Photonic meta-crystals
0 
Abstract
Photonic crystals (PCs) and metamaterials are periodic artificial structures with different scales that modulate light–matter interactions. Considering their complementary advantages, the concept of photonic meta-crystals is proposed. In these hybrid structures, such as hypercrystals (composed of hyperbolic metamaterials and PCs), the photonic band gap provided by PCs can be blue-shifted with more degrees of freedom, and the weak coupling of hyperbolic metamaterials to the environment can be enhanced. This review introduces photonic meta-crystals in sequence, based on the classification of electromagnetic parameters in metamaterials. Recent advances in photonic meta-crystals are also presented in the context of topological semimetals.
Keywords
INTRODUCTION
In electronic systems, the interactions between electrons and atoms in practical materials seem elusive due to the enormous magnitude near 1023 cm-3. Nevertheless, approximations like the Born-Oppenheimer adiabatic approximation, Hatree-Fock mean-field theory, and periodic potential theory provide an elegant way to simplify the problem into the motion of a single electron in an effective periodic potential, which led to the concept of energy bands established by F. Bloch in 1928[1]. More specifically, the periodic potential tends to originate from the regular arrangement of atoms with discrete spatial translation symmetry, corresponding to crystalline lattices in metals and semiconductors. The great success of energy band theory has motivated significant developments in the microelectronics industry and inspired further exploration into extensive fields, such as photonic counterparts. Compared with electrons, photons exhibit several characteristics fulfilling the first two approximations: on the one hand, they have no mass and travel at the highest velocity; on the other hand, they do not interact with each other. By introducing periodic potentials through alternating dielectric layers, the concept of the photonic crystal (PC) was independently proposed by Yablonovitch[2] and John[3] in 1987. When the lattice constant is comparable to the wavelength of light, multiple Bragg scattering mechanisms can inhibit spontaneous emission and support photon localization within the photonic band gap. Due to their characteristics, photons inherently avoid redundant energy consumption caused by Joule heating, making them well-suited for use in integrated and miniaturized devices. However, the flexible modulation of photons remains challenging due to the absence of photon-photon interactions. The photonic band gap in PCs provides a direct method to control photons, leading to various applications in recent years, including fibers[4-8], lasers[9,10], signal processing[11-13], and image differentiation[14-17].
For the periodic structure, when reducing the lattice constant to a subwavelength scale, the dominant Mie scattering gives rise to optically induced electric or magnetic resonances based on displacement currents[18,19], leading to the opening of a Mie band gap below the lowest Bragg band gap[20]. Under these conditions, the entire structure can be effectively treated as a homogeneous medium according to effective medium theory (EMT). Here, the electromagnetic field components are regarded as continuous and constant within each layer, complying with the boundary conditions derived from Maxwell’s equations[21]. Intriguingly, these artificially designed structures, known as metamaterials[22], exhibit distinct electromagnetic responses that surpass those of conventional dielectrics, which typically possess positive permittivity ε > 0 and permeability μ > 0. Through meticulous and rational design, metamaterials can realize counterintuitive phenomena previously deemed impossible, such as electromagnetic cloaking[23-25], negative refraction[26-28], and superlensing[29-31].
