Polaritons are commonly described as light–matter hybrid quasiparticles. Polaritons inherit their attributes from both their light and matter constituents. More rigorously, a polariton is a quantum mechanical superposition of a photon with a matter excitation, the latter being a collective mode in solids and superconducting circuits or an electron in atoms, molecules or even superconducting qubits. As such, the notion of polaritons is a unifying universal concept between the fields of quantum materials (QMs) and quantum optics/electrodynamics. Until fairly recently, these subfields of contemporary physics evolved largely independently of each other. Among the unintended consequences of these divisions is the ambiguity in polaritonic terminology with the same terms used markedly differently in QMs and cavity quantum electrodynamics (QED) with atomic systems. Here, we attempt to summarize (in alphabetical order) some of the polaritonic nomenclature in the two subfields. We hope this summary will help readers to navigate through the vast literature in both of these fields . Apart from its utilitarian role, this summary presents a broad panorama of the physics and technology of polaritons transcending the specifics of particular polaritonic platforms (Boxes 1 and 2). We invite readers to consult with reviews covering many important aspects of the physics of polaritons in QMs , , , atomic and molecular systems , and in circuit QED , , as well as general reviews of the closely related topic of strong light–matter interaction , , , , , . A constantly updated version is available at https://infrared.cni.columbia.edu.
Anderson–Higgspolaritons , . The matter constituent of these polaritons originates from the amplitude mode in superconductors  (Figure 1). Anderson–Higgs polaritons are yet to be experimentally observed.
Bardasis–Schrieffer polaritons. The matter constituent of Bardasis–Schrieffer (BaSh) polaritons is associated with the fluctuations of subdominant order parameter in superconductors , , charge density wave systems , and excitonic insulators . This novel theoretical concept still awaits experimental confirmation. The requisite experiments include nanospectroscopy and nanoimaging of polaritonic dispersion in the terahertz (THz) frequency range below the energy gap of superconductors. These are challenging scanning probe measurements, as they have to be carried out at cryogenic temperatures. Nano-THz imaging at cryogenic temperatures have been recently fulfilled , paving the wave to the exploration of polaritonic phenomena in superconductors (see also Cooper pair plasmon polaritons and Josephson plasmon polaritons).
Berreman polaritons: Phonon polaritons in anisotropic materials and multilayer structures are also referred to as epsilon-near-zero or ENZ polaritons , , . ENZ materials, artificial structures, and nanocavities reveal exotic electromagnetic responses with a broad range of technological applications , , , , . For example, ENZ nanocavities facilitate ultrastrong coupling between plasmonic and phononic modes , as well as the so-called photonic doping .
Berry plasmon polaritons: chiral plasmonic modes whose dispersion is explicitly impacted by the Berry curvature and anomalous velocity in chiral media , , . Berry plasmon polaritons are yet to be experimentally observed.
Bose–Hubbard polaritons: cavity QED polaritons with matter component associated with transitions across the Mott gap in the system of interacting atoms  (see also Mott polaritons).
Bragg polaritons. Bragg reflectors (Box 1 panel G, Figures 2 and 4) are routinely utilized to implement polaritonic cavities. Bragg polaritons pertain to systems in which multiple excitonic layers and/or quantum wells are periodically integrated in a DBR cavity ,  (see also polaritonic lattices). The inherent anisotropy of Bragg multilayer structures may enable hyperbolic electrodynamics  (see hyperbolic polaritons).
Cavity (microcavity) polaritons. Weisbuch et al. devised and implemented the first semiconductor (micro)cavity device revealing Rabi splitting of exciton polaritons (Boxes 1 and 2). Semiconductor microcavites emerged as a powerful platform for the investigation of strong light–matter interaction in semiconductors , . Microcavity structures reveal intriguing phenomena including polariton parametric amplification  and its spontaneous counterpart, the parametric photoluminescence . Parametric photoluminescence is a purely quantum process. An appealing attribute of polariton parametric photoluminescence is that signal-idler polariton pairs are produced in nonclassical states with quantum correlations. The quest for Bose–Einstein condensation of microcavity polaritons has produced a stream of breakthrough results ,  (see also exciton polaritons and their condensates). Microcavity exciton polaritons display quantum effects including entanglement  and polariton blockade ,  and may serve as a platform for the implementation of qubits .
Channel polaritons are supported by materials and structures with a straight channel cut in polaritonic medium . Channel polaritons were utilized for the implementation of waveguide components including interferometers and ring resonators . Polaritons guided along the nanoslit are predicted to form hybrid polaritons, giving rise to both bonding and antibonding modes .
