Abstract

We demonstrate local circular polarization in surface vortices of an optical near-field generated by superposing two cross-propagating evanescent waves with transverse electric fields on a planar dielectric surface. The circularly rotating local electric fields are converted into circularly polarized propagating light waves in free space via a near-field interaction with a sub-wavelength size local probe. The results show that optical near-fields generated under the influence of a material environment with local rotational symmetry carry angular pseudo-momentum with respect to the symmetry axis. The local circular polarization is of fundamental significance in spin-related and magneto-optical phenomena in nanophotonics.

© 2008 Optical Society of America

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  1. R. A. Beth, "Direct Detection of the Angular Momentum of Light," Phys. Rev. 48, 471 (1935).
    [CrossRef]
  2. R. A. Beth, "Mechanical Detection and Measurement of the Angular Momentum of Light," Phys. Rev. 50, 115-125 (1936).
    [CrossRef]
  3. K. Cho, H. Hori, and K. Kitahara, in Nano-Optics, S. Kawata, M. Ohtsu, M. Irie, eds., (Springer, Berlin, 2002), Chap. 1.
  4. H. Hori, in Optical and Electronic Process of Nano-Matters, M. Ohtsu, eds., (Kluwer Academic Publishers, Dordrecht, 2001), Sec. 1.9.2.
  5. M. Kristensen and J. P. Woerdman, "Is photon angular momentum conserved in dielectric medium?," Phys. Rev. Lett. 72, 2171-2174 (1994).
    [CrossRef] [PubMed]
  6. H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinstein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particle from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1995).
    [CrossRef] [PubMed]
  7. R. Peierls, More Surprises in Theoretical Physics (Princeton University Press, Princeton, 1991), Secs. 2.4 and 2.6.
  8. D. F. Nelson, "Momentum, pseudomomentum, and wave momentum: Toward resolving the Minkowski-Abraham controversy," Phys. Rev. A 44, 3985-3996 (1991).
    [CrossRef] [PubMed]
  9. T. Matsudo, H. Hori, T. Inoue, H. Iwata, Y. Inoue, and T. Sakurai, "Direct detection of evanescent electromagnetic waves at a planar dielectric surface by laser atomic spectroscopy," Phys. Rev. A 55, 2406-2412 (1997).
    [CrossRef]
  10. T. Matsudo, Y. Takahara, H. Hori, and T. Sakurai, "Pseudomomentum transfer from evanescent waves to atoms measured by saturated absorption spectroscopy," Opt. Comm. 145, 64-68 (1998).
    [CrossRef]
  11. M. Ohtsu and H. Hori, Near-Field Nano-Optics (Academic/Plenum, New York, 1999).
    [CrossRef]
  12. E. Wolf and M. Nieto-Vesperinas, "Analyticity of the angular spectrum amplitude of scattered fields and some of its consequences," J. Opt. Soc. Am. A 2, 886-889 (1985).
    [CrossRef]
  13. T. Inoue and H. Hori, "Representations and Transforms of Vector Field as basis of Near-Field Optics," Opt. Rev. 3, 458-462 (1996).
    [CrossRef]
  14. T. Inoue and H. Hori, "Theoretical Treatment of Electric and Magnetic Multipole Radiation Near a Planar Dielectric Surface Based on Angular Spectrum Representation of Vector Field," Opt. Rev. 5, 295-302 (1998).
    [CrossRef]
  15. T. Inoue and H. Hori, "Quantization of evanescent electromagnetic waves based on detector modes," Phys. Rev. A 63, 063805 (2001).
    [CrossRef]
  16. Y. Ohdaira, K. Kijima, K. Terasawa, M. Kawai, H. Hori, and K. Kitahara, "State-selective optical near-field resonant ionization spectroscopy of atoms near a dielectric surface," J. Microscopy 202, 255-260 (2001).
    [CrossRef]
  17. H. Hori, K. Kitahara, and M. Ohtsu, "Comment on the possibility of longitudinal electromagnetic wave on the surface of dielectrics," Abstracts of the 1st Asia Pacific Workshop on Near-Field Optics, Seoul, 49 (1996).
  18. S. F. Alvarado and P. Renaud, "Observation of spin-polarized-electron tunneling from a ferromagnet into GaAs," Phys. Rev. Lett. 68, 1387-1390 (1992).
    [CrossRef] [PubMed]

2001 (2)