Although PCs and metamaterials each possess distinctive advantages, their individual limitations restrict comprehensive control over light. PCs effectively create band gaps through Bragg scattering; however, they are constrained by blue shift dispersion under oblique incidence and lack flexibility in engineering arbitrary electromagnetic parameters. On the other hand, metamaterials enable unconventional optical phenomena like negative refraction but frequently encounter challenges related to narrow operational bandwidths and significant energy dissipation. Recent advancements in photonic meta-crystals (PMCs), formed by integrating PCs and metamaterials (as illustrated in Figure 1), have opened new avenues for manipulating light. By combining the broadband dispersion control capabilities of PCs with the customized electromagnetic properties of metamaterials, PMCs overcome critical limitations inherent to each individual technology. Specifically, these hybrid systems compensate for spectral shifts resulting from Bragg scattering through the use of hyperbolic metamaterials[32], enhance light-matter interactions via zero-index materials[33,34], and alleviate the narrow bandwidth[35] and intrinsic losses typical of conventional metamaterials. This synergistic integration facilitates innovative functionalities, including nonreciprocal transport[36] and topological protection[37], which will be extensively discussed throughout this review. In the first part of this review, we explore the physical properties of PMCs arising from the integration of various classes of metamaterials. Under transverse magnetic (TM) excitation, these metamaterials can be broadly categorized by their effective permittivity and permeability. The integration of these metamaterials into PCs can yield diverse optical behaviors depending on their electromagnetic characteristics and structural configurations. One representative category is left-handed materials (LHM), characterized by simultaneously ε > 0 and μ > 0. When integrated into photonic crystals, they can produce omnidirectional photonic band gaps that are insensitive to the angle of incidence, owing to the zero average refractive index condition[38]. Such structures also support negative refraction[26-28], superlensing[39,40], and reversed Doppler and Cherenkov effects[41-47]. Single-negative (SNG) materials, which exhibit either ε < 0, μ > 0 or ε > 0, μ < 0, provide further means to manipulate reflection phase and band topology when integrated into photonic crystal structures. Pairings of epsilon-negative (ENG) and mu-negative (MNG) materials can support resonant tunneling and complete transmission when phase and impedance are properly matched[48]. In addition, asymmetric designs enable flexible control of dispersion and near-field tuning[49-51]. Zero-index materials (ZIMs), characterized by ε = 0 and/or μ = 0, support nearly uniform phase propagation and enable wave tunneling through structures of arbitrary geometry[52-55]. Their strong field enhancement benefits nonlinear processes[31,57,77], and supports cloaking[58], photonic doping[59,60], and analog optical computing[61]. Hyperbolic metamaterials (HMMs) exhibit anisotropic permittivity tensors, where type-I satisfy
Figure 1. The family of metamaterials and a schematic illustration of photonic meta-crystals. The diagram on the right presents a structural roadmap depicting the integration process and functional evolution of these metamaterials within photonic meta-crystals. LHM: Left-handed material; SNG: single-negative; ZIM: zero-index material; HMM: hyperbolic metamaterial; PMC: photonic meta-crystal.
PMC WITH LHM
In 1968, V. G.Veselago proposed a peculiar material with ε < 0 and μ < 0, and predicted several fantastic phenomena, including negative refraction, the inverse Doppler effect, and the reversed Cherenkov radiation[63]. In this case, the electric field E, the magnetic field H, and the wave vector k form a left-handed set, corresponding to a negative index
Figure 2. (A) Photograph of the left-handed metamaterial (LHM), quoted with permission from Shelby et al.[26]; (B) The phase front of the light shows the negative refraction angle, quoted with permission from Valentine et al.[27]; (C) Comparison between the conventional lens, metasurfaces lens, and two superlenses with negative refraction and photonic crystal slab, quoted with permission from Liu et al.[40]; (D) Schematic showing the normal Doppler effect in normal materials (n > 0) and inverse Doppler effect in LHM (n < 0), quoted with permission from Chen et al.[43]; (E) Schematic representation of conventional and reversed Cherenkov radiation (CR) excited via a moving charge, quoted with permission from Guo et al.[47]; (F) Schematic of the PC containing LHM with the ray diagram for the end-fire wave propagation and suppression of radiation of a local source placed inside, quoted with permission from Shadrivov et al.[64].
The negative refraction[36-40]
As shown in Figure 2B, when light passes through the surface, the incident ray in medium 1 with refractive index n1 > 0 and the refracted ray in medium 2 with index n2 < 0 appear on the same side of the normal line, following Snell’s law n1 sin θ1 = n2 sin θ2. Under this condition, a simple parallel-sided LHM slab can act as a superlens with double focusing, transverse invariance, and aberration-free performance in principle[39]. However, this design relies on the slab being thick enough to support a propagation phase, and fabricating a bulky LHM is difficult. Although negative refraction has been well demonstrated at microwave frequencies, its realization in the optical range faces major challenges, mainly due to high ohmic losses in metals and the difficulty of scaling structures such as split-ring resonators to deep-subwavelength dimensions. In addition, achieving isotropic and broadband negative index responses requires careful suppression of anisotropy and parasitic coupling. To overcome these limitations, researchers have explored alternative strategies including dielectric resonators, planar metamaterials, and metasurfaces that mimic left-handed behavior with improved scalability and reduced loss. Notably, Liu et al. propose a reciprocal lens based on the PC slab, as shown in Figure 2C, where the ray can be laterally shifted by modulating the phase in momentum space[40].