Charge transfer polaritons. The formation of plasmon polaritons in graphene or semiconductors relies on the high carrier density that can be introduced by electrostatic gating , , ferroelectric polarization , chemical doping , or photoexcitation . Alternatively, the requisite carrier density can be introduced by charge transfer across the interface between proximal materials with dissimilar work functions. Such charge transfer plasmon polaritons have been demonstrated for graphene residing on another van der Waals material RuCl3 . Experiments on metallic nanoparticles show that charge transmitted between the pair of nanoparticles through a conducting pathway leads to a characteristic plasmonic response  termed charge transfer plasmons. Interlayer exciton in transition metal dichalcogenide (TMDC) heterostructures (e.g., MoSe2/WSe2) also involves charge transfer from one layer to another; the relevant microcavity polaritons  are classified as charge transfer exciton polaritons.
Charged polariton. Charged polaritons posess a nonvanishing electric charge. This interesting concept was introduced in the context of the cavity exciton polaritons in GaAs/AlAs quantum wells that also hosted two-dimensional electron gas with the density ne. Spectroscopic experiments in a study by Forg et al.  have identified several distinct properties of charged exciton polaritons, including the scaling of the coupling strength analogous to the properties of atomic QED system . The effective mass of charged polaritons exceeds the band mass of a GaAs quantum well by a factor of 200. Tiene et al.  have theoretically demonstrated the unique utility of charged microcavity polaritons for exploring the physics of electron–hole systems with charge imbalance, which are difficult to access with alternative experimental methods. They demonstrated how the Fermi sea of excess charges modifies both the exciton properties and the dielectric constant of the cavity medium, which in turn affects the photon component of the many-body polariton ground state (Figure 2). See also the closely related entries of Fermi-edge exciton polaritons and trion polaritons.
Cherenkov polaritons. In the Cherenkov effect , a charged particle moving with a velocity faster than the phase velocity of light in the medium radiates light. The emitted radiation forms a cone with a half angle determined by the ratio of the two velocities. Genevet et al.  demonstrated that by creating a running wave of polarization along a one-dimensional metallic nanostructure consisting of subwavelength-spaced rotated apertures that propagates faster than the surface plasmon polariton phase velocity, one can generate surface plasmon wakes that serve as a two-dimensional analog of Cherenkov radiation. The Cherenkov physics is also relevant to the properties of phonon polaritons , . Infrared nanoimaging experiments reveal Cherenkov phonon polariton wakes emitted by superluminal one-dimensional plasmon polaritons in a silver nanowire on the surface of hexagonal boron nitride . See also Exciton polariton X-waves on superluminal properties in the system of exciton polaritons.
Cooper pairs polaritons (in QMs and cold fermionic cavity systems). Cooper pair plasmon polaritons emerge in superconductors. The matter component of these polaritons is associated with the superfluid density (from a study by Basov et al. ). The dispersion of Cooper pairs plasmon polaritons in layered cuprate high-Tc superconductors has been investigated theoretically ,  but is yet to be explored in experiments. Recently, the formalism of the Bardeen Cooper and Schrieffer theory of superconductivity has been applied to describe the quasiparticle excitations of a cold fermion system coupled to a cavity. Depending on the excitation density and atomic interaction, the excited atoms and holes and in the Fermi sea may form bound Cooper pairs strongly coupled with cavity photons. This latter kind of polaritons were also termed Cooper pair polaritons .
Dark polaritons in QMs: polaritons are characterized by a wavevector that lies beyond the light line. The lower branches of polaritons in many/most QM systems are dark by this criterion and do not couple to free space photons because of the notorious “momentum mismatch” problem (Box 1 F, H, Figure 1). Light excition of dark polaritons can be mediated by nanoscale defects such as a protrusions, divots, or cracks, exploiting the high spatial frequencies inherent to these deeply subwavelength objects. Better controlled strategies can also provide the missing momentum needed for coupling to dark polartons . These include prism and grating coupling, and the use of plasmonic optical nanoantennas , , , , , , , . Notably, sharp scan probe tips can act as such antennas , , , , , , allowing polaritonic waves to be launched and visualized. Scanning probe antenna-based nano-optics has emerged as an indespensible research tool enabling spectroscopy and visualization of polaritons in QMs , , .
Dark-state polaritons in atomic ensembles: typically, this refers to polaritons in atomic ensembles that propagate in the regime of electromagnetically induced transparency (EIT) , , , . The darkness arises from the photon mixing strongly with a collective atomic excitation, resulting in a state with only a minute photonic component. See also EIT polaritons below. In ordered atomic arrays, dark (also often referred to as subradiant) states emerge due to interference in photon emission and absorption. At the single photon level, these darks states are collective spin excitations with a wave vector that lies beyond the light line, preventing the coupling with radiation modes (exactly the same phenomenon of “momentum mismatch” described above for QMs) , , , . Polaritons arising in atomic lattices have applications in quantum information storage and processing .
Demons: or density modes were introduced by David Pines , an early protagonist of plasmons research. Demons are particularly relevant to the response of the Dirac fluid in graphene in hydrodynamic regime  and adiabatic plasmon amplification .
Dirac plasmon polaritons are formed by hybrids of infrared photons with Dirac electrons in graphene , , , . Direct nanoimaging experiments uncovered extraordinarily long propagation lengths of highly confined Dirac polaritons and have established fundamental limits underlying their decoherence and losses .
