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Is this correct:

"that is, refractive index n decreases with increasing wavelength λ. In this case, the medium is said to have normal dispersion. Whereas, if the index increases with decreasing wavelength the medium has anomalous dispersion."

There appears to be two different definitions of anomalous dispersion. The first:

 Normal dispersion means refractive index increases as frequency increases, i.e. dn/df > 0.
 Anomalous dispersion means dn/df < 0.

The second:

 Normal dispersion means not only dn/df > 0, but also refractive index is linearly related to frequency, dn/df = const.
 Anomalous dispersion means a refractive index that is a nonlinear function of frequency.

It is glasses with the second type of anomalous dispersion that make apochromatic lenses possible. See Tamron's discussion http://www.tamron.com/lenses/optical.asp . I'm not an optical engineer, so my assumption that normal dispersion is "linear" may not be accurate, but it's fairly close. ChrisMaple (talk) 04:37, 13 January 2010 (UTC)Reply[reply]

I've never heard of the second definition you give; what is your citation for that definition? I don't see that definition given explicitly anywhere in your link. Note that no material has dn/df = constant if you look in a sufficiently large bandwidth, and in general d²n/df² in general only vanishes at isolated frequency points, so your second definition seems like it would very rarely be strictly applicable. — Steven G. Johnson (talk) 06:20, 13 January 2010 (UTC)Reply[reply]

The second definition is absolutely wrong! The property of having a linear relation between refractive index and frequency, which as Steven points out is not generally the case, I have called "first order dispersion" in my own work (however that is not a universally accepted term, I just don't know of any other!). See my further discussion of that issue below (GVD section). Anomolous dispersion is a particular feature of the refractive index in the immediate vicinity of an absorbtion line (which is the only reason that it is possible, since it would otherwise predict a signal velocity greater than c).

Interferometrist (talk) 15:28, 2 April 2010 (UTC)Reply[reply]

I'm sort of out of my depth here. In the Material Dispersion In Optics section I see a chart with the caption: The variation of refractive index vs. vacuum wavelength for various glasses. The wavelengths of visible light are shaded in red. There is no red shading. Blue shading looks like the visible range at first glance. But units shown are off by a factor of 1000. Micrometers would be correct, but people usually use nanometers for visible light wavelength (I think ~400 nm to ~700 nm would fall within the visible range of the typical human eye, or ~.4 um to ~.7 um might be rightly applied due to space constraints). Actual limits to the range are probably correct, my numbers are guesses. Scale and shading appear incorrect.Jeffreagan (talk) 05:48, 20 January 2018 (UTC) Jeffreagan (talk) 05:48, 20 January 2018 (UTC)Reply[reply]

I recently added what I thought was the more general formula for the group velocity:

${\displaystyle v_{g}=v-\lambda {\frac {\partial v}{\partial \lambda ))}$

which user:Stevenj has removed saying it's not generally true, only in the case of low dispersion. I though this came from the definition of the phase and group velocities:

${\displaystyle v=\omega /k}$

and

${\displaystyle v_{g}={\frac {\partial \omega }{\partial k))}$

hence:

${\displaystyle v_{g}=v+k{\frac {\partial v}{\partial k))}$

and from ${\displaystyle k=2\pi /\lambda }$, giving:

${\displaystyle v_{g}=v-\lambda {\frac {\partial v}{\partial \lambda ))}$.

So, what am I missing? Are my velocity definitions wrong? (I accept that none of the equations are valid for inhomogeneous media.) -- Bob Mellish 17:58, 5 October 2005 (UTC)Reply[reply]

Ah, now I see what you meant. My problem is with the ${\displaystyle k=2\pi /\lambda }$. Ordinarily, in equations like this (or in most of optics for that matter) λ means the vacuum wavelength, i.e. ${\displaystyle \lambda =2\pi c/\omega }$. Using the wavelength in the material is problematic — not only for inhomogeneous media, but also for anisotropic homogeneous media — but mainly I think people don't use the medium-dependent λ because it is just more convenient to talk in terms of conserved quantities. (I wish this article would start with the general definitions and then give the specific formulas for special cases like homogeneous media, but I don't have time to do major re-working myself right now.) —Steven G. Johnson 04:59, 6 October 2005 (UTC)Reply[reply]

It looks like essentially every usage of λ in the article means vacuum wavelength, but it never says that explicitly. Sigh. —Steven G. Johnson 05:02, 6 October 2005 (UTC)Reply[reply]

• Hrrm, I didn't think of k being wrong. Yes, vacuum wavelength makes more sense to use. Unfortunately I've forgotten most of the derviation of this stuff, if you've got a good modern reference I could look it up and try to improve the article, if you're too busy. Personally I'd prefer it to start with the simple cases and move to the most complex ones, but then I've never worked with photonic crystals or the like. -- Bob Mellish 16:35, 7 October 2005 (UTC)Reply[reply]

The classic reference on all of this stuff is:

Léon Brillouin, Wave Propagation and Group Velocity (Academic: New York, 1960).