The inverse Doppler effect[41-43]
When a source with the frequency ω0 moves away from the receiver at velocity v, the received frequency becomes
The reversed Cherenkov radiation[44-47]
When fast-moving charged particles with the velocity v bombard the LHM, the direction of coherent radiation is reversed, with the Cherenkov angle θ satisfying
Considering a one-dimensional PC composed of two alternating layers of LHM (nA < 0) and conventional dielectrics (nB > 0), the propagation of electromagnetic waves through such structures can be mathematically described by the transfer matrix method. The characteristic matrix of the j th layer is given by:
where kj = njω/c and
PMC WITH SNG MATERIALS
SNG materials can be categorized into ENG, (with ε < 0, μ > 0) and MNG, (with ε > 0, μ < 0). As discussed in the previous section, an isolated SNG layer can, to some extent, serve as an intermediate step or simplified substitute for LHMs. Take the LHM design[36] as an example, the MNG split-ring resonators are placed at the nodes of the magnetic field generated by the ENG wire array, in order to minimize their near-field coupling. Under this configuration, the EMT remains applicable[65]. Moreover, complementary SNG media can replace the LHM-based cloaking shell[66], and two parallel ENG slab waveguides under TM excitation can serve as an alternative to the LHM-based configuration excited by natural light, effectively enhancing optical gradient forces, as shown in Figure 3A[49]. The engineered configurations of SNG materials open new dimensions in photonic control beyond conventional dielectric structures, and their extraordinary manifestations can be observed through the following aspects:
Figure 3. (A) A metamaterial slab that amplifies the evanescent tails to enhance the optical gradient force, quoted with permission from Ginis et al.[49]; (B) The bi-periodic honeycomb array with a negative index band (the red line in the lower left panel) and the subwavelength focusing of a super lens, quoted with permission from Kaina et al.[50]; (C) The symmetry features in the near-field wave systems and the metasources to demonstrate the near-field photonic routing based on the interface mode between ENG and MNG metamaterials, quoted with permission from Long et al.[51]; (D) The band structure, effective parameters (ε and μ), and reflection phase φR of the infinite-periodic PC (ABBA)N, quoted with permission from Shi et al.[67]; (E) The transmission spectrum of a system composed of PC1 on the left-hand side and PC2 on the right-hand side (the left panel), the band structure (solid black curve) and Zak phase (labeled in green) of PC1 (the middle panel) and PC2 (the right panel), quoted with permission from Xiao et al.[68]. ENG: Epsilon-negative; MNG: mu-negative; PC: photonic crystal.
Tunable negative refraction
When the symmetry of the SNG PC lattice is broken, multiple scattering leads to folding of the lower polariton band in the first Brillouin zone, and opens a narrow transparency window with negative-index dispersion, as shown in Figure 3B[50]. This effect enables super-resolution imaging, high-Q filtering, and enhanced nonlinear optics. When implemented on silicon or III-V platforms, it provides a compact alternative to conventional metamaterials with precise dispersion control.
