finesse.components.mirror.Mirror.ABCD

Mirror.ABCD(from_node, to_node, direction='x', symbolic=False, copy=True, retboth=False)[source]

Returns the ABCD matrix of the mirror for the specified coupling.

In both cases below, the sign of the radius is defined such that \(R_c\) is negative if the centre of the sphere is located in the direction of propagation.

Transmission

../../../../_images/abcd_mi.svg

For transmission this is given by,

\[M_{t} = \begin{pmatrix} 1 & 0 \\ \frac{n_2 - n_1}{R_c} & 1 \end{pmatrix}, \]

where \(n_2\) and \(n_1\) are the indices of refraction of the spaces connected to the mirror and \(R_c\) is the radius of curvature of the mirror.

The matrix for transmission in the opposite direction of propagation is identical.

Reflection

../../../../_images/abcd_mr.svg

In the case of reflection the matrix is,

\[M_{r} = \begin{pmatrix} 1 & 0 \\ -\frac{2n_1}{R_c} & 1 \end{pmatrix}. \]

Reflection at the back surface can be described by the same type of matrix by setting the \(C\) element to \(C = 2n_2/R_c\).

See Connector.ABCD() for descriptions of parameters, return values and possible exceptions.