Talk:Negative-index metamaterial

Misleading redirect: "Negative index media" are not subset of "Metamaterials", and vice versa
There are homogeneous media that should exhibit negative refraction. See e.g. Agranovich 2004, who suggests that many ordinary materials with excitonic resonances should behave like this, and concludes with another example of negative group velocity of Surface plasmon on simple silver-coated aluminum.

On the other hand, there are also metamaterials that are not designed to provide any negative refraction. Other metamaterials do provide negative refraction, but their spatial dispersion prevents from speaking about anything like "negative index of refraction". The redirect from Negative_index_of_refraction is therefore double wrong.

By the way, I believe the group of pages discussing metamaterials, photonic-crystals, transformation optics, superlens, cloaking and related topics etc. needs a complete rewrite. Note how much time was wasted in the discussion about cloaking above! Cloaking indeed does NOT require negative refraction and I am convinced it absolutely needs not to be mentioned here. It should be contained in Metamaterial_cloaking (which itself might better merge with Transformation_optics etc.). --FDominec (talk) 09:22, 31 March 2014 (UTC)


 * FDominec is correct. It is wrong to say that a negative index of refraction does not occur in nature. To add to the example above, this paper contains measurements of such waves in plasmas (Armstrong 1984 ) and indeed predates Agranovich by some margin. If it not objected to, both the redirect and wording of this article should be changed to de-emphasise the property of negative refractive index as that only of a metamaterial. Phuech (talk) 14:36, 03 November 2014 (UTC)


 * In line with the above, I've changed the hatnote at Refractive index§Negative refractive index from 'main' to 'see also'. And with reliable sources to support these,, please by all means make the changes – I am more than happy to support such changes! — Sasuke Sarutobi (talk) 18:59, 3 November 2014 (UTC)


 * I believe you are absolutely wrong. You do not get both epsilon and mu <0 certainly at any optical frequencies. Yes, you do very much get epsilon < 0 (in plasmas, metals) which is what you must be talking about. However the issue is BULK negative index materials, and that requires mu<0 which just doesn't happen. In fact at optical frequencies mu=1 almost exactly (I'm not even aware of ANY measurement where it is significantly different from 1 at optical frequencies), and certainly not <0!! If disputed, I'm willing to look at the source cited, but first FDominec should recheck it to see that he/she misinterpreted epsilon<0 for n<0.


 * Also, note that negative refractive index implies the PHASE velocity being negative, not group velocity. Interferometrist (talk) 12:24, 4 November 2014 (UTC)

I also disagree, and think the mere supposition that what might be an effectively left-handed material, due to exitonic resonances, makes for "homogenous" examples is a bit of a misleading ruse, since, even in its realization, this would still require the resonant superstructure of an effective meta-material.

More importantly, the biggest problem with this article and this topic is that it is based on the unfortunate, non-physical, silly weasel words of "negative index materials," which has just been a buzz word for a bunch of cheezeballs to make glitzy, sensational press releases (need I invoke all the intellectually bankrupt press-releases on "faster than speed of light" nonsense from these same grand-standers?). It is just a dumb, misleading terminology.

The terms "metamaterials", "left-handed materials" are far more accurate, more physical, and far less misleading. Why not stick with what is real? Wikibearwithme (talk) 00:22, 8 September 2016 (UTC)


