Geometrical Aspects in Optical Wavepacket Dynamics

Abstract

We construct a semiclassical theory for propagation of an optical wavepacket in non-conducting media with periodic structures of dielectric permittivity and magnetic permeability, i.e., non-conducting photonic crystals. We employ a quantum-mechanical formalism in order to clarify its link to those of electronic systems. It involves the geometrical phase, i.e., Berry phase, in a natural way, and describes an interplay between orbital motion and the internal rotation. Based on the above theory, we discuss the geometrical aspects of the optical Hall effect. We also consider a reduction of the theory to a system without periodic structure and apply it to the transverse shift at an interface reflection/refraction. For generic incident beams with elliptic polarizations, an identical result for the transverse shift of each reflected/transmitted beam is given by the following different approaches; (i) analytic evaluation of wavepacket dynamics, (ii) total angular momentum (TAM) conservation {\it for individual photons}, and (iii) numerical simulation of wavepacket dynamics. It is consistent with a result by classical electrodynamics. This means that the TAM conservation for individual photons is already taken into account in wave optics, i.e, classical electrodynamics. Finally, we show an application of our theory to a two-dimensional photonic crystal, and propose an optimal design for the enhancement of the optical Hall effect in photonic crystals.

REVTeX, 31 pages, 7 figures, 3 tables, references updated

References in corpus (4)

• Dissipationless Quantum Spin Current at Room Temperature
• Conservation of Angular Momentum, Transverse Shift, and Spin Hall Effect in Reflection and Refraction of Electromagnetic Wave Packet
• Optical Magnetoelectric Effect in Multiferroic Materials: Evidence for a Lorentz Force Acting on a Ray of Light
• Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect

Cited by in corpus (6)

• Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet
• Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium
• Spin Hall effect of a light beam in left-handed materials
• Gradient expansion approach to multiple-band Fermi liquids
• Conservation laws and angular transverse shifts of the reflected and transmitted light beams
• Finsler Spinoptics