Multimode Waveguide Polaritons

• Multimode waveguide polaritons are hybrid states formed by coherently coupling material resonances (e.g., excitons, plasmons) to multiple guided modes.
• They exhibit multiple avoided crossings and distinct dispersion branches due to intermode overlap and mode-dependent propagation constants.
• Engineered via design parameters like thickness, index contrast, and patterning, these polaritons enable tunable nonlinear optics, phase control, and nonreciprocal transport.

Multimode waveguide polaritons are hybrid light–matter eigenstates formed when one or more material resonances couple coherently to more than one guided electromagnetic mode of a slab, slot, patterned multilayer, or related waveguide, so that the resulting spectrum contains several avoided crossings, multiple polariton branches, and mode-dependent propagation constants, field profiles, and losses. In the reported literature, the relevant matter resonances include quantum-well excitons, surface plasmon polaritons, phonon polaritons, and periodic emitter arrays, while the multimode character can arise from several TE or TM guided modes, Bloch-folded photonic bands, two coupled interfaces of a slot waveguide, or, in a distinct sense, two orthogonally polarized surface-polaritonic modes (Ciers et al., 2016, Abdol et al., 2020, Bürger et al., 26 May 2026, Asgarnezhad-Zorgabad et al., 2019, Sun et al., 2019).

1. Conceptual basis

For a single guided photonic mode with dispersion $E_C(k)$ coupled to an exciton at energy $E_X$, the polariton branches obey

$$E_{\mathrm{UP/LP}}(k)=\frac{E_C(k)+E_X}{2}\pm\sqrt{\left(\frac{E_C(k)-E_X}{2}\right)^2+g^2},$$

with Hopfield coefficients determined by the detuning and the coupling rate $g$; in the III-nitride slab-waveguide realization, these relations apply to the TE0 mode, and in a multimode slab one writes a separate coupled-oscillator problem for each TE/TM guided mode, yielding one LPB/UPB pair per guided mode (Ciers et al., 2016). In semiconductor waveguides with heavy-hole excitons, the same two-level structure is used to describe TE and TM guided polaritons, with measured Rabi splittings $\Omega_{R,\mathrm{TE}} \approx 13.4\ \mathrm{meV}$ and $\Omega_{R,\mathrm{TM}} \approx 5.2\ \mathrm{meV}$ in one electrically controlled GaAs platform (Suárez-Forero et al., 2020).

The multimode generalization is a matrix problem. In the microscopic multilayer framework, one introduces several photonic branches $\omega_m(k_\parallel)$, several excitonic branches $\omega_{xj}(k_\parallel)$, and a coupling matrix $G_{mj}=g_{mj}(k_\parallel)$, so that the polariton frequencies are the eigenvalues of a non-Hermitian block matrix with photonic and excitonic diagonal blocks and off-diagonal light–matter couplings; the same formalism is explicitly adapted from Fabry–Perot cavities to planar waveguides by replacing standing-wave mode functions with guided-mode profiles $\mathcal{E}_m(z)$ (Mandal et al., 2023). In patterned multilayer waveguides, the full non-Hermitian generalized Hopfield–Bogoliubov matrix retains radiative loss rates $E_X$0, excitonic loss rates $E_X$1, and anti-resonant blocks, so that multimode polariton dispersion follows from $E_X$2 (Zanotti et al., 2022).

A central distinction concerns coupling regime. In the visible planar-waveguide study of exciton-tunable multimode engineering, “multimode strong coupling” denotes the regime in which an exciton couples to several photonic modes but each polariton branch remains predominantly associated with one photonic parent, whereas “superstrong coupling” is defined by $E_X$3, so that a single branch acquires sizeable contributions from multiple photonic modes and can develop a continuous S-shaped dispersion. The same work explicitly distinguishes this superstrong-coupling criterion from ultrastrong coupling, which would require $E_X$4 (Bürger et al., 26 May 2026).