Dyakonov surface polaritons: the surface modes that propagate along the interface between isotropic and uniaxial materials is known as Dyakonov surface polaritons , , . A special case of Dyakonov polaritons is realized in anisotropic crystals of layered van der Waals materials. One example is that of the hyperbolic surface phonon polaritons propagating along the edges of slabs prepared from hexagonal boron nitride , , .
Edge magneto plasmons. Two-dimensional (2D) electron gas subjected to the magnetic field normal to the plane of the 2D conductors reveals two distinct field-dependent resonances: the cyclotron resonance mode with frequency increasing with the magnetic field and another mode that redshifts with the applied field. The latter mode has been linked to the edge plasmons of the charged sheet and can be viewed as the 2D analog of surface plasmons in three-dimensional (3D) systems . Specifically, edge magneto plasmons can propagate along the physical boundary of the 2D conductors , . Edge magneto plasmons constitute a spectacular manifestation of the dynamical Hall effect. Edge magneto plasmons are chiral. Their chirality is a direct implication of the applied Lorentz force . Graphene reveals rich plasmonic phenomena in the presence of magnetic fields , , , , .
Edge plasmon polaritons: one-dimensional plasmonic modes propagating along the physical boundaries of two-dimensional materials (Figure 3) is called edge plasmon polaritons. They reveal an approximately 10% shorter wavelength compared to the interior of the plasmonic medium . Qualitatively, the shorter wavelength can be ascribed to the effective reduction of the Drude weight since free carriers exist only on one side of the physical boundary. Dyakonov hyperbolic phonon polaritons are a lattice analog of edge plasmon polaritons. Berini reported on an in-depth numerical analysis of edge and corner plasmon polariton modes in thin conducting slabs . Whispering-galley polaritons is a special example of an edge polaritons that loops around the ridge of polartonic medium  or along the circumference of nanoholes , .
EIT polaritons propagate in atomic systems under conditions of EIT. A remarkable aspect of EIT polaritons is that they can be slowed down to 10s of meters per second  or even brought to a standstill , . EIT polaritons can be dark (decoupled from radiation, more “atom-like”) or bright (coupled to radiation, more “photon-like”). The darkness/brightness of the polaritons is controlled by an external laser beam. EIT polaritons can be strongly interacting, if coupled to Rydberg states (see Rydberg polaritons below). The EIT phenomenon is also observed in materials and nanostructures. Examples include:
ENZ polaritons: epsilon-near-zero or ENZ polaritons are equivalent to Berreman polaritons above.
Exciton polaritons and their condensates. Exciton polaritons are bosonic quasiparticles originating from photons hybridized with hydrogen-like bound electron–hole pairs. Semiconductor microcavities (Box 1 and Figure 4A) offer an outstanding platform for the investigation of exciton polaritons and the attendant strong light–matter coupling, provided a high-quality microcavity is nearly resonant with an excitonic transition. Trapped photons may be emitted and reabsorbed multiple times before being lost to dissipation or cavity leakage. Absorption and re-emission of photons in the cavity give rise to light–matter mixed eigenstates . When sufficiently long-lived, exciton polaritons may form coherent quantum states , , , , , , . Bose–Einstein condensates (BECs) of exciton polaritons are appealing quantum liquids in part because their coherent state is created and controlled by light , , . The binding energies of excitons in organic molecules , TMDCs, and lead halide perovskites can be as high as 0.75 eV , , , , , , , , ; these extraordinary high binding energies underlie the theoretical predictions of condensation and superfluidity at T = 300 K , , . BECs of exciton polaritons were predicted to form spatially and temporarily ordered states: time crystals . Exciton polariton condensates may also enable energy-efficient lasers .
Exciton polariton X-waves: wavepackets of exciton polaritons that sustain their shape without spreading, even in the linear regime. In a study by Gianfrate et al. . Self-generation of an X-wave out of a Gaussian excitation spot is obtained via a weakly nonlinear asymmetric process with respect to two directions of the nonparabolic polariton dispersion. Notably, X-waves were found to propage with supluminal peak speed with respect to the group velocity of the polaritonic system.
Fermi edge exciton polaritons ,  are observed in microcavities where the active semiconductor is heavily doped to form the Fermi edge. Fermi edge exciton polaritons are formed of electron hole pair excitations involving electron and hole states with in-plane wave vectors around the Fermi edge: kIIe = kIIh ∼ kF, where kF is the Fermi wavevector. In some literature, this latter form of polaritonic states are referred to Mahan exciton polaritons , recognizing a prediction of excitonic bound states in doped semiconductors beyond the critical density of the insulator to metal transition states by Mahan , . See also Quantum Hall polaritons below.
Floquet polaritons. The concept of Floquet engineering refers to the control of a system using a time periodic optical field and is being broadly applied in atomic physics, as well as in the field of QMs . The notion of Floquet polaritons pertains to polaritons in a system of Floquet-engineered atomic states  or electronic states in solids . The concept of Floquet engineering by time period optical fields has been extended to coherent phonons in QMs . Chiral Floquet polaritons are predicted  to form in chiral cavities, in which fundamental matter symmetries are broken (Box 2).
