Talk:Dispersion (optics)

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Contents 1 Material dispersion in optics 2 Group velocity formula 3 How to solve a problem of light dispersion in Optics? 4 waveguide dispersion vs. modal dispersion 5 Dark Side of the Moon 6 Conceptual animation 7 Measuring Dispersion

[edit] Material dispersion in optics

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."

[edit] Group velocity formula

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

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 = ω / k

and

hence:

and from k = 2π / λ, giving:

.

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)

Ah, now I see what you meant. My problem is with the k = 2π / λ. Ordinarily, in equations like this (or in most of optics for that matter) λ means the vacuum wavelength, i.e. λ = 2πc / ω. 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)

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)

• 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)

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)

• 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)

[edit] How to solve a problem of light dispersion in Optics?

[edit] waveguide dispersion vs. modal dispersion

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

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)

[edit] Dark Side of the Moon

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)

[edit] Conceptual animation

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)

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)

[edit] Measuring Dispersion

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)

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)

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)

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)