2. Geometries and sources of mode multiplicity

Mode multiplicity is realized, or deliberately suppressed, by waveguide thickness, index contrast, periodic folding, lateral confinement, or interface coupling. In the III-nitride slab-waveguide platform, the structure was intentionally designed so that only TE0 and TM0 were guided and all higher-order modes were cut off; this near-single-mode choice avoided exciton coupling into multiple guided channels, but the same analysis states that thicker cores or larger index contrast would admit TE1/TM1 and higher modes, each potentially forming its own polariton branch (Ciers et al., 2016). By contrast, the visible planar-waveguide study explicitly analyzes $E_X$5 cores supporting two TE modes, $E_X$6 cores supporting three to four TE modes, and $E_X$7 cores supporting up to TE4, with the excitonic layer embedded near a core boundary to maximize intermode overlap (Bürger et al., 26 May 2026).

In slot geometries, the multimode character is not simply a count of transverse slab modes. A Weyl-semimetal slot waveguide made of two semi-infinite Weyl semimetals separated by a dielectric spacer supports multiple SPP branches because two interfaces are coupled through the factor $E_X$8, and the number, reciprocity class, and asymptotic frequencies of the modes depend on the spacer thickness $E_X$9, chemical potential $$E_{\mathrm{UP/LP}}(k)=\frac{E_C(k)+E_X}{2}\pm\sqrt{\left(\frac{E_C(k)-E_X}{2}\right)^2+g^2},$$0, and anomalous Hall parameter $$E_{\mathrm{UP/LP}}(k)=\frac{E_C(k)+E_X}{2}\pm\sqrt{\left(\frac{E_C(k)-E_X}{2}\right)^2+g^2},$$1 (Abdol et al., 2020). In anisotropic vdW slabs, the waveguide eigencondition $$E_{\mathrm{UP/LP}}(k)=\frac{E_C(k)+E_X}{2}\pm\sqrt{\left(\frac{E_C(k)-E_X}{2}\right)^2+g^2},$$2 yields several branches $$E_{\mathrm{UP/LP}}(k)=\frac{E_C(k)+E_X}{2}\pm\sqrt{\left(\frac{E_C(k)-E_X}{2}\right)^2+g^2},$$3 at a fixed frequency, and in a $$E_{\mathrm{UP/LP}}(k)=\frac{E_C(k)+E_X}{2}\pm\sqrt{\left(\frac{E_C(k)-E_X}{2}\right)^2+g^2},$$4 $$E_{\mathrm{UP/LP}}(k)=\frac{E_C(k)+E_X}{2}\pm\sqrt{\left(\frac{E_C(k)-E_X}{2}\right)^2+g^2},$$5-MoO$$E_{\mathrm{UP/LP}}(k)=\frac{E_C(k)+E_X}{2}\pm\sqrt{\left(\frac{E_C(k)-E_X}{2}\right)^2+g^2},$$6 slab on SiO$$E_{\mathrm{UP/LP}}(k)=\frac{E_C(k)+E_X}{2}\pm\sqrt{\left(\frac{E_C(k)-E_X}{2}\right)^2+g^2},$$7 the reported branches are labeled PhP-M0, M1, M2, and M3 (Sun et al., 2019). In GST/SiC thin films, the TE mode order is controlled by the minimum thickness $$E_{\mathrm{UP/LP}}(k)=\frac{E_C(k)+E_X}{2}\pm\sqrt{\left(\frac{E_C(k)-E_X}{2}\right)^2+g^2},$$8, with TE0 robust for $$E_{\mathrm{UP/LP}}(k)=\frac{E_C(k)+E_X}{2}\pm\sqrt{\left(\frac{E_C(k)-E_X}{2}\right)^2+g^2},$$9 and higher-order TE modes appearing at larger thicknesses (Passler et al., 2019).

