On a Simple Derivation of the Fresnel Diffraction Formula and a Transfer Function Approach to Wave Propagation
American Journal of Physics
The Fresnel diffraction formula is straightforwardly obtained by solving a partial differential equation (PDE) for envelope propagation using Fourier transform techniques. The PDE, in turn, can be derived from the dispersion relation of a linear medium by employing a simple operator formalism. The transfer function and impulse response of propagation follows as a spin‐off and is used to solve illustrative problems. Huygens’ principle is visualized as a consequence of the convolution property of linear systems.
Copyright © 1990, American Association of Physics Teachers
American Association of Physics Teachers
Banerjee, Partha P. and Poon, Ting-Chung, "On a Simple Derivation of the Fresnel Diffraction Formula and a Transfer Function Approach to Wave Propagation" (1990). Electrical and Computer Engineering Faculty Publications. 157.