T. Inoue and H. Hori, "Quantization of evanescent electromagnetic waves based on detector modes," Phys. Rev. A 63, 063805 (2001).
[CrossRef]

Y. Ohdaira, K. Kijima, K. Terasawa, M. Kawai, H. Hori, and K. Kitahara, "State-selective optical near-field resonant ionization spectroscopy of atoms near a dielectric surface," J. Microscopy 202, 255-260 (2001).
[CrossRef]

1998 (2)

T. Inoue and H. Hori, "Theoretical Treatment of Electric and Magnetic Multipole Radiation Near a Planar Dielectric Surface Based on Angular Spectrum Representation of Vector Field," Opt. Rev. 5, 295-302 (1998).
[CrossRef]

T. Matsudo, Y. Takahara, H. Hori, and T. Sakurai, "Pseudomomentum transfer from evanescent waves to atoms measured by saturated absorption spectroscopy," Opt. Comm. 145, 64-68 (1998).
[CrossRef]

1997 (1)

T. Matsudo, H. Hori, T. Inoue, H. Iwata, Y. Inoue, and T. Sakurai, "Direct detection of evanescent electromagnetic waves at a planar dielectric surface by laser atomic spectroscopy," Phys. Rev. A 55, 2406-2412 (1997).
[CrossRef]

1996 (1)

T. Inoue and H. Hori, "Representations and Transforms of Vector Field as basis of Near-Field Optics," Opt. Rev. 3, 458-462 (1996).
[CrossRef]

1995 (1)

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinstein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particle from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

1994 (1)

M. Kristensen and J. P. Woerdman, "Is photon angular momentum conserved in dielectric medium?," Phys. Rev. Lett. 72, 2171-2174 (1994).
[CrossRef] [PubMed]

1992 (1)

S. F. Alvarado and P. Renaud, "Observation of spin-polarized-electron tunneling from a ferromagnet into GaAs," Phys. Rev. Lett. 68, 1387-1390 (1992).
[CrossRef] [PubMed]

1991 (1)

D. F. Nelson, "Momentum, pseudomomentum, and wave momentum: Toward resolving the Minkowski-Abraham controversy," Phys. Rev. A 44, 3985-3996 (1991).
[CrossRef] [PubMed]

1985 (1)

1936 (1)

R. A. Beth, "Mechanical Detection and Measurement of the Angular Momentum of Light," Phys. Rev. 50, 115-125 (1936).
[CrossRef]

1935 (1)

R. A. Beth, "Direct Detection of the Angular Momentum of Light," Phys. Rev. 48, 471 (1935).
[CrossRef]

Alvarado, S. F.

S. F. Alvarado and P. Renaud, "Observation of spin-polarized-electron tunneling from a ferromagnet into GaAs," Phys. Rev. Lett. 68, 1387-1390 (1992).
[CrossRef] [PubMed]

Beth, R. A.

R. A. Beth, "Mechanical Detection and Measurement of the Angular Momentum of Light," Phys. Rev. 50, 115-125 (1936).
[CrossRef]

R. A. Beth, "Direct Detection of the Angular Momentum of Light," Phys. Rev. 48, 471 (1935).
[CrossRef]

Friese, M. E.

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinstein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particle from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

He, H.

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinstein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particle from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinstein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particle from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

Hori, H.

Y. Ohdaira, K. Kijima, K. Terasawa, M. Kawai, H. Hori, and K. Kitahara, "State-selective optical near-field resonant ionization spectroscopy of atoms near a dielectric surface," J. Microscopy 202, 255-260 (2001).
[CrossRef]

T. Inoue and H. Hori, "Quantization of evanescent electromagnetic waves based on detector modes," Phys. Rev. A 63, 063805 (2001).
[CrossRef]

T. Matsudo, Y. Takahara, H. Hori, and T. Sakurai, "Pseudomomentum transfer from evanescent waves to atoms measured by saturated absorption spectroscopy," Opt. Comm. 145, 64-68 (1998).
[CrossRef]

T. Inoue and H. Hori, "Theoretical Treatment of Electric and Magnetic Multipole Radiation Near a Planar Dielectric Surface Based on Angular Spectrum Representation of Vector Field," Opt. Rev. 5, 295-302 (1998).
[CrossRef]

T. Matsudo, H. Hori, T. Inoue, H. Iwata, Y. Inoue, and T. Sakurai, "Direct detection of evanescent electromagnetic waves at a planar dielectric surface by laser atomic spectroscopy," Phys. Rev. A 55, 2406-2412 (1997).
[CrossRef]

T. Inoue and H. Hori, "Representations and Transforms of Vector Field as basis of Near-Field Optics," Opt. Rev. 3, 458-462 (1996).
[CrossRef]

Inoue, T.

