Talk:Ray transfer matrix analysis

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There appears to be a contradiction in this page.

1) From a thermodynamic consideration, AD-BC=1

2) The ray transfer matrix for a beam going from refractive index n1 to n2 is given by:

A=1, B=0, C=0 and D=n1/n2

This gives AD-BC=n1/n2

which is not equal to 1 in most cases.

I have been looking into this a bit, but still have no idea what the answer is.

So after reading Siegman's Lasers (Ch. 15) I learnt that in general AD-BC = n1/n2, which explains everything. I revised the article. Good catch. -- Pgabolde 15:59, 17 February 2006 (UTC)

1 Ray transfer matrices for gaussian beams
2 Normalisation of the Matrices
3 Renaming the article
4 Error in table?
5 matrix for curved mirror

[edit] Ray transfer matrices for gaussian beams

There is one subtility regarding the propagation of a gaussian beam from one region, region 1, with index of refraction n₁ to another region, region 2, with index of refraction n₂. The definition of 1/q involves the wavelength $λ$ , and it should be noted that $λ$ is different between region 1 and region 2 by a factor of $n_2\over n_1$ . It is necessary to take this into account when calculating the beam width in region 2 in order to have the beam width continous at the surface between region 1 and region 2. It took me a while to figure this out. Perhaps this should be added to the article?

[edit] Normalisation of the Matrices

In "Lasers" by Siegman, the ray transfer matrices are "reduced", meaning that the slopes of the rays are multiplied by the local refractive index. The consequence is that Snell's law is built into the matrices and the matrix for changing refractive index is just the identity matrix. This tends to make some things easier, and other things quite strange, for example the reflection from a curved surface depends on the local refractive index!

[edit] Renaming the article

I suggest renaming this article "Matrix formalism (optics)". I believe this is simpler, and perhaps more common name than "Ray transfer matrix analysis". Ahmes 10:31, 20 May 2006 (UTC)

I've never heard it called that, except as a general term (i.e. as one of any number of techniques in optics that uses matrices to do something). I prefer the term "ray transfer matrix", since that at least tells you what the matrix is doing. --Bob Mellish 18:48, 20 May 2006 (UTC)

Agreed. The term "ray transfer matrix" is the most commonly understood. Graceej 11:04, 29 November 2006 (UTC)

[edit] Error in table?

In the table it says: "In Propagation in free space or in a medium of constant refractive index" and the matrix: (1 d)(0 1)

But in a dielectric I think it is (1 d/n)(0 1) where n is the refractive index. So is it right to write "or in a medium of constant refractive index"?

The propagation in free space is the same as the propagation in a medium with a constant refractive index. i edited the remark for the translation matrix in the table of the ray transfer matrizes. See here. Here is an example of the method: http://www.ee.byu.edu/cleanroom/ABCD_Matrix_tut.phtml --141.35.186.111 19:46, 8 August 2007 (UTC)

[edit] matrix for curved mirror

The matrix element on the bottom left (2/R) needs to be negative for a focussing mirror. How you define R (negative or positive for convex or concave) is somewhat arbitrary.