Is pertubation a linear operation?

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SUMMARY

The discussion centers on the classification of perturbation theory in electromagnetic coupling, particularly within waveguide structures. The user questions whether the coupling interactions are non-linear and how this affects the perturbation operation used to derive coupling results. They assert that perturbation theory, similar to its application in quantum mechanics, typically begins with a linear approximation, even in the context of non-linear problems. The user seeks algebraic expressions to describe coupling and decoupling in these systems.

PREREQUISITES
  • Understanding of perturbation theory in electromagnetic coupling
  • Familiarity with waveguide structures and their operational principles
  • Basic knowledge of linear and non-linear interactions in physics
  • Concepts of quantum mechanics and linear approximations
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  • Research perturbation theory applications in electromagnetic fields
  • Study the mathematical formulations of coupling and decoupling in waveguides
  • Explore non-linear dynamics in waveguide interactions
  • Investigate the role of linear approximations in solving non-linear problems
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Physicists, electrical engineers, and researchers involved in electromagnetic theory, particularly those working with waveguide structures and perturbation analysis.

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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