Talk:Transfer-matrix method (optics)

Comment

I debated proposing a merge with Ray transfer matrix analysis, but I think this technique is distinct enough to benefit from having its own article. Do others agree?--Srleffler (talk) 23:03, 3 June 2008 (UTC)

I'm not sure to what prior debate you're referring. When I was searching on Wikipedia for existing material on TMM, it appeared to me that TMM is a very generic technique that is applied to problems with very little in common other than that the effect on a system state can be described by a matrix. See google. For example, it is also used in Anderson localization, which is not likely to resemble what's described here.

I think Wikipedia is lacking an article on the generic principle of transfer matrix method. The statistical mechanics TMM article could move to Transfer-matrix method (statistical mechanics) and instead there could be a general introduction at Transfer-matrix method, referring to the more specific articles.

Han-Kwang (t) 06:40, 4 June 2008 (UTC)

The "debate" was with myself. This is a common figure of speech in English; a synonym for "considered" or "thought about". I was not referring to a prior debate on Wikipedia.--Srleffler (talk) 06:46, 4 June 2008 (UTC)

I guess the method is the same as the Abeles_matrix_formalism but without the correct credits given. Altough one has to be careful as the form as it is presented in Abeles_matrix_formalism is only applicable to x-rays and is thus a simplified case of the method described here but this restriction is not present in Abeles original paper. 129.206.42.213 (talk) 14:52, 20 April 2009 (UTC)

I agree, definitely the same thing as Abeles matrix formalism. This article does the derivation with one set of assumptions (normal incidence, smooth interfaces, no absorption, etc.), and that article does the derivation with a different set of assumptions (unpolarized light, no absorption, etc.), but it's really the same method. I put in a merge tag. --Steve (talk) 15:39, 20 April 2009 (UTC)

Move proposal

I propose moving this article from Transfer-matrix method (optics) to Transfer-matrix method (wave optics). The term "transfer-matrix method (optics)" applies equally to this article and Ray transfer matrix analysis. --Steve (talk) 17:48, 12 July 2009 (UTC)

L

Variable L is used in two different aspects, leftness and thickness of a layer. This is confusing. One of them should be renamed. —Preceding unsigned comment added by 131.234.208.189 (talk) 16:15, 25 November 2009 (UTC)

Traveling waves?

The first equation of this article (equation for E(z)) is described as a "traveling wave". However, this cannot be a traveling wave as it has no time dependence. This exponential part of this equation should be of the form exp[i(kz-ωt)] or something similar if it is meant to be a plane wave. The lack of time dependence propagates throughout the article. — Preceding unsigned comment added by 139.80.48.19 (talk) 03:01, 14 September 2011 (UTC)

This is common in treatment of wave propagation. The time dependence is separable: the full equations are divided through by exp(-iωt) to make the math simpler. The article probably should not do this without explanation, however.--Srleffler (talk) 03:49, 14 September 2011 (UTC)

Error?

The base change from Er, El to E,F is depending on k, which depends on the medium. Therefore, for multiple layers, one cannot just compute the product of propagation matrices. A base change is necessary from k(n) to k(n+1) between each layer. This base change being equivalent to Fresnel equations for interfaces. Abeles introduces an elegant formulation for this : it separates the interface matrix (n,n+1) into a product of two matrices, one depending on n only, the other one on n+1 only. By combining these matrices with the propagation matrix, he defines a formalism where the matrix for multiple layers is a product of matrices, with only one matrix per layer, and which is not depending on neighbor layers. This implies using a common base for all layers, k being removed from the definition of F. — Preceding unsigned comment added by 88.164.16.51 (talk) 09:46, 17 April 2013 (UTC)

I thought the article was saying... Step 1: Forget about Er and El. Solve for E and F in each layer using the transfer matrix method. Step 2: Now that you have E and F in each layer, find Er and El in each layer. It seems correct to me ... Er and El play no role whatsoever in step 1. Am I misunderstanding? --Steve (talk) 12:21, 17 April 2013 (UTC)

Missing pieces

There are several key missing pieces for in this article. The most major omission is that angle dependence is not mentioned at all. The way the article is written, it sounds like transfer matrices are only useful for on-axis incident light! Second I think it would be best to have an example where we exploit the nice property of transfer matrices simply multiplying together, i.e., the example should have multiple interfaces.

Finally the very simple mathematical basis and mathematical generalization is not emphasized, instead we have a mess of complicated equations. In general the transfer matrix method can be used to quickly find solutions of any Matrix differential equation where the coefficient matrix is piecewise constant. The transfer matrices themselves are simply matrix exponentials of the product of coefficient matrix and distance. Maxwell's equations for stratified media are only an example of this. --Nanite (talk) 09:57, 8 May 2015 (UTC)

Suggested Revisions

There are several issues with this article. First, there is no definition of ${\textstyle Z_{c}}$. According to Ref. 1 this should be the wave impedance, but then ${\textstyle iZ_{c}\neq -1/k}$, in contrast to what is suggested by the example. Indeed, a base transition is necessary to obtain the real valued matrix form as in the example: ${\textstyle (E_{i},H_{i})\rightarrow ({\tilde {E_{i}}},{\tilde {H_{i}}})}$ with ${\textstyle {\tilde {E_{i}}}=-i({\sqrt {\varepsilon _{0}/\mu _{0}}})k_{0}^{-1}E_{i}}$ and ${\textstyle {\tilde {H_{i}}}=H_{i}}$. Since only a constant is multiplied to the electric field component, this is possible without loss of generality. The important issue is that the formulas for ${\textstyle t}$ and ${\textstyle r}$ refer to this gauge. They cannot be correct for the transfer matrix as given in the beginning of the article, due to the different dimensions of the terms. See also Ref. 1 of the article. — Preceding unsigned comment added by 129.247.247.239 (talk) 08:15, 15 October 2018 (UTC)