ECE615_Lecture_22

ECE615_Lecture_22 - In simple cases we use power expansion:...

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Unformatted text preview: In simple cases we use power expansion: But does not work for all cases, such as Saturable Absorption. Lecture 22 Nonlinear Optics in the Two-Level Approximation (1) (2) 2 (3) 3 ( ) ( ) ( ) ( ) ... P t E t E t E t = + + + 2 n c 1 s I I = + a b is weak-field absorption. is saturation intensity (and optical constant for the material). Expands to: Only converges for , which is not always realistic. Use nonperturbative approach. 1 2 I n c E = s I ( 29 ( 29 ( 29 2 3 1 ... s s s I I I I I I =- +- + s I I < Collection of 2-level atoms: (1) no damping effects ( ) H H V t = + a a E = b b E = 0, | | nm n nm H E n H m = = ( ) ( ) V t E t = - aa bb aa bb V V = = = = (omit the signs of vectors and dot-product) 2 * ( ) ba ab ba V V E t = = - aa ab ba bb = * ab ba = [ ] ( 29 ( 29 ( 29 , = nm nm nm nm nv vm nv vm v i i H H H i H V - = - = - -- [ ] nm nm nm nv vm nv vm v i i V V = --- ( 29 ( 29 ( 29 ba ba ba ba bb aa bb ba ab ba ab aa ab ba ab ba i i V i V V i V V = - +- =- =- 1 aa bb aa bb + = + = 3 (1) Closed two-level atom upper level (2) decays to the lower level at a rate lifetime of the upper level is given by Typically, the decay of the upper level would be due to spontaneous emission (population remains within system, i.e. closed....
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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 University-West Lafayette.

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ECE615_Lecture_22 - In simple cases we use power expansion:...

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