Converting between Wavelength and Frequency in Resonators

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SUMMARY

The discussion centers on the relationship between wavelength and frequency in resonators, specifically using the equation Δλ/λ = Δν/ν to relate linewidths. Niles confirms that this equation is valid, stating that the percentage error in wavelength corresponds to the percentage error in frequency due to the constant speed of light (c). Additionally, the Free Spectral Range (FSR) for a resonator of length L=3 microns is calculated to be 50 THz, prompting a query on how to convert this frequency separation into wavelength separation.

PREREQUISITES
  • Understanding of basic wave mechanics, specifically the relationship between wavelength and frequency.
  • Familiarity with the concept of Free Spectral Range (FSR) in optical resonators.
  • Knowledge of the speed of light and its role in wave equations.
  • Basic proficiency in handling equations involving ratios and percentage errors.
NEXT STEPS
  • Study the derivation and implications of the Free Spectral Range (FSR) in optical systems.
  • Learn how to convert frequency separations to wavelength separations in resonators.
  • Explore the impact of linewidth on resonance quality and stability in optical devices.
  • Investigate the applications of wavelength and frequency conversions in photonics and telecommunications.
USEFUL FOR

Students and professionals in physics, optical engineering, and telecommunications who are working with resonators and need to understand the conversion between wavelength and frequency.

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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