Whispering Gallery Waves Research Articles

Numerical solution of the problem on whispering gallery waves in a neighborhood of a simple zero of the effective curvature of the boundary

A method of numerically solving the problem on whispering gallery waves in a neighborhood of a simple zero of the effective curvature of the boundary is described, and results are presented of calculating the wave field in the case of the first and second whispering gallery waves.

Problem of whispering gallery waves in a neighborhood of a simple zero of the effective curvature of the boundary

The mathematical formulation of the problem on the propagation of whispering gallery waves in a neighborhood of a simple zero of the effective curvature of the boundary is given for the principal term of the short-wave asymptotics, and the uniqueness of the solution of this problem is demonstrated.

Geometrical Theory for Surface Waves

The virtues of geometrical diffraction theory and of uniform asymptotic methods can be combined. Instead of merely matching the local geometry with the geometry of a canonical problem, the exact solution to the canonical problem is used as an approximation to the problem at hand. The wave equation is not employed directly, but the principle of energy conservation is used to determine certain amplitudes. This idea is illustrated by applying it to WKB solution of an ordinary differential equation, deriving the equation for geometrical optics, finding whispering gallery modes, finding the whispering gallery waves excited by a source, and by constructing creeping waves and their excitation coefficients.

Asymptotic solutions for high-frequency trapped wave propogation

A technique is developed by which high-frequency trapped scalar wave problems are reduced to finding solutions for a sequence of equations which are independent of the frequency. The technique is applied to whispering gallery waves, ducted waves, edge waves and surface waves. Several successful comparisons are made between the asymptotic expansions of exact analytic solutions and the results obtained by using the technique while one numerical comparison shows that such results can be extremely accurate even when the frequency is low. The range of validity of the solutions is discussed with particular reference to numerical solutions.