T. Inoue and H. Hori, "Quantization of evanescent electromagnetic waves based on detector modes," Phys. Rev. A 63, 063805 (2001).
[CrossRef]

T. Inoue and H. Hori, "Theoretical Treatment of Electric and Magnetic Multipole Radiation Near a Planar Dielectric Surface Based on Angular Spectrum Representation of Vector Field," Opt. Rev. 5, 295-302 (1998).
[CrossRef]

T. Matsudo, H. Hori, T. Inoue, H. Iwata, Y. Inoue, and T. Sakurai, "Direct detection of evanescent electromagnetic waves at a planar dielectric surface by laser atomic spectroscopy," Phys. Rev. A 55, 2406-2412 (1997).
[CrossRef]

T. Inoue and H. Hori, "Representations and Transforms of Vector Field as basis of Near-Field Optics," Opt. Rev. 3, 458-462 (1996).
[CrossRef]

Inoue, Y.

T. Matsudo, H. Hori, T. Inoue, H. Iwata, Y. Inoue, and T. Sakurai, "Direct detection of evanescent electromagnetic waves at a planar dielectric surface by laser atomic spectroscopy," Phys. Rev. A 55, 2406-2412 (1997).
[CrossRef]

Iwata, H.

T. Matsudo, H. Hori, T. Inoue, H. Iwata, Y. Inoue, and T. Sakurai, "Direct detection of evanescent electromagnetic waves at a planar dielectric surface by laser atomic spectroscopy," Phys. Rev. A 55, 2406-2412 (1997).
[CrossRef]

Kawai, M.

Y. Ohdaira, K. Kijima, K. Terasawa, M. Kawai, H. Hori, and K. Kitahara, "State-selective optical near-field resonant ionization spectroscopy of atoms near a dielectric surface," J. Microscopy 202, 255-260 (2001).
[CrossRef]

Kijima, K.

Y. Ohdaira, K. Kijima, K. Terasawa, M. Kawai, H. Hori, and K. Kitahara, "State-selective optical near-field resonant ionization spectroscopy of atoms near a dielectric surface," J. Microscopy 202, 255-260 (2001).
[CrossRef]

Kitahara, K.

Y. Ohdaira, K. Kijima, K. Terasawa, M. Kawai, H. Hori, and K. Kitahara, "State-selective optical near-field resonant ionization spectroscopy of atoms near a dielectric surface," J. Microscopy 202, 255-260 (2001).
[CrossRef]

Kristensen, M.

M. Kristensen and J. P. Woerdman, "Is photon angular momentum conserved in dielectric medium?," Phys. Rev. Lett. 72, 2171-2174 (1994).
[CrossRef] [PubMed]

Matsudo, T.

T. Matsudo, Y. Takahara, H. Hori, and T. Sakurai, "Pseudomomentum transfer from evanescent waves to atoms measured by saturated absorption spectroscopy," Opt. Comm. 145, 64-68 (1998).
[CrossRef]

T. Matsudo, H. Hori, T. Inoue, H. Iwata, Y. Inoue, and T. Sakurai, "Direct detection of evanescent electromagnetic waves at a planar dielectric surface by laser atomic spectroscopy," Phys. Rev. A 55, 2406-2412 (1997).
[CrossRef]

Nelson, D. F.

D. F. Nelson, "Momentum, pseudomomentum, and wave momentum: Toward resolving the Minkowski-Abraham controversy," Phys. Rev. A 44, 3985-3996 (1991).
[CrossRef] [PubMed]

Nieto-Vesperinas, M.

Ohdaira, Y.

Y. Ohdaira, K. Kijima, K. Terasawa, M. Kawai, H. Hori, and K. Kitahara, "State-selective optical near-field resonant ionization spectroscopy of atoms near a dielectric surface," J. Microscopy 202, 255-260 (2001).
[CrossRef]

Renaud, P.

S. F. Alvarado and P. Renaud, "Observation of spin-polarized-electron tunneling from a ferromagnet into GaAs," Phys. Rev. Lett. 68, 1387-1390 (1992).
[CrossRef] [PubMed]

Rubinstein-Dunlop, H.

