Primordial Metamaterials: Beyond Local EMT

• Primordial metamaterials are composite electromagnetic media characterized by nonlocal behavior when the structural period approaches the materials’ intrinsic nonlocality length.
• Experimental designs using semiconductor multilayers and nonlocal transfer-matrix methods reveal additional-wave interference that fundamentally deviates from classical effective medium theory.
• Analog-cosmology models and quantum metamaterial architectures expand the scope, offering novel interpretations and practical applications beyond conventional dipolar homogenization.

“Primordial metamaterials” designates several related but non-identical concepts in metamaterials research. In the most precise recent usage, it denotes composite electromagnetic media structured on the scale of the inherent spatial nonlocality of their constituents, so that additional waves and strong macroscopic nonlocality dominate the response even when the structural period is deeply subwavelength (Ware et al., 26 Jun 2025, Podolskiy et al., 15 Jul 2025). In earlier and adjacent usages, the term or its conceptual equivalent has also referred to metamaterials built from more microscopic degrees of freedom than standard dipolar effective media, including artificial quantum two-level systems, higher multipoles, and optical spaces engineered to mimic compactified or Big-Bang-like spacetimes (Macha et al., 2013, Fradkin et al., 2024, Smolyaninov et al., 2011, Smolyaninov, 2010). This suggests a broader category of work in which metamaterial behavior is traced back to a more primitive constitutive level than conventional local effective-medium theory.

1. Terminological scope and regime structure

Across the cited literature, “primordial” is used in three principal senses. The most sharply formalized one is the nonlocal-composite regime introduced in “Primordial Metamaterials” and “Primordial Media: the shrouded field of composite materials,” where the defining scale relation is $d \sim l_p$, with $d$ the structural period and $l_p$ the intrinsic nonlocality length of the component materials (Ware et al., 26 Jun 2025, Podolskiy et al., 15 Jul 2025). A second usage appears in analog-gravity and analog-cosmology work, where metamaterials act as laboratory models of primordial spacetime, compactification, topology change, or an emergent arrow of time (Smolyaninov et al., 2011, Smolyaninov, 2010). A third usage is editorial rather than taxonomic: “primordial” marks foundational architectures in which the macroscopic response is built directly from artificial atoms, higher multipoles, or elementary space–time control handles rather than from standard local dipolar homogenization (Macha et al., 2013, Fradkin et al., 2024).

Usage	Representative systems	Characteristic idea
Nonlocal composite regime	layered nonlocal plasmonic/dielectric media	$d \sim l_p$, additional waves, failure of EMT
Analog-cosmological media	hyperbolic metamaterials, compactified optical spaces	effective spacetime, Big Bang-like or multiverse analogs
Foundational constitutive architectures	qubit arrays, quadrupole media, PMMs	artificial atoms, higher multipoles, or primitive matching rules

In the regime map of the nonlocal theory, the four cases are stated explicitly as local effective medium, $l_p \ll d \ll \lambda$; nonlocal effective medium, $d \ll l_p \ll \lambda$; photonic crystal, $l_p \ll d \sim \lambda$; and primordial metamaterial, $l_p \sim d$ (Podolskiy et al., 15 Jul 2025). That classification is important because it rejects the conventional assumption that shrinking the period of a composite necessarily drives it toward an ordinary homogeneous response.

2. Primordial metamaterials as a nonlocal electromagnetic regime

In the nonlocal formulation, the constitutive law is written as

$$\vec{D}=\hat{\epsilon}\vec{E}- \frac{c^2}{\omega^2} \frac{\partial}{\partial z}\left(\alpha(z)\frac{\partial E_z}{\partial z}\right)\hat{z},$$

where $\hat{\epsilon}$ is the local permittivity tensor and $d$0 is a dimensionless nonlocality parameter (Podolskiy et al., 15 Jul 2025). In this description, $d$1 encodes an intrinsic microscopic length scale through

$d$2

The central physical consequence is that TM-polarized waves no longer satisfy a quadratic dispersion relation. Instead, the homogeneous-medium TM dispersion becomes quartic in $d$3,

$d$4

which supports two distinct TM waves: the ordinary “main” extraordinary wave and an additional nonlocal branch (Podolskiy et al., 15 Jul 2025).

