Understanding the Negative Sign in Laser Linewidth Calculation

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Discussion Overview

The discussion revolves around the interpretation of the negative sign in the calculation of laser linewidth, specifically how changes in wavelength relate to changes in frequency. Participants explore the implications of these relationships in the context of laser physics.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant calculates the frequency from wavelength using ν=c/λ and expresses confusion about the negative sign in the linewidth formula Δν=cΔλ/λ².
  • Another participant suggests that the negative sign arises because an increase in wavelength corresponds to a decrease in frequency.
  • A different participant questions whether they are misunderstanding the concept, noting that while Δν represents a linewidth in frequency, Δλ should also be considered in terms of its sign.
  • One participant emphasizes that differences have a sign, indicating that width is an absolute value of a difference.
  • A later reply indicates that the explanation provided helped clarify the confusion regarding the negative sign.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the negative sign, with some agreeing on its physical interpretation while others remain uncertain about the implications of the signs in the context of linewidth and wavelength changes.

Contextual Notes

Participants do not fully resolve the conceptual nuances regarding the interpretation of the negative sign and its physical meaning in the context of laser linewidth calculations.

dziech
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Hi guys,

It's one of the questions I'm asking myself needlessly but I really wonder about this ;)

Say I have a laser at a wavelength λ. I can calculate the frequency by ν=c/λ. Then the linewidth Δν=cΔλ/λ2 that can be found through differentiation of two sides of the equation. The question is, where does the minus go though? It should be Δν=-cΔλ/λ2 should it not? I can't think of what does the negative physically mean here and that's my question.
 
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If the wavelength increases, the frequency decreases, hence the minus sign. That's all !
 
Am I just thinking of this the wrong way? I mean, Δν is a linewidth in frequency. Say it's 60GHz, the Δλ should be like 0.2nm at 1um, but it would be -0.2nm wouldn't it? Or should I think of it as Δν change in linewidth? But that doesn't make obvious sense to me. It's one of the questions I should probably not think about too much but my brain keeps doing things to me ;D
 
differences have a sign: a-b = -(b-a)

width is an absolute value of a difference
 
That clicked! :D I can finally sleep peacefully ;) Thanks!
 
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