dorsal/arxiv
View SchemaModified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect
| Authors | K. Yu. Bliokh, Yu. P. Bliokh |
|---|---|
| Categories | |
| ArXiv ID | physics/0402014 |
| URL | https://arxiv.org/abs/physics/0402014 |
| DOI | 10.1103/PhysRevE.70.026605 |
| Journal | Physical Review E 70, 026605 (2004) |
Abstract
In this paper we present a modification of the geometrical optics method, which allows one to properly separate the complex amplitude and the phase of the wave solution. Appling this modification to a smoothly inhomogeneous isotropic medium, we show that in the first geometrical optics approximation the medium is weakly anisotropic. The refractive index, being dependent on the direction of the wave vector, contains the correction, which is proportional to the Berry geometric phase. Two independent eigenmodes of right-hand and left-hand circular polarizations exist in the medium. Their group velocities and phase velocities differ. The difference in the group velocities results in the shift of the rays of different polarizations (the optical Magnus effect). The difference in the phase velocities causes the increase of Berry phase along with the interference of two modes leading to the familiar Rytov law about the rotation of the polarization plane of a wave. The theory developed suggests that both the optical Magnus effect and the Berry phase are accompanying nonlocal topological effects. In this paper the Hamilton ray equations giving a unified description for both of these phenomena have been derived and also a novel splitting effect for a ray of noncircular polarization has been predicted. Specific examples are also discussed.
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"abstract": "In this paper we present a modification of the geometrical optics method,\nwhich allows one to properly separate the complex amplitude and the phase of\nthe wave solution. Appling this modification to a smoothly inhomogeneous\nisotropic medium, we show that in the first geometrical optics approximation\nthe medium is weakly anisotropic. The refractive index, being dependent on the\ndirection of the wave vector, contains the correction, which is proportional to\nthe Berry geometric phase. Two independent eigenmodes of right-hand and\nleft-hand circular polarizations exist in the medium. Their group velocities\nand phase velocities differ. The difference in the group velocities results in\nthe shift of the rays of different polarizations (the optical Magnus effect).\nThe difference in the phase velocities causes the increase of Berry phase along\nwith the interference of two modes leading to the familiar Rytov law about the\nrotation of the polarization plane of a wave. The theory developed suggests\nthat both the optical Magnus effect and the Berry phase are accompanying\nnonlocal topological effects. In this paper the Hamilton ray equations giving a\nunified description for both of these phenomena have been derived and also a\nnovel splitting effect for a ray of noncircular polarization has been\npredicted. Specific examples are also discussed.",
"arxiv_id": "physics/0402014",
"authors": [
"K. Yu. Bliokh",
"Yu. P. Bliokh"
],
"categories": [
"physics.optics",
"cond-mat.other",
"physics.gen-ph"
],
"doi": "10.1103/PhysRevE.70.026605",
"journal_ref": "Physical Review E 70, 026605 (2004)",
"title": "Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect",
"url": "https://arxiv.org/abs/physics/0402014"
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