Frenkel exciton polaritons. The matter constituent of these polaritons originates from Frenkel excitons characterized by the Bohr radii of the same order as the size of the unit cell. Frenkel exciton polaritons are common in organic semiconductors . The high exciton binding energy (∼eV) and large oscillator strength may lead to room temperature exciton polariton condensates , , .
Fuchs–Kliewer interface polaritons: phonon polaritons occurring at surfaces and interfaces  with the matter part are originating from Fuchs–Kliewer surface phonons . Huber et al.  employed nanoinfrared methods to visualize propagating Fuchs–Kliewer surface phonon polaritons in SiC. Surface phonon polaritons are observed in insulating and semiconducting materials including hBN , , SiC , , , , GaAs , and many others.
Helical plasmon polaritons: were predicted to form in topologically nontrivial Weyl semimetals . Plasmon polariton dispersion may enable the detection of a chiral anomaly: a charge imbalance between the Weyl nodes in the presence of electric and magnetic fields . The Fermi surface of Weyl semimental features open disjoint segments – the Fermi arcs – associated with the topolical surface states. The resulting Fermi arc plasmon polaritons are predicted to be chiral and to reveal unidirectional propagation . Helical plasmon terminology was also applied to describe one-dimensional plasmon polaritons associated with the helical state in domain walls of topologically nontrivial conductors including anomalous quantum Hall systems . Helicity dependence of plasmon polaritons is discussed in the context of unidirectional propagation in plasmonic metastructures controlled by the circular polarization of light , .
Hopfield polaritons: a bold theoretical concept of light–matter hybridization proposed by John Hopfield in his doctoral thesis back in 1958 (in a study by Hopfield ). Hopfield also coauthored the first experimental paper on polaritons devoted to the study of phonon polariton dispersion in GaP by means of Raman scattering . Other early contributions to the theory of polaritons (short of introducing this term) were made by Fano , Huang , and Tolpygo .
Hybrid polaritons. Different types of polaritons hosted by the same material are prone to hybridization . For example, intersubband polaritons and phonon polaritons hybridize in semiconductor quantum wells , , . Hybridization can also occur in multilayered structures. In all-dielectric layered structures, phonon polaritons associated with the neighboring layers couple to form hybrid modes , , . Semiconductor heterostructures ,  and especially van der Waals heterostructures offer a fertile platform for the implementation of hybrid polaritons , . One such example (Figure 5B and C) is graphene surrounded by insulating layers of hexagonal boron nitride hBN or silicon dioxide. Plasmons associated with graphene layers hybridize with phonon polaritons in proximal SiO2 or hBN layers to form plasmon–phonon polaritons , , , . Hybrid polaritons at the interface of graphene with high-Tc superconductors were proposed as a tool to probe Anderson–Higgs electrodynamics . Hybrid polariton at the interface of graphene with a charge density wave materials were theoretically proposed to “melt” the density wave order . Hybrid modes produced by plasmons in graphene and molecular vibrations of absorbates on the graphene surface may enable high-selectivity sensing mechanisms , . A special case of hybrid modes is hybrid longitudinal–transverse phonon polaritons . Polaritonic heterostructures with phase change materials enable persistent switching of polaritonic response under thermal and optical stimuli .
Hyperbolic polaritons. Anisotropic media are predicted to support an interesting class of polaritonic light–matter modes referred to as “hyperbolic” because their isofrequency surface is a hyperboloid , , , , , , , , . These modes exist over a range of frequencies where the in-plane permittivity and the out-of-plane (c-axis) permittivity are of the opposite sign. Hyperbolic electrodynamics and hyperbolic polaritons can originate from a variety of physical processes including phonons , , , , , , , , , , ,  intersubband transitions in quantum wells , ,  plasmons , , , , , , excitons , and Cooper pairs (see Cooper pair polaritons). Hyperbolic polaritons dramatically enhance the local photonic density of states and are predicted to give rise to strong nonlinearities . Hyperbolic polaritons enable canalization imaging  with image effectively transferred by high-momentum subdiffractional polaritonic rays from back to front surface of the polaritonic medium , , , .
Image polaritons: virtual polariton modes produced by image charges at the interface of a polaritonic medium and a metal are called image polaritons. Lee et al.  have experimentally demonstrated low loss response of image polaritons at the interface of hBN separated with a thin spacer from a metallic substrate (Figure 5D).
