Bragg scattering from point interactions: An explicit formula for the reflection coefficient

A. S. Kuraptsev, Igor M. Sokolov, Ya. A. Fofanov

We analyze resonant light scattering from a dense and disordered ensemble of motionless point-like scatters with uniform (on average) spatial distribution of the density. The average interatomic distance is considered comparable with the resonant wavelength and the mean free path of photon. The inhomogeneity of dipole-dipole interaction near the surface is discussed. Angular distribution of the light scattered from a medium in a slab geometry is calculated. The total reflected light power [Formula: see text] and the reflectivity [Formula: see text] depending on the optical thickness of a medium [Formula: see text] are analyzed. It is shown that in the case of small optical thickness ([Formula: see text]) [Formula: see text] and [Formula: see text]. With further increasing of the optical thickness we observe oscillations of the dependencies [Formula: see text] and [Formula: see text]. The attenuation coefficient of these oscillations is discussed.

Juha Javanainen

Lawrence E. Thomas

Arlen Anderson

By calculating the reflection and transmission coefficients for a square potential barrier in terms of a series of scatterings at step potential discontinuities, a multiple scattering approach to potential problems is presented. This approach is applied to WKB potential problems by interpreting the WKB connection formulas in terms of reflection and transmission coefficients at each turning point. An algorithm for the systematic construction of the energy Green’s function is given. The significance of complex coordinate turning points is demonstrated. The equivalence of this approach and that of the Gaussian approximation of the path integral is mentioned briefly.

Kikuo Cho, Takahiro Arakawa

Stefano Longhi

We introduce a new class of parity-time ( )-symmetric complex crystals which are almost transparent and one-way reflectionless over a broad frequency range around the Bragg frequency, i.e., unidirectionally invisible, regardless of the thickness L of the crystal. The -symmetric complex crystal is synthesized by a supersymmetric (SUSY) transformation of a Hermitian square well potential, and exact analytical expressions of transmission and reflection coefficients are given. As L is increased, the transmittance and reflectance from one side remain close to one and zero, respectively, whereas the reflectance from the other side secularly grows like owing to unidirectional Bragg scattering. This is a distinctive feature as compared to the previously studied case of the complex sinusoidal -symmetric potential at the symmetry breaking point, where transparency breaks down as .