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Unformatted text preview: 31 TE modes in dielectric slab waveguides As frequency f increases well beyond the microwave range, the cutoff wavelength c = 2 a 1 = c f of the TE 10 of mode will dip towards m scales. Guiding structures with m scales can be more naturally implemented as dielectric slabs as opposed to hollow waveguides. Optical integrated circuits contain many such channels of dielectric slab waveguides . In this lecture we will examine briefly the guidance conditions and dispersion characteristics encountered in dielectric slab waveg- uides. Consider a slab of dielectric material of refractive index n 1 = 1 r of a width d embedded in a dielectric with a smaller refractive index n 2 = 2 r . Propagati ng modes of frequency f can be trapped and guided in the slab with the refractive index n 1 > n 2 , z x d n 2 n 2 n 1 > n 2 i Guidance requires i > c = sin- 1 n 2 n 1 so long as the mode can be represented as a superposition of un- guided TEM waves reflected from plane boundaries of regions with index n 1 and n 2 with an incidence angle i larger that c , where c = sin- 1 n 2 n 1 is the critical angle for total internal reflection (TIR). Recall that when TIR occurs, the reflected wave has the same amplitude as the incident wave, while an evanescent transmitted 1 wave is found in the second region. If i < c no guidance can occur since the transmitted fields in that case would be propagating...
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