ECE615_Lecture_12

ECE615_Lecture_12 - Lecture 12 Nonlinear Optical...

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Nonlinear Optical Interactions with Focused Gaussian Beams 2 2 2 2 2 2 2 2 0 1 n n n E P n E c t c t ε - = ɶ ɶ ɶ Paraxial Wave Equation (1) are nonplane waves Considered in the approximation in which all interacting waves are infinite plane waves. In practice, the incident radiation is usually focused. ( 29 ( , ) ( ) exp k . . n n n E r t A r i z t c c ϖ = - + a a a ɶ , n n E P ɶ ɶ 1 (2) (3) is transverse Laplacian operator here in cylindrical coordinates Use slowly varying amplitude approximation (4) - paraxial wave equation n ( 29 ( , ) ( ) exp k . . n n n n P r t P r i z t c c = - + a a a ɶ 2 2 2 2 2 2 2 2 2 2 2 2 1 1 T T r z x y r r r r φ   ∇ = ∇ + ∇ = + = +     2 T ( 29 2 2 2 2 2 0 2 k exp k n n n T n n A i A P i z z c k k k n n ∆ = -
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ECE615_Lecture_12 - Lecture 12 Nonlinear Optical...

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