Talk:Ray transfer matrix analysis

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)

Importance
Among those that work with optics and especially systems of the aforementioned, these equations are used daily. Yet, they are rarely incoporated into grade/high school academics. Because this is used on a daily basis in the optics field but rarely taught in schools I believe it should recieve a "mid" ranking. --Frozenport (talk) 01:12, 26 June 2008 (UTC)

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 $$\lambda$$, and it should be noted that $$\lambda$$ 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?

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!

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)

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)

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.

reflection from flat mirror
This appears to be either incorrect or poorly defined. This identity matrix {{1,0},{0,1}} indeed describes reflection from a flat mirror, but only a flat mirror with a face parallel to the z plane (where the ABCD matrices are normally defined in a cartesian plane with z representing the horizontal direction, r representing the vertical direction, and theta being defined as delta r/delta z). If the mirror face is parallel to the r plane (the more common occurrence) the matrix would be {{1,0},{0,-1}}. None of this accounts for a mirror of arbitrary angle.

--71.178.207.74 (talk) 00:37, 20 January 2009 (UTC)mjd

I went to the talk page to see if anybody else had noticed. I am going to edit the matrix to display the proper [1,0;0,-1] should we add the proper matrix for mirror of arbitrary angle?90.185.47.8 (talk) 08:54, 17 May 2015 (UTC)

Comments for Examples in Gaussian Beam section
The articles includes two examples of Gaussian Beam propagation, through free space and a thin lens. Both have a statement afterward regarding the radius, but the statements are incorrect in the general case, and for any condition of which the statements are reasonable, there is no additional context provided so that the intended meaning is rather useless and/or misleading. Because an in-depth explanation is probably not appropriate for the article, I plan on removing the statements altogether unless someone shares a good explanation. My own arguments follow:

Free space:
The free-space example concludes with $$q_2 = q_1+d$$ and then says "traveling through free space increases the radius by d". But the wave-front radius is only related to the real part of the reciprocal of the q parameter, not the real part of the q parameter itself. Although the q parameter can be defined like in the article as its reciprocal, the q parameter can also be defined like $$q = \delta z + i\ z_R$$, where $$z_R$$ is the Raleigh length and $$\delta z$$ represents a displacement from the beam waist. In this view, we have that $$\delta z_2 = \delta z_1 + d$$. Regarding the wave-front radius, some complex algebra tells us that $$\frac{1}{R_1} = \frac{\delta z}{{\delta z}^2 + z_R^2}$$ and $$\frac{1}{R_2} = \frac{\delta z + d}{{(\delta z + d)}^2 + z_R^2}$$. Only when $$d \gg z_R$$ and $$\delta z_1 \neq 0$$ is the statement in question applicable, but when working with collimated beams (or nearly so), the Rayleigh length $$z_R$$ is not small especially compared to free-space propagation distances. That statement is also meaningless when starting the beam propagation from the waist where $$\delta z_1 = 0$$ and the radius is infinite (i.e. a wave front is a planar surface).

Thin lens:
The comment for this examples says "Again, only the real part of q is affected: the radius of curvature is reduced by 1/f." But this time, rather than the real part of q itself, it is the real part of the reciprocal that changes. They are not the same thing and its incorrect to just casually refer to them as the same thing. The real and imaginary parts of the q parameter and separately its reciprocal have different interpretations. Likewise, the reciprocal of the radius is reduced by 1/f, not the radius. $$Re[\frac{1}{q_2}] = Re[\frac{1}{q_1}] - \frac{1}{f} = \frac{1}{R_1} - \frac{1}{f} $$. (A little algebra shows that the radius is really "reduced" by $$\frac{R_1^2}{f - R_1}$$.)

cperk (talk) 14:08, 16 July 2015 (UTC)

Linear Optics
I followed a link to Linear optics hoping to find out what the phrase means; it redirects here, but this article does not make any reference to that phrase - the word 'linear' appears nowhere except in a See Also link at the end. If the redirect is correct, could someone please add a definition of Linear Optics at some suitable place in the article? Hv (talk) 14:54, 12 September 2016 (UTC)


 * I just moved the redirect: Now linear optics redirects to nonlinear optics.


 * Linear optics is the opposite of nonlinear optics. --Steve (talk) 16:56, 12 September 2016 (UTC)

Angles Theta
The angles are measured as slopes, which is mentioned nowhere and not obvious at all. Sure, everyone will figure out its measured neither in degrees nor rad. But that the slope belongs there is not clear from the drawings. The german article luckily explicitly mentions that. I've never seen a slope being indicated in a drawing like an angle. That's horribly confusing. — Preceding unsigned comment added by 129.69.48.35 (talk) 15:50, 19 November 2019 (UTC)

Which matrix format?
As we all know, there are various systems for laying out the matrices: e.g. Meyer-Arendt, Hecht, Gerrard/Busch. They differ in sign conventions but also in order of the elements A, B, C, D. The choice is a matter of personal preference. The article should say which system it is using, and note that there are other systems. Don't leave the reader wondering why it doesn't match the textbook he happens to be using, or poking around in the citations for clues. (If there is now some optical industry standard governing this, I guess I haven't heard about it.) Mgryan (talk) 21:40, 15 March 2024 (UTC)