Waveguide Theory Based on Wave Optics•Waveguides were discussed in terms of geometric optics or ray optics (Snell’s law total reflection etc)or ray optics (Snell s law, total reflection etc) •Geometric or ray optics fails to describe certain optical phenomena (interference, diffraction, polarization, etc)•More rigorous description is wave optics, or physical optics (under what conditions is geometric optics valid?)•In wave optics, waveguides are dealt with by solving Maxwell’s equations directly with appropriate boundary conditionsEEE537 Fall 2010 C.Z. Ning, ECEE ASU 1
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Planar Waveguide: Polarization ConstrainsGeneral solution of the field in a 2D waveguide with propagation direction along z]z)-i(ω[e)yx,(βtxpEE−=]z)-i(ω[e)yx,(βtxpHH−=β: propagation constant for propagating wave with given free space wavelength: ππλc22How do you determineβ?ωk0==EEE537 Fall 2010 C.Z. Ning, ECEE ASU Part of task of waveguide theory: solve wave equation with boundary conditions!How do you determine 2