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ECE615_Lecture_10

ECE615_Lecture_10 - Lecture 10 Manley Rowe Relations For...

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Lecture 10 Manley –Rowe Relations For lossessmedia (1) (2) * * 0 2 i i i i i i dI dA dA n c A A dz dz dz ε = + 1 ϖ 2 ϖ 3 ϖ * 0 2 i i i i I n cA A ε = * * * * 1 0 eff 1 3 1 2 0 eff 1 3 1 2 4 exp( k ) . . 8 Im exp( k ) dI d iA A A i z c c d A A A i z dz ε ϖ ε ϖ = - ∆ + = - - ∆ * * 2 8 Im exp( k ) dI d A A A i z ε ϖ = - - ∆ 1 (3) Manley-Rowe (1959) 0 eff 2 3 1 2 dz * * * 3 0 eff 3 3 1 2 0 eff 3 3 1 2 8 Im exp( k ) 8 Im exp( k ) dI d A A A i z d A A A i z dz ε ϖ ε ϖ = - = - ∆ 1 2 3 I I I I = + + ( 29 * * 3 1 2 0 eff 1 2 3 3 1 2 0 8 Im exp( k ) dI dI dI dI d A A A i z dz dz dz dz ε ϖ ϖ ϖ = = + + = - + - - ∆ 0 3 1 2 1 2 3 I I I d d d dz dz dz ϖ ϖ ϖ = = - i i I ϖ Intensity of wave in photons per unit area per unit time
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Beams exchange photons, but total number is constant. Alternate representation of M-R relations: (a) (b) Three conserved quantities Rate of photon creation at equals rate of
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