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
Optical fields in free space carry momentum and angular momentum parallel to each other due to relativity requirements for transverse waves propagating at the speed of light [1,2]. This readily provides perfect polarization of photonic spin and restricts its application only to the axis along the direction of propagation. The situation is different in the sub-wavelength vicinity of an optical source, i.e., in the optical near-field regime, where the optical fields under the influence of the material environment exhibit a quite different nature from those in free space [3–10]. Optical near-fields correspond to electromagnetic fields generated in the vicinity of an illuminated object so as to establish induced polarization and associated surface charge consistent with the optical near-fields. Reflecting the nature of composite modes of optical fields and material excitation, the physical quantities associated with optical near-field interactions exhibit quite different features in comparison with optical radiation in the far field (Fig. 1(a)). Regarding momentum and angular momentum, defined as conserved quantities under parallel displacement and rotation in homogeneous space, respectively, we cannot adopt these quantities directly in optical near-fields without spatial homogeneity. Instead, we can use quasi-conserved quantities under the restricted symmetry of the local subsystem relevant to the interactions under consideration [7–10]. For optical near-field interactions, we can consider pseudo-momentum and angular pseudo-momentum under restricted spatial translational and rotational symmetries, respectively [9–11].
Interactions of matter with evanescent electromagnetic waves represent the fundamental processes of optical near-field interactions, since optical near-fields, in general, are described by a series of evanescent waves in terms of an angular spectrum representation of scattered fields [12–15]. We have already demonstrated the pseudo-momentum conservation in atomic recoil during resonant absorption of photons from evanescent waves near a planar dielectric surface [9,10]. The high-resolution pump-probe laser spectroscopy of Cs atoms at the D 2 resonance line showed that the magnitude of the pseudo-momentum transferred to the atom corresponds to the wave number of the evanescent wave and is larger than the momentum of free photons. We can also consider angular pseudo-momentum conserved in the optical near-field interactions of local electronic systems of sub-wavelength size, provided that the relevant electronic and optical systems have a common symmetry axis for the local spatial rotation within the spatial extent of each subsystem (Fig. 1(b)). In this case, the angular pseudo-momentum can be transferred to the local electronic system via orbital angular motions driven by the circularly rotating local electric fields. For example, when we consider optical near-field interaction of an atomic particle near a planar surface, the axis of circular polarization should be taken in the surface normal direction.
In this paper, we report that a circularly rotating local electric field near a dielectric planar surface is observable in an optical surface vortex generated by a superposition of two cross-propagating TE-polarized evanescent waves, whose axis of rotation is perpendicular to the direction of wave-propagation [16,17]. We demonstrate that such a circularly rotating local electric field can be scattered into circularly polarized propagating waves by a dielectric probe of sub-wavelength size. This suggests that the local circular polarization drives a rotating electric polarization in the probe, corresponding to the excitation of orbital angular motion in the local electronic system. The local circular polarization will therefore be useful for spin manipulation of nanometer-sized electronic systems via spin-orbit interactions [17,18], optical excitation of rotational motion in microscopic objects and photo-reactive molecules, and control of polarization-preferred chemical reactions aiming at nanometer scale material fabrication.
2. Generation and observation of local circular polarization in optical near-field
The experimental setup shown in Fig. 2(a) was employed to generate optical surface vortices with the predicted vortex-like electric field-vector distribution surrounding dark spots of zero field amplitude in optical near-field shown in Fig. 2(b). Frequency-stabilized single-mode diode laser light at wavelength 852.1 nm was divided into two linearly polarized beams of equal amplitude, which were made incident on the bottom of a 45 degree quartz prism of a truncated pyramidal shape so as to produce two TE-polarized evanescent waves having a definite relative phase with equal penetration depths and the directions of propagation orthogonal to each other. The vortex-like electric field-vector distribution moves in the direction of the combined wave vector with a velocity approximately equal to the speed of light. The spatial phase difference between the two evanescent waves, Δϕ, determines local polarizations in the sub-wavelength region: for Δϕ=π/2, the local electric field exhibits the nature of left (σ -) or right (σ +) circular polarization with respect to the surface normal, and for Δϕ=π or 2π, local linear polarizations appear in the transverse electric field. Elliptical polarization arises for intermediate phase differences, for which corresponding polarizations are not shown in Fig 2 (b) for simplicity. The spatial period of repetition is approximately equal to the wavelength of the incident light. A sub-wavelength sized local probe can see the local circular polarization which was directed perpendicular to the wave vector of the combined wave, i.e., the orthogonal nature of the pseudo-momentum and angular pseudo-momentum in the optical near-field interactions between sub-wavelength sized objects.
Two different types of sub-wavelength size local probes were employed to scatter the optical near-field into propagating light observable in the far field: an isolated small dielectric sphere of 50 nm in radius (Tokuyama Corp., SX series, SiO2) placed directly on the prism surface (Fig. 3(a)), and a sharpened, metal-coated conical tip of an optical fiber-probe of a scanning near-field optical microscope (Fig. 4(a)). The small sphere enables direct comparison of the results with Mie-scattering theory, whereas the probe tip serves as an authentic single scattering center. To convert the local polarizations into those of scattered light observable in the far field, we should maintain cylindrical symmetry with respect to the normal of the prism surface in the probing system including a polarization analyzer. This assures a direct correspondence of the local symmetry under spatial rotation with those of the scattered fields. The polarization analyzer transformed the right and left circular polarizations into orthogonal linear polarizations, both of which were detected by a single cooled charge coupled device (CCD; dark current, 0.1 electron/pixel/s; Fig.3(b)). Integrated over each beam spot corresponding to the separated polarization components, the CCD output provided intensities corresponding, respectively, to the right (σ +) and left (σ -) circular polarization components of the scattered light from the probe. The degree of local circular polarization P=(I +- I -)/(I ++I -)×100 at the probe was estimated from the observed intensities I +(I -) of σ + (σ -) circularly polarized scattered light.
