Derive an expression for ratio of proportionality constants

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Reference no: EM13984928

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).

Reference no: EM13984928

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