Interband polaritons. The matter constituent of these polaritons originates from contributions of the optical response associated with transitions across the energy gap in the electronic spectrum of a material. These include transitions across the energy gap in semiconductors  and superconductors or transitions involving minibands/flat bands in moire superlattices of van der Waals materials , , ,  (see also Moire polaritons). The frequency dependence of σ2(ω)xω, where σ2(ω) is the imaginary part of the complex conductivity, is informative for the analysis of interband polaritons , . Spectra of σ2(ω)xω reveal a series of steps separated by plateaus, with each step uncovering the energy scale associated with separate interband contributions. In the limit of ω → 0, the product σ2(ω)xω quantifies the spectral weight of intraband processes to the plasmon polaritons. Interband effects play a central role in theoretical proposals for the implementation of population inversion , gain and superluminal plasmon polaritons .
Intersubband polaritons. Dini et al. ,  reported the first experimental observation of the vacuum-field Rabi splitting of an intersubband transition inside a planar microcavity hosting two-dimensional electron gas. Nonlinearities associated with intesubband transitions in semiconductors can be dramatically enhanced by in hybrid structure with plasmonic metasurfaces  (see also hybrid polaritons).
Josephson plasmon polariton: an inherent attribute of strongly anisotropic layered superconductors is the Josephson plasmon polariton. The matter constituent of Josephson plasmon polaritons originates from interlayer Josephson plasmon in layered superconducting materials such as cuprates , . Josephson plasmons are the electromagnetic signature of three-dimensional superconductivity in highly anisotropic layered high-Tc superconductors . Josephson plasma waves can be parametrically amplified under illumination with pulsed THz fields , paving the way for active Josephson polaritonics.
Kane polaritons: surface plasmon polaritons formed with Kane quasiparticles is the Kane polaritons. Kane polaritons were recently observed in pump–probe experiments on narrow gap II–VI semiconductors .
Landau polaritons. The matter component of Landau polaritons originates from cyclotron resonances and transitions between quantized Landau levels relevant in low-dimensional electron gases subjected to high magnetic fields , . See also magneto plasmon polariton.
Luttinger liquid polaritons: plasmon polaritons in one-dimensional conductors recently revealed by infrared nanoimaging of single-wall and multiple-wall carbon nanotubes . Interacting electrons confined in one dimension are generally described by the Luttinger liquid formalism , . Anomalous dependence of the plasmonic quality factor on gate voltage was interpreted in terms of plasmon–plasmon interaction in carbon nanotubes .
Magnon polaritons. The matter constituent of these polaritons originate from antiferromagnetic ,  and ferromagnetic resonances . In weak magnetic fields, surface magnon polaritons are predicted to acquire nonreciprocal properties. Macedo and Camley  analyzed the propagation of surface magnon polaritons in anisotropic antiferromagnets. Sloan et al.  predicted that surface magnon polaritons will strongly enhance the spin relaxation of quantum emitters in the proximity of antiferromagnetic materials such as MnF2 or FeF2. Kruk et al.  developed artificial structures with hyperbolic magnetic response with principal components of the magnetic permeability tensor having the opposite signs. Magnetic materials also support hybrid polaritons, including hybrid magnon–phonon polaritons recently observed in ErFeO3/LiNbO3 multilayers .
Magneto plasmon polaritons: coupled modes of magneto plasmons and THz/infrared photons , . Theoretically predicted unconventional properties of magneto polaritons in Weyl semimetals include hyperbolic dispersion and photonic stop bands . The nanoinfrared imaging and visualization of magneto plasmon polaritons remains an unresolved experimental challenge. Once technical obstacles are circumvented, it may become possible to directly explore both the focusing and the nonreciprocity predicted for magneto plasmon polaritons . Plasmonic system driven by intense a.c. field is predicted to reveal spontaneous symmetry breaking and nonlinear magnetism .
Microcavity polaritons: see cavity polaritons.
Moire polaritons. Atomic layers comprising van der Waals materials can be reassembled into heterostructures with nearly perfect interfaces , , . A unique control knob specific to vdW systems is the twist angle θ between the adjacent layers. Varying θ forms moiré superlattices that can radically modify the electronic structure and attendant properties , , , , , , , , , , , , , , . Plasmons, phonons, and excitons are all altered in moire superlattices prompting changes of the corresponding polaritons. G/hBN[cross-Ni-Moire]. Infrared nanoimaging data display rich real space patterns of polaritonis with selected examples of moire polaritons displayed in Figure 6. Morie design principle can be applied to epitaxially grown thin films on dielectric substrates . Recent experiments on interlayer excitons in TMDC heterobilayers have revealed the trapping of these excitons on the moire potential landscape , , , . When placed in an optical cavity, such moire trapped excitons may form an exciton polariton lattice and serve as analog quantum simulators (QSs) (see polaritonic lattices and quantum simulators).
Molecular polaritons. Organic semiconductors and molecules embedded in optical (nano)cavities under strong and ultrastrong coupling promote the dynamical formation of molecular polaritons: hybrid energy eigenstates composed of entangled photonic, electronic, and vibrational degrees of freedom , , . Molecular polaritons were demonstrated to enhance energy transfer  and DC conductivity . Progress with nanostructures enabled a demonstration of the strong–light matter coupling with a single molecule embedded in a plasmonic cavity . Molecular molaritons enable control of optical nonlinarities via manipulations of cavity characteristics . Molecular polaritons can form hybrid polaritons by coupling to surface plasmons , for example. We remark that molecular polaritons are commonly referred to as vibrational polaritons.