Resonant tunneling and transparency
Although the isolated ENG or MNG material is opaque, the situation may be different in the heterostructure composed of a lossless ENG-MNG pair. When the matching condition of the impedance X1 = -X2 and the effective-phase β1d1 = β2d2 is fulfilled, the resonance amplifies the evanescent wave and leads to complete tunneling with high transparency[48]. Here,
Near-field photonic routing
Near-field photonic routing utilizes the interface between ENG and MNG metamaterials to control electromagnetic waves at subwavelength scales. By designing metasources with parity (
Intriguingly, the band gaps in PC can be analogous to SNG materials; hence, an interface mode like the Tamm state can form at the boundary when joining two PCs with band gaps of the same frequency but different components[67]. Specifically, the component can be defined by the reflection phase φR of the reflection coefficient
PMC WITH ZIM
As a transitional category between conventional matters and SNG/NIM, the family of ZIMs can be classified into epsilon-near-zero (ENZ, with ε ≈ 0, μ ≠ 0), mu-near-zero (MNZ, with ε ≠ 0, μ ≈ 0), and epsilon-and-mu-near-zero (EMNZ, with ε ≈ 0, μ ≈ 0), as is shown in Figure 4A[33]. Conveniently, ZIMs can be found near the resonant frequency of the electric and/or magnetic dipole mode, like ENZ in a bulk metal near the plasma frequency, as shown in Figure 4B. However, metal tends to possess significant intrinsic ohmic losses, which leads to short propagation length. To alleviate the impact of ohmic losses, novel natural materials such as two-dimensional (2D) materials are being explored[34]. Two artificial structures are mainly adopted: (1) In a rectangular waveguide with width w, the effective relative permittivity εeff/ε0 = n2 – c2 / (4f2w2) satisfies the condition of ENZ at the cutoff frequency f = c/(2w)[69]. (2) In the PC with a square lattice, the band structure manifests dispersion of a Dirac cone with the pseudospin-1 triply degenerate point, where an electrical monopole mode and a transverse magnetic dipole mode dominate the properties of EMNZ, as shown in Figure 4C[36,52]. When breaking the C4vand time-reversal symmetry by introducing an elliptical cylinder and applying an external magnetic field, the dispersion evolves into pseudospin-1/2 doubly degenerate, and the determinant (instead of the value) of the effective permeability keeps zero[70]. In addition, the out-of-plane radiation loss of PC is further eliminated based on the destructive interference of the bound state in the continuum (BIC)[71]. The various experiment realizations of ZIMs provide powerful platforms to explore and demonstrate the novel features, and several examples are listed below:
Figure 4. (A) Schematic illustration of the adjustability of EMNZ properties, quoted with permission from Dai et al.[33]; (B) The Lorentz model and Drude model of the ENZ materials, quoted with permission from Kinsey et al.[34]; (C) In a PC slab with a square lattice, an electrical monopole mode (the upper right panel) and a transverse magnetic (the lower left panel) form EMNZ, quoted with permission from Li et al.[36]; (D) Geometry of a 2D waveguide structure with an ENZ section to support the tunneling effect, quoted with permission from Silveirinha et al.[57]; (E) Sectional view of the ZIM cloaking shell covered by a metasurface, quoted with permission from Chu et al.[58]; (F) Photonic doping in the ENZ material, quoted with permission from Liberal et al.[59]; (G) Dispersion coding in the ENZ material based on photonic doping, quoted with permission from Zhou et al.[60]; (H) The enhanced absorption cross section when a resonator is doping, quoted with permission from Zhou et al.[76]; (I) ZIM can solve phase mismatching in the process of nonlinear propagation, quoted with permission from Suchowski et al.[77]; (J) Both BIC and ZIM realized in the daisy PC, quoted with permission from Minkov et al.[85]; (K) BIC (also called embedded eigenstate here) in a ENZ-dielectric-ENZ three-layered waveguide, quoted with permission from Monticone et al.[86]; (L) Concept of the secure targeted wireless power transfer, quoted with permission from Zanganeh et al.[87]; M: Magnetized gradient ENZ layer (the lower left panel) to realize broadband nonreciprocity breaking the classical Kirchhoff’s law (the upper panel), quoted with permission from Liu et al.[90]. EMNZ: Epsilon-and-mu-near-zero; PC: photonic crystal; ENZ: epsilon-near-zero; 2D: two-dimensional; ZIM: zero-index material; BIC: bound state in the continuum.
