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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 ~ ~ ε = ε xx ˆ x ˆ x + ε yy ˆ y ˆ y + ε zz ˆ z ˆ z where ε xx , ε yy , and ε zz are all real constants > 0. Now assume that we introduce a propagating wave of frequency ω . (a) If the magnetic field of the wave takes the form ~ H = H exp(- j ~ β · ~ r ) , where ~ β = β 1 (ˆ z cos( θ ) + ˆ x sin( θ )), what is the wave dispersion (re- lation between β 1 and ω )? 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 ~ β · ~ r ) , where ~ β = β 2 (ˆ z cos( θ ) + ˆ x sin( θ )), what is the wave dispersion (re- lation between β 2 and ω )? Is the phase velocity of the wave con-)?...

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