Engineering and Applied Sciences Applied Physics 216 Lecture 20: Lecture 20
21 Feb 2017
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Ap 216 lecture 20 scalar waves, helmholtz equation, fourier optics. In the last lecture we studied the scalar wave equation for which. 22 and found the general solution in terms of retarded and advanced greens functions. Many sources of radiation can be considered to be monochromatic, ie containing only a single frequency. This is either because the charge densities and currents that give rise to the radiation vary in time sinusoidally at one frequency or because the radiation has been sent through a frequency filter. Assume the sources oscillate with a time frequency component , i. e f x e . F x t i t (2) and we look for solution of equation (1) of the form x t x e i t (comment on the use of complex exponentials. ) Inserting equations (2) and (3) in (1) gives the inhomogeneous helmholtz equation. 32 whose greens function g(x , x ". Expanding and representing g by gives x x.
