Four waves mixing together are explained by four different coupled equation (Ref : GP Agarwal) But the methods to solve this equations are either by Split step Fourier Transform or FDTD. Why there is no direct solution possible from the Maxwel's Wave Equation?
I know this:
R.Conte and S.Bugaychuck, "Explicit solutions of the Four-wave mixing model" in J.Phys.A: Math. Theor. 42 (2009) 1922003.
Hope this helps
Closed-form solutions are possible in the domain of simplifying the situation, such as the assumption of an undepleted pump. In fact, the coupled equation framework assumes that the meaning of 'modes' make senses. However, if the physical situation is quite complicated where as the modes couldn't be clearly defined, the coupled mode theory would yield increasing error. Working in the Maxwell's equation framework allows handling of broader situations. However, again the mathematical construct is perhaps beyond any human's capability in the past history. Perhaps, you can try solve it?
Yes you question is absolutely correct..Only thins is to minimize the complexity.
If your better system and computational knowledge you solve this in matla. ... If you provide the papers related to this i can help you ...because i am very interested to do this type of problems...
I know this: R.Conte and S.Bugaychuck, "Explicit solutions of the Four-wave mixing model" in J.Phys.A: Math. Theor. 42 (2009) 1922003. Hope this helps
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