Patterning adds another route. In periodically patterned multilayer waveguides, the in-plane lattice folds several guided photonic modes into the first Brillouin zone and opens photonic band gaps, after which embedded quantum-well excitons couple to the folded Bloch modes to form multimode photonic crystal polaritons (Zanotti et al., 2022). In nanowire photonic-crystal waveguides with one quantum dot per unit cell, the reported geometry supports one below-light-line guided band in the analyzed case, but the formulation is explicitly generalized to multiple guided branches $g$0, each giving rise to upper and lower polariton branches and, if several branches lie within the emitter bandwidth, to inter-mode avoided crossings (Angelatos et al., 2015).

Platform	Origin of multimode structure	Representative control
III-nitride slab waveguide	Higher-order TE/TM modes in thicker or higher-contrast slabs	Core thickness, index contrast
Visible planar semiconductor waveguide	Multiple TE modes with active layer at core boundary	$g$1, $g$2, grating period
Weyl-semimetal slot waveguide	Coupled SPPs of two interfaces	Spacer thickness $g$3, $g$4, $g$5
Patterned multilayer PhC waveguide	Brillouin-zone folding of several guided modes	Lattice symmetry, fill factor, QW placement
Anisotropic vdW or GST slab	Multiple slab roots of the guided-mode condition	Thickness, substrate/superstrate, frequency

A separate terminological case appears in the hybrid plasmonic waveguide with DEIT control, where “multimode” means two orthogonally polarized surface-polaritonic modes, right-circular and left-circular, rather than distinct spatial eigenmodes; the spatial content remains a single bound SPP at the interface (Asgarnezhad-Zorgabad et al., 2019).

3. Dispersion engineering and hybridization regimes

The reported dispersions show that multimode waveguide polaritons are shaped not only by exciton–photon detuning but also by intermode overlap. In the III-nitride slab waveguide, the measured normal-mode splitting is $g$6 at $g$7, with an average of $g$8 between $g$9 and $\Omega_{R,\mathrm{TE}} \approx 13.4\ \mathrm{meV}$0, corresponding to $\Omega_{R,\mathrm{TE}} \approx 13.4\ \mathrm{meV}$1; however, strong coupling is effectively single-mode because the overlap of the TM0 $\Omega_{R,\mathrm{TE}} \approx 13.4\ \mathrm{meV}$2 field with the active region is nearly two orders of magnitude smaller than the TE0 $\Omega_{R,\mathrm{TE}} \approx 13.4\ \mathrm{meV}$3 overlap, so TM0 plays a negligible role (Ciers et al., 2016).

The visible multimode planar-waveguide study gives a more explicit hierarchy of coupling regimes. For $\Omega_{R,\mathrm{TE}} \approx 13.4\ \mathrm{meV}$4, the adjacent photonic-mode spacing is $\Omega_{R,\mathrm{TE}} \approx 13.4\ \mathrm{meV}$5 and the couplings are $\Omega_{R,\mathrm{TE}} \approx 13.4\ \mathrm{meV}$6–$\Omega_{R,\mathrm{TE}} \approx 13.4\ \mathrm{meV}$7, giving $\Omega_{R,\mathrm{TE}} \approx 13.4\ \mathrm{meV}$8–$\Omega_{R,\mathrm{TE}} \approx 13.4\ \mathrm{meV}$9 and a multimode strong-coupling regime. For $\Omega_{R,\mathrm{TM}} \approx 5.2\ \mathrm{meV}$0, $\Omega_{R,\mathrm{TM}} \approx 5.2\ \mathrm{meV}$1 and $\Omega_{R,\mathrm{TM}} \approx 5.2\ \mathrm{meV}$2–$\Omega_{R,\mathrm{TM}} \approx 5.2\ \mathrm{meV}$3, giving $\Omega_{R,\mathrm{TM}} \approx 5.2\ \mathrm{meV}$4–$\Omega_{R,\mathrm{TM}} \approx 5.2\ \mathrm{meV}$5 and superstrong coupling. For $\Omega_{R,\mathrm{TM}} \approx 5.2\ \mathrm{meV}$6, $\Omega_{R,\mathrm{TM}} \approx 5.2\ \mathrm{meV}$7 and $\Omega_{R,\mathrm{TM}} \approx 5.2\ \mathrm{meV}$8–$\Omega_{R,\mathrm{TM}} \approx 5.2\ \mathrm{meV}$9, giving $\omega_m(k_\parallel)$0–$\omega_m(k_\parallel)$1 and deep superstrong coupling. The mechanism is explicit: orthogonality is intentionally broken by restricting the active material to a subregion $\omega_m(k_\parallel)$2 where different TE-mode fields overlap strongly, with reported overlap parameters $\omega_m(k_\parallel)$3, $\omega_m(k_\parallel)$4, and $\omega_m(k_\parallel)$5 in representative cases (Bürger et al., 26 May 2026).