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinstein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particle from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

Sakurai, T.

T. Matsudo, Y. Takahara, H. Hori, and T. Sakurai, "Pseudomomentum transfer from evanescent waves to atoms measured by saturated absorption spectroscopy," Opt. Comm. 145, 64-68 (1998).
[CrossRef]

T. Matsudo, H. Hori, T. Inoue, H. Iwata, Y. Inoue, and T. Sakurai, "Direct detection of evanescent electromagnetic waves at a planar dielectric surface by laser atomic spectroscopy," Phys. Rev. A 55, 2406-2412 (1997).
[CrossRef]

Takahara, Y.

T. Matsudo, Y. Takahara, H. Hori, and T. Sakurai, "Pseudomomentum transfer from evanescent waves to atoms measured by saturated absorption spectroscopy," Opt. Comm. 145, 64-68 (1998).
[CrossRef]

Terasawa, K.

Y. Ohdaira, K. Kijima, K. Terasawa, M. Kawai, H. Hori, and K. Kitahara, "State-selective optical near-field resonant ionization spectroscopy of atoms near a dielectric surface," J. Microscopy 202, 255-260 (2001).
[CrossRef]

Woerdman, J. P.

M. Kristensen and J. P. Woerdman, "Is photon angular momentum conserved in dielectric medium?," Phys. Rev. Lett. 72, 2171-2174 (1994).
[CrossRef] [PubMed]

Wolf, E.

J. Microscopy (1)

Y. Ohdaira, K. Kijima, K. Terasawa, M. Kawai, H. Hori, and K. Kitahara, "State-selective optical near-field resonant ionization spectroscopy of atoms near a dielectric surface," J. Microscopy 202, 255-260 (2001).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Comm. (1)

T. Matsudo, Y. Takahara, H. Hori, and T. Sakurai, "Pseudomomentum transfer from evanescent waves to atoms measured by saturated absorption spectroscopy," Opt. Comm. 145, 64-68 (1998).
[CrossRef]

Opt. Rev. (2)

T. Inoue and H. Hori, "Representations and Transforms of Vector Field as basis of Near-Field Optics," Opt. Rev. 3, 458-462 (1996).
[CrossRef]

T. Inoue and H. Hori, "Theoretical Treatment of Electric and Magnetic Multipole Radiation Near a Planar Dielectric Surface Based on Angular Spectrum Representation of Vector Field," Opt. Rev. 5, 295-302 (1998).
[CrossRef]

Phys. Rev. (2)

R. A. Beth, "Direct Detection of the Angular Momentum of Light," Phys. Rev. 48, 471 (1935).
[CrossRef]

R. A. Beth, "Mechanical Detection and Measurement of the Angular Momentum of Light," Phys. Rev. 50, 115-125 (1936).
[CrossRef]

Phys. Rev. A (3)

D. F. Nelson, "Momentum, pseudomomentum, and wave momentum: Toward resolving the Minkowski-Abraham controversy," Phys. Rev. A 44, 3985-3996 (1991).
[CrossRef] [PubMed]

T. Matsudo, H. Hori, T. Inoue, H. Iwata, Y. Inoue, and T. Sakurai, "Direct detection of evanescent electromagnetic waves at a planar dielectric surface by laser atomic spectroscopy," Phys. Rev. A 55, 2406-2412 (1997).
[CrossRef]

T. Inoue and H. Hori, "Quantization of evanescent electromagnetic waves based on detector modes," Phys. Rev. A 63, 063805 (2001).
[CrossRef]

Phys. Rev. Lett. (3)

S. F. Alvarado and P. Renaud, "Observation of spin-polarized-electron tunneling from a ferromagnet into GaAs," Phys. Rev. Lett. 68, 1387-1390 (1992).
[CrossRef] [PubMed]

M. Kristensen and J. P. Woerdman, "Is photon angular momentum conserved in dielectric medium?," Phys. Rev. Lett. 72, 2171-2174 (1994).
[CrossRef] [PubMed]

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinstein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particle from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

Other (5)

R. Peierls, More Surprises in Theoretical Physics (Princeton University Press, Princeton, 1991), Secs. 2.4 and 2.6.

K. Cho, H. Hori, and K. Kitahara, in Nano-Optics, S. Kawata, M. Ohtsu, M. Irie, eds., (Springer, Berlin, 2002), Chap. 1.

H. Hori, in Optical and Electronic Process of Nano-Matters, M. Ohtsu, eds., (Kluwer Academic Publishers, Dordrecht, 2001), Sec. 1.9.2.

