Converting between Wavelength and Frequency in Resonators

AI Thread Summary
The discussion focuses on converting between wavelength and frequency in resonators, specifically addressing how to find the frequency linewidth Δν from a given wavelength linewidth Δλ. The relation Δλ/λ = Δν/ν is confirmed as correct, indicating that the percentage error in wavelength corresponds to the percentage error in frequency. A user inquires about calculating the separation in wavelength for a resonator with a specific length, noting that the previous equation is not applicable in this context. The Free Spectral Range is mentioned as a critical factor, with a specific example of 50 THz separation for a resonator length of 3 microns. Understanding these conversions is essential for accurate measurements in optical resonators.
Niles
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Homework Statement


Hi

Say I have an energy level centered around λ with some linewidth Δλ, and I wish to find the corresponding frequency linewidth Δν. What I would use is the following relation

Δλ/λ = Δν/ν.

Is this correct?

Thanks in advance.


Niles.
 
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Yes. It amounts to saying the % error in wavelength is the same as the % error in frequency. This is true because c = f*λ, λ = c/f. No error in c, % errors add when multiplying or dividing.
 
Thanks! If I have a resonator with length e.g. L=3 micron, then the resonances are separated by (the Free Spectral Range c/2L) 50 THz. If I want to find the corresponding separation in wavelength, then how would I do that? I can't use my equation in the previous post, since that is associated with an error.
 

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