Superposition principle in arbitrary medium

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Discussion Overview

The discussion centers on the applicability of the superposition principle for wave equations, particularly in the context of electromagnetic waves traveling through non-homogeneous and anisotropic media. Participants explore whether waves can be represented as sums of waves along principal axes defined by the dielectric tensor.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions if the superposition principle holds in non-homogeneous and anisotropic media, specifically regarding the representation of waves in arbitrary directions.
  • Another participant notes that the superposition principle is violated in nonlinear materials, citing examples such as the Stark and Kerr effects, and mentions the Wolf effect as a potential exception.
  • A subsequent post seeks clarification on whether superposition holds as a general rule in linear media.
  • One participant affirms that superposition holds in linear media, stating they are unaware of any exceptions.

Areas of Agreement / Disagreement

Participants express differing views on the conditions under which the superposition principle applies, particularly regarding linear versus nonlinear media. The discussion remains unresolved on the broader implications for non-homogeneous and anisotropic media.

Contextual Notes

Participants have not fully explored the implications of specific nonlinear effects on the superposition principle, and there may be assumptions about the linearity of the medium that are not explicitly stated.

Heirot
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Does the superposition principle for wave equations (say electromagnetic) hold also for non homogeneous and anisotropic media? I.e. can one always represent a wave traveling in an arbitrary direction as a sum of waves propagating along the principal axes of, e.g. dielectric tensor \epsilon_{ik}?

Thanks
 
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The superposition principle is violated in nonlinear materials- some basic examples are the Stark and Kerr effects.

Another effect is the spectral changes that occur as partially coherent light propagates in free space (sometimes called the Wolf effect)- but this may not count as a violation of superposition.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2915902/

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVF-46JGT6V-GM&_user=10&_coverDate=09%2F01%2F1990&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1500898854&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=4d4d39ef9500de32bd2e9337d46bda5b&searchtype=a
http://www.opticsinfobase.org/abstract.cfm?uri=josaa-7-9-1591
 
So, as long as the medium is linear, superposition holds as a rule?
 
Yes- at least, I am unaware of any exceptions.
 

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