Understanding the Negative Sign in Laser Linewidth Calculation

[dziech]

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.

 

[BvU]

If the wavelength increases, the frequency decreases, hence the minus sign. That's all !

 

[dziech]

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

 

[BvU]

differences have a sign: a-b = -(b-a)

width is an absolute value of a difference

 

[dziech]

That clicked! :D I can finally sleep peacefully ;) Thanks!