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ECE615_Lecture_25

ECE615_Lecture_25 - Lecture 25 Optical Wave Mixing in...

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(1) Saturation Spectroscopy setup: One determines how the response of the medium to the probe wave is modified by the presence of the pump wave. Lecture 25 Optical Wave Mixing in Two-Level Systems strong pump weak probe ϖ ϖ δ ϖ δ measure transmission of probe wave atomic vapor (2) Multiwave mixing 1 strong pump weak probe ϖ ϖ δ ϖ δ atomic vapor ϖ δ - ϖ ϖ ϖ δ ϖ ϖ δ - a b Forward 4-wave mixing (generation of the symmetric sideband at frequency ) ϖ δ -
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At low intensities of the pump laser: (perturbation theory) absorption and dispersion experienced by the probe wave is somewhat reduced by the presence of the pump ) At high intensities of the pump laser: (perturbation theory is not enough) atomic energy levels are strongly modified => new resonances. 2 pump ( ) I I ϖ δ - Solution of the Density Matrix Equations for a 2-level Atom in the Presence of Pump and Probe Fields ( 29 exp . . E E c c i t ϖ = + - ɶ w ρ ρ = - complex dipole amplitude : expectation value 2 bb aa ab ba p μ σ = ( 29 exp . . d p p c c i t ϖ = + - ɶ ɶ p ɶ 2 2 1 ba i i p p Ew T μ ∆ - = - ɺ ( 29 * 1 4 Im eq w w w pE T - = + ɺ
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Solution: exact for the field and the lowest order in the amplitude the steady-state solution is in the form: -the solution when only the pump field is present ba w w ∆ = - ( 0 1 exp E E E i t δ = + - 0 E 1 E ( ( 0 1 1 exp exp p p p p i t i t δ δ - = + + - ( ( 0 1 1 exp exp w w w w i t i t δ δ - = + + - 0 0 , p w 0 E [ ] ( 29 [ ] 0 1 ( ) exp exp . . E t E E c c i t i t ϖ ϖ δ = + + - - + ɶ 0 1 E E oscillations of the pump-probe frequency difference 3 0 1 p p ± 0 1 w w ± * 1 1 w w - = ( 0 1 ( ) 2 cos w t w w t δ φ = + phase ( ( ) 2 2 2 0 2 2 2 2 1 2 1 1 eq w T w T TT + ∆ = + ∆ + Ω
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( ( ) 2 2 2 0 2 2 2 2 1 2 1 1 eq w T w T TT
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