The tunneling effect[52-55,58-61,70-81]
Owing to the infinite effective spatial wavelength
Similar differences also exist between EMNZ and ENZ/MNZ materials when considering doping impurities. For the environment outside the EMNZ material, impurities do not impact the passing electromagnetic wave, as if they are invisible, leading to potential applications such as cloaking, as shown in Figure 4E[52,58]. On the other hand, Liberal et al. propose that impurities in the ENZ material can modify the effective permeability of the entire medium. Intriguingly, owing to large phase velocities and static-like field distributions, this impact is independent of either the position of the impurities or the external geometry of ENZ materials, as shown in Figure 4F[59], which benefits robust information technology like dispersion coding in Figure 4G[60] and performing calculus[61].
To compensate for the divergent impedance mismatching between the ENZ material and the surrounding environment, Luo et al. designed a pair of parity-time-symmetry metasurfaces to sandwich the ENZ slab, effectively eliminating the scattering caused by impurities[80]. For impurities inside the ZIM, the absorption cross section can be significantly enhanced when a resonator is doping, as shown in Figure 4H[76], and the scattering cross section can be significantly enhanced when a scatter is doping[81].
The parameter enhancement[56,57,82]
In the nonlinear process, a major problem is the phase mismatch between nonlinear fields, which results in destructive interference and low generation efficiency. More specifically, material dispersion leads to a lack of photon momentum conservation. In ZIM, the photon momentum p = h/λ is zero, preventing the conservation for any combination of directions, as shown in Figure 4I[77]. Moreover, based on the boundary condition of Maxwell’s equations,
Likewise, the property of field enhancement is also utilized to improve the nonreciprocity arising from the magneto-optical effect. For example, by inducing a magnetized ENZ defect into a 1D PC, the defect modes in the band gap are shifted for forward and backward incidences. A similar phenomenon is also observed in heterostructures composed of a magnetized ENZ material and a truncated PC, and the Fano-type interference with sharp spectral variation further enhances the shift.
The BIC[83-90]
As predicted by von Neumann and Wigner, the BIC is characterized by zero leakage and zero linewidth[83]. For ZIM slabs, the mechanism of BIC is employed to reduce the out-of-plane radiation loss. One approach is based on the symmetry-protected modes. A square lattice with C4vsymmetry supports a single 2D irreducible representation E, which corresponds to modes that couple to external plane waves. In comparison, the C6vgroup has two distinct 2D irreducible representations E1 and E2 where modes belonging to E2 do not couple to external plane waves. In that case, the triply degenerate point of EMNZ PC can be composed of modes from E2, along with the 1D irreducible representations B1 and B2, as in the daisy PC shown in Figure 4J[84,85]. Another approach is based on the resonance-trapped modes. Considering the top and bottom interfaces of the slab as two mirrors, the thickness of this Fabry-Perot cavity can be tuned to induce destructive interference in each radiation channel[72,84].
Except for the PC slab, a kind of three-layered waveguide “ENZ-dielectric-ENZ” has been widely discussed to generate BIC (also called embedded eigenstates, EEs) in the past decade. At the frequency of the Fabry-Perot resonance in the dielectric layer, the ENZ layer with high impedance limits the leakage mode, as shown in Figure 4K[86], which promotes the targeted wireless power transfer (WPT) more securely, as shown in Figure 4L[87]. When a non-Hermitian parameter, like the loss in the ENZ layers, is considered, a pair of scattering singularities emerges from the BIC, and each singularity is protected by the topological charge
Beyond these theoretical mechanisms, ENZ-based architectures have also been widely leveraged in practical photonic devices. Several representative advances by Caputo and collaborators have demonstrated the versatility of ENZ metamaterials in nanoscale fabrication and functional photonic applications. One of the earlier works introduced multilayer ENZ nanocavities to enhance two-photon direct laser writing, achieving sub-50 nm resolution and enabling the fabrication of ultrathin metalenses and complex 3D nanostructures[91]. Building on similar photonic structures, the group later developed anticounterfeiting tags by embedding QR codes beneath plasmonic multilayers on paper substrates. These tags exhibited unique speckle patterns and structural colors, functioning as physical unclonable functions (PUFs) for secure optical authentication[92]. Subsequently, ENZ nanocavities were combined with metasurfaces to engineer Fano-Rabi resonances with ultra-narrow spectral features and high refractive index sensitivity, offering promising capabilities for label-free biochemical sensing[93]. In a further step, the researchers introduced tunable optical coupling by inserting a birefringent liquid crystal layer between ENZ cavities, enabling polarization-sensitive spectral splitting and reconfigurable resonance modes[94]. These works collectively demonstrate a transition from passive ENZ-based nanostructures to tunable, multifunctional photonic systems, reinforcing the relevance of ENZ metamaterials in the broader context of meta-crystal research.