You can also find some discussion in Jackson (Classical Electrodynamics) etc. However, even so most of this discussion is limited to homogeneous media. In general, the group velocity is defined as dω/dk, where k is the Bloch wavevector in a periodic system (of which a homogeneous system is a special case). In a periodic system, on the other hand, there is no perfectly satisfactory definition of phase velocity, since k is only defined up to a reciprocal lattice vector. A proof that dω/dk is equal to the energy velocity for dispersionless, lossless systems (including periodic systems and also including waveguides) can be found in Sakoda, Optical Properties of Photonic Crystals (Springer: Berlin, 2001). This can be extended to systems with material dispersion (using the proper definition of energy density in a dispersive medium, as can be found in Jackson), but I'm not aware of any single reference that contains the complete derivation for all cases (arbitrary inhomogeneity and dispersion). Once you include loss, of course, or when you are looking at evanescent modes (complex k), then the group velocity is no longer the energy velocity; this is described in the Brillouin reference, which also describes the front velocity and other concepts. A good description (without too much math) of the phenomena and consequences of dispersion (both material and waveguide, but not in general periodic media) in communications systems can be found in Ramaswami and Sivarajan, Optical Networks: A Practical Perspective (Academic Press, 1998); this is an excellent introductory textbook overall (although a little specialized to fibers, in which things simplify because the inhomogeneity is weak). In particular, Ramaswami also gives a more general definition of the dispersion parameter D, which is especially pertinent to this article. —Steven G. Johnson 18:49, 7 October 2005 (UTC)Reply[reply]

• Heh, I actually have the Brillouin book right here; I grabbed that equation from page 3 (eqn. 9b). I've been reading it with aim to improving the front velocity and signal velocity articles. I'll try seeing if the library has the other works you mention. -- Bob Mellish 18:59, 7 October 2005 (UTC)Reply[reply]

• To Steve/Bob: So is the equation v(group) = v(phase) - lambda*[d(v(phase))/d(lambda)] , true always? If yes, the correct expression for v(group) in terms of the refractive index is : v(group) = c*[(1/n) + (lambda)*(d(n)/d(lambda))/n^2], which is only approximately equal (upto first order term) to the formula typed out in the article currently i.e. v(group) = c*[n - (lambda)*(d(n)/d(lambda))]^(-1). So which one is the correct formula and which one is the approximate one? -- Mvpranav —Preceding unsigned comment added by Mvpranav (talk • contribs) 23:28, 10 December 2008 (UTC)Reply[reply]

what's the difference? Pfalstad 15:47, 4 January 2006 (UTC)Reply[reply]

Modal dispersion comes because the waveguide supports multiple modes at the same frequency that travel at different speeds. Waveguide dispersion refers to the fact that for a single mode the speed depends on the relative size of the wavelength and the waveguide geometry, which causes the solution's field pattern to change. —Steven G. Johnson 17:37, 4 January 2006 (UTC)Reply[reply]

Anyone agree with a mention or even a photo of Pink Floyd's album Dark Side of the Moon, which of course featured dispersion on the cover? Wwwhhh 02:37, 27 July 2006 (UTC)Reply[reply]

I thought we could use something more visually appealing to explain dispersion, so I came up with this little animation. Maybe it's too conceptual to the point of being entirely misleading, so I'm putting it here first so you can be the judge. Oh, and if I screwed up with anything, keep in mind I've been awake for 30 hours. :P — Kieff 21:05, 20 January 2007 (UTC)Reply[reply]

Nice animation, but has a couple of issues. (1) the refraction angles at the left and right surfaces don't match. The green component (3rd from above) travels through the glass horizontally, which means that it should come out at the same angle as how it went in. (2) The ratios of the velocities inside/outside the prism don't seem to match the refraction angles, although i didn't check very carefully. If you draw the light as wavefronts rather than dots - or as two rows of dots - , both (1) and (2) should be satisfied. I think this type of properties should be visualised correctly. Although it would require the GIF animation to be an enormous number of frames, which would be a disadvantage. (3) Using a prism for visualisation actually demonstrates two effects at the same time: temporal dispersion and refraction. It might actually be more to the point to only have a beam traveling through a slab or rod of glass rather than a prism. Han-Kwang 21:04, 19 March 2007 (UTC)Reply[reply]

