*σ*denotes one of two possible basic spin state of the emitted field (Fig. 5(d)). The observed effect is due to a spin-orbit interaction resulting from the dynamics of the surface waves propagating along the structure whose local anisotropy axis is rotated in space. The spin symmetry breaking is caused by the absence of inversion symmetry in our system. In general, time reversal symmetry (TRS) in a crystal results in energy relation

*x*direction

3. K. Ishizaka, M. S. Bahramy, H. Murakawa, M. Sakano, T. Shimojima, T. Sonobe, K. Koizumi, S. Shin, H. Miyahara, A. Kimura, K. Miyamoto, T. Okuda, H. Namatame, M. Taniguchi, R. Arita, N. Nagaosa, K. Kobayashi, Y. Murakami, R. Kumai, Y. Kaneko, Y. Onose, and Y. Tokura, “Giant Rashba-type spin splitting in bulk BiTeI,” Nat. Mater. **10**(7), 521–526 (2011). [CrossRef] [PubMed]

3. K. Ishizaka, M. S. Bahramy, H. Murakawa, M. Sakano, T. Shimojima, T. Sonobe, K. Koizumi, S. Shin, H. Miyahara, A. Kimura, K. Miyamoto, T. Okuda, H. Namatame, M. Taniguchi, R. Arita, N. Nagaosa, K. Kobayashi, Y. Murakami, R. Kumai, Y. Kaneko, Y. Onose, and Y. Tokura, “Giant Rashba-type spin splitting in bulk BiTeI,” Nat. Mater. **10**(7), 521–526 (2011). [CrossRef] [PubMed]

12. N. Dahan, Y. Gorodetski, K. Frischwasser, V. Kleiner, and E. Hasman, “Geometric doppler effect: spin-split dispersion of thermal radiation,” Phys. Rev. Lett. **105**(13), 136402 (2010). [CrossRef] [PubMed]

20. N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. **11**(5), 2038–2042 (2011). [CrossRef] [PubMed]

21. B. C. Hsu and J.-F. S. Van Huele, “Spin dynamics for wave packets in Rashba systems,” Phys. Rev. B **80**(23), 235309 (2009). [CrossRef]

*k*momentum direction and found non-split modes. The measured dispersion was identical to the cases involving a homogeneous lattice (L1 and L3), as expected from the homogeneity in the

_{y}## 6. Conclusions

*spinoptics*.

## Acknowledgments

## References and links

1. | P. Zeeman, “On the influence of Magnetism on the Nature of the Light emitted by a Substance,” Philos. Mag. |

2. | E. I. Rashba, “Properties of semiconductors with an extremum loop. 1. Cyclotron and combinational resonance in a magnetic field perpendicular to the plane of the loop,”Sov. Phys. Solid State |

3. | K. Ishizaka, M. S. Bahramy, H. Murakawa, M. Sakano, T. Shimojima, T. Sonobe, K. Koizumi, S. Shin, H. Miyahara, A. Kimura, K. Miyamoto, T. Okuda, H. Namatame, M. Taniguchi, R. Arita, N. Nagaosa, K. Kobayashi, Y. Murakami, R. Kumai, Y. Kaneko, Y. Onose, and Y. Tokura, “Giant Rashba-type spin splitting in bulk BiTeI,” Nat. Mater. |

4. | G. Dresselhaus, “Spin–orbit coupling effects in zinc blende structures,” Phys. Rev. |

5. | R. A. Beth, “Mechanical Detection and Measurement of the Angular Momentum of Light,” Phys. Rev. |

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

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

8. | K. Y. Bliokh, “Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium,” J. Opt. A. |

9. | Y. Gorodetski, S. Nechayev, V. Kleiner, and E. Hasman, “Plasmonic Aharonov-Bohm effect: Optical spin as the magnetic flux parameter,” Phys. Rev. B |

10. | Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, “Observation of optical spin symmetry breaking in nanoapertures,” Nano Lett. |

11. | Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. |

12. | N. Dahan, Y. Gorodetski, K. Frischwasser, V. Kleiner, and E. Hasman, “Geometric doppler effect: spin-split dispersion of thermal radiation,” Phys. Rev. Lett. |

13. | J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature |

14. | E. D. Palik, |

15. | J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics |

16. | T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary Optical Transmission through Sub-Wavelength Hole Arrays,” Nature |

