Is pertubation a linear operation?

[rkrishnasanka]

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.

 

[WWGD]

Do you have a formula / algebraic expression to describe the coupling and/or decoupling?

 

[rkrishnasanka]

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.

 

[HallsofIvy]

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.