Abstract

The two-dimensional stationary-wave equation (Helmholtz equation) can be solved by a simple linear-optical filtering experiment for arbitrary source distributions. The experiment can be considered as direct visualization of Huygens’s principle, i.e., each point of an initial wave front can be regarded as the source of an elementary wave. Many phenomena can be visualized: diffraction, interference (including Talbot effect, Bragg effect) with monochromatic and polychromatic light, birefringence, etc. Optical filtering can be applied to other linear differential equations with constant coefficients too, such as the Poisson equation and the diffusion equation.

© 1988 Optical Society of America

Field equations, Huygens’s principle, integral equations, and theorems for radiation and scattering of electromagnetic waves in isotropic chiral media

Akhlesh Lakhtakia, Vasundara V. Varadan, and Vijay K. Varadan
J. Opt. Soc. Am. A 5(2) 175-184 (1988)

Vectorial approach to Huygens's principle for plane waves: circular aperture and zone plates

Julio A. Romero and Luis Hernández
J. Opt. Soc. Am. A 23(5) 1141-1145 (2006)

Diffraction by a circular aperture: an application of the vectorial theory of Huygens's principle in the near field

J. A. Romero and L. Hernández
J. Opt. Soc. Am. A 25(8) 2040-2043 (2008)

Huygens’s principle and rays in uniaxial anisotropic media. I. Crystal axis normal to refracting surface

Maximino Avendaño-Alejo, Orestes N. Stavroudis, and Ana Rosa Boyain y Goitia
J. Opt. Soc. Am. A 19(8) 1668-1673 (2002)

Reflection formulae for ray tracing in uniaxial anisotropic media using Huygens’s principle

Luis A. Alemán-Castañeda and Martha Rosete-Aguilar
J. Opt. Soc. Am. A 33(11) 2198-2205 (2016)