Talk:Distributed Bragg reflector

Reflectivity

Dopeydog,

Is it correct, the reflectivity formula is for the center wavelength of the stopband?

Also, the graph often loses detail (for example, all of the text and lines) when scaled. This seems to depend on the browser, screen resolution, etc. Can your program produce a black-on-white version? (I'm assuming you're the "Me" who submitted the graph).

--The Photon 05:07, 14 August 2006 (UTC)

I may have confused matters with my edit. The formula for bandwidth used several variables which were not defined in the article. I took my best guess as to what he intended. (Note to Dopeydog: In Wikipedia, as in academic writing, always define even the most trivial of variables. You may not assume that the reader knows what you mean by $\lambda$, $\nu$, etc.)--Srleffler 05:22, 14 August 2006 (UTC)

Reflectivity formula in article citing is here: http://dl.dropbox.com/u/9348241/0963-9659_4_5_018.pdf see equation (18) 82.6.103.94 (talk) 19:01, 29 August 2012 (UTC)

Non optical

this page seems to be focusing solely on the optical side of things, there's a different formula for corrugated metal waveguides determining the central frequency of refelection.

also i edited the bit at the end just to include free electron masers as these mirrors are excellent in such devices.—Preceding unsigned comment added by Hermanzegerman (talk • contribs) 05:22, March 1, 2007

I'm not familiar with these corrugated metal waveguides. Are they still "distributed Bragg reflectors"?--Srleffler 13:12, 1 March 2007 (UTC)

Definately, they still have Bragg reflecting devices distributed across their surface. There's lots of papers on coaxial, cylindrical and planar DBRs in FELs, Gyratrons and the like. They're big RF pulsed power devices popular in Russia and China for their potential in directed energy systems.Barryferguson6 11:13, 4 September 2007 (UTC)

High-quality

The high-quality note was removed. This is unfortunate, as it is an important characteristic of such devices. These mirrors can have reflectivities (in the appropriate band) much closer to 100% than a metal mirror.--Torsionalmetric (talk) 19:36, 4 May 2009 (UTC)

Metal mirrors are not exactly state of the art. DBRs are not better reflectors than modern dielectric mirrors. I removed it, though, because "high quality" is vague. If the assertion was that they have unusually high reflectance, the article should have said so. If there is some specific and unambiguous way that DBRs can be said to have higher quality than other reflectors, I would be open to trying to work that back in.--Srleffler (talk) 00:46, 5 May 2009 (UTC)

Ahhhh, my apologies. I was confusing DBRs and modern dielectrics. Should some words be added to the first paragraph that they are a derivative or precursor to modern dielectrics? 138.210.84.242 (talk) 17:44, 5 May 2009 (UTC)

I'm not sure how best to characterize the distinction between a DBR and a dielectric mirror, except of course that DBRs are used in waveguides and "dielectric mirrors" are used in free space. They operate on similar principles, although the designs are different in practice. I'm not sure if they are best characterized as two names for the same thing, completely distinct things (by some definition), or overlapping. I have the impression that DBRs use layers that are exactly a quarter wavelength thick, while thin film dielectric mirrors use coatings whose layer thicknesses are numerically optimized to produce the desired coating curve. --Srleffler (talk) 22:37, 5 May 2009 (UTC)

Merger_proposal

In my opinion, there's no reasons to have dielectric mirror and distributed bragg reflector in different articles. it's 100% the same underlying pysical principle. Dielectric mirrors are a used of Bragg interference effect to create mirrors "in free space" in general, whereas DBR are more often heard of for laser cavity mirrors, but they are the same, and it would nice reorganizing a bit all this, what is your opinion ?Matthieu.berthome (talk) 07:19, 3 July 2009 (UTC)

I would rather not merge these two. DBRs are used in fibers and other waveguides, while dielectric mirrors are used for free-space mirrors (i.e. at the boundary between a substrate medium and air). While the underlying physics is the same, they are distinct technologies. I am not even sure that they are the same, aside from that. See above: I believe DBRs use many layers of exactly quarter-wave thickness, while dielectric mirrors typically do not.--Srleffler (talk) 20:13, 3 July 2009 (UTC)