Mott polaritons (QM) were also introduced in context of the resonant coupling between strongly correlated electrons in solid Mott insulators integrated in a single-mode cavity .
Phonon polaritons: is a collective excitation comprised (infrared) light coupled with a polar lattice vibration. Like other polaritons, phonon polaritons can be understood in terms of an anticrossing of the dispersion curves of light and matter constituents (Figure 5). Early observations of phonon polaritons (see Hopfield polaritons) in bulk crystals and films were made using a variety of spectroscopic methods , . More recent work  has focused on the generation, detection, and on picosecond polaritons dynamics , , , , . By matching the phonon polariton velocity in LiNbO3 crystal to the group velocity of the fs punp pulse Yeh et al.  have been able to generate intense THz fields of the order of 10 μJ energy. Advanced nanoimaging/spectroscopy methods , ,  were employed for the real-space visualization of phonon polariton standing ways. Phonon polaritons play a major role in nanoscale thermal transport at nanoscale and mesoscale , , , , , , . Phonon polaritons in the anisotropic oxide material MoO3 reveal both elliptical and hyperbolic dispersions , , . The dispersion and propagation of phonon polaritons can be controlled by nanostructuring  and twist-angle (moire) engineering (Figure 6). The recent discovery of parametric phonon amplification in SiC paves the way for the exploration of nonlinear and active phonon polariton phenomena . Surface phonon polaritons (see also Fuchs–Kliewer interface polaritons) reveal a dispersion branch located between longitudinal and transverse vibrational modes (see hybrid polaritons). Dai et al.  detected surface phonon polaritons in monolayers of hBN.
Plasmon polaritons: probably the most thoroughly studied class of polaritons. A surface plasmon polariton is a transverse magnetic (TM)-polarized optical surface wave that, for example, propagates along a flat metal–dielectric interface, typically at visible or infrared wavelengths , , . Plasmon polaritons have rich implications for technology , , , . Nonlinear , ,  and quantum , , , ,  properties of plasmonic structures are in the vanguard of current research. Plasmon polaritons can be controlled at femto-second timescales , , , , ,  enabling access to novel physics and applications , . Plasmonic waveguides have been incorporated with light-emitting materials, paving the way for integrated plasmonic and photonic structures . Plasmon polaritons have been harnessed to implement high-quality factors such as whispering gallery microcavities . In parallel, many research groups are searching for new plasmonic media with the properties optimized for different classes of plasmonic effects , , , . Van der Waals materials, and especially graphene, are emerging as outstanding plasmonic media in light of their inherent tunability with different stimuli (see Dirac plasmons). Acoustic plasmon polaritons are a special example of hybrid polaritons whose frequency-momentum ω(q) dispersion is predicted to be linear , , , , . Acoustic plasmon plaritons have been demonstrated , ,  in structures, where graphene resides in close proximity to metallic surfaces. Spoof surface plasmons polaritons were introduced describe plasmon polaritons on the surface of artificial metallic structures and metamaterials . Airy surface plasmon polaritons are the surface counterparts of nondiffracting airy waves  and have been demonstrated by direct nanoimaging . Chiral plasmon polaritons  were predicted to occur in twisted bilayer graphene  (Figure 7).
Plexcitons are a specific example of hybrid polaritons. The matter constituent of plexcitons originates from plasmon exciton coupled modes , , , , , ,  Historically, plexciton studies have focused primarily on localized states , . Propagating plexciton states also exist and offer potential for compact quantum information carriers as well as opportunities for mediating emitter–emitter coupling , , . Composite structures and multilayers can feature plexcitons. An interesting recent example of plexciton study has been conducted in the setting of scanning probe nano-optical imaging and spectroscopy (Figure 8). This work by May et al. , along with a study by Groß et al. , implemented the scanning optical cavities formed between a nano-optical antenna and the substrate. The authors investigated CdSe/ZnS quantum dots using this scanning cavity approach and observed plexitonic Rabi splitting of 163 meV.
Polaritons parametric amplification, gain, and lasing have been demonstrated for exciton polaritons in microcavities , , , . Resonant coupling between photons and excitons in microcavities can efficiently generate significant single-pass optical gains . Polaritonic lasing has been implemented and analyzed in different material systems hosting plasmon polartions and exciton polaritons . Amplification of demons  has been predicted as well but is yet to be experimentally demonstrated.
Polaritonic circuits, devices, arrays, and systems. Both light and matter constituents of polaritons are amenable to controls with external stimuli . The use of exciton polaritons as building blocks for future information processing such as spin switches , spin memory , transistors , logic gates , resonant tunneling diodes , routers , and lasers  has recently been demonstrated. The first polaritonic systems are also emerging and include QSs and networks for neuromorphic computers . TMDC material WSe2 integrated into microcavity devices acts as efficient light emitting device .