H. Hori, K. Kitahara, and M. Ohtsu, "Comment on the possibility of longitudinal electromagnetic wave on the surface of dielectrics," Abstracts of the 1st Asia Pacific Workshop on Near-Field Optics, Seoul, 49 (1996).

M. Ohtsu and H. Hori, Near-Field Nano-Optics (Academic/Plenum, New York, 1999).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Nature of local circular polarization in optical near-fields and angular momentum transfer between electronic system and optical near-fields. (a) Circular polarizations (photon spin) of electromagnetic waves in free space and those in optical near-fields exhibit quite different features. While the axis of the circular polarization is directed parallel to the wave vector (momentum) in free space, that of optical near-fields is directed normal to the surface and orthogonal to the lateral wave vector (pseudo-momentum) due to the restricted spatial rotational and translational symmetry of the coupled mode of light and matter at the material surface. (b) A schematic picture showing angular momentum transfer in optical near-field interactions being dependent on both the local rotational symmetry of the electronic systems and optical systems relevant to the interaction. The angular pseudo-momentum of optical near-fields can be transferred to a local electronic system of sub-wavelength size, and vice versa, when the rotational symmetry axes of those local systems are taken in the same directions.

Fig. 2.
Fig. 2.

Generation of local circular polarization in surface vortices of optical near-fields with vortex-like electric field-vector distribution surrounding dark spots of zero field amplitude on a planar dielectric surface. (a) Simple optical setup to generate circularly rotating local electric field in optical near-field. Two laser beams divided from a single-mode semiconductor laser (wavelength 852.1 nm, power 9.6 mW, beam diameter 0.68 mm, beam divergence 1.5×10-3 rad) were incident on the surface of a pyramidal prism (refractive index n=1.452 at 852.1 nm, bottom surface 24× 24 mm2, truncated top surface 6×6 mm2) at the angle of total internal reflection, and two TE-polarized evanescent waves were superposed in the direction orthogonal to each other. The relative phase of the laser beams was controlled by a piezoelectric transducer (PZT) attached to one of the reflecting mirrors. (b) Predicted distribution of surface vortices of electric field and circularly rotating local electric field. On a line corresponding to the specific phase difference, Δϕ=π/2, between the cross-propagated evanescent waves, the local electric field in the surface optical vortices exhibits the nature of left (-) or right (+) circular polarization with respect to the surface normal. Linear polarizations appear for Δϕ=π or 2π, and elliptical polarization arises for intermediate phase differences (not shown). The spatial repeating period is approximately equal to the wavelength λ of the incident light.

Fig. 3.
Fig. 3.

Observation of local polarization in surface vortices of optical near-field using a single small dielectric sphere. (a) Enlarged view of the sphere probe placed in the local field. The local circular polarizations are scattered and transformed into circularly polarized light propagating in free space. (b) Sectional view of collimation optics and polarization analyzer. The scattered light was collected by an aspherical lens and was spatially filtered. The circular polarization components were separated and detected by a cooled CCD. (c) Top view of the optical setup built on a Zerodur glass substrate, showing drift of phase difference between two evanescent waves monitored by a Michelson interferometer. (d) The observed intensity variations of right- and left-circular polarization components involved in the scattered fields from the single sphere probe (radius ~50 nm) as a function of phase difference Δϕ between the two incident evanescent waves. Solid and dashed lines, respectively, are sinusoidal fits for the right (I +) and left (I -) circular components. (e) The degree of circular polarization P obtained from (d).

Fig. 4.
Fig. 4.

Optical setup and observation of local circular polarization by means of optical fiber probe with a sharpened tip. (a) Placement of optical fiber probe held in a direction perpendicular to the prism surface. This alignment maintains cylindrical symmetry of the probing system around the normal of the prism surface. (b) Collimation optics for scattered light propagated into the prism. An aspherical lens was attached to the truncated top of the pyramidal prism. (c) The entire optical system. The setup was modified from that of the sphere probe system to easily produce the cross-propagating evanescent waves. The edge of the pyramidal prism was directed normal to the plane formed by the two incident beams. (d) The observed intensity variations of right- and left-circular polarization components involved in the scattered fields from the optical fiber probe. The apex of the conical tip of the optical fiber probe was held ~360 nm above the prism surface. (e) The degree of circular polarization P obtained from (d).

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