Is This Method for Laser Cavity Length Calculation Accurate?

[Biest]

Hi,

So I have a lab question for which I have to drive a formula to find the optical cavity length of a laser, $$L$$. I have results from testing the fringe patterns when I move one of the mirrors in a Michelson interferometer. It shows the typical $$\frac{\sin x}{x}$$ pattern. To find the cavity length, I use the distance between two high amplitude peaks, $$d$$, and the refractive index of the material inside the cavity, silicon in this case so 4.01. What I did was this, since the distance between peaks is the time between a wave has traveled $$2L$$, I figured that this formula has to be true:

$$\frac{2Ln}{c} = \frac{d}{c}$$

which will give me

$$2Ln = d$$


Is this accurate?

Thank you very much in advance.

Cheers,

Biest

 

[Twigg]

If I'm inferring what you did in lab correctly, you must have a Michelson interferometer with a variable path length difference ($d$) and you are using a multimode laser as a light source. You scan the interferometer path length difference and you record the intensity of the fringe. As you scan the path length difference of the interferometer, you will find path lengths for which some of the laser modes constructively interfere. The distance between two adjacent laser modes that constructively interfere tells you the FSR of the laser cavity.

If $d$ here means the total difference in path length between the reference arms (as opposed to the difference in mirror position measured relative to the beamsplitter), then yes your formulas are correct: $2Ln = d$.