Posted this earlier onver on the image page 65.202.227.114 (talk)mjd 2008-03-14 09:14EDT I think the "refracting dots" model is more intuitive, but there are some issues that I think should be considered. Your white dots entering the left side of the prism could be considered light "packets" and as such have a wavefront associated with them. They may or may not be coherent - which is unimportant - but they have a definite phase relationship associate with the wavefront, which is also approximately a plane wave. The chromatic dots leaving the prism have a curved wavefront which is exactly correct, and both the curvature and overall tilt of the wavefront are very instructive. What happens inside the prism is quite a bit more problematic. An inquisitive student would notice that the various wavefronts entering the prism are segregated and recombined into new wavefronts before exiting the prism, which is of cource incorrect. It is precisely that the wavefront itself is refracted according to wavelength or frequency in the material that is the take-home message for this sub-topic, and one that great pains should be taken to illustrate correctly. Wonderful graphical work, in any event. 65.202.227.91 (talk) 18:22, 6 March 2008 (UTC)mjd 2008-03-06 13:21ESTReply[reply]

Retrieved from "http://en.wikipedia.org/wiki/Image_talk:Light_dispersion_conceptual.gif"

A version with waves is now available. — Kieff | Talk 04:16, 24 December 2007 (UTC)Reply[reply]

The version with waves is flawed and should not be used. The red rays are clearly moving faster than the purple ones outside the prism. Unless the space outside the prism is supposed to be some odd medium with very high dispersion, this is incorrect. The version of the image with little balls had this detail correct.--Srleffler (talk) 00:11, 17 February 2008 (UTC)Reply[reply]

This is now fixed. — Kieff | Talk 03:36, 27 February 2008 (UTC)Reply[reply]

Hi, I wanted to add a part about measuring waveguide dispersion. do you think it should be a new page or a part of this page? Sr903 20:28, 19 March 2007 (UTC)Reply[reply]

I'd say Waveguide is a better place to discuss dispersion in waveguides. I actually think the waveguide discussion should not be so prominent at the top of this page, but rather in a section, but I might be biased by my background in spectroscopy rather than telecom. Han-Kwang 21:04, 19 March 2007 (UTC)Reply[reply]

I see your point but as someone from more of a telecom background. How about a page named Waveguide Dispersion? We could then redirect Fiber Optic Dispersion. In the Telecom world Dispersion is a big thing and I would expect to see the amount of content on this subject growing.Sr903 14:19, 20 March 2007 (UTC)Reply[reply]

Any comprehensive discussion of dispersion has to include both material dispersion and structural (a.k.a. waveguide) dispersion. One problem with the current page, however, is that the discussion of waveguide dispersion is misleading. "Waveguide dispersion" isn't just any dispersion that happens to take place in a waveguide. It's dispersion that occurs because you have a waveguide, which breaks the scale-invariance with respect to the wavelength, and it happens in addition to material dispersion (although they aren't literally additive except in low-contrast media such as doped-core fibers...the combination is more complicated in general). More generally, you get structural dispersion in any inhomogeneous medium that is periodic or uniform along the direction of propagation (which is necessary to get a well-defined group velocity).

There are other problems with the current page as well, for example it pointlessly specializes the equations of group velocity and the dispersion parameter to homogeneous media, rather than starting with the general definitions.

Group-velocity dispersion is a very general phenomenon. An encyclopedia article on such a general phenomenon should describe its general features, definitions, and sources first, and then give more detailed equations for specialized cases like homogeneous materials, doped-core optical fibers, etcetera, possibly in sub-articles. The top-level article should most certainly not be written from a narrow perspective, but this is unfortunately the present situation.

