Negative Refraction, Left-Handed, Negative Refractive Index Material, NIM's, or Metamaterial Headlines Going Back as far as to 1904

Some negative refractive index material headlines long before Veselago work and going back as far as to 1905...

     



     Negative-refraction materials, also called briefly as NIM's, or "left handed materials," LHM, or metamaterials, refract light in a way which is contrary to the normal "right handed" rules of electromagnetism. LHM researchers hope that the peculiar properties will lead to superior lenses, and might provide a chance to observe some kind of negative analog of other prominent optical phenomena, such as the Doppler shift and Cerenkov radiation. When the dielectric constant, eps, and magnetic permeability, mu, are both negative waves can still propagate in such a medium, since the product eps*mu remains positive. In this case, the refractive index in the Snell's law is negative, an incident wave experiences a negative refraction at an interface, and we have a backward wave for which the phase of the waves moves in the direction opposite to the direction of the energy flow. The first study of general properties of wave propagation in such a negative refractive index medium has been usually attributed to the work of Russian physicist V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of eps and mu", Soviet Phys. Usp. 10, 509-514 (1968) [Usp. Fiz. Nauk 92, 517-526 (1967); for further Veselago's articles click here]. However, the subject has been studied since 1904, at least...

     H. Lamb [see his article "On group-velocity", Proc. London Math. Soc. 1, 473-479 (1904)] may have been the first person to suggest the existence of backward waves (the waves which phase moves in the direction opposite from that of the energy flow). Lamb´s examples involved mechanical systems rather than electromagnetic waves. Seemingly, the first person who discussed the backward waves in electromagnetism was A. Schuster in his book An Introduction to the Theory of Optics (Edward Arnold, London, 1904). On pp. 313-318 of his book Schuster briefly notes Lamb´s work and gives a speculative discussion of its implications for optical refraction, should a material with such a properties ever be found. He cited the fact that within the absorption band of, for example, sodium vapour a backward wave will propagate. But, because of the high absorption region in which the dispersion is reversed, he was pessimistic about the applications of negative refraction. Around the same time, H.C. Pocklington in his article "Growth of a wave-group when the group velocity is negative", Nature 71, 607-608 (1905) showed that in a specific backward-wave medium, a suddenly activated source produces a wave whose group velocity is directed away from the source, while its velocity moves toward the source.

     The latter property was rediscovered by almost 50 years later by G.D. Malyuzhinets, "A note on the radiation principle", Zh. Tekh. Fiz. 21, 940-942 (1951). General properties of wave propagation in a medium with negative refractive index have been discussed by D.V. Sivukhin, "The energy of electromagnetic waves in dispersive media", Opt. Spektrosk. 3, 308-312 (1957). Some unusal aspects of the transition radiation and Cherenkov radiation in the frequency region characterized by negative group velocities have been revealed by V. E. Pafomov in a series of his articles JETP 33(4), 1074-1075 (1957), JETP 30(4), 761-765 (1956), and Soviet Physics-JETP 36(6), 1853-1858 (1959) [the original russian articles can be requested from Sergei Galiamin]. The use of negative refractive medium as a plane-parallel lens (though not yet perfect) has been investigated by R.A. Silin in his article "Possibility of creating plane-parallel lenses", Opt. Spektrosk. 44, 189-191 (1978) (an english translation is available thanks to OSA, which has been publishing translation of the Russian journal). Noteworthy in this regard is an earlier review by R.A. Silin, "Optical properties of artificial dielectrics", Izv. VUZ Radiofiz. 15, 809-820 (1972), which appeared almost thirty year before the current revival of interest in the properties of wave propagation in a medium with negative refractive index. The review focuses on artificial dielectrics formed as various periodic arrangements of conductive and dielectric elements. Propagation properties are explained in terms of equi- or iso-frequency surfaces. It is argued that flat parallel slabs of artificial dielectrics may convert a divergent beam into convergent one, total reflection may appear at small incidence angles and at larger incidence angles partial reflection, increasing incidence angle may result in decreasing refraction angle. Depending on the incidence angle, birefringence may occur. All these three authors give credit to an earlier theoretical and experimental works of L.I. Mandel'shtam [He discovered Raman scattering several days before Raman, but only Raman was awarded by the Nobel prize. See here for details]:

  1. Group velocity in crystalline arrays, Zh. Eksp. Teor. Fiz. 15, 475-478 (1945)
  2. Complete Collected Works (Akad. Nauk SSSR, Moscow, 1947), Vol. 2, p. 334
  3. Complete Collected Works (Akad. Nauk SSSR, Moscow, 1950), Vol. 5, p. 419