In Weyl-semimetal slot waveguides, dispersion engineering is controlled by gyrotropy. Symmetric Voigt–Voigt waveguides support two reciprocal SPP bands, one below and one above $\omega_m(k_\parallel)$6; symmetric Faraday–Faraday waveguides support two bands below $\omega_m(k_\parallel)$7; asymmetric Voigt–Voigt structures with $\omega_m(k_\parallel)$8 or $\omega_m(k_\parallel)$9 generate giant nonreciprocity and wide unidirectional windows; and hybrid Voigt–Faraday structures support unidirectional modes above $\omega_{xj}(k_\parallel)$0 together with a continuous nonreciprocal band below $\omega_{xj}(k_\parallel)$1 displaying both Voigt and Faraday features (Abdol et al., 2020). In hybrid waveguide–plasmon polaritons, an avoided crossing between a broad LSPP and a narrow guided mode produces a transmutation from plasmon-like to waveguide-like character as the detuning changes sign, with near-zero extinction and strong local fields near zero detuning (Rodriguez et al., 2013).

Patterning further enriches the branch topology. In photonic-crystal polaritons, Bragg folding and exciton coupling create several avoided crossings, while symmetry-protected or accidental bound states in the continuum satisfy $\omega_{xj}(k_\parallel)$2 and yield very high-$\omega_{xj}(k_\parallel)$3 or effectively lossless polariton branches at zero or finite in-plane wavevector. The same framework associates topological charge transfer and off-$\omega_{xj}(k_\parallel)$4 BICs with symmetry breaking of the lattice (Zanotti et al., 2022).

4. Propagation, loss, disorder, and nonlinear dynamics

Propagation performance varies strongly with modal composition. In the III-nitride slab waveguide, photon-like polaritons with $\omega_{xj}(k_\parallel)$5 exhibit decay lengths $\omega_{xj}(k_\parallel)$6, with an absorption-derived upper bound $\omega_{xj}(k_\parallel)$7 from $\omega_{xj}(k_\parallel)$8. The extracted lifetimes satisfy

$\omega_{xj}(k_\parallel)$9

with $G_{mj}=g_{mj}(k_\parallel)$0 at $G_{mj}=g_{mj}(k_\parallel)$1 and fitted $G_{mj}=g_{mj}(k_\parallel)$2, leading to $G_{mj}=g_{mj}(k_\parallel)$3–$G_{mj}=g_{mj}(k_\parallel)$4 for LPB states with exciton fraction $G_{mj}=g_{mj}(k_\parallel)$5–$G_{mj}=g_{mj}(k_\parallel)$6. The same platform reports $G_{mj}=g_{mj}(k_\parallel)$7-PL homogeneity $G_{mj}=g_{mj}(k_\parallel)$8 over $G_{mj}=g_{mj}(k_\parallel)$9, inhomogeneous broadening of $\mathcal{E}_m(z)$0, and a Stokes shift of $\mathcal{E}_m(z)$1, all of which are explicitly linked to low disorder and long-range guided transport (Ciers et al., 2016).