—Steven G. Johnson 17:59, 20 March 2007 (UTC)Reply[reply]

Is it just me, or doesn't the page specify what are the units of dispresion? (Ran Shenhar 2 May 2007)

I added the general definition of the dispersion parameter D, including waveguide and material dispersion, and the physical interpretation as pulse spreading per unit distance per unit bandwidth, and the typical units (for optical fibers) of ps / nm km. —Steven G. Johnson (talk) 04:51, 17 February 2008 (UTC)Reply[reply]

Much of this article is about what I understand to be refraction. Refraction concepts are included, such as refractive index, without explanation except by way of link. Even if the articles are not merged, there should at least be some discussion of the relation between dispersion and refraction; how they are the same and how they are different. Robert P. O'Shea (talk) 14:43, 20 March 2008 (UTC)Reply[reply]

I'd say there isn't much connection between dispersion and refraction; you can have either without the other. The Material dispersion in optics section explains the effect of dispersion on refraction (i.e. it gives rise to angular dispersion). The other sections don't relate to refraction at all, except for the very small Dispersion in gemology and Dispersion in imaging sections. Maybe these should be sub-sections of Material dispersion in optics? Perhaps the prism picture in the lead is suggestive of a stronger connection with refraction than is apparent from reading the whole article. --catslash (talk) 15:25, 20 March 2008 (UTC)Reply[reply]

I agree, they are independent concepts. One can have refraction in a non-dispersive medium. One can also have dispersion without refraction (e.g. we talk about material dispersion and pulse spreading in a homogeneous medium, where there are no interfaces to refract through; another example would be waveguide dispersion in a hollow metallic waveguide, where there is reflection but no refraction). —Steven G. Johnson (talk) 15:39, 20 March 2008 (UTC)Reply[reply]

Thanks for clarifying the difference. But my point stands. Essentially all of the introductory paragraphs of the article describe what most people would understand as refraction. There needs to be some reconciliation in the article of the two concepts, rather than simply confining it to the discussion. I've put back the mergeto note as a bookmark to people who know that the two concepts are different to explain how in the article and as a bookmark to people who don't know that the two concepts are different to see some deficiencies in this article. Robert P. O'Shea (talk) 09:39, 2 April 2008 (UTC)Reply[reply]

I've modified the introduction to make it clear that prisms/rainbows are just one familiar example of a dispersion phenomenon, and are by no means the only example. (Still, even for the original version of the intro, your comment was hyperbole—exactly two sentences referred to prisms/refractions, and both sentences gave them as examples; the rest of the intro did not mention refraction at all.) —Steven G. Johnson (talk) 04:13, 3 April 2008 (UTC)Reply[reply]

I would like to see more clear treatment of the case of angular dispersion (the prism example; interface between media with different phase velocities) and a subsequent generalization to waveguide dispersion (which can be viewed as an extension of the single-interface refraction problem to one having two parallel interfaces and utilizing the internally refracted rays). Anyone? Ryan Westafer (talk) 00:29, 29 November 2010 (UTC)Reply[reply]

Can someone disprove (or strengthen) this statement? "Material dispersion is equivalent to the case of refraction through infinitesimally distributed (relative to the wavelength) interfaces of arbitrary spacing and angle with respect to the incident wave (k)."

For instance, when a system has "internal" (characteristic dimension smaller than the wavelength) degrees of freedom, energy might couple to corresponding refracted, reflected, and/or trapped modes (angles, polarizations, defect states, etc.). Then the transmitted wave exhibits propagation loss with respect to the incident wave mode (polarization, angle, etc.).

If one knows the sub-wavelength details of the medium, one can compute its average or "effective medium" parameters (refractive index, etc.) corresponding to 0th order dispersion (n=0 Fourier expansion of the space harmonics of the sub-wavelength inhomogeneities). Ryan Westafer (talk) 00:56, 29 November 2010 (UTC)Reply[reply]

A dielectric medium with a sub-wavelength microstructure can be dispersive in two circumstances: (a) the size of the microscopic elements is a significant fraction of the wavelength (say at least 1/20) and/or (b) the microscopic elements themselves have a frequency-dependent response (are dispersive). Barring these circumstances, different wavelengths will be indistinguishable on the scale of the microstructure, and so will elicit the same behaviour - the bulk medium will therefore show no dispersion. Not at all sure if this answers your question. --catslash (talk) 14:27, 29 November 2010 (UTC)Reply[reply]

The equation

${\displaystyle D=-{\frac {\lambda }{c))\,{\frac {d^{2}n}{d\lambda ^{2))}.}$

looks wrong, like a mixup between two correct versions:

${\displaystyle D=-{\frac {\lambda }{c))\,{\frac {d^{2}n}{d\lambda d\nu )).}$ where ${\displaystyle \nu }$ is frequency

${\displaystyle D={\frac {\lambda ^{3)){c^{2))}\,{\frac {d^{2}n}{d\lambda ^{2))}.}$

