ECE615_Lecture08

ECE615_Lecture08 - Lecture 8 The Wave Equation for...

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Unformatted text preview: Lecture 8 The Wave Equation for Nonlinear Optical Media Laser field induces polarization at new frequency components. Generation of new components are described by Maxwells equations. dipole radiation pattern 1 2 1 2 + 1 2 + 3 1 2 = + 1 N atoms: if the relative phasing of the dipoles is correct, the field radiation by each dipole will add constructively in the forward direction, leading to radiation in the form of a well-defined beam. Acts as a phased array of dipoles if the phase-matching condition is satisfied. Forward intensity is N 2 larger than single atom. 1 2 + Consider a second-order NL process such as sum-frequency generation (SFG). Maxwells Equations (omit the arrow sign, for simplicity) (1) (2) (3) (4) D B B E t D H J t = = = - = + = 2 with no free charges and no free currents the material is nonmagnetic (5) Polarization vector ( ) nonlinearly depends on (6) substituting (4), then (5) (7) J = = B H = r D E P E = + = P E ( 29 or B E E B t t = - = - 2 2 2 2 2 2 2 2 2 2 2 1 1 1 E D D E P t c t c t c t = - = - = -- remember that: but since so so (7) becomes (8) If we define where all nonlinear contributions are in 2 2 2 2 2 2 2 1 1 E E P c t c t - =...
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ECE615_Lecture08 - Lecture 8 The Wave Equation for...

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