Exact Solution to Helmholtz Equation for Inhomogeneous Medium: Its Application in Optical Communication

In order to study the capability of amplifying the input optical signal of certain materials, we investigate the Helmholtz equation which describes a system of inhomogeneous media. After exploring its SU(1,1) algebraic structure, we obtain the exact solutions of this Helmholtz equation by means of the algebraic dynamical method. Based on the exact solutions, we analyse the capability of optical amplifiers, which is an important issue in modern optical communication. We take the wave number k₀(z) and the expansion coefficient k₂(z) to be the trigonometric functions, exponential functions and power functions of variable z, respectively. It is found that the material following the exponential functions is the best one for optical amplifiers.