I'd prefer the latter, which is found at page 962 in the book "Fundamentals of Photonics" by B.E.A. Saleh & M.C Teich (Wiley-interscience 2007). ${\displaystyle \lambda }$ and ${\displaystyle c}$ are the values in vacuum. Assuming --ErikM (talk) 10:54, 8 January 2009 (UTC)Reply[reply]

Maybe there are two different conventions, depending on if you use the sign from a frequency derivative of a wavelength derivative. The article now says If D is less than zero, the medium is said to have positive dispersion. If D is greater than zero, the medium has negative dispersion. but with the formula from Saleh & Teich^[1] (actually for what they call ${\displaystyle D_{\nu ))$) the naming seems more reasonable: If D is less than zero, the medium is said to have negative dispersion. If D is greater than zero, the medium has positive dispersion. —Preceding unsigned comment added by ErikM (talk • contribs) 11:10, 8 January 2009 (UTC)Reply[reply]

The formula in the article is correct. Your formula is also correct. They correspond to different definitions of the dispersion parameter D. Both definitions are given in Saleh and Teich. I think you have a different edition of Saleh than mine because our page numbers don't match up. Saleh calls the definition you are using ${\displaystyle D_{\nu ))$ (equation 5.6-20 in my edition) and the definition the Wikipedia article uses ${\displaystyle D_{\lambda ))$ (equation 5.6-21 in my edition). The latter definition is more widely used in the fiber/telecom industry. Also, the latter definition corresponds to the more general definition given in the Wikipedia article (generalized to inhomogeneous media, i.e. including both material and waveguide dispersion):^[2]

${\displaystyle D=D_{\lambda }=-{\frac {2\pi c}{\lambda ^{2))}{\frac {d^{2}\beta }{d\omega ^{2))}={\frac {2\pi c}{v_{g}^{2}\lambda ^{2))}{\frac {dv_{g)){d\omega ))}$

To get the homogeneous-medium equation in the article, substitute ${\displaystyle \beta =n\omega /c}$ and recall via the chain rule that ${\displaystyle {\frac {d}{d\omega ))=-{\frac {\lambda ^{2)){2\pi c)){\frac {d}{d\lambda ))}$. The definition you are using corresponds more generally to:

${\displaystyle D_{\nu }=2\pi {\frac {d^{2}\beta }{d\omega ^{2))}=-{\frac {\lambda ^{2)){c))D_{\lambda ))$

(equation 5.6-9 in my edition of Saleh). The difference is whether one wants to describe pulse spreading per unit frequency bandwidth (${\displaystyle D_{\nu ))$) or per unit wavelength bandwidth (${\displaystyle D_{\lambda ))$), as explained in Saleh. —Steven G. Johnson (talk) 19:13, 8 January 2009 (UTC)Reply[reply]

The current (2019-09-02) wikipedia text tells: "If D is greater than zero, the medium is said to have positive dispersion (normal dispersion). If D is less than zero, the medium has negative dispersion (anomalous dispersion). If a light pulse is propagated through a normally dispersive medium, the result is the shorter wavelength components travel slower than the longer wavelength components." Also the dispersion parameter defined there is:

${\displaystyle D=-{\frac {\lambda }{c)){\frac {d^{2}n}{d\lambda ^{2))))$

that is ${\displaystyle D_{\lambda ))$ from the discussion above. But in this case the text is wrong because ${\displaystyle D_{\lambda }>0}$ corresponds to anomalous dispersion ^[3]. Can we change the text into "If ${\displaystyle D}$ is negative, the medium is said to have normal dispersion. If ${\displaystyle D}$ is positive, the medium has anomalous dispersion. If a light pulse is propagated through a normally dispersive medium, the result is the shorter wavelength components travel slower than the longer wavelength components"? Ang1972 (talk) 10:04, 2 September 2019 (UTC)Reply[reply]

Hi Stevej, Your recent edits to the lead could be read as meaning that dispersion and group velocity dispersion are the same thing. They are of course interdependent, but if you quantify them, then in general they'll be different numbers. If the dispersion relation was something like ${\displaystyle \omega =\omega _{0}+A\beta }$ (over a limited band obviously), then there would be "phase velocity dispersion", but no group velocity dispersion. Regarding periodic structures; each space-harmonic of a given mode has the same group velocity, and a different phase velocity (but it still has a well-defined phase velocity).--catslash (talk) 00:17, 9 April 2009 (UTC)Reply[reply]

In periodic structures, the phase velocity is a problematic quantity that is not uniquely defined. By different "space harmonics" I suppose you mean different Brillouin zones, but you should realize that these are merely different labels for exactly the same mode and field pattern. Hence the ambiguity.

