# Laser Modes/Free Spectral Range

1. Mar 15, 2005

### zeta101

Hi,

As we know, lasers have longitudinal modes, the seperation between neighbouring modes (measured in frequency) is:

$$\Delta \nu = \frac{c}{2L}$$

and by using the fact that:

$$\frac{\Delta \nu}{\nu} = \frac{\Delta \lambda}{\lambda}$$

we obtain the seperation between neightbouring modes as (in wavelength):

$$\Delta \lambda = \frac{\lambda^2}{2L}$$

Now, the question I have is that I have read that there is something called the Free Spectral Range (FSR) which is defined as the seperation between longitudinal modes (and has the same formula as $$\Delta \lambda$$...however for various reasons I think that the FSR is a term than can only be used to describe Fabry-Perot Interferometers (which, as I understand just simulate a laser cavity and will only transmit modes that obey the "integer number of half wavelengths")...

Erm, yes the question I have, what I want to know is can I use the term FSR in place of longitudinal modes when talking about laser cavities and is the $$\Delta \lambda$$ equation above correct for laser cavities (and thus for FPI's too?)

Thanks!

James

Last edited: Mar 15, 2005
2. Mar 15, 2005

### Claude Bile

The reason the equations look similar is because we are looking for a resonance condition between two mirrors.

In a FP etalon, we are passing light through the cavity and looking at the resultant fringe pattern. In a laser, we are using an active medium to generate light within the cavity.

If we removed the active medium, a parallel plate cavity would behave as a FP etalon and we could apply things like FSR and so on to it, however practical lasers use at least one curved mirror, usually two.

So no, you cannot interchange the term FSR with the term longitudinal mode.

Regarding your second question, the equation is correct for a Fabry Perot etalon placed within a laser cavity to give an additional resonance condition, thus separating the longitudinal modes further. The equation you gave is correct for FP etalons in general, however it is not usually put in that fashion, mainly because all wavelengths satisfy that condition, it is the variation of ray angle with wavelength that is interesting.

Regards,
Claude.

3. Mar 16, 2005

### zeta101

thank you for the reply Claude.

So the FSR is the longitudinal spacing of the modes only when the mirrors (or reflecting surfaces) are planar? otherwise we just just the term longitudinal spacing?

About my second question, I was asking if the $$\Delta \lambda$$ equation is correct for a laser cavity on its own, i know that it is true for FPI's (although not interesting as you pointed out). The project I'm working on has the mode spacing (for a laser) defined this way (as it helps with explanations of other things) but I have read in a book and in a user manual for a grating stabilised laser about the FSR as if its something that can be attributed to laser cavities.

The actual laser i am using is an extended cavity semiconductor laser, so it has a laser diode in (which has 2 planar reflecting facets correct?) and then an angled diffraction grating, which is also planar (but as i said its not 90deg to the optical axis). If i am dealing with such a laser would you now say it is correct to use the term FSR? otherwise i will be at a loss with the literature i have.

Thanks again :)

4. Mar 16, 2005

### Claude Bile

Yes, the equation is correct for a laser.

The term FSR can be applied to a laser cavity, but the term cannot be interchanged with the term longitudinal mode.

As far as I know, any stable cavity can have the term FSR applied to it, but in this context the term FSR simply means, as you put it, longitudinal mode separation, which is different to how the term FSR is used with FP etalons. However, there are other factors that also define the longitudinal mode spacing, for example the active laser medium and the presence of intracavity devices.

When using the term FSR for your cavity, you must be very precise about what you are referring too, as both the laser cavity and the diffraction grating both have FSR's, and the longitudinal mode spacing will be different again.

Keep in mind that FSR refers to the laser cavity, wheras 'longitudinal mode' refers to the laser itself.

I hope I am not confusing you.

Claude.

5. Mar 16, 2005

### zeta101

Thanks, it makes a lot more sense now, and also, thinking about what the actual words mean in FSR, the range (ie a distance) that is free of spectral lines? (ie the distance betweeen spectral lines, or different modes since the modes correspond to slightly different wavelengths).

I am aware that the external cavity laser will have both an FSR for the laser diode cavity and for the external cavity, this has a significance for the project.

Does this sound reasonable?
James

6. Mar 17, 2005

### Claude Bile

The term FSR is borrowed from Fabry Perot interferometers, and describes the maximum spectral range one can arbitrarily resolve without neighbouring maxima interfering with the measurement. In a FPI, the smaller the FSR, the greater the resolution and vice versa.

The FSR would be equivalent to the spacing between peak maxima in the spectrum.

Having two FSR's sounds entirely reasonable.

Claude.