Interactive Forum (closed)

Christophe Caloz (formerly a member of MTT-15) has put together some results from an interactive discussion on the terminology in the area of metamaterials.

He considers two terminologies which have been debated: »metamaterials« and »left-handed«. The latter very much depends on the point of view and applications targeted.

Metamaterial Terminology

MTT-15 position

The terminology »metamaterial« is appropriate to designate effective electromagnetic structures, i.e. structures operating in a frequency range where the average lattice size p is much smaller than the guided wavelength (p << λ_g/4 or, equivalently, where the unit cell is lumped), since such structures may be rigorously characterized in terms of their effective constitutive parameters ε and μ.

It is not restricted to structures with a ε,μ < 0.

It may be considered as an extension of the traditional terminology »artificial dielectrics« to include novel properties and effects.

It should not be used to designate non-effective structures for which, when periodic, the terminology »periodic structures« is the appropriate one.

	PROS	CONS
METAMATERIALS (MTMs) ~ 2000	very general for effective structures (lattice << λ) exhibiting interesting ε and μ dispersive responses regroups all engineered materials under the same umbrella reasonable consensus	too vague renames old concepts and make them appear new (e.g. chiral and bi-anisotropic media) some people include Bragg structures in MTMs while Bragg structures are not effective and do not have defined ε and μ (i.e. are not materials but only »structures«)
ARTIFICIAL DIELECTRICS (ADs) Bose, 1989 (twisted jute) Lindman, 1914, (chiral helixes) Cock, Cohn, Collin, 1940–1960, (loaded dielectrics, radoms)	appropriate for MTMs (as effective structures): all MTMs are ADs.	may occult the novelty in recent MTMs (e.g. negative refractive index, super-resolution, infinite wavelength propagation, enhanced complex mode coupled-line coupling, full-space scanning, leaky-wave radiation, etc.)
PERIODIC STRUCTURES (PSs) Brillouin, 1946 (passive) Pierce, 1950 (tubes)		a MTM (as an effective structure) does not owe its properties to periodicity and does not need to be periodic. applies only to Bragg regime (lattice ≅ mλ/2), opposed to MTM regime passive PSs: only space harmonics can be backward ≠ modes → very different and less efficient tubes PSs: backward waves (BWO) = interaction of EM waves with an e-beam → no passive medium
FILTERS (1D case) Matthaei, Young, Jones, 1964		every structure in the world is a filter (e.g. metal at optical frequencies, waveguides, amplifiers, etc.) MYJ filters (except Bessel) → magnitude response following a mathematical prototype ⇒ all cells different and generally not subwavelength ⇒ not a uniform medium or material but only a 2-port circuit ⇒ phase response is wiggly (no continous ε and μ even if were effective) 1D MTM has all properties of 3D (Felsen, Marcuvitz) considering just different directions see applications (antennas, couplers, imagers, etc.)

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Left-handed Terminology

MTT-15 position

Both terminologies »left-handed« (LH) and »negative refractive index« (NRI) are appropriate to designate metamaterials with negative ε and negative μ.

LH is applicable for all metastructures, including 1D, while NRI is ideal for 2D and 3D structures where refractive effects are specifically used.

The terminologies »double negative« (DNG), »backward-wave« and »Veselago« are not recommended.

	PROS	CONS
LEFT-HANDED (LH) Veselago, 1967	fundamental triad in Maxwell's equations initial terminology of Veselago in his classical 1967 paper	possible confusion with bi-isotropic (chiral) media made of geometrical LH or right-handed »atoms«, while the geometrical »atoms« of LH media have no handedness.
NEGATIVE REFRACTIVE INDEX (NRI) ~ 2003	optimal for refractive phenomena	sees only n and forgets Z, purely physicists vision. not relevant for 1D LH structures where only β and Z are really meaningful to describe the phenomena and design devices
DOUBLE NEGATIVE (DNG) ~ 2003	avoids possible confusions	does not tell what is negative may suggest that DNR is mandatory for NRI, which is wrong (e.g. anisotropic media) same limitation as NRI for 1D structures
BACKWARD WAVE (BW)	applies both to 1D and 2D-3D structures	confusion with space harmonics and active tubes little information on constitutive parameters
VESELAGO	tribute to pioneer Veselago	no information on material properties Veselago is the most important contributor, but not the unique one (Pocklington, Mandelshtam, Sivukhin, and many recent ones)

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Should 1D Metastructures be called Metamaterial Structures?

MTT-15 position

1D metastructures, which are by definition operated in an effective frequency range, engineered (like artificial transmission lines) in terms of their effective constitutive parameters (ε/μ or, equivalently, β/Z) and exhibiting unusual properties, should be called »metamaterial structures«. They may alternatively be called »meta transmission lines«. In contrast, they should not be called »metamaterials«.

1D structures which are used as filters (i.e. for their pass-band and stop-responses) should not be called »metamaterial structures«, but »filters«, even if they are designed using non traditional filter techniques

	YES	NO
APPEARANCE/FUNCTION	have a sub-wavelength structure (in their MTM band of operation) operated (as MTM structures) neither near cutoff nor in stop bands are (should) not be used as filters »the whole world is a filter« (including 3D MTMs, of course)	look like (periodic) filters generally do not have a volumetric structure they ultimately filter
DESIGN	phase/dispersion engineering, whereas conventional filters are designed for magnitude specifications (rare exceptions); MYJ not applicable similar to artificial transmission lines (e.g. lumped microwave components) characterized by β and Z, i.e. »continuous«
RESPONSE	same fundamental properties as 2D and 3D (CRLH) as a consequence of effective homogeneity
SOME UNIQUE PROPERTIES (NOT IN FILTERS)	distinct backward-wave propagation complex mode enhanced coupling infinite wavelength propagation full-space leaky-wave propagation phase conjugating »NRI« interfacing artificial-TL multiband/enhanced-BW impulse dispersion engineering

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