Polaritonic lattices, and QSs. A variety of experimental approaches have been utilized to implement one- and two-dimensional arrays of interacting polaritons. In the field of microcavity exciton polaritons gate arrays, spatially dependent optical potential as well as surface acoustic waves , have been utilized to generate arrays/lattices . One-dimensional exciton polariton superlattices reveal weak lasing assigned to a novel type of a phase transition in this interacting system . Arrays of evanescently coupled cavities hosting neutral atoms  have been proposed as QSs, where the photon blockade provided by the atom limits the occupancy of each cavity to one, allowing for the implementation of the Bose–Hubbard model. QSs require controllable quantum systems that efficiently simulate a Hamiltonian of interest, which may encode phases with a significant degree of entanglement and is not amenable to calculations by classical computer , , , , , . Lattices of exciton polaritons , , , , ,  have emerged as a promising platform for QS, along with ultracold atoms , , trapped ions , , , and superconducting circuits , . Moire superlattices of plasmon polaritons (Figure 6) present yet another example of polaritonic lattices. Moire superlattices were realized in graphene devices with nanostructured gate electrodes , as well as in moire superlattices of twisted graphene layers .
Polaritonic interference, refraction, collimation, front shaping, and waveguiding. All these common wave phenomena are relevant to polaritons (Figure 9). In van der Waals materials, domain wall boundaries can act a polaritonc reflectors , , , or conductors . Zia and Brongersma  demonstrated Young’s double-slit experiments with surface plasmon polaritonss. Beyond analogs of geometrical optics effects, polaritons offer at least two novel routes for image formation. First, hyperbolic polaritons enable canalization imaging , with images effectively transferred by high-momentum subdiffractional polaritonic rays from the back to the front surface of the polaritonic medium , , ,  (Figure 9C). Second, polaritons are amenable to guiding and steering using methods of transformation optics. Polaritonic waveguides have been implemented over a broad range of frequencies from THz  and infrared regions to visible light. Peier et al. observed phonon–polariton tunneling across the airgap . Advanced polaritonic launchers and metalenses (Figure 9D) are well suited for defining the trajectories of polaritonic surface “beams” , . In highly nonlinear regime polaritons are predicted to display self-focusing effects and to form solitons .
Polariton–polariton interactions. The interaction of polaritons stems from their underlying matter constituents. In close analogy with other interacting systems, polariton–polariton interactions renormalize the dispersion and also prompt a blue shift of the emission energy as the polariton density increases , . Polariton–polariton interaction effects have been recently demonstrated for microcavity exciton polaritons , . See also quantum Hall polaritons.
Polaron polaritons. In TMDC monolayers, the itinerant electrons dynamically screen exciton to form new quasiparticle branches – the attractive and repulsive polaron – each with a renormalized mass and energy , . Microcavity polaritons with the matter constituent linked to these polaron branches are referred to as polaron polaritons .
Quantum Hall polaritons are a product of coupling cavity photons to the cyclotron resonance excitations of electron liquids in high-mobility semiconductor quantum wells or graphene sheets , . The edge channels of the quantum Hall effect offer a platform for probing interference and entanglement effects in the setting of a condensed matter system since the edge states propagation is ballistic, one-dimensional, and chiral. This platform enables experimental implementation of electron quantum optics , , ,  and may be suitable for the realization of flying qubits. In a parallel development, Smolka et al. . investigated cavity exciton polaritons in the presence of high-mobility 2D electron gas subjected to external magnetic field and discovered novel correlated electron phases. Knuppel et al.  reported on strong polariton–polariton interactions in the fractional quantum Hall regime.
Rydberg polaritons (QED): photons dressed by highly excited atomic Rydberg states under conditions of electromagnetic induced transparency. These polaritons can either reside in a cavity or propagate throughout an atomic ensemble. In a cavity, Rydberg dressing bestows an atomic ensemble with the character of a two-level system: the excitation of a single Rydberg polariton prevents the creation of a second one, in the so-called “Rydberg blockade” regime. Under conditions of electromagnetic induced transparency, polaritons can propagate within an optically dense atomic cloud. These polaritons can then be made to interact with each other via Rydberg dressing: the first Rydberg polariton alters the transparency condition for the second one, preventing its propagation within a certain “blockade radius” , , , . Rydberg polaritons are appealing for quantum logic functionalities  and for realizing synthetic materials via many-body states of light , .
Rydberg polaritons (QM): a special example of exciton polaritons with matter constituent associated with strongly interacting Rydberg states of excitons . Candidate systems include TMDC monolayers ,  and cuprous oxide, where Rydberg states with principal quantum numbers of up to n = 25 are feasible .
Soliton polaritons. Propagating wavepackets in semiconductor micorcavities are referred to as soliton polaritons (Figure 10C). In quantum optics, topological soliton polaritons refer to composite objects made of fermions trapped in an optical soliton. The prototypical one-dimensional (1D) model of solitons posessing nontrivial topology is the model of Su–Schrieffer–Heeger (SSH) chains . Variants of the SSH Hamiltonian have been emulated in the 1D lattices of microcavity exciton polaritons  and also in the system of quantum emitters coupled to a photonic waveguide . Topological phases of polritons in cavity waveguides were analyzed in a study by Downing et al. .
