- #1
kelly0303
- 573
- 33
Hello! I need to calculate the ABCD matrix for a thick concave mirror, in the situation in which the light comes from the plane side of the mirror, and it is the concave part that is coated (for reference, I have a Fabry Perot cavity with 2 concave mirrors, and I want to mode match the laser coming from outside). The mirror has a radius of curvature R, a thickness d and an index of refraction n. The way I was thinking to do it, was to treat the mirror as a thick slab of index of refraction n and thickness d, which has the ABCD matrix:
$$
\begin{pmatrix}
1 & d/n\\
0 & 1
\end{pmatrix}
$$
plus a concave lens of focal length ##-R/2##, with R here being positive, so f being negative (I assumed it is concave, as the light coming from the direction I need here would diverge upon reflection) which has the ABCD matrix:
$$
\begin{pmatrix}
1 & 0\\
2/R & 1
\end{pmatrix}
$$
Overall, the total ABCD matrix would be:
$$
\begin{pmatrix}
1 & 0\\
2/R & 1
\end{pmatrix} \times
\begin{pmatrix}
1 & d/n\\
0 & 1
\end{pmatrix} =
\begin{pmatrix}
1 & d/n\\
2/R & 1+\frac{2d}{nR}
\end{pmatrix}
$$
Is this right? Can someone tell me how to fix it, in case it is wrong? Thank you!
$$
\begin{pmatrix}
1 & d/n\\
0 & 1
\end{pmatrix}
$$
plus a concave lens of focal length ##-R/2##, with R here being positive, so f being negative (I assumed it is concave, as the light coming from the direction I need here would diverge upon reflection) which has the ABCD matrix:
$$
\begin{pmatrix}
1 & 0\\
2/R & 1
\end{pmatrix}
$$
Overall, the total ABCD matrix would be:
$$
\begin{pmatrix}
1 & 0\\
2/R & 1
\end{pmatrix} \times
\begin{pmatrix}
1 & d/n\\
0 & 1
\end{pmatrix} =
\begin{pmatrix}
1 & d/n\\
2/R & 1+\frac{2d}{nR}
\end{pmatrix}
$$
Is this right? Can someone tell me how to fix it, in case it is wrong? Thank you!