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Physical Review

A Quantum-Mechanical Definition of Refractive Index

S. M. Neamtan

Published Apr 15, 1954• 11 citations
Publisher

Abstract

The refractive index is defined in terms of momentum and energy changes in first-order transitions of a system consisting of the particles of a refractive medium in interaction with the electromagnetic field.
DOI
10.1103/physrev.94.327

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Abstract A quantum mechanical system consisting of one photon interacting with N atoms not far from resonance is considered and an (approximately) stationary solution found for the eigenstates and energy of the interacting system. It is shown that the interaction energy (light shift) is simply related to the atomic polarizability. A consideration of the expectation value of the operator representing the first-order correlation function of an optical field yields a quantum-mechanical interpretation of refractive index.
The refractive index of a system is often viewed as the collective response of a medium to an electromagnetic field. Nevertheless, even if targeted at a single atom, the incoming light undergoes the dispersion. By studying the propagation of a single photon interacting with a two-level atom, we examine the dispersion behavior, calculate the phase and group velocity of the photon wave packet, and further analyze the dispersion experienced by the photon. These findings are critical for advancing long-distance quantum communications.
A method for controlling the refractive index that is based on the backward rescattering of the scattered and amplified electromagnetic waves is proposed and analysed. The resulting field is a sum of the initial (probe) wave and the rescattered wave. The effective wave number of the total wave can be varied by varying the gain. This variation in the wave number can be treated as a variation in the refractive index, although the physical properties of the medium do not change. The effective refractive index for the total wave propagating in such a device was called the virtual refractive index.
Accurate modeling of optical nonlinearities is crucial to describe macroscopic laser propagation in a medium, including sum frequency generation, spectral broadening due to self-phase modulation, various ionization processes and soliton formation. For incident laser light the response of the medium is given by the induced polarization of the microscopic system. The polarization is usually expanded in a Taylor series for the electric field amplitude, which is truncated after the first non-linear term being of third order for isotropic media. A third-order nonlinearity leads to the well-known optical Kerr effect, where the refractive index of the medium becomes intensity dependent via n = n0+ n2I. This leads to an inherent problem when modeling laser propagation in two or more spatial dimensions, linked to the formal divergence (n2> 0) of the refractive index for increasing intensity.