Pendry's 2004 'chiral route to negative refraction' showed that a single chiral resonance in an otherwise ordinary dielectric makes the refractive index negative for one circular polarization, removing the need for simultaneously negative permittivity and permeability, and predicted two signature consequences: a polarization-selective perfect lens when the circular-polarization index reaches n±=−1n_{\pm}=-1 with the medium impedance-matched to free space, and a divergence of the photonic density of states at the chiral resonance. The enabling capability — strong, low-loss chirality and chiral negative refraction — has since been demonstrated from microwave through terahertz to near-infrared frequencies, but the two predicted end-point effects have never been experimentally verified. The problem is to realize the chiral medium at the impedance-matched n±=−1n_{\pm}=-1 condition with sufficiently low loss and to experimentally demonstrate near-field subwavelength focusing for one circular polarization together with the resonance-enhanced photonic density of states and its observable consequences for radiation rates and coupling.

Background

In an isotropic chiral medium (a medium whose constituents are not superposable on their mirror image, exhibiting optical activity), the eigenmodes of propagation are right- and left-circularly polarized waves, with refractive indices n±=εμ±κn_{\pm}=\sqrt{\varepsilon\mu}\pm\kappa, where ε\varepsilon is the permittivity, μ\mu the permeability, and κ\kappa the chirality parameter that couples electric and magnetic fields. In 2000, Pendry showed that a slab with refractive index n=−1n=-1 and impedance matched to the surrounding medium acts as a 'perfect lens': it restores both propagating and evanescent (near-field) wave components of a source, allowing imaging with resolution not limited by diffraction, limited in practice only by loss. At the time, negative refraction was obtained by driving ε<0\varepsilon<0 and μ<0\mu<0 simultaneously, which requires two separate resonances that are difficult to overlap and whose magnetic resonance is hard to realize with low loss above microwave frequencies. Pendry's 2004 Science paper 'A Chiral Route to Negative Refraction' pointed out that a resonant chirality parameter κ\kappa alone makes n±n_{\pm} negative for one circular polarization while εμ\sqrt{\varepsilon\mu} stays positive, so a single resonance suffices; the wave impedance Z±=μ/εZ_{\pm}=\sqrt{\mu/\varepsilon} is independent of κ\kappa, so the medium can be impedance-matched to free space (Z±=+Z0Z_{\pm}=+Z_0, where Z0Z_0 is the impedance of free space) and hence reflectionless. He further noted that near the chiral resonance the photonic density of states (the number of electromagnetic modes per unit frequency and volume, which controls spontaneous-emission rates and coupling to emitters) is predicted to diverge, and that realizing such media at optical frequencies requires strong chirality, low loss, and scalable three-dimensional fabrication such as helical conductive structures. Subsequent work confirmed the enabling physics: giant chirality at gigahertz frequencies in bilayered chiral structures (Rogacheva et al. 2006), the first experimental chiral negative-index metamaterial with n=−5n=-5 from a single chiral resonance at terahertz frequencies (Zhang et al. 2009), a direct experimental proof of negative refraction through a three-dimensional metallic-helix array (Wu et al. 2010), a gold-helix optical metamaterial acting as a broadband circular polarizer with roughly single-wavelength thickness (Gansel et al. 2009), low-loss broadband chiral negative index at microwave frequencies (Song et al. 2017), and conjugated-gammadion (planar four-fold chiral) chiral negative-index metamaterials at terahertz frequencies (Zhao et al. 2011). Theoretical studies have analyzed focusing by chiral slabs and chiral media with unit negative refractive index (Jin and He 2005; Semchenko et al. 2008; Tretyakov 2009), and reviews summarize the field's progress (Li, Mutlu and Ozbay 2013). By contrast, the non-chiral double-negative perfect lens has only ever been partially realized, as the loss-limited silver 'superlens' of Fang et al. (2005). What has not been achieved, for either route and specifically for the chiral route, is the end-point regime Pendry's analysis singled out: an impedance-matched slab at n±=−1n_{\pm}=-1 for one circular polarization, and an accounting of the divergent photonic density of states at the chiral resonance.

Problem Statement

Realize a low-loss resonantly chiral metamaterial, at any frequency band from microwave to optical, tuned to the endpoint condition identified by Pendry's chiral route — refractive index n±=−1n_{\pm}=-1 for one circular polarization with wave impedance Z±=+Z0Z_{\pm}=+Z_0 matched to free space — and experimentally verify the two predictions of the 2004 analysis that remain unconfirmed: (1) near-field, polarization-selective perfect-lens behavior of a slab of this medium, namely imaging of a source through the slab with resolution below the diffraction limit for the favored circular polarization (with the orthogonal polarization behaving conventionally), the restoration of the evanescent components of the source being the signature of this perfect-lens behavior; and (2) the behavior of the photonic density of states at and near the chiral resonance, where the 2004 analysis predicts a divergence, with a quantitative account of how loss and finite unit-cell size regularize the divergence. Both effects are to be obtained from one and the same chiral metamaterial, whose effective index and impedance are simultaneously engineered to the matched n±=−1n_{\pm}=-1 condition, with loss low enough that near-field focusing and density-of-states enhancement are observable above absorption and local-field artifacts.

References

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