Once could certainly talk about phase-velocity dispersion as distinct from group-velocity dispersion, in cases where the former is well-defined. The latter seems much more common as a precise numerical quantity, however. Do you have any references that define a quantity analogous to D for phase-velocity dispersion?

— Steven G. Johnson (talk) 06:27, 3 August 2009 (UTC)Reply[reply]

I don't know if I have a good reference (outside of what I have written, mainly unpublished) but in my nomenclature there are two (and more) levels of dispersion. "First-order dispersion" is exactly what you are refering to, in which case dn/df is constant (over a region) and this causes 1)a change in the group velocity relative to the phase velocity; 2) a change in the phase of the wavepacket at its center. However the latter effect is not easily observed in most conexts which I'm sure is why it has received little attention.

"Second order dispersion" in my system is equivalent to "group velocity dispersion" in which the group velocity, as well as being different from the phase velocity, is a function of optical frequency. This DOES cause pulse broadening which is more easily observable (such as the degradatation of signals in communications). In my decomposition 2nd order dispersion, the term for second order dispersion adds to the refractive index a constant times ((f^-1) - 1)(f^-2) -- I hope you can read that! Higher orders of dispersion create terms like ((f^-1) - 1)^N * (f^-2) with N>1.

In this context (including first order dispersion in the definition of dispersion) the statement early in the article that "Dispersion is sometimes called .... group-velocity dispersion (GVD) to emphasize the role of the group velocity." is inaccurate. GVD is just better appreciated but does not describe all dispersion in a strictly mathematical sense.

Interferometrist (talk) 15:28, 2 April 2010 (UTC)Reply[reply]

First-, second-, etcetera, order dispersions are just the first-, second-, etcetera derivatives of the dispersion relation ω(k) (in a periodic medium, the k label is ambiguous under addition of reciprocal lattice vectors, and hence there is no unambiguous phase velocity, but the derivatives are unambiguous). First-order "dispersion" is just the first derivative, which is the group velocity (or its inverse, depending on which variable you differentiate); first-order "dispersion" alone causes no pulse-spreading whatsoever and refers to no "change" in the group velocity. See e.g. here. The terms are confusing, but as far as I can tell if you just say "dispersion" by itself in optics (as opposed to "dispersion relation"), you're referring to a phenomenon where different colors get separated in some way. — Steven G. Johnson (talk) 15:52, 2 April 2010 (UTC)Reply[reply]

Something is missing to this article, namely a sub-section of travelling ultrashort pulses and the partial differential equation that governs the carrier envelope of these pulses subject to dispersion. Such a presentation is essential. I found this out because the ultrashort pulse section has a link to this site on dispersion but the material is not sufficient.

There are lots of different ways to simulate ultrashort pulses. If any partial differential equation deserves to be called "the" equation, it would be Maxwell's equations and not any particular approximation. People also make various approximations, usually Taylor series expansions of the dispersion relation, and plug these approximations into Fourier transforms or slowly varying envelope approximations (SVEA), but there's no reason to single out a particular order Taylor series SVEA from a particular paper as "the" method here.

Unfortunately, our SVEA article basically sucks right now (it has an incredibly narrow perspective on what is really a very broad subject), but that's not a topic for the Dispersion article to address.

I've added a brief section on higher-order dispersion (which is the name for what you are trying to get at, and is not specific to ultrashort pulses). I doubt any more detail is appropriate for this article at this point -- considering that our discussion of second-order dispersion (D) is so brief, it doesn't make sense to go on about higher-order effects in great detail until/unless the lower-order effects are treated in more depth.

— Steven G. Johnson (talk) 18:53, 6 August 2009 (UTC)Reply[reply]

Steven, this tug-of-war has to stop! :-)

First of all, this treatment is not just 1+1. The pulse propagates in the z-direction and the coefficients themselves depend on the angle theta from the z-axis. So this is a 3-dimensional problem assuming cylindrical symmetry. So the treatment is quite general. Given that people gave complained that the formulae on this site are wrong, the computer algebra treatment ensure correctness of the coefficients. The paper is just used as a reference for the coefficients. I know this paper and I can assure you that it applies to ultra-short pulses or pulses propagating over long distances where terms to higher order (i.e. 3rd order) are needed. Let us come to an agreement before continuing any further action is taken. —Preceding unsigned comment added by 171.71.55.181 (talk) 20:00, 6 August 2009 (UTC)Reply[reply]

Sorry, you're right that the equation you wrote down was not 1+1 dimensional. Of course, that means it's also wrong if you're talking about waveguides, which are (in the SVEA) 1+1 dimensional. Take your pick. (And you hardly need a computer algebra system to write down a Taylor expansion.)