The primordial regime arises when the period $d$5 of a composite becomes comparable to the internal nonlocal wavelength set by $d$6. In that regime, the additional waves are no longer negligible evanescent corrections confined near interfaces. They become propagating Bloch constituents of the composite, and their interference dominates the band structure. The cited work therefore defines primordial metamaterials as composites “dominated by the interference of additional waves and whose properties, as a result, are not described by an effective medium theory — even when the layers are very thin” (Podolskiy et al., 15 Jul 2025).

A key analytical result is that the limits of vanishing nonlocality and vanishing structural period do not commute. In the local limit one recovers the familiar layered-medium averages,

$d$7

whereas in the nonlocal homogenized limit the effective parameters become

$d$8

Because these are generically different, the intermediate $d$9 regime cannot be reduced either to ordinary local EMT or to a smooth nonlocal effective medium (Podolskiy et al., 15 Jul 2025). This is the formal basis for regarding primordial metamaterials as a distinct electromagnetic phase of composites rather than a minor correction to homogenization.

3. Theoretical and experimental realization in nonlocal semiconductor multilayers

The experimental realization reported in “Primordial Metamaterials” uses molecular-beam-epitaxy-grown InAs/AlAsSb multilayers designed so that the structural period lies on the scale of the constituent nonlocality length (Ware et al., 26 Jun 2025). The structures consist of five periods of AlAsSb / n-InAs / AlAsSb / n$l_p$0-InAs on an unintentionally doped InAs substrate, preceded by a 200 nm InAs buffer grown at $l_p$1 and terminated by a 10 nm InAs cap layer. The lightly doped n-InAs layer is specified with target $l_p$2 and $l_p$3, while the highly doped n$l_p$4-InAs layer has $l_p$5 and $l_p$6 (Ware et al., 26 Jun 2025).

The optical characterization is angle- and polarization-resolved FTIR transmission in the mid-IR. TE-polarized spectra serve as a control and show minimal sensitivity to the barrier thickness, consistent with the model assumption that the dominant nonlocality is along $l_p$7 and affects TM modes. TM spectra show the defining primordial signature: a single ENZ-associated transmission dip evolves into a split doublet as the barriers are thinned. In the constant-period study, the reported sequences are $l_p$8 nm, $l_p$9 nm, and $d \sim l_p$0 nm for AlAsSb / n-InAs / AlAsSb / n$d \sim l_p$1-InAs. In the constant-barrier study, the three structures are $d \sim l_p$2 nm, $d \sim l_p$3 nm, and $d \sim l_p$4 nm, corresponding to total periods of 240 nm, 160 nm, and 80 nm, respectively (Ware et al., 26 Jun 2025).

The theoretical description uses a nonlocal transfer-matrix method in which each layer supports two TM modes, a primary and an additional one, and the interface conditions include continuity of $d \sim l_p$5, $d \sim l_p$6, $d \sim l_p$7, and $d \sim l_p$8. In the homogeneous limit, the nonlocal constitutive law yields

$d \sim l_p$9

so that the multilayer problem intrinsically contains an additional-wave channel (Ware et al., 26 Jun 2025).

The reported interpretation is that coupling between additional waves in adjacent nonlocal layers reduces the effective wavevector mismatch sufficiently for a nonlocal mode to become optically visible in far-field transmission. That is why, in the smallest-period sample, a nonlocal feature appears at wavelengths well below the effective-medium ENZ wavelength. The same work emphasizes that this occurs in room-temperature, lossy semiconductor structures, not in idealized low-loss excitonic systems, and that the response cannot be captured by any local effective permittivity model even when the period is of order $l_p \ll d \ll \lambda$0 (Ware et al., 26 Jun 2025).

4. Primordial metamaterials as analogs of primordial spacetime

A distinct but influential usage treats metamaterials as laboratory analogs of primordial cosmology. In “Modeling of Time with Metamaterials,” hyperbolic metamaterials are engineered so that one spatial coordinate plays the role of an effective time variable for extraordinary light (Smolyaninov et al., 2011). For a uniaxial medium with $l_p \ll d \ll \lambda$1, $l_p \ll d \ll \lambda$2, and $l_p \ll d \ll \lambda$3, the extraordinary field $l_p \ll d \ll \lambda$4 satisfies a Klein–Gordon-like equation. With the identification $l_p \ll d \ll \lambda$5, the monochromatic spatial field distribution is read as the full history of a $l_p \ll d \ll \lambda$6-dimensional universe: $l_p \ll d \ll \lambda$7 In cylindrical implementations, the radial coordinate $l_p \ll d \ll \lambda$8 is similarly interpreted as time, with $l_p \ll d \ll \lambda$9 acting as a Big-Bang-like origin and outward-diverging plasmon rays acting as world lines in an expanding universe (Smolyaninov et al., 2011).