     Various artificial dielectrics composed of periodically spaced lattices of metallic rods, also known as wire grid, wire mesh, or rodded structures, have been intensively studied by electromagnetics community in early fifties of the last century. Although they do not possess a negative index of refraction, they exhibit a plasma-like behaviour [W. Rotman, Plasma simulation by artificial dielectrics and parallel-plate media, IEEE Trans. Antennas Propag. 10, 82-95 (1962)] and their index of refraction can be less than unity [J. Brown, Artificial dielectrics having refractive indices less than unity, Proc. IEEE, Monograph no. 62R, vol. 100, Pt. 4, pp. 51-62 (1953)].

     Another example of remarkable but forgotten work is that by Remigius Zengerle, now professor at the University of Kaiserslautern in Germany. Long before an ``official discovery" of photonic crystals, and shortly after finishing his PhD thesis at the Max-Planck-Institute for Solid State Physics in Stuttgart (between 1977 and 1979), he presented his work on the optical Bloch waves in (singly and doubly) periodic planar waveguides on the conference on Integrated and Guided-Wave Optics held in Incline Village, NV, USA, on 28-30 Jan. 1980. (See the contribution by R. Ulrich and R. Zengerle, Optical Bloch waves in periodic planar waveguides, (IEEE, New York, 1980), pp. TuB1/1-4, in the conference technical digest.) Among other, the contribution discusses interference, transitions to nonperiodic guides, beam steering, negative refraction, and focusing as possible applications. Take notice, the authors presented theoretical simulations together with experimental verification of their predictions. More accessible is a later publication by R. Zengerle, Light propagation in singly and doubly periodic planar waveguides, J. Mod. Optics. 34(12), 1589-1617 (1987), which is a condensed form of Zengerle's PhD thesis. He clearly demonstrates (both theoretically and experimentally) negative refraction in the visible in certain areas of the backward bending dispersion relation (see, for instance, photograph 10a) and focusing properties of the doubly periodic planar waveguide between unmodulated regions with parallel straight boundaries (see, for instance, photographs in Figs. 13-14). A clear graphical representation of the observable propagation effects is given in terms of wave-vector diagrams, showing the directional dispersion of the elementary waves in periodic structures. Examples of applications of planar periodic (singly and doubly periodic) structures as highly selective frequency filters, optical multiplexers as well as frequency-tunable beam narrowing, focusing, and expanding devices (decade later rediscovered as superprisms) are given together with measured data. (Read recent The Anatomy of Negative Refraction by Igor Tsukerman for the summary of the early work together with an overview of technical details.)

     Shortly after R. Zengerle had completed his PhD thesis, an article by R. E. Camley and D. L. Mills, Surface polaritons on uniaxial antiferromagnets, Phys. Rev. B 26, 1280-1287 (1982) appeared. Among other issues, the authors also discussed the case of an antiferromagnetic metal. At a first glance, the title does not look promissing for those interested in negative-refractive index materials. However, metal implies a negative dielectric constant, whereas antiferromagnet implies a negative permeability. In the antiferromagnetic metal case, when both dielectric constant and magnetic permeability are negative, R. E. Camley and D. L. Mills then made the following observation: "In this case we find that the phase velocity of both the bulk and surface polaritons is oppositely directed to the group velocity" (see p. 1281, right column, last but one paragraph; p. 1284, left column, last paragraph - right column, l. 1). At both occasions they added that such a behavior was to be expected and refered to Veselago.

     Almost one decade later, H. Khosravi, D. R. Tilley, and R. Loudon (see their article Surface polaritons in cylindrical optical fibers, J. Opt. Soc. Am. A 8, 112-122 (1991) for more details) established negative group velocity regions of surface polaritons in cylindrical optical fibers of angular momentum m=1 over a limited fiber radii range. The integrated power flow for m=1 (see Fig. 14 therein for the power flow density and Fig. 16 for the integrated power flow) is negative for the range of momentum q values for which the slope of the corresponding dispersion curve is negative. This shows that the energy velocity [Eq. (55) therein and displayed in Fig. 18 for m=1] is in quantitative agreement with the group velocity v_g=d omega/d q found as the slope of the dispersion curve (for m=1 displayed in Fig. 7 therein). Later on, these conclusions have been confirmed in the work by B. Prade and J. Y. Vinet, Guided optical waves in fibers with negative dielectric constant, J. Lightwave Technology 12(1), 6-18 (1994).

