Mode Matching a Cavity: Best Practices Explained

[Malamala]

Hello! What is the best way to mode match a cavity in practice? I know the laser spot size before it enters the cavity, but I don't know what the beam spot size should be inside the cavity, so I am not sure how I should adjust the size of the laser spot such that it matches the one that builds up inside the cavity. I tried to just maximize the power output from the cavity several times, but every time the mode leaving the cavity is a higher order one (not the T00 that I want), so I am not sure how to proceed. Can someone advise me on this? Thank you!

 

[Twigg]

Sorry this post will be super rough.

1) You can calculate the ideal spot size of the beam as it enters the cavity. I don't have time to go in depth (sorry :/), but the math for a simple two-mirror cavity is the same as for an infinite series of thin lenses separated by the cavity length. Each lens represents one reflection off the curved cavoty mirror. The condition for mode matching is that the spot size needs to be the same at every lens in the series. My preference is to set up a system of ABCD matrices and solve for the q-parameter of the incident beam. For your bowtie, you can ignore the non-curved mirrors. All that matters is the two curved mirrors and the distance traversed between them.

2. If you're getting higher order modes, the problem is alignment not spot size. Add some wedges and a CCD camera to the transmitted beam so you can see which mode you have.

3. Every time you change the spot size, you need yo re-do the alignment. Its a 5 parameter walk (1 spot size + 4 alignment). It sucks but thems the way it is.

4) How are you measuring transmitted power? A picture of your technique would be nice

 

[Twigg]

Just wanted to supplement the information I posted about calculating the mode-matching conditions.

You can treat your bowtie cavity the same as a Fabry-Perot cavity, where the spacing of the Fabry-Perot is given by the distance the travels in the bowtie between the two curved mirrors. The mathematical condition for mode-matching a Fabry-Perot cavity is given by: $$\left( \begin{matrix} kq \\ k \end{matrix} \right) = \left( \begin{matrix} 1 & d \\ -1/f & 1 - d/f \end{matrix} \right) \left( \begin{matrix} q \\ 1 \end{matrix} \right)$$
where d is the distance between curved mirrors and f is the focal length of the curved mirrors (half the radius of curvature)
Solve the above equation for k and q. The value of k is meaningless, but it's a necessary step in finding the value of q. This q is the q-parameter of gaussian optics.

This procedure gives the you q-parameter just inside the cavity. You can ignore the difference between inside and outside of the cavity. This math will get you close to where you need to be, and the rest will be solved experimentally by fine-tuning.