This is ridiculous sophistry! First you criticize it for being 1+1 (which it isn't) and then you criticize it for not being 1+1 for SVEA. That paper is correct, I can assure you. It was peer-reviewed and published in Optics Letters. The paper itself uses SVE defines well its domains of application. You have a pulse propagating in the z-direction. You have cylindrical symmetry. Nothing is lost. The SVE approximation used overlaps greatly with what your very web-site and its links are describing.

The basic problem here is that highlighting a particular SVEA based on a particular-order Taylor expansion as "the" way to handle higher-order dispersion is simply wrong. And if you're going to write an infinite-order Taylor expansion, you might as well not Taylor expand at all (e.g. in a split-step method you can plug in the whole dispersion spectrum without Taylor expansion). And when the pulses get really short, you eventually have to give up on the SVEA and should be using the full Maxwell's equations anyway, especially in a waveguide. Going into great detail on one particular approach does not belong in this article; it would belong in the (currently lamentable) SVEA article, if anywhere.

Nothing is "wrong" with a Taylor series. The first order coefficients beta_1 and beta_2 were well known in the literature. No pretense was made that this was "the" way although you claim yours is the "way!. This paper extended the Taylor series to higher-order and can in principle yield the coefficients to any desired order. Again you're contadicting yourself: your writeup also mentions the use of a Taylor series!

(Besides which, it's pretty crazy to give any detailed equations for third and higher-order dispersion when we haven't even shown explicitly how to compute pulse evolution with second-order dispersion.)

For the given Physics described in that paper, nothing was actually lost.

— Steven G. Johnson (talk) 20:11, 6 August 2009 (UTC)Reply[reply]

This is fruitless. No agreement can be reached and it is clear you are pushing through a particular method: your own. The tug of war will be endless. It is clear I am not dealing with an honest individual in good faith. No point in any further communication.

What method do you think I'm pushing? The paragraph I wrote describes several methods (including SVEA). You're not making sense.

The point that I have been consistently making is that it doesn't make sense to single out a specific method here, especially one restricted to particular circumstances (whether an SVEA for homogeneous media or an SVEA for waveguides), nor is this article the right place to go into a particular variant of an SVEA (out of many variants in the vast literature on this topic) in great depth, nor is an SVEA in terms of the Taylor expanded dispersion relations the only way to approach this problem. (I never said it was wrong when applied under appropriate circumstances. Just that it, like every method, has its limitations, and singling it out as the method is what is wrong. The only method that, in principle, is correct under all (classical) circumstances is solving the full Maxwell equations, but as a practical matter it is often desirable to use approximations when they are valid.) (You are the one who called this SVEA variant "the partial differential equation" governing this problem (emphasis added).)

Your resort to ad hominem arguments is out of place. — Steven G. Johnson (talk) 04:39, 7 August 2009 (UTC) PS. On Wikipedia, it is considered poor style/etiquette to intersperse your comments with someone else's. Don't break up someone else's comments — make your comments as a contiguous block. It is also good to sign up for a username.Reply[reply]

It is not an ad hominem remark to point out the endless contradictions and attributions you make within your arguments. One merely needs to walk through the discussion blog to see complaints and your endless responses of merely rebuttal and action taken strictly on whatever terms you dictate. You still keep going on about Maxwell's equations when this is the very starting point about that the Optics Letters paper which was (i) authoritative, (ii) correct and (iii) found to be very useful in the community. I NEVER claimed it was "the" method. This is your jihad. I never claimed there were no alternatives. You clearly do not know how to communicate effectively with other people and no it's NOT A method you are pushing, it is simply your (narrow) point of view (however contradictory it is) that you are enforcing no matter what. No compromise, no collaboration, no fruitful outcome is possible in such cases. BTW, that is a discernment, no an ad hominem remark. You bring up etiquette and don't even respect it. The neutrality of this particular site is therefore highly in doubt. —Preceding unsigned comment added by 171.71.55.181 (talk) 16:43, 7 August 2009 (UTC)Reply[reply]

