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Unformatted text preview: Lecture 7 TimeDomain Description of Optical Nonlinearities FrequencyDomain (FD) descriptions of nonlinearities apply to monochromatic input fields. FD relates the nonlinear polarization to the input field TimeDomain (TD) descriptions of nonlinearities apply to arbitrary input fields. FD relates the nonlinear polarization to the input field TD is useful for short pulses and transient fields. FD and TD descriptions are entirely equivalent, and are chosen for convenience. ( ) P ϖ ( ) E ϖ ( ) P t ( ) E t 1 (1) where is linear response function relating response at time to input at time for all as required by causality (1) (1) ( ) ( ) ( ) P t R E t d ε τ τ τ ∞ = ∫ ɶ ɶ (1) ( ) R τ (1) P ɶ ( ) t E ɶ ( ) t τ (1) ( ) R τ = τ < TimeDomain to FrequencyDomain through Fourier Transform (FT/IFT) FT: (2) IFT: (3) Inverse Fourier Transform (IFT) of (1) (4) ( 29 ( ) ( ) exp E E t i t dt ϖ ϖ ∞∞ = ⋅ ∫ ɶ ( 29 1 ( ) ( ) exp 2 E t E i t d ϖ ϖ ϖ π ∞∞ = ⋅ ∫ ɶ...
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This note was uploaded on 01/10/2011 for the course ECE 615 taught by Professor Shalaev during the Fall '10 term at Purdue.
 Fall '10
 Shalaev
 Frequency

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