The realization of a left-handed electromagnetic medium — an effective medium with simultaneously negative effective permittivity and permeability — by Smith, Padilla, Vier, Nemat-Nasser and Schultz in 2000 opened the way to testing the counterintuitive electrodynamic effects that Veselago predicted in 1968 for such media. Most of the open issues raised by that paper have since been closed by direct experimental or quantitative work: effective-parameter retrieval from reflection and transmission measurements is now standard, the role of losses in left-handed bands has been characterized, isotropic three-dimensional left-handed metamaterials have been built, and negative refraction, reversed Cherenkov radiation, and the inverse Doppler effect have all been observed. The surviving open core is the one reversal that has never been definitively demonstrated: whether the radiation pressure exerted by an electromagnetic wave on a left-handed (negative-index) medium reverses sign, so that the medium is pulled toward the source ('radiation tension') rather than pushed away. The problem is to measure the sign and magnitude of the net optical force or momentum transfer on a realistic dispersive, dissipative, structured negative-index metamaterial, separated from absorption and thermal artifacts, and to reconcile the outcome with a defensible account of electromagnetic momentum density and force density in such media, where theory remains contested and even predicts that the sign can depend on the subwavelength structure.

Background

An electromagnetic 'metamaterial' is an artificial composite of subwavelength conducting or dielectric elements that behaves as an effective medium, characterized by an effective permittivity εeff(ω)\varepsilon_{\mathrm{eff}}(\omega) and permeability μeff(ω)\mu_{\mathrm{eff}}(\omega), for wavelengths much larger than the unit cell. Periodic arrays of thin continuous wires act as a dilute plasma with negative εeff\varepsilon_{\mathrm{eff}} below an effective plasma frequency, while Pendry's split ring resonators (SRRs) — small resonant rings with capacitive gaps, nonmagnetic but magnetically excited — produce a resonant μeff(ω)\mu_{\mathrm{eff}}(\omega) that is negative on the high-frequency side of the resonance. Veselago showed in 1968 that a medium with simultaneously negative ε\varepsilon and μ\mu (a 'left-handed' medium, since the field triad E\mathbf{E}, H\mathbf{H}, k\mathbf{k} forms a left-handed set, with antiparallel phase and group velocities) would invert familiar electrodynamic phenomena: reversed Doppler shift, reversed Cherenkov radiation, anomalous (negative) refraction, and reversal of radiation pressure into 'radiation tension'. Smith et al. demonstrated the first such composite at microwave frequencies in 2000 — SRRs interleaved with continuous wires, exhibiting a propagation band where both effective constants are negative — and explicitly set out what remained open: their dispersion relations set the dissipation factor Γ=0\Gamma=0; extracting the complex εeff(ω)\varepsilon_{\mathrm{eff}}(\omega) and μeff(ω)\mu_{\mathrm{eff}}(\omega) experimentally would require 'an intricate reflection and transmission measurement to fit the material constants' that they did not perform; the demonstrated structure was deliberately anisotropic, with the isotropic three-dimensional medium deferred; and the Veselago reversals remained to be observed. Subsequent literature closed these threads one by one: Smith, Vier, Kroll and Schultz computed the effective constants numerically (2000) and Smith, Schultz, Markoš and Soukoulis (2002) implemented the transmission/reflection inversion that became the standard 'retrieval procedure'; Markoš, Rousochatzakis and Soukoulis (2002) traced the transmission losses of the SRR/wire composites largely to absorption in the dielectric circuit board; isotropic three-dimensional left-handed metamaterials were demonstrated by Koschny, Zhang and Soukoulis (2005), Grbić and Eleftheriades (2005), and Wang et al. (2009); Shelby, Smith and Schultz observed negative refraction (2001), Xi et al. (2009) and Duan et al. (2017) observed reversed Cherenkov radiation, and Seddon and Bearpark (2003) and Chen et al. (2011) observed the inverse Doppler effect in left-handed and negative-index systems. The radiation-pressure reversal is the exception. Veselago's argument, and the classic Balazs thought experiment (Balazs 1953: a light pulse entering a transparent slab and displacing it, which fixes the momentum carried in matter), have been reanalyzed for dispersive, dissipative negative-index slabs by Chau and Lezec (2012) (following their companion analysis of the positive-index case, Chau and Lezec 2011), whose postulates — the Abraham momentum density (momentum density carried by the energy flux, as opposed to the rival Minkowski form proportional to field intensity), a generalized Lorentz force law, and absorption-driven mass transfer — were disputed in a published comment (Kemp 2012); Bethune-Waddell and Chau (2015) showed that simulations of existing radiation-pressure experiments cannot yet pin down the energy and momentum of light in matter; Markel (2020) gave a relativistic re-analysis critical of the standard force-density formulations; and Partanen and Tulkki (2022) state that the negative radiation pressure of light in negative-index metamaterials 'still lacks experimental verification' and that its sign may depend on the subwavelength structure. Experimental reports exist only at conference level (Lezec and co-workers, 2009 and 2011, on a left-handed plasmonic metamaterial).

Problem Statement

Determine, by direct experiment on a left-handed (negative-index) metamaterial, whether the radiation pressure exerted by an incident electromagnetic wave reverses sign — that is, whether the medium is pulled toward the source (Veselago's 'radiation tension') rather than pushed away — and reconcile the measured outcome with a consistent account of the electromagnetic momentum density and force density in a realistic dispersive, dissipative, spatially structured negative-index effective medium. This is the surviving open core of the open issues raised by Smith et al. (2000) after their demonstration of the first left-handed medium: of the electrodynamic effects they proposed to test, anomalous (negative) refraction, reversed Cherenkov radiation, and the inverse Doppler effect have since been observed, while the reversal of radiation pressure still lacks experimental verification. The measurable is the net force, impulse, or momentum transfer on a left-handed specimen relative to a positive-index control, with the scattering contribution separated from absorption-driven and thermal artifacts, together with its sign and magnitude; since current theory predicts that the sign may depend on the subwavelength structure of the composite, the outcome is to be reconciled with a defensible account of the electromagnetic momentum density and force density for the same specimen.

References

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