Complex amplitude of E-field and phase changes

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SUMMARY

The discussion focuses on the behavior of the complex amplitude of the electric field (E-field) in electromagnetic waves when interacting with dielectrics, specifically referencing the Fresnel equations. It establishes that a positive complex amplitude, represented as E0eiΦ, indicates no phase change upon reflection, while a negative amplitude results in a phase change of π. This phase change occurs because the reflected E-field is inverted relative to the incoming E-field, which is mathematically expressed as exp(iπ) = -1.

PREREQUISITES
  • Understanding of electromagnetic waves and their properties
  • Familiarity with complex numbers and their representation in physics
  • Knowledge of the Fresnel equations and their application in optics
  • Basic concepts of phase changes in wave mechanics
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  • Study the derivation and applications of the Fresnel equations in different dielectric materials
  • Explore the implications of phase changes in wave interference patterns
  • Learn about the reflection and transmission coefficients in various media
  • Investigate the role of complex amplitudes in other wave phenomena, such as sound waves
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Physicists, optical engineers, and students studying electromagnetism or wave optics who seek to deepen their understanding of wave behavior at dielectric interfaces.

km707
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Hi,

I'm looking through my notes on em waves in dielectrics and the fresnel equations and I've been stuck on this for a while.

It states that if the complex amplitude = E0eiΦ is positive there is no phase change. However when the value is negative, the phase change Φ is π.. Why is that?

Thanks in advance!
 
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It just means that after reflection from the surface of an insulator, then the reflection coefficient (the fraction between the incoming and reflected amplitude) might be either negative or positive. If positive, there is no phase change. If it is negative, then it means that the reflected E-field "points the other way" compared to the incoming E-field - which is just a π-change in phase (recall exp(iπ) = -1).
 

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