     A recent discovery by Zhang, Fluegel and Mascarenhas shows a new type of medium interface that features negative refraction or, depending on the angle of incidence, positive (conventional) refraction. This switch-hitting optical ability (the technical name for it is amphoteric refraction) is a first. Furthermore, the same type of interface can be used to (negatively or positively) refract a ballistic beam of electrons (i.e., electrons traveling, as waves, over a very short distance in a straight line). The amphoteric refraction can be observed on the interface of two slabs of uniaxial YVO4 crystals, provided that the respective crystals optical axis are properly oriented. An additional feature of the interface is that it inhibits all reflection. This opens the door for a reflection-less lens which would be of enormous value in, for example, the transport of high-power laser beams. A recent comment by H.-F. Yau, J.-P. Liu, B. Ke, C.-H. Kuo, and Z. Ye, Comment on "Total Negative Refraction in Real Crystals for Ballistic Electrons and Light", Phys. Rev. Lett. 91, 157404 (2003) [see also cond-mat/0312125] clarifies that the amphoteric refraction can be observed even with a single uniaxial crystal and that it is purely due to the anisotropy of refractive media. They also argued that the superlensing effect will not be observed since, in contrast to true negative refraction media, the negative refraction in the amphoteric case only occurs in a narrow range of incident angles.

     Recent article by C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix, IEEE Trans. Antennas Propag. 51, 2596-2603 (2003) speculated that complicated structures comprising split ring resonators and wires are not necessary for the design of a negative-refraction material which, in principle, can be obtained as a composite of spheres. This would open up the possibility of fabricating an homogeneous and isotropic negative refractive index metamaterials much more simply than it has been proposed up until now. Together with Vassilis Yannopapas we have recently expanded on the ideas of Holloway et al and showed that even a composite of inherently non-magnetic homogeneous spheres can provide a negative refractive index metamaterial. See our article published in J. Phys.: Condens. Matter. 17, 3717-3734 (2005) (minor erratum) [pdf]. The absence of inherently magnetic materials in our porposal is a key difference which makes it possible to achieve a negative refractive index band even in the deep infrared region. Note that materials that exhibit magnetic response are:

Magnetic polarisation in materials follows indirectly either from the flow of orbital currents or from unpaired electron spins. In magnetic systems, resonant phenomena, analogous to the phonons or collective modes that lead to an enhanced electric response at infrared or higher frequencies, tend to occur at far lower frequencies, resulting in relatively little magnetic material response at THz and higher frequencies. Though R. Zengerle has already achieved negative refraction in planar waveguides in the visible, our design is a 3D isotropic design which can be realized by both periodic and disordered structures. The resulting negative refractive index structure is a truly subwavelength structure with wavelength-to-structure ratio as high as 14:1, which appears to be almost by 50% higher than that achieved so far using split ring resonators and wires.

     Our results are explained in the context of the extended Maxwell - Garnett theory (see my accompanying F77 code EFFE2P) and reproduced by the ab-initio calculations based on first-principle multiple scattering theory. The role of absorption in the constituent materials is discussed. The centre wavelength lambda of the negative refractive index band can be tuned over a wide frequency range from deep infrared to terahertz (1-10 THz) frequency ranges. This can lead to efficient optical components for terahertz beams, which are required in many scientific and technological applications, ranging from the imaging of biological materials to manipulating quantum states in semiconductors, from drug discovery and medical imaging to security screening.

     Here you can download my Windows executable effe, which calculates an effective medium properties for a composite of coated Au@SiO2 spheres in air with volume fraction 34%. The executable is to be used for wavelengths typically at least one order of magnitude longer than the sphere radius. Refractive index of SiO2 is taken to be 1.45. The refractive index of gold for wavelengths up to 2 micrometers is determined using Palik's data (download material data file Audat.dat) and for longer wavelengths a Drude fit is used according to parameters by M. A. Ordal et al, Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, V, and W in the infrared and far infrared Appl. Opt. 22, 1099-1119 (1983). Although all the constituents are nonmagnetic, you will find that the effective medium does show magnetic properties. The idea of generating an effective magnetic response from a composite comprising inherently nonmagnetic materials had already been implicit in the work of L. Lewin, The electrical constants of a material loaded with spherical particles, Proc. Inst. Elec. Eng. 94, 65-68 (1947), which was later generalized by N. A. Khizhnyak, Artificial anisotropic dielectrics formed from two-dimensional lattices of infinite bars and rods, Sov. Phys. Tech. Phys. 29, 604-614 (1959). (A brief description of these two and other early headlines on effective medium properties or homogenization of photonic crystals you will find here.)


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