Solving coupled wave equations

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The discussion focuses on challenges in solving coupled wave equations related to parametric amplifiers, particularly the assumptions of an undepleted pump wave and the impact of linear absorption on the signal and idler. A user points out a typo in equations 2.7 and 2.8, suggesting corrections to improve clarity. There is confusion about transitioning from equation 2.8 to 2.9, despite earlier equations being clear. A response indicates that the vector in equation 2.8 is general, implying the matrix must be zero, which affects the determinant. Overall, the conversation highlights the complexities of understanding the mathematical framework in this context.
linfocus
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1.
Just going through some material about parametric amplifiers but I have difficulties to see where the solution comes in given text.

In equations it is assumed undepleted pump wave and in equations there is loss caused by linear absorption for signal and idler.


2.
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p.s. There is a typo on the equation 2.7. With alpha and gamma it should be i instead of s. And in equation 2.8 the matrix element on the left and down should be E_p* instead of just E_p.


3.
For some reason I just don't get it how get from 2.8 to 2.9. Till 2.8 it was all clear. This is just bugging me badly.
 
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welcome to pf!

hi linfocus! welcome to pf! :smile:

the vector in (2.8) is general, so the matrix must be 0, so its determinant must be 0 :wink:

(writing X = \Gamma + α+ may help in the calculation)
 
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