If merging, then merge the two articles as "distributed bragg reflectors" as DBRs not always consist of dielectrics, but also often of semiconductor material. Therefore, describing the mechanism without restricting to dielectrics would be better, i guess. A pure explanation based on index contrast will hold! 134.102.20.212 (talk) 14:15, 20 January 2010 (UTC)

Reflectivity formula

Isn't there something weird with the formula, or some text left out. The width of the dielectric layers must show up somewhere. --Ravn-hawk (talk) 16:13, 7 December 2009 (UTC)

The layers are a quarter wavelength thick, by design.--Srleffler (talk) 03:18, 8 December 2009 (UTC)

Shouldn't there be a reference associated with the reflectivity formula? Especially since there is no discussion of the assumptions made in its derivation. --dvaselaar (talk) 17:39, 14 March 2010 (UTC)

Yes.--Srleffler (talk) 01:02, 15 March 2010 (UTC)

According to that reference I added, in equation (18) p.669 the formula doesn't have an exponent (^2) after the brackets and it is exactly the same formula. Another one (in McLeod, "thin film optical filters" 2nd Ed. McGrawHill) that does contain the (^2) doesn't include the surrounding medium and has different exponents, if the reference is there I think the formula should read as in the source, therefore I'm removing the outermost ^2. --Kilologin (talk) 17:24, 28 April 2010 (UTC)

You have to be careful when comparing formulas from different sources, and make sure you understand the notation. There are two kinds of reflectivity: amplitude and intensity. The intensity reflectivity is proportional to the square of the amplitude reflectivity (the constant of proportionality depends on the notational scheme used). By removing the ^2, you have probably changed the meaning of the variable R from intensity to amplitude. The article should be clear about the definition of R. While the article Reflectivity says that the latter is always amplitude, I doubt this is universally true.

I don't have access to either of the sources mentioned, so I can't verify the formula.--Srleffler (talk) 03:29, 29 April 2010 (UTC)

I've been finding other approaches (approximations) not only depending on the mathematical method used to obtain the formula but also in how the wave equations were postulated (i.e. vectors, matrices, etc. absorption, no-absorption, etc.) For example a slightly different one can be found in page 185 here: http://books.google.com/books?id=D0S9hxzPJq8C&printsec=frontcover#v=onepage&q&f=false). For example, one that solves the Maxwell equations for stratified medium (1D photonic structure) is called MIT photonic bands (http://ab-initio.mit.edu/book/), freely available online, which outputs seem to be far more complicated that the well known approximation shown in the article. —Preceding unsigned comment added by Kilologin (talk • contribs) 04:16, 4 May 2010 (UTC)

MacCleod's formula is for a stack of alternating layers that both starts and ends with a high-index layer. This article claims that the formula given is for a "number of repeated pairs of low/high refractive index material," which I take to mean that the stack starts with a high-index layer and ends with a low-index one, or vice versa.--Srleffler (talk) 04:25, 4 May 2010 (UTC)

R there is the reflection coefficient, and the reference citing the formula doesn't have that squared value. Therefore, the squared bit should be removed, if you think the formula should have it then provide the reference for it. I'm not changing it again because I did it once and the change was reverted, but it should be not squared, please access the article here : http://dl.dropbox.com/u/9348241/0963-9659_4_5_018.pdf 82.6.103.94 (talk) 18:59, 29 August 2012 (UTC)

You seem not to understand: Sheppard's paper gives the reflection coefficient r, which is the ratio of the reflected and incident electric fields. This article gives the reflectivity, R, which is the ratio of the reflected and incident power or intensity. These are not the same thing, but trivially R = r². You can tell that Sheppard's r is for the electric field because in many of the formulas it is complex (see Fig. 3 in the paper). Reflectivity R is always real. You can tell that the formula in this article is for reflectivity because it says so.

We could rewrite the article to talk about amplitude instead of intensity, but I do not think this would be beneficial. It is less directly useful to the casual reader.--Srleffler (talk) 04:31, 30 August 2012 (UTC)