There is finally some kind of resolution to this dispute in that the material removed by — Steven G. Johnson has been revised and placed in the section on Ultrashort pulses where it has been accepted (and vindicated). Hopefully, this will bring peace of mind to all. Having said all that, this does not remove the fact that we witnessed a serious and intense debacle. Though I understand that Johnson initiated the article and his efforts should be applauded, nowhere does it say that he is the final authority on the subtle and complex subject of optical dispersion. Excess of zeal can be very destructive. TonyMath (talk) 20:44, 26 April 2011 (UTC)Reply[reply]

(--ErikM (talk) 11:14, 8 January 2009 (UTC))Reply[reply]

The Wikipedia article on Kramers-Kronig relations links to this article and that article back to this one. But other than that, there is no reference to Kramers-Kronig on this page. What gives? This is not a useful reference. Nor do I see any formula on this page that even remotely looks like a Kramer-Kronig Formula. 67.95.202.34 (talk) 04:33, 7 February 2009 (UTC)Reply[reply]

Note that Kramers–Kronig is exclusively about material dispersion (and other linear susceptibilities), which is only a subset of what is discussed on this page. I agree that it would be nice, in the section on material dispersion, to mention that material dispersion is indirectly related to absorption loss by the Kramers–Kronig relations, and link to the latter. I doubt that we should actually give the Kramers–Kronig formulas here. (Unfortunately, last time I checked, the K–K page on Wikipedia seemed pretty awful, but that's a topic for that page, not this one.) — Steven G. Johnson (talk) 06:30, 3 August 2009 (UTC)Reply[reply]

I've added a mention of K–K to the section on material dispersion, as I proposed. (It looks like the K–K article is not so bad these days, although it could use a more accessible introduction.) — Steven G. Johnson (talk) 19:27, 6 August 2009 (UTC)Reply[reply]

While I agree that "dispersion" in optics automatically refers to the frequency dispersion, also a note of the spatial dispersion should be added. As a matter of fact, this phenomenon is present in many solids, being responsible for different phenomena, and its study has a long history. If nobody objects, I will try to write some notes in the future.FDominec (talk) 15:09, 30 July 2015 (UTC)Reply[reply]

Pinging FDominec. If you consider this split still necessary please mention it in the talk page of a relevant WikiProject. If not, please remove the tag. A. C. Santacruz ⁂ Talk 09:47, 14 September 2021 (UTC)Reply[reply]

It would be good to have a diagram of refractive index surrounding an absorption resonance peak (i.e. a picture of anomalous dispersion), and some more explanation of why the dispersion curve has the features it does (e.g., precisely where anomalous dispersion is encountered; and the mechanism behind normal dispersion being normal). Cesiumfrog (talk) 22:21, 20 December 2015 (UTC)Reply[reply]

I agree with the Nov.2015 suggestion that 'Dispersion measure' be split out into a separate article. DM is not just about pulsars any more. Since the Mar. 15, 1980 article by Linscott/Erkes and particularly since FRBs Lorimer et.al. Nov 2 2007, the dispersion measure has become a valuable tool for discovering what's in the neighborhood of many kinds of pulse sources. Too important to be relegated to a skimpy paragraph at the end of a broad introductory optics article. Twang (talk) 00:51, 5 January 2017 (UTC)Reply[reply]

I have renamed section so that this can count as split proposal discussion. (If anyone still wants to discuss a split) Footlessmouse (talk) 10:32, 29 August 2020 (UTC)Reply[reply]

I think this page would be greatly improved by the addition of a history section describing the original discovery of dispersion and the scientists involved with the formalization of the subject. I will probably try to add some of this in the next couple months, but there may be others more capable of adding it in short order. DavidJonBloom (talk) 04:07, 6 April 2021 (UTC)Reply[reply]

Refractive index formulae 41.78.136.116 (talk) 17:44, 28 November 2021 (UTC)Reply[reply]

Wherefrom does the factor p comes in

${\displaystyle {\frac {\partial ^{p)){\partial \omega ^{p))}k(\omega )={\frac {1}{c))\left(p{\frac {\partial ^{p-1)){\partial \omega ^{p-1))}n(\omega )+\omega {\frac {\partial ^{p)){\partial \omega ^{p))}n(\omega )\right)}$?

And the same question for the phase. Madyno (talk) 16:17, 10 November 2022 (UTC) Sorry, got it. Madyno (talk) 16:24, 10 November 2022 (UTC)Reply[reply]