Spin polaritons: this term was coined in the context of polariton microcavity diode lasers operating via injection of spin polarized currents .
Spin plasmon polaritons are relevant to the plasmonic response of spin-polarized electron gas . Alternatively, spin–orbit interaction may lift the degeneracy between the spin states and give rise to transitions responsible for peculiar dispersion features of spin plasmon polaritons . The surface plasmon of a helical electron liquid is predicted to carry spin and is also referred to as a spin plasmon polariton .
Transformation optics with polaritons. Transformation optics refers to a general principle for designing a complex electromagnetic medium with tailored properties by carefully crafting the spatial patterns of the local optical index , . This general principle has been extended to polaritons  and polartonic cavities , and specifically to plasmon polaritons in graphene . Losses present the most significant experimental roadblock for practical transformational polaritonics. Recent advances with highly confined but low-loss plasmon polaritons  and phonon polaritons  fulfill important experimental preconditions for the realization of transformation optics ideas in polaritonic systems.
Tamm surface plasmon polaritons are associated with Tamm states at metallic surfaces . Common surface plasmon polaritons are formed with a TM polarization at the boundary of metallic and dielectric surfaces and lie to the right of the light cone. Tamm polaritons are found with both TM and transverse electric polarizations, and their dispersion can be within the light cone , .
Trion polaritons. The matter constituent of these polaritons is formed by charged excitons or trions (see also charged polaritons). Trion polaritons are commonly found in the response of TMDC semiconductors ,  and also in carbon nanotubes .
Tunneling plasmon polaritons were predicted  and observed  in an atomically thick tunable quantum tunneling devices consisting of two layers of graphene separated by 1 nm of h-BN. By applying a bias voltage between the graphene layers, one creates an electron gas coupled to a hole gas. Even though the total charge of the devices is zero, this system supports propagating graphene plasmons.
Valley polaritons. The matter constituent of these polaritons originates from valley polarized excitons in TMDC semiconductors (Figure 4B and exciton polaritons). The electronic structure of two-dimensional TMDC semiconductors endows this class of materials with the spin–valley degree of freedom that provides an optically accessible route for the control and manipulation of electron spin , , .
Vibrational polaritons: see molecular polaritons.
Wannier or Wannier–Mott polaritons borrow their matter part from Wannier excitons in semiconductors .
Waveguides and photonic crystals for polaritons. Waveguides and photonic crystals allow one to design and control the properties of photons, and thus of polaritons, both in quantum optics and QMs. In waveguide QED, different type of emitters (neutral atoms, quantum dots, color centers, superconducting qubits) are coupled to a one-dimensional (1D) optical channels , such as fibers , , photonic crystals , , and transmission lines ,  (Box 1 and Figure 11A). Channel with a bandgap give rise to atom–photon bound states (i.e., polaritonic bound states), provided the atomic resonance frequency is close to the band edge. Beyond the band-edge, photons are bound to the atoms, forming localized polaritonic cavities that can be harnessed for realizing quantum simulation and quantum information processing (Box 1). If the coupling between photons and atoms is strong enough, bound states emerge even if the atomic resonance frequency lies inside the band (i.e., as a “bound states in the continuum”) due to multiple scattering , . In the field of QMs, photonic crystal structures were fabricated using common phonon–polariton oxide systems LiTaO3 and LiNbO3 (Figure 11B). Pump–probe experiments in Figure 11B revealed the key attributes of the dispersion control by these periodic structures. A significant deficiency of conventional photonic crystals is that they do not allow for dynamical dispersion engineering. Xiong et al. circumvented this limitation and demonstrated a broadly tunable two-dimensional photonic crystal for surface plasmon polaritons [cross-ref-xiond]. Infrared nanoimaging revealed the formation of a photonic bandgap and an artificial domain wall which supports highly confined one-dimensional plasmonic modes.
Zenneck–Sommerfeld waves and Norton waves: an early example of a guided electromagnetic wave at the interface of media with negative and positive dielectric function , , , the same condition that is required for the formation of polaritonic modes in THz, infrared, and optical frequencies. The original prediction of Zenneck–Sommerfeld waves pertained to the radiofrequency wave at the interface of air and the Earth. In this analysis, the surface of the Earth was regarded as a lossy dielectric. The concept of Zenneck–Sommerfeld waves and closely related Norton waves has been applied to a broad class of wave patterns on the surface of metallic , , ,  and dielectric materials .
Research at Columbia is supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award DE-SC0019443. D.N.B. is Vannevar Bush Faculty Fellow ONR-VB: N00014-19-1-2630 and Moore Investigator in Quantum Materials #9455.
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: Research at Columbia is supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award DE-SC0019443.
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