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Field Distribution
The transverse distribution um(y) of the electric-field complex amplitude of a TE mode in a slab waveguide is given by:
um (Y) ∝ (cos(2Π.sinθm/λ) → m = 0,2,4,6 ...
(sin (2Π.sinθm/λ) → m = 1,3,5, ...for -d/2 ≤ y ≤ d/2
and
um(Y) ∝ (exp (-ymy) → y > d /2.
exp (ymy) → y < -d/2
Derive an expression for the ratio of the proportionality constants. Plot the distribution of the m = 0 TE mode for a slab waveguide with parameters n1 = 1.48, n2 = 1.46, d = 0.5 pm, and λ0 == 0.85 μm, and determine its confinement factor (percentage of power in the slab).
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