 * The profound problem of this article is that it is inherently based on a popular, but questionable approximation of local constitutive parameters. This may be acceptable in microwaves, where we can easily make e.g. SRRs much smaller than wavelength. At short wavelengths, all metamaterials known so far exhibit strong spatial dispersion (4) (aside of great dissipative losses!), where $$\varepsilon = \varepsilon(\omega, \mathbf{k})$$. By the way, even in the isotropic case whenever one uses permittivity dependent on wavenumber $$k = |\mathbf{k}|$$, all magnetic effects can be accounted for in the spatial dispersion and $$\mu$$ can be completely eliminated form Maxwell equations (1). The very notion of the scalar refractive index ceases to make much sense when spatial dispersion is so strong, that it enables opposite signs of group and phase velocities. As I noted above, this happens not only in metamaterials, but is also predicted for waves near excitonic levels in some homogeneous media (2). Aside from this, also the vectors of phase velocity, group velocity (not speaking about the signal velocity) and energy propagation velocity can have very exotic combinations of their orientation (3).
 * I am afraid a proper treatment of periodic structures in terms of homogenized effective parameters is far more complicated than is commonly understood. I am very in favor for that Wikipedia provides solid theoretical background, avoiding self-assuring simplifications (5). Should not we write a wikibook on this topic? :)
 * References:
 * (1) Landau, Lifshitz et al., 1984: Electrodynamics of continuous media, paragraph 103-106
 * (2) Agranovich, Gartstein 2006: Spatial dispersion and negative refraction of light
 * (3) Mikki, Kishk 2009: Electromagnetic wave propagation in nonlocal media: Negative group velocity and beyond
 * (4) Klingshirn 2007: Semiconductor optics, p. 455 etc.
 * (5) Munroe 2011: http://xkcd.com/978/
 * FDominec (talk) 17:55, 5 December 2014 (UTC)


 * FDominec, this sounds quite interesting. I stumbled accross your discussion here while reading up on spatial dispersion. In fact I plan to start the article spatial dispersion which at the moment doesn't exist.
 * What do you mean that metamaterials have strong spatial dispersion, do you mean they cannot be described by spatially local $$\epsilon$$, $$\mu$$?
 * I understand we are free to represent the bound currents $$\nabla \times \mathbf M$$ from magnetization instead as bound currents $$-i\omega\mathbf P$$ from electric polarization. Or vice versa: for that part of electric polarization current which is divergenceless (no bound charge) we can represent it as a magnetic bound current. But do you think there is any preference to use one or the other? For example I think it's mathematically convenient that we often can "hide" surface bound currents by placing them in $$\mathbf M$$. Then, the transverse $$H$$ field is continuous across the surface. Certainly you're right that negative $$\mu$$ is not the only mathematical encoding that produces negative group velocity.
 * Nanite (talk) 08:15, 8 March 2015 (UTC)


 * Nanite, the notion of spatial dispersion is surely worth a Wikipedia article. It should be also somehow linked to nonlocality, and it should be marked clearly when the theory refers to an electromagnetic wave only. Your mention of the possibility to re-express polarisation in terms of nonlocal magnetisation is pertinent, but if an article is to be written, I would recommend keeping it simple and showing only the example from Landau&Lifshitz where magnetisation is expressed by means of nonlocal polarisation.
 * When the misleading/cluttered articles are to be rewritten as I proposed above, a rigorous theory based on isofrequency contours and spatial-dispersive medium parameters should be explained first (in separate articles?), and then the approximation of local permittivity and permeability and other common MM notions can follow based on the firm theory.
 * I am a bit afraid this is going to be a really hard topic to explain in Wikipedia, though not impossible if it is done in a well-thought didactic way. If anybody is interested, I can post ca. 10 kB from my thesis where I build the spatial-dispersive theory down from Maxwell equations. FDominec (talk) 21:22, 8 March 2015 (UTC)

Hi FDominec, thanks for the tips. I agree things are best kept simple and L&L seem to cover it fairly well in section 103 (though I wonder about the issues of boundary conditions, which they have avoided...). I also found various papers, e.g., this arxiv which notes the more general transformation in Eq 9. They say this is fairly well known, and "[the choice mu=1 is] particularly useful in the presence of spatial dispersion, where there is no set of local (independent of k) parameters epsilon and mu. Then it is convenient to specify the medium properties by a single (but nonlocal) quantity epsilon." However, also they say "For spatially nondispersive media where epsilon and mu are independent of k, it is often more convenient to retain these two parameters, as they are much simpler to use in practical situations formulated in the spatial domain."

I read your earlier comment again and I see what you mean, in this context. In optical metamaterials the permittivity has a strong spatial dispersion, and so they might as well absorb their permeability into it for simplicity.