To observe the polarization distribution, the local polarization at the probe was altered by varying the phase difference Δϕ between the cross-propagating evanescent waves. That is, the entire polarization pattern was swept according to a continuous change of Δϕ. Before putting the probe on the prism surface, the unpolarized background levels in the scattered light were measured to be 1.36×10-13 ±2.3×10-15 W for the sphere probe setup and 5.50×10-15 ±8.7×10-17 W for the fiber probe setup, which remained constant during phase scanning. For the sphere probe, the scattered field was analytically calculated by using the angular spectrum representation of vector spherical waves [13,14]. As a result, the scattering cross-section into the far-field is given approximately by , where ξ is the helicity with respect to the normal to the prism surface, angle Θ is one half of the angular aperture for an optical detector collecting the scattered field, and σ 0 is the total cross section mainly determined by the Mie coefficient for the sphere probe and penetration depth of the evanescent waves (in our setup, σ 0 ~ 6.2×10-17 m2). The value of Δϕ was measured from interference fringes produced by a Michelson interferometer formed by the reflected beams from the input facets of the prism (Fig. 3(c)). The optical setup was built on a Zerodur glass substrate, which reduced the temperature drift of Δϕ corresponding to an optical path difference of less than 6 nm per minute in typical room-temperature operation (Fig. 3(c)).
3. Experimental results and discussions
Figures 3(d) and 3(e) show typical results obtained for a small silica sphere with a radius of 50 nm, where the laser incidence angle of 45.0±1/ 60 degrees corresponds to an evanescent wave penetration depth of 478 nm. In practice, spheres are randomly scattered on the prism surface by dropping a diluted ethanol solution containing the spheres, followed by air drying. The suitability of this technique was confirmed using a reference sample observed by transmission electron microscopy. A small sphere was selectively observed through a circular aperture of diameter 25 µm supported 25 µm above the prism surface by a thin spacer of stainless steel, in order not to obstruct the evanescent waves and to limit the half-angle aperture Θ of observation to about 0.30 radian (Fig. 3(b)). The scattered light passing through the aperture was tightly focused by an aspheric lens and collimated by a plano-convex lens after transmission through a spatial filter. Despite the very weak observed intensity of ~1.8×10-14 W, the result showed a nearly sinusoidal curve, providing experimental evidence of circularly rotating local optical fields. That is, the right-circular, linear, and left-circular polarizations were sequentially observed according to the variation of the phase difference Δϕ between the cross-propagating evanescent waves, and the repetition period of the polarization pattern was in good agreement with the predicted distribution shown in Fig. 2(b). The observed intensity was in good agreement with the theoretical value of 2.8×10-14 W, accounting for the nominal loss of 46% of the optical components employed. The observed degree of circular polarization was also lowered possibly by slight misalignment of the polarization analyzer and stray light scattered at the prism surface, as well as at each optical component.
Figures 4(d) and 4(e) show typical results obtained for a commercially available optical fiber probe with a conical shape held perpendicular to the surface in order to maintain cylindrical symmetry of the probing system with respect to the normal of the prism surface. Here, the scattered light into the pyramidal prism was collimated by an aspheric lens (NA=0.25, diameter 6.4 mm, f=7.92 mm) attached to the truncated top of the prism (Figs. 4(b) and 4(c)). The apex of the fiber probe, much smaller than the optical wavelength, was held 360 nm above the prism surface, corresponding approximately to the 1/e intensity maximum of the total scattered field. The results clearly show an anti-correlated sinusoidal variation of the right- and left-circular polarizations according to the phase difference, in spite of the extremely weak intensity of ~2.6×10-15 W. The observed repetition period of the polarization corresponded to a spatial displacement of ~870 nm, with the degree of circular polarization possibly lowered due to misalignment of the optical fiber probe and polarization analyzer. The consistency of these results leads to the conclusion that circularly rotating local electric fields were produced and converted into the propagating light with corresponding circular polarizations via near-field interactions. The angular momentum transferred into the far field can be compensated by an angular distortion in the material system of the probe and glass substrate relevant to the optical near-field interaction. This will allow the optical near-field interactions to be distinguished from simple interference of cross-propagating light waves in free space.
In this paper, we have demonstrated that a circularly rotating local optical field can be produced by a pair of cross-propagating TE-polarized evanescent waves. The results suggested that the local circular polarization drives rotating electric polarizations in the probe, corresponding to the excitation of the orbital angular motion in the local electronic system. The local polarizations of optical near-fields have potential applications in manipulating the spin state and rotational state of mesoscopic systems, as well as a wide range of uses in nanophotonics.
This work was partly supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture and also by CREST, JST. The authors also thank the Matsuo Foundation for financial support.
References and links
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, and M. Irie, eds. (Springer, Berlin, 2002), Ch. 1.
4. H. Hori, in Optical and Electronic Process of Nano-Matters, M. Ohtsu, eds. (Kluwer Academic Publishers, Dordrecht, 2001), Sec. 1.9.2.
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.
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).