Laterally confined semiconductor guides demonstrate that optical confinement can dominate over geometric spreading. In etched rectangular waveguides, the reported propagation lengths are $\mathcal{E}_m(z)$2 for a straight channel and $\mathcal{E}_m(z)$3 for a bend of radius $\mathcal{E}_m(z)$4, whereas in a strip-loaded waveguide with a $\mathcal{E}_m(z)$5 ITO strip of width $\mathcal{E}_m(z)$6 the propagation length reaches $\mathcal{E}_m(z)$7. The letter attributes the shorter rectangular-waveguide lengths mainly to wet-etch sidewall roughness, especially in bends, and the longer strip-loaded length to the absence of etched sidewalls (Liran et al., 2018).

Strongly nonlinear multimode dynamics have been reported in a different waveguide class. In the DEIT-controlled hybrid plasmonic interface, the two circularly polarized probe components form coupled SPW modes with $\mathcal{E}_m(z)$8 and $\mathcal{E}_m(z)$9, group-velocity dispersion coefficients $E_X$00, and self-defocusing nonlinearities $E_X$01. In the near-Manakov regime, these support dark rogue waves, polarization-modulation instability, bimodal polaritonic frequency combs, and phase singularities at the zero-intensity condition $E_X$02; switching times down to $E_X$03 are reported for the phase-rotation functionality (Asgarnezhad-Zorgabad et al., 2019).

In mid-infrared phonon-polaritonic slabs, the relation between confinement and dissipation is likewise mode dependent. For the TE0 waveguide polariton in GST/SiC, the reported maximum field enhancement is $E_X$04 at $E_X$05, while the quality factors at $E_X$06 are $E_X$07 and $E_X$08 in a-GST, dropping to $E_X$09 and $E_X$10 in c-GST because the crystalline phase has larger loss $E_X$11.

5. Control knobs, diagnostics, and modeling

Thickness, active-region placement, and periodic loading are primary design variables. In the visible SSC study, the recommended compromise is $E_X$12, which preserves high intermode overlap while maintaining large $E_X$13; in the GaAs waveguide-polariton laser, the cavity is defined by two $E_X$14 gold gratings of pitch $E_X$15 separated by $E_X$16–$E_X$17, generating discrete Fabry–Perot manifolds with measured free spectral ranges of $E_X$18 for $E_X$19, $E_X$20 for $E_X$21, and $E_X$22 for $E_X$23 (Bürger et al., 26 May 2026, Suárez-Forero et al., 2020).

Electrical, excitonic, and topological control all appear in the surveyed systems. In the electrically controlled waveguide polariton laser, applied voltages from $E_X$24 to $E_X$25 yield laser-energy shifts of $E_X$26 at $E_X$27 and $E_X$28 at $E_X$29, and at $E_X$30 the lasing switches to the next FP manifold because the exciton approaches the bluest FP mode and changes the relative linewidths; the same paper estimates an electrical switching energy of $E_X$31 and reports lasing at $E_X$32 and $E_X$33 (Suárez-Forero et al., 2020). In the exciton-tunable multimode waveguides, the reported figures of merit predict $E_X$34 phase shifts for $E_X$35 over $E_X$36 on lower branches and $E_X$37 on upper branches, while modal switching in the $E_X$38 SSC example requires exciton blueshifts of $E_X$39–$E_X$40 (Bürger et al., 26 May 2026). In Weyl-semimetal slots, thickness $E_X$41, chemical potential $E_X$42, and the magnitude or orientation of $E_X$43 tune band positions, nonreciprocity, and the size of unidirectional windows (Abdol et al., 2020). In GST/SiC, non-volatile phase switching produces measured red shifts of $E_X$44 for the TE0 mode and $E_X$45 for the SPhP at $E_X$46 (Passler et al., 2019).