I am a bit new to this E&M field, coming from a background of mesoscopics. In mesoscopics nonlocality can be very widespread. It's interesting that while E&M is normally taught as a local theory, nonlocality does come in from time to time even at room tempearture. By the way, a point of terminology: I would say that spatial dispersion is a restricted type of nonlocality: for spatial dispersion, the system should be homogeneous and infinite so it is possible to fourier transform the system in space. In other words spatial dispersion should be something expressible as a wavenumber dependence, just like temporal dispersion has a frequency dependence. (The more general type of nonlocality would apply also to irregularly shaped systems.) Is my thinking correct?

--Nanite (talk) 21:48, 9 March 2015 (UTC)


 * Dear Nanite, it is a good point (which I did not realize) that spatial dispersion describes one specific sort of nonlocal behaviour that exists in homogeneous infinite media only. In fact, spatial dispersion is relatively common in optics, one example being Doppler broadening in gases, but it can often be approximated by frequency dispersion.
 * As a result, I believe SD gets less attention than it would deserve in E&M courses. When one holds a hammer, all problems look like a nail; when a generation of physicists is taught the local theory, almost everybody tries to describe metamaterials in terms of local parameters. This however causes much confusion, because as far as I know, above GHz range, we are only able to make metamaterials that are spatially dispersive (and lossy). If no fundamental breakthrough comes, I guess it will remain true in the next decades.
 * I therefore happily support the idea of writing a robust and readable article on spatial dispersion, though I can not promise to invest much time in it now. The article can in general relate to any waves propagating in a (nonlocal homogeneous) medium, so the theory can be composed of wave equation and convolution with nonlocal response function. The second part of the article could focus on the electromagnetic wave, extending the subject to the electromagnetic "L&L §§103-106" theory (I tried to sketch it here) and mentioning several examples, including gases and metamaterials. What do you think about this? FDominec (talk) 23:37, 9 March 2015 (UTC)


 * That sounds perfect! Presently in my studies I am coming accross spatial dispersion in the context of spatially dispersive conductivity (e.g., Landau damping) and I would give that a mention. I would also like to show a simple example of spatially dispersive response both in fourier and as a spacetime animation. I am not sure which response function would be illustrative here, any ideas?
 * --Nanite (talk) 08:42, 13 March 2015 (UTC)


 * Finally got around to it, spatial dispersion is now an article. I hope you can find some time to improve the article further. Cheers, --Nanite (talk) 12:43, 6 December 2015 (UTC)

External links modified
Hello fellow Wikipedians,

I have just modified 1 one external link on Negative index metamaterials. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive http://web.archive.org/web/20100117145839/http://physics.aps.org:80/articles/v2/91 to http://physics.aps.org/articles/v2/91

When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at ).

Cheers.—cyberbot II  Talk to my owner :Online 03:26, 2 April 2016 (UTC)

Institutional Research
Is there any point in the 'Institutional Research' section? This has grown to a significant field of research internationally, with research going on in likely hundreds if not thousands of institutions. - Yikkayaya (talk) 12:13, 23 January 2017 (UTC)


 * I think there is no point in keeping the 'Institutional Research' section. And I still believe that whole article should be rewritten from scratch, because its structure suggests its text was gathered as learning notes and is not well organized. It also overlaps with the Metamaterial article. --FDominec (talk) 17:29, 25 January 2017 (UTC)


 * It does indeed need a rewrite. I am unfortunately far out of my field here. Yikkayaya (talk) 10:24, 31 January 2017 (UTC)

External links modified (February 2018)
Hello fellow Wikipedians,

I have just modified one external link on Negative-index metamaterial. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added tag to http://www.physics-online.ru/PaperLogos/1/files/Full_text_English_version.pdf
 * Added tag to http://www.csm.unavarra.es/Publicaciones/Images/Pub474.pdf
 * Added tag to http://www.physics.princeton.edu/~mcdonald/examples/optics/garrett_pra_1_305_70.pdf
 * Added archive https://web.archive.org/web/20160303224255/http://www.fulviofrisone.com/attachments/article/404/6875x_c001.pdf to http://www.fulviofrisone.com/attachments/article/404/6875x_c001.pdf
 * Added tag to http://www.physics.princeton.edu/~mcdonald/examples/optics/garrett_pra_1_305_70.pdf

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

Cheers.— InternetArchiveBot  (Report bug) 11:26, 15 February 2018 (UTC)