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Feb10_numerical aperture_slab_with notes

# Feb10_numerical aperture_slab_with notes - 2 n i 2-β 2 x...

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Today Numerical Aperture (65-67) Start slab waveguides (44-55)

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Numerical Aperture What is the maximal incident angle for which light will couple into the waveguide?
Angle of Incidence as Function of Critical Angle

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Numerical Aperture of a GaAs/AlAls Waveguide

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Numerical Aperture of a Silicon Waveguide
Slab Waveguide

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Slab Waveguide 2 E y + K 0 2 n i 2 E y = 0 In each region the wave equation is given by:
Wave Propagation in a Slab Solution: E y = E 0 e ± β 2 - K 0 2 n i 2 x for β K 0 n i E 0 e ± j K 0 2 n i 2 - β 2 x for β < K 0 n i

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Wave Propagation in a Slab Solution: E y = E 0 e ± β 2 - K 0 2 n i 2 x for β K 0 n i E 0 e ± j K 0 2 n i 2 - β 2 x for β < K 0 n i How can we change β?
What is the range of wavectors allowed? E y = E 0 e ± β 2 - K 0 2 n i 2 x for β K 0 n i E 0 e ±

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Unformatted text preview: 2 n i 2-β 2 x for β< K n i E y ( x ) = A e-γ c x x Bcos K f x ( 29 + C sin K f x ( 29 < x <-h D e c x + h ( 29 x <-h What are the values of when there is guiding? β n = β 2-K 2 n i K f = K 2 n i 2-β 2 A e-γ c x x Bcos K f x ( 29 + C sin K f x ( 29 < x <-h D e c x + h ( 29 x <-h Lets just look at the guiding region n = β 2-K 2 n i K f = K 2 n i 2-β 2 Effective index and Degree of confinement vs. angle of propagation...
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