PMC WITH HMM
In most situations of the above-mentioned discussions, the material anisotropy shown in Figure 5A[28,95], whether natural or artificial, is neglected. For metamaterials, substituting periodicity with continuous translation symmetry in one or two spatial dimensions, such as in metal-dielectric multilayer film or nanowire array, may lead to extreme anisotropy. According to EMT, the permittivity can be described as
Figure 5. (A) The IFC in the HMM, quoted with permission from Poddubny et al.[28]; (B) The metal-dielectric multilayer film, quoted with permission from Wood et al.[30]; (C) The nanowire array (the left panel) and the negative refraction analyzed through the IFC (the right panel), quoted with permission from Liu et al.[32]; (D) The enhanced spontaneous emission in multilayer HMM, quoted with permission from Lu et al.[35]; (E) The enhancement during the topological transition between elliptic and hyperbolic dispersions, quoted with permission from Schulz et al.[62]; (F) The transition between positive and negative refractions in HMM, quoted with permission from High et al.[102]; (G) The magnifying super lens, quoted with permission from Liu et al.[104]; (H) The strategy of complex frequency composed of multiple real frequencies (the upper panel) and related imaging of the super lens (the lower panel), quoted with permission from Guan et al.[105]; (I) The band structures and schematics of the HMM (the upper panel) and the 2D hypercrystal (the lower panel), quoted with permission from Galfsky et al.[106]; (J) The schematic of the 1D hypercrystal (the upper panel) and the dispersionless band gap (the lower panel), quoted with permission from Xue et al.[108]; (K) The phase variation compensation in the IFC (the upper panel) and the forward dispersionless and backward monotonic increasing band gap in magnetized 1D hypercrystal (the lower panel), quoted with permission from Hu et al.[109]. IFC: Isofrequency contour; HMM: hyperbolic metamaterial; 2D: two-dimensional.
The enhanced spontaneous emission[27,38,62,100,101]
The photonic density of states (DOS) is related to the volume between the dispersion of ω(k) and ω(k) + dω[100]. Therefore, the HMM with an open IFC theoretically exhibits infinite DOS, where high wavevectors also contribute. Although the DOS of HMMs in practice is limited by several factors, including the ohmic losses of the metal components, the dispersion of the dielectric components, the finite period of the metamaterial, the finite size of source, and the finite distance between the source and the metamaterial[27], the spontaneous emission can still be enhanced by using a grating-like HMM with the outcoupling effect, as shown in Figure 5D[35]. Furthermore, spontaneous emission can be flexibly modulated by altering the filling ratio, which leads to improvement during the topological transition between elliptic and hyperbolic dispersions, as shown in Figure 5E[62]. Additionally, HMMs exhibit anomalous scaling laws: cavities with different sizes can share the same resonant frequency, and higher-order resonance modes can oscillate at lower frequencies. This property offers a strategy for reducing the size of HMM structures to increase the quality factor and enhance the light-matter interactions[101].
