Solving coupled wave equations

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SUMMARY

This discussion focuses on solving coupled wave equations in the context of parametric amplifiers, specifically addressing the assumptions of undepleted pump waves and linear absorption losses for signal and idler waves. Key equations referenced include equation 2.7, which contains a typographical error regarding the use of 'i' instead of 's', and equation 2.8, where the matrix element should be corrected to E_p*. The transition from equation 2.8 to 2.9 is highlighted as a point of confusion, with the determinant of the matrix needing to be zero for the solution to be valid.

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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 = [itex]\Gamma[/itex] + α+ may help in the calculation)
 

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