A. Zh. Khachatrian

Reflection of a plane electromagnetic wave obliquely incident on a one-dimensional isotropic dielectric medium with an arbitrary refractive index

A new method is suggested for finding the reflection and transmission amplitudes of an arbitrarily polarized electromagnetic plane wave incident on a one-dimensional finite size dielectric medium. Within the transfer matrix method it is shown that the problem reduces to a set of first-order differential equations with the scattering amplitudes being functions of the size of the medium. We also show that when the unknown functions are chosen as a suitable combination of a scattering amplitudes, the problem reduces to a Cauchy problem for the wave equations describing the s- and p-polarized waves.

Connection between the immersing and transfer-matrix methods in one-dimensional scattering problems

We show that application of the immersing and transfer-matrix methods to one-dimensional problems of particles scattering leads to the system of two linear equations for the functions F and Φ expressed by means of the transmission and reflection amplitudes. The expressions of these functions are derived. The offered method is illustrated by the finding of transmission and reflection coefficients for the potential barrier with a constant height. The developed method can be applied in solving the quasi-one-dimensional and two-dimensional problems of scattering.

Determination of bound state energies for a one-dimensional potential field

Abstract A method for determination of bound state energies for an asymmetric quantum well with an arbitrary shape of the bottom is suggested. It is shown that how the equation determining the energy levels can be easily derived if one knows the electron transmission and reflection amplitudes corresponding to the part of potential inside the well. The results are applied to three difference test problems.

Stationary motion of a quantum particle in the field of a one-dimensional arbitrary potential

A new approach to the problem of description of the stationary motion of a quantum particle in the field of a one-dimensional arbitrary potential is developed. It is shown that the wave function of infinite motion, with the accuracy to two arbitrary constants, can be expressed by means of an arbitrary single solution for some set of linear differential equations of the first order. It is shown that one general property of the Schrödinger equation solutions lies in the basis of many known methods of the problem consideration, such as the method of integral equations, transfer-matrix method, imbedding method, and method of combination of scattering parameters. Within the framework of the proposed approach, the connection between the above-mentioned methods becomes more transparent.

Efficient second-harmonic generation in a double-quantum-well structure

Second-harmonic generation in a double-quantum-well nanostructure is analyzed. Optimization of the structure design from the viewpoint of attaining the highest intensity of the second-harmonic wave at the output is considered. Relationships between the quantum-well parameters in a structure satisfying the double-resonance condition are established. The dependence of the optical characteristics of the system on the quantum-well parameters is studied and the problem of optimization of the second-harmonic intensity is solved. It is demonstrated that the highest conversion efficiency is attained under the conditions where the second-harmonic generation coefficient is maximum.

Three-layer antireflection diamond-like carbon films on glass

The three-layer diamond-like carbon films grown on the glass from the decomposition of toluene and nitrogen by Plasma Enhanced Chemical Vapor Deposition technique. The optimal parameters of three-layered structures with the minimum reflection in the range of 400–750 nm were theoretically calculated using the generalized transfer-matrix technique. The dependence of the refractive index of grown films on the plasma power and nitrogen concentration in the gas mixture was investigated.

Stationary motion of a quantum particle in an arbitrary one-dimensional potential

A consistent approach to the description of a stationary motion of a quantum particle in an arbitrary one-dimensional potential has been developed. It has been proved that the wave function of an infinite motion can be expressed accurate to up two arbitrary constants with the use of one particular solution to the system of first-order linear differential equations. It has been shown that many well-known methods, such as the integral equation method, the transfer matrix method, the embedding method, and the method of combination of scattering parameters, are based on a general property of the solutions to the Schrödinger equation. Within the proposed approach, the relation between these methods becomes more transparent and their description can be well within a unified context.

Electron Wave Function In The Field Of One-Dimensional Irregular Layered Structure

A method is proposed to find the wave function of an electron moving infinitely in the field of an arbitrary 1D layered structure with two different homogeneous semi-infinite boundaries. It is shown that in general the problem reduces to solution of a set of two linear recurrent equations. The proposed approach is discussed on a base of two cases: a structure of periodically placed identical rectangular potentials and a nonordered structure with certain distortion of periodicity and potential identity.

Scattering of an Electromagnetic Wave on a Dielectric Layer Bounded on Two Sides by Two Different Homogeneous, Semi-Infinite Media

The problem of the passage of a plane electromagnetic wave through an arbitrary, inhomogeneous dielectric layer bounded on two sides by two different homogeneous, semi-infinite media is considered. Algebraic relations are obtained between the amplitudes of transmission and reflection (the scattering amplitudes) for the problem under consideration and the wave scattering amplitudes when the layer is bounded on both sides by a vacuum. It is shown that for s and p polarized fields the scattering problem (a boundary-value problem) can be formulated as a Cauchy problem directly for the s and p wave equations. It is also shown that the problem of finding the field inside the layer also reduces to a Cauchy problem in the general case.