ECE615_Lecture_11

ECE615_Lecture_11 - 1 ℓ fraction of total power z = ℓ...

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Lecture 11 If highly reflecting mirrors are placed around the nonlinear medium to form an optical resonator, gain of the parametric amplification process can occur. This is known as a parametric oscillator (PO). 1 1 ϖ 2 3
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1 2 ( , ) ( , ) ( , ) E z t E z t E z t = + ɶ ɶ ɶ Second Harmonic Generation (SHG) (1) ( 29 ( , ) ( ) exp . . j j j E z t E z i t c c ϖ = - + ɶ ( 29 ( ) ( ) exp k j j j E z A z i z = - 2 (2) k j j j n c = 1 2 (1) ( ) j j n ε = 2 (1) 2 2 2 2 2 2 2 0 ( ) 1 j j j j E E P z c t c t - = ɶ ɶ ɶ (2) χ 1 2 1 2 = 0 z = z L =
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1 2 ( , ) ( , ) ( , ) NL P z t P z t P z t = + ɶ ɶ ɶ ( 29 ( , ) ( ) exp . . j j j P z t P z i t c c ϖ = - + ɶ [ ] * * 1 0 eff 2 2 0 eff 2 1 2 1 ( ) 4 4 exp (k k ) P z d E E d A A i z ε = = - ɶ 2 2 2 0 eff 1 0 eff 1 1 ( ) 2 2 exp( 2k ) P z d E d A i z = = ɶ 2 * 1 eff 1 2 p( k ) i d dA A i z - ∆ (3) (4) (5) Note that (4),(5) have different degeneracy factors. We obtain coupled-amplitude equations: 2 1 2 1 exp( k A A dz c = 2 2 2 eff 2 1 2 2 exp( k ) k i d dA A i z dz c = 1 2 k=2k k -
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k 0 ∆ = Previously with also with perfect phase matching In the general case, the solution can be expressed in terms of the Jacobi elliptic ( 29 (2) 2 2 2 2 1 sinc k 2 I I L L χ const A = 2 L α L 2 I functions. 1 0 2 ϖ
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Unformatted text preview: 1 ζ ℓ fraction of total power z = ℓ ( 29 1/2 1 2 1 eff 1 2 (0) n n c d A = = ℓ distance over which fields exchange energy Estimate value for for typical system with power and spot size Assume optimal focusing, i.e. spot size chosen so that depth of focal region is equal to the length Then 2 1 1 0 1 2 2 P I n cA w ε π = = ζ P w w b L 2 1 1 2 w n b L λ ≡ = 1/2 2 2 w 2 w NLO crystal and which for typical values 1 P A c L = 1/2 2 2 eff 3 1 2 1 16 d LP z cn n = = ℓ 12 6 eff 4 10 1 cm =1 W 0.5 10 m =2 m V d L P n--= × = = × 0.14 z = = ℓ b L =...
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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.

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ECE615_Lecture_11 - 1 ℓ fraction of total power z = ℓ...

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