17. | C. F. Bohren and D. R. Huffman, |

18. | K. D. Ko and C. K. Toussaint Jr., “A simple GUI for modeling the optical properties of single metal nanoparticles,” J. Quant. Spectrosc. Radiat. Transf. |

19. | D. H. Goldstein, |

20. | N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. |

21. | B. C. Hsu and J.-F. S. Van Huele, “Spin dynamics for wave packets in Rashba systems,” Phys. Rev. B |

**OCIS Codes**

(230.5440) Optical devices : Polarization-selective devices

(240.6690) Optics at surfaces : Surface waves

(310.6628) Thin films : Subwavelength structures, nanostructures

(290.6815) Scattering : Thermal emission

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: July 27, 2011

Revised Manuscript: September 27, 2011

Manuscript Accepted: September 28, 2011

Published: November 2, 2011

**Citation**

Kobi Frischwasser, Igor Yulevich, Vladimir Kleiner, and Erez Hasman, "Rashba-like spin degeneracy breaking in coupled thermal antenna lattices," Opt. Express **19**, 23475-23482 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-23-23475

Sort: Year | Journal | Reset

### References

- P. Zeeman, “On the influence of Magnetism on the Nature of the Light emitted by a Substance,” Philos. Mag.43, 226–239 (1897).
- E. I. Rashba, “Properties of semiconductors with an extremum loop. 1. Cyclotron and combinational resonance in a magnetic field perpendicular to the plane of the loop,”Sov. Phys. Solid State2, 1109 (1960).
- K. Ishizaka, M. S. Bahramy, H. Murakawa, M. Sakano, T. Shimojima, T. Sonobe, K. Koizumi, S. Shin, H. Miyahara, A. Kimura, K. Miyamoto, T. Okuda, H. Namatame, M. Taniguchi, R. Arita, N. Nagaosa, K. Kobayashi, Y. Murakami, R. Kumai, Y. Kaneko, Y. Onose, and Y. Tokura, “Giant Rashba-type spin splitting in bulk BiTeI,” Nat. Mater.10(7), 521–526 (2011). [CrossRef] [PubMed]
- G. Dresselhaus, “Spin–orbit coupling effects in zinc blende structures,” Phys. Rev.100(2), 580–586 (1955). [CrossRef]
- R. A. Beth, “Mechanical Detection and Measurement of the Angular Momentum of Light,” Phys. Rev.50(2), 115–125 (1936). [CrossRef]
- O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science319(5864), 787–790 (2008). [CrossRef] [PubMed]
- K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics2(12), 748–753 (2008). [CrossRef]
- K. Y. Bliokh, “Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium,” J. Opt. A.11, 094009 (2009).
- Y. Gorodetski, S. Nechayev, V. Kleiner, and E. Hasman, “Plasmonic Aharonov-Bohm effect: Optical spin as the magnetic flux parameter,” Phys. Rev. B82(12), 125433 (2010). [CrossRef]
- Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, “Observation of optical spin symmetry breaking in nanoapertures,” Nano Lett.9(8), 3016–3019 (2009). [CrossRef] [PubMed]
- Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett.101(4), 043903 (2008). [CrossRef] [PubMed]
- N. Dahan, Y. Gorodetski, K. Frischwasser, V. Kleiner, and E. Hasman, “Geometric doppler effect: spin-split dispersion of thermal radiation,” Phys. Rev. Lett.105(13), 136402 (2010). [CrossRef] [PubMed]
- J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature416(6876), 61–64 (2002). [CrossRef] [PubMed]
- E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, 1985).
- J. A. Schuller, T. Taubner, and M. L. Brongersma, “Optical antenna thermal emitters,” Nat. Photonics3(11), 658–661 (2009). [CrossRef]
- T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary Optical Transmission through Sub-Wavelength Hole Arrays,” Nature391(6668), 667–669 (1998). [CrossRef]
- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 2004).
- K. D. Ko and C. K. Toussaint., “A simple GUI for modeling the optical properties of single metal nanoparticles,” J. Quant. Spectrosc. Radiat. Transf.110(12), 1037–1043 (2009). [CrossRef]
- D. H. Goldstein, Polarized Light, (CRC Press, 2011).
- N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett.11(5), 2038–2042 (2011). [CrossRef] [PubMed]
- B. C. Hsu and J.-F. S. Van Huele, “Spin dynamics for wave packets in Rashba systems,” Phys. Rev. B80(23), 235309 (2009). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.