If n is infinity, wavelength is equal to what?

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SUMMARY

The discussion centers on the relationship between the refractive index (n) and wavelength in the context of surface plasmon dispersion relations. According to the equation presented in the referenced paper by Barnes et al. (2006), the wavelength is proportional to the square root of n. However, participants clarify that allowing n to approach infinity does not yield an infinite wavelength; instead, it results in a finite limit when considering the permittivity (ε) parameters in the equation.

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Amany Gouda
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in the dispersion relation of the surface plasmon

the wavelength is proportional to square root of n. according to equation 5 in this paper:
https://Newton.ex.ac.uk/research/emag/pubs/pdf/Barnes_JOA_2006.pdf
if n goes to infinity, then what will be the value of wavelength.
Thank you
 
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I don't see any n that could go to infinity in equation 5, and if you let one of the ε go to infinity (keeping the other constant) the square root has a finite limit.
 
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