The same paper defines a statistical arrow of time from the angular distribution of intensity on circles of fixed radius. Using

$d \ll l_p \ll \lambda$0

and the intensity-based approximation

$d \ll l_p \ll \lambda$1

the reported entropy increases monotonically with effective cosmological time in disordered samples, aligning the statistical arrow with the expansion direction (Smolyaninov et al., 2011).

In “Metamaterial ‘Multiverse’,” the primordial analogy is framed instead in terms of effective optical spaces with different topology and dimensionality (Smolyaninov, 2010). The paper constructs optical analogs of $d \ll l_p \ll \lambda$2 and $d \ll l_p \ll \lambda$3, where extraordinary waves experience compactified dimensions and Kaluza–Klein-like spectra. For the $d \ll l_p \ll \lambda$4 construction, the compact coordinate gives eigenmodes

$d \ll l_p \ll \lambda$5

with dispersion

$d \ll l_p \ll \lambda$6

In that framework, the integer $d \ll l_p \ll \lambda$7 functions as an effective $d \ll l_p \ll \lambda$8 charge, while topology-changing phase transitions between optical spaces such as $d \ll l_p \ll \lambda$9 are proposed to generate a flash of light through a dynamical-Casimir-like mechanism (Smolyaninov, 2010).

These analog-cosmology usages do not define primordial metamaterials by nonlocality. They instead define them by the capacity to emulate primordial-universe kinematics, compactification, or the emergence of time in an effective optical metric.

5. Foundational microscopic and multipolar architectures

In superconducting circuit QED, “Implementation of a Quantum Metamaterial” presents a system in which the macroscopic response is built directly from artificial atoms rather than classical resonant inclusions (Macha et al., 2013). The experiment embeds 20 superconducting flux qubits in a coplanar waveguide resonator of length $l_p \ll d \sim \lambda$0 with fundamental frequency $l_p \ll d \sim \lambda$1. The collective system is modeled by the Tavis–Cummings Hamiltonian, and the transmitted phase reveals the collective resonant coupling of up to 8 qubits. In this usage, the metamaterial is “primordial” because its microscopic building blocks are genuine quantum two-level systems whose level structure, tunability, and coupling arise from Josephson physics rather than from classical LC analogies (Macha et al., 2013).

A comparable shift toward more primitive constitutive variables appears in higher-multipole homogenization. “Quadrupole Mie-resonant metamaterial” demonstrates a dense 2D photonic crystal of water-filled dielectric cylinders whose second TE Mie resonance is governed by magnetic quadrupole response rather than by dipolar $l_p \ll d \sim \lambda$2 and $l_p \ll d \sim \lambda$3 alone (Fradkin et al., 2024). The medium is characterized by electric dipole, magnetic dipole, and magnetic quadrupole susceptibilities $l_p \ll d \sim \lambda$4, $l_p \ll d \sim \lambda$5, and $l_p \ll d \sim \lambda$6, and its interface conditions become

$l_p \ll d \sim \lambda$7

The associated Fabry–Perot slab can exhibit zero reflection at normal incidence, a result that depends on the quadrupole boundary parameter and therefore lies beyond dipolar homogenization (Fradkin et al., 2024).

Other papers use “primordial” to describe foundational metamaterial architectures rather than a single regime. “Photonic crystals as metamaterials” treats photonic crystals as an early or foundational route to Veselago-type behavior, distinguishing a propagation-equivalent regime at $l_p \ll d \sim \lambda$8 from a deep-subwavelength effective-medium regime at $l_p \ll d \sim \lambda$9 (Foteinopoulou, 2020). “Metallo-dielectric core-shell nanospheres as building blocks for optical 3D isotropic negative-index metamaterials” proposes spherical Ag@Si or Ag@Ge inclusions whose electric and magnetic dipole resonances overlap, yielding a fully 3D, isotropic negative-index metamaterial in the range within $l_p \sim d$0-$l_p \sim d$1 microns (Paniagua-Domínguez et al., 2011).