The experimental diagnostics are equally mode specific. Outcoupling from gratings is reconstructed through relations such as

$E_X$47

used in III-nitride guided-polariton spectroscopy (Ciers et al., 2016). Patterned multilayer polaritons are modeled by guided-mode expansion plus a non-Hermitian Hopfield matrix and validated against S-matrix or RCWA spectra (Zanotti et al., 2022). Multimode visible waveguides are analyzed by RCWA combined with a generalized Hopfield model (Bürger et al., 26 May 2026). In anisotropic vdW slabs, the near-field fringe spacing obeys $E_X$48 and $E_X$49, allowing direct extraction of guided polariton dispersion from s-SNOM images (Sun et al., 2019). For periodic quantum-dot chains, the exact finite-size Green function is obtained from a Dyson-equation construction without approximation (Angelatos et al., 2015).

6. Functional roles, conceptual boundaries, and outlook

The reported functions of multimode waveguide polaritons span coherent sources, phase control, routing, nonreciprocal transport, low-loss propagation, and waveguide QED. Concrete examples include electrically controlled polariton lasing in a guided Fabry–Perot manifold (Suárez-Forero et al., 2020), long-range laterally confined polaritonic channels and bends (Liran et al., 2018), exciton-controlled phase shifters and mode switches in SSC planar waveguides (Bürger et al., 26 May 2026), wide-band unidirectional SPP transport in asymmetric Weyl-semimetal slots (Abdol et al., 2020), bimodal polaritonic frequency-comb generation and high-speed phase rotation in DEIT-controlled hybrid plasmonic waveguides (Asgarnezhad-Zorgabad et al., 2019), and low-loss or effectively lossless photonic-crystal polariton branches associated with BICs (Zanotti et al., 2022). In nanowire photonic-crystal polariton waveguides, coupling a target quantum dot with $E_X$50 to the dominant finite-chain polariton resonance gives $E_X$51 and a clear Rabi doublet, while a $E_X$52 emitter coupled in the Fabry–Perot region produces a spectral triplet because two nearby FP resonances participate simultaneously (Angelatos et al., 2015).

Several recurring misconceptions are resolved by the literature itself. First, “multimode” does not always mean multiple spatial eigenmodes: in the hybrid plasmonic rogue-wave study, the platform is explicitly “bimodal” because of right- and left-circular polarization modes, whereas the spatial mode is a single bound SPP (Asgarnezhad-Zorgabad et al., 2019). Second, not every waveguide polariton platform advertised as relevant to multimode physics is multimode in its realized device: the III-nitride slab was deliberately engineered to remain effectively single-mode for strong coupling, and multimode waveguide polaritons are presented there as a route achievable by thicker cores or altered contrasts rather than as the measured operating point (Ciers et al., 2016). Third, the superstrong-coupling regime discussed for multimode planar waveguides is not the ultrastrong-coupling regime, because the operative criterion is the comparison between Rabi splitting and intermode spacing rather than the absolute ratio $E_X$53 (Bürger et al., 26 May 2026). Fourth, the s-polarized GST/SiC TE waveguide mode is polariton-like in dispersion and confinement but is distinct from a conventional SPhP, since planar SPhPs are intrinsically limited to p-polarization (Passler et al., 2019).

A plausible implication is that multimode waveguide polaritons provide a single design space in which modal order, polarization, dispersion topology, propagation constant, and loss can all be co-engineered by layered geometry and localized active matter. The surveyed works point in that direction through low-disorder III-nitride slabs with room-temperature prospects (Ciers et al., 2016), finite-$E_X$54 low-loss polariton BICs and topological charge control in patterned multilayers (Zanotti et al., 2022), and SSC waveguides in which a small exciton shift reshapes modal composition and phase over propagation lengths of only tens of micrometers (Bürger et al., 26 May 2026).