Is pertubation a linear operation?

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The discussion centers on the classification of perturbation theory in the context of electromagnetic coupling in waveguide structures. There is a debate on whether the coupling interaction is non-linear, and its implications for the perturbation operation used to derive coupling results. The original poster believes that perturbation is a linear operation, similar to its application in quantum mechanics, where non-linear problems often begin with a linear approximation. They seek clarification on whether a deeper interaction exists between the waveguides and request formulas for coupling and decoupling. The conversation highlights the complexities of applying linear perturbation theory to potentially non-linear interactions in electromagnetic systems.
rkrishnasanka
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My question stems from a discussion I had with my colleague today. In Electomagnetic coupling , like in waveguide structures. We apply pertubation theory to find out the coupling between various modes that get coupled in the device.

My colleague said that the coupling interaction was non-linear. Its interesting but I don't know if the interaction can be classified as an non-linear interaction. Also what would it mean for the pertubation operation that is used for theoretically getting the result of the coupling. Would it be an linear approximation to a nonlinear interaction. Is there a deeper interaction between the waveguides that I'm missing out.
 
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Do you have a formula / algebraic expression to describe the coupling and/or decoupling?
 
WWGD said:
Do you have a formula / algebraic expression to describe the coupling and/or decoupling?

I'll put up the derivation tomorrow. I'd like to know if I'm missing out something. I was under the impression that the perturbation used in the entire derivation was still a linear operation. Just like it is Quantum mechanics also.
 
Every (differentiable) function can be approximated by a linear function over some short region. Typically what is done with non-linear problems is to start with a linear approximation.
 

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