Talk:Dispersion (optics)

message: 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)
replies: text: 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)
replies: text: 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)
thread_title: Material dispersion in optics

message: I recently added what I thought was the more general formula for the group velocity:
: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: 
:v = \omega / k
and
:v_g = \frac{\partial \omega}{\partial k}
hence:
:v_g = v + k \frac{\partial v}{\partial k}
and from k = 2\pi / \lambda, giving:
: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)
replies: text: Ah, now I see what you meant.  My problem is with the k = 2\pi / \lambda.   Ordinarily, in equations like this (or in most of optics for that matter) λ means the vacuum wavelength, i.e. \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)
replies: text: 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)

text: 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)
thread_title: Group velocity formula

message: what's the difference?  Pfalstad 15:47, 4 January 2006 (UTC)
replies: text: 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)
thread_title:  waveguide dispersion vs. modal dispersion 

message: 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)
thread_title:  Dark Side of the Moon 

message: 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)
replies: text: 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)

text: 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)
replies: text: This is now fixed. — Kieff | Talk 03:36, 27 February 2008 (UTC)
thread_title:  Conceptual animation 

message: (--ErikM (talk) 11:14, 8 January 2009 (UTC)
thread_title:  References 

message: 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)
replies: text: 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)
replies: text: 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)
thread_title: Kramers–Kronig

message: 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)
replies: text: Pinging . 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)
thread_title:  Dispersion and Spatial dispersion 

message: 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)
thread_title:  Anomalous dispersion 

message: 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)
thread_title: Split proposal

message: 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)
thread_title:  Addition of a History Section 

message: Refractive index formulae 41.78.136.116 (talk) 17:44, 28 November 2021 (UTC)
thread_title:  Dispersion 

message: Wherefrom does the factor p comes in
:\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)
thread_title:  Factor p 

message: The section "Generalized formulation of the high orders of dispersion – Lah-Laguerre optics" has two primary refs. One is a preprint and the other has 9 citations. The section consists of one paragraph, three pages of formulas, and one figure from one of the papers.
I think the topic should be covered in one sentence or not at all. Johnjbarton (talk) 18:15, 23 April 2024 (UTC)
thread_title:  WP:Undue content Generalized formulation of the high orders of dispersion – Lah-Laguerre optics