The negative refraction[32,102,103]
Considering an incident light with momentum ki and the Poynting vector Si from the isotropic dielectric, the conservation of the tangential momentum determines two possible refraction momentum kr and kr’ after passing through the interface between the dielectric and the HMM. Then, the causality principle determines Sr flowing away from the interface, which corresponds to a negative refraction angle
The super lens[103-109]
In far-field imaging, the high-frequency information is evanescent and lost in the dielectric. In comparison, the HMM with an open IFC can support this kind of information, and transfer the near-field information to the other side, thereby breaking the diffraction limit of light. A cylindrical HMM is designed to magnify the image, as shown in Figure 5G[104]. While the functionality of the super lens is well described by EMT, it is important to note that EMT assumes deeply subwavelength structuring and a local electromagnetic response. However, in practice, these assumptions may become less accurate when the structural periodicity approaches the operating wavelength or when high-k modes dominate the imaging process. Under such conditions, the actual dispersion and energy transport behavior may deviate from EMT-based predictions, especially near the topological transition region. To improve modeling accuracy, full-wave simulations are typically used in parallel with EMT during the design stage. Moreover, naturally hyperbolic materials such as α-MoO3 and h-BN offer a promising alternative, achieving broadband hyperbolic dispersion without relying on structural averaging. To compensate for intrinsic losses, a recent study proposed an excitation with a complex frequency composed of multiple real frequencies, as shown in Figure 5H[105].
While HMMs exhibit topology in the form of open IFCs, this geometrical topology differs from the band topology discussed in topological photonics. The former arises from anisotropic dispersion and leads to phenomena such as high-k modes and enhanced density of states, whereas the latter is characterized by global invariants such as the Berry phase or the Zak phase, which guarantee robust surface or edge states. Incorporating HMMs into PCs provides a natural bridge between IFC engineering and band topology, enabling new topological phases such as Type-I, II, and III nodal semimetals. This synergy underpins many recent advances in PCMs and sets the stage for the discussion of topological phenomena in the following section.
To some extent, the advantages of HMM and PC are complementary. By integrating HMM with PC, the concept of the photonic hypercrystal has been proposed[103]. On the one hand, HMMs possess a broadband DOS, but the high-momentum modes lie below the light line, trapping most of the emitted power inside the HMM. By patterning a 2D lattice of holes, the periodicity can fold these modes inside the light line like PCM, and provide high light-scattering efficiency with the surrounding environment, as shown in
PMC AND TOPOLOGY
Beyond Landau’s classic approach based on spontaneously broken symmetries, topological theory provides a new perspective on the classification paradigm, including gapped phases such as topological insulators[110], and gapless phases such as topological semimetals[111]. After the realization of topological insulators[112-114], photonic systems, especially PCs and metamaterials, have also been proven to be versatile platforms to demonstrate the phases of topological semimetals, which can be further classified into nodal points[115,116], nodal lines[117,118], and nodal surfaces[119] according to the dimensions of band degeneracy areas. A growing frontier in this field is to emulate relativistic quasiparticles that feature band degeneracies with linear dispersions, such as fourfold Dirac fermions and even twofold Weyl fermions. However, most of the designs are based on 2D lattices, and it is highly desirable in practice to use a simpler 1D lattice to realize similar band structures.
In 1D PCs with inversion symmetry, the imaginary part of the surface impedance ς is dictated by the cumulative Zak phases of the bulk bands below the nth gap:
Figure 6. (A) The sketch of the in-plane dispersion around the Dirac nodal ring (the upper left panel), the experimental setup (the upper right panel), the transmission spectra of the PC to observe the Dirac nodal ring (the lower left panel, the situation of the TM mode is similar), and the double-bowl state for the truncated PC (the lower right panel, the situation of the TM mode is similar), quoted with permission from Hu et al.[37]; (B) The schematic of PC without the inversion symmetry (the upper left panel), the gapped ridge state (the upper right panel), and the toroidal-shaped Berry fluxes for vortexes for two structures (the lower panel), quoted with permission from Deng et al.[120]; (C) The degree of freedom of rotation and translation in the hypercrystal; (D) The bilateral drumhead surface state (the upper panel) is pinned by a pair of reflection-phase topological charges (the middle panel), and the charge pair approaches each other, but cannot annihilate completely, which forms a quasi-BIC (the lower panel), quoted with permission from Hu et al.[122]. PC: Photonic crystal; TM: transverse magnetic; BIC: bound state in the continuum.
