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Unformatted text preview: ECE 222B, Winter 2010 Homework Set 2: Problems 1, 2, and 3 are due Tuesday, January 26th. Problem 4 will not be turned in. 1. Assume that an anisotropic crystal has a permittivity tensor ~ ~ = xx x x + yy y y + zz z z where xx , yy , and zz are all real constants > 0. Now assume that we introduce a propagating wave of frequency . (a) If the magnetic field of the wave takes the form ~ H = H exp(- j ~ ~ r ) , where ~ = 1 ( z cos( ) + x sin( )), what is the wave dispersion (re- lation between 1 and )? Is the phase velocity of the wave con- stant? Calculate ~ D and ~ E , and express them in terms of frequency, wavenumber, and magnetic field. Are ~ E and ~ D parallel to each other? Under what conditions? (b) If the electric flux density of the wave takes the form ~ D = D exp(- j ~ ~ r ) , where ~ = 2 ( z cos( ) + x sin( )), what is the wave dispersion (re- lation between 2 and )? Is the phase velocity of the wave con-)?...
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