Is pertubation a linear operation?

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Discussion Overview

The discussion revolves around the nature of perturbation theory in the context of electromagnetic coupling in waveguide structures. Participants explore whether the perturbation operation can be classified as linear, especially in relation to potential non-linear interactions in coupling various modes within the device.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions whether the coupling interaction in waveguide structures can be classified as non-linear and what implications this has for the perturbation operation used in theoretical analyses.
  • Another participant seeks a formula or algebraic expression to describe the coupling and decoupling processes, indicating a desire for a more concrete mathematical framework.
  • A later reply suggests that the perturbation used in the derivation is still a linear operation, drawing a parallel to its application in quantum mechanics.
  • Another participant notes that every differentiable function can be approximated by a linear function over a short region, implying that non-linear problems often begin with a linear approximation.

Areas of Agreement / Disagreement

Participants express differing views on whether the perturbation operation is linear or non-linear, indicating that multiple competing perspectives remain unresolved.

Contextual Notes

The discussion does not resolve the assumptions regarding the nature of the perturbation operation or the specific mathematical expressions involved in the coupling and decoupling processes.

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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