While significant progress has been made in designing topological phases within photonic meta-crystals, several practical challenges that limit their implementation in real-world systems remain. These include the limited tunability of band structures in static lattices, the difficulty of achieving nonreciprocal transport without bulky configurations or strong bias fields, and the integration challenges posed by resonant or large-footprint components. These limitations can hinder the realization of compact, reconfigurable, and broadband topological functionalities in integrated photonic platforms. Recent studies have started to address these issues. For example, reconfigurable van der Waals heterostructures, such as trilayer α-MoO3, enable real-time control over topological dispersion through multiple robust photonic magic angles, providing a flexible alternative to traditional rigid photonic crystals[97]. In addition, shear polaritons observed in β-Ga2O3 provide an intrinsic mechanism for directional wave propagation, without requiring structural asymmetry or complex patterning[99]. Furthermore, broadband nonreciprocal absorption has been demonstrated in magnetized gradient ENZ films, enabling directional light control in ultrathin, non-resonant structures that are suitable for on-chip integration[89]. These advances not only help overcome current limitations in PMC-based designs but also highlight their increasing potential in integrated, reconfigurable, and topologically robust optical systems.
CONCLUSIONS
PC and metamaterial, both periodic structures composed of unit cells with different characteristic scales, have promoted the explorations of novel phenomena over the past two decades, some of which even violate and reshape conventional cognitions. To some extent, the advantages of PC and metamaterial are complementary, and their combination is becoming a paradigm in the photonics community. Photonic meta-crystals, by integrating these features, have emerged as a powerful hybrid paradigm that enables unprecedented tunability of photonic band structures. This review has provided a comprehensive classification of PMCs based on their electromagnetic responses, including LHMs, SNG materials, ZIMs, and HMMs. Compared to earlier reviews that examined PCs or metamaterials in isolation, this article bridges both theoretical foundations and experimental realizations of PMCs, presenting a unified framework that links electromagnetic parameters to emerging functionalities. In particular, PMCs offer distinctive advantages in enabling topological phenomena - such as photonic Dirac/Weyl semimetals, double-bowl states, and quasi-BICs - through precise engineering of symmetry, band degeneracies, and reflection-phase topology. Furthermore, the extreme field enhancement in ZIM-based structures greatly facilitates nonlinear optical amplification, reducing device size and energy thresholds. The introduction of magneto-optical effects and gain/loss modulation also provides new pathways for achieving broadband nonreciprocal light transport, which is crucial for isolators and unidirectional emitters. However, fabrication processes that bridge two scales with significant differences may be more complicated. Recent advances in van der Waals materials indicate their potential as candidates for metamaterials, possibly offering a feasible way for the next generation of robust and miniaturized devices. Looking forward, PMCs hold great potential for transformative impact in integrated photonics and quantum optics. In integrated systems, they can act as topologically protected waveguides, low-threshold nonlinear switches, or nonreciprocal elements in photonic circuits. In quantum regimes, the engineered density of photonic states and tunable emission dynamics of PMCs may enable efficient single-photon sources, quantum interfaces, and entanglement-preserving photonic channels. The vast design space offered by anisotropy, periodicity, magnetism, and gain/loss further facilitates exploration in emerging fields such as optical neural networks, programmable metasurfaces, and quantum sensing. Overall, this review highlights the unique physical mechanisms, multifunctional capabilities, and practical prospects of PMCs, positioning them as a frontier architecture for topological photonics, nonlinear optics, and next-generation integrated and quantum photonic systems.
DECLARATIONS
Authors’ contributions
Conceptualization and supervision: Chen, H.; Guo, Z.
Writing-original draft, writing-review and editing: Hu, S.; Li, P.; Chen, H.; Guo, Z.
Funding acquisition: Guo, Z.
Availability of data and materials
Not applicable.
Financial support and sponsorship
This work was supported by the National Key R&D Program of China (Nos. 2021YFA1400602 and 2023YFA1407600), the National Natural Science Foundation of China (Nos. 12004284 and 12374294), and the Chenguang Program of Shanghai Education Development Foundation and Shanghai Municipal Education Commission (No. 21CGA22).
Conflicts of interest
All authors declared that there are no conflicts of interest.
Ethical approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Copyright
© The Author(s) 2025.
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