Space–time and matching-oriented architectures have also been cast in primordial terms. “4D Optically Reconfigurable Volumetric Metamaterials” describes a volumetric metamaterial-based scatterer whose effective permeability is controlled dynamically with light via SRRs loaded with a varactor and a photodiode, producing an artificial gigahertz magnon resonance and a $l_p \sim d$2 resonance shift under illumination (Dobrykh et al., 2021). “Perfectly Matched Metamaterials” defines passive, inhomogeneous media that perform purely refractive field transformations while remaining all-angle reflectionless in a 2D S-polarized or TEM setting; the analytical demonstrations span $l_p \sim d$3 to $l_p \sim d$4 GHz with efficiencies above $l_p \sim d$5 or $l_p \sim d$6, depending on device thickness (Ruiz-Garcia et al., 24 Nov 2025). In both cases, the “primordial” aspect is the exposure of a minimal constitutive control handle—time-varying bulk resonance in one case, exact local matching and independent $l_p \sim d$7/$l_p \sim d$8 control in the other.

6. Conceptual boundaries, misconceptions, and open directions

A common misconception is that “primordial metamaterials” names a single universally accepted class. The literature summarized here does not support that reading. In the nonlocal-composite theory, the term has a precise operational definition tied to the noncommuting limits of $l_p \sim d$9 and $$\vec{D}=\hat{\epsilon}\vec{E}- \frac{c^2}{\omega^2} \frac{\partial}{\partial z}\left(\alpha(z)\frac{\partial E_z}{\partial z}\right)\hat{z},$$0, to the condition $$\vec{D}=\hat{\epsilon}\vec{E}- \frac{c^2}{\omega^2} \frac{\partial}{\partial z}\left(\alpha(z)\frac{\partial E_z}{\partial z}\right)\hat{z},$$1, and to the dominance of additional-wave interference (Podolskiy et al., 15 Jul 2025). In the analog-cosmology literature, by contrast, the term refers to laboratory models of primordial spacetime, compactification, and topology change in an effective optical metric rather than to a nonlocal constitutive regime (Smolyaninov et al., 2011, Smolyaninov, 2010).

A second misconception is that any deep-subwavelength composite should be homogenizable. The recent nonlocal work argues explicitly that this intuition is “fundamentally flawed, even at the qualitative level,” because shrinking the unit cell does not remove primordial behavior when the period remains comparable to the intrinsic nonlocality length (Podolskiy et al., 15 Jul 2025). In that sense, the primordial regime is not merely a stronger version of standard spatial dispersion; it is a breakdown of both local EMT and the smooth nonlocal EMT that applies when $$\vec{D}=\hat{\epsilon}\vec{E}- \frac{c^2}{\omega^2} \frac{\partial}{\partial z}\left(\alpha(z)\frac{\partial E_z}{\partial z}\right)\hat{z},$$2.

The older analog-spacetime papers also impose clear limits. Their optical metrics are effective ones, not dynamical solutions of Einstein’s equations. The modeled topology change occurs in a fixed laboratory medium, not in physical spacetime; gravity does not backreact; and the constructions do not realize quantum gravity or full $$\vec{D}=\hat{\epsilon}\vec{E}- \frac{c^2}{\omega^2} \frac{\partial}{\partial z}\left(\alpha(z)\frac{\partial E_z}{\partial z}\right)\hat{z},$$3-dimensional cosmology (Smolyaninov et al., 2011, Smolyaninov, 2010). Likewise, the superconducting quantum metamaterial experiment is explicitly a proof-of-principle in a dephasing-dominated regime rather than the full Dicke superradiant strong-coupling limit (Macha et al., 2013). The perfectly matched metamaterial formalism is derived for a 2D, S-polarized or TEM configuration with anisotropic unit cells, not as a general unrestricted theorem for arbitrary 3D media (Ruiz-Garcia et al., 24 Nov 2025).

The open directions identified in the cited work are correspondingly diverse. In the nonlocal setting they include generalization to other geometries, stronger nonlocality, inverse design with explicit additional-wave control, and device concepts based on emission engineering, multi-resonant spectra, or thermal-radiative control (Podolskiy et al., 15 Jul 2025, Ware et al., 26 Jun 2025). In the multipolar setting they include systematic exploitation of quadrupole, toroidal, and higher-order constitutive variables (Fradkin et al., 2024). In the space–time setting they include richer optical metrics, nonlinear analog cosmology, and spatiotemporal modulation (Smolyaninov et al., 2011, Dobrykh et al., 2021). The most stable encyclopedic conclusion is therefore not that primordial metamaterials form a closed class, but that they identify points where metamaterials cease to be well described as merely local effective media and instead expose a more elementary layer of constitutive physics.