Capacitive Strain Sensors: Fundamentals & Applications

• Capacitive strain sensors are devices that detect mechanical deformation by measuring variations in capacitance induced by physical strain.
• They offer high sensitivity, low power consumption, and ease of fabrication, making them ideal for structural health monitoring, wearables, and robotics.
• Recent advancements include wireless integration and enhanced signal processing techniques for real-time monitoring and improved accuracy.

Surface polaritons are hybrid electromagnetic modes localized at interfaces between dissimilar materials, typically involving strong coupling between collective charge, lattice, or spin excitations and photons. Quantum-geometric coupling refers to the interplay between these polaritonic modes and the nontrivial geometry of the quantum states constituting the system—most notably, encoded in the quantum geometric tensor, which encompasses both the quantum metric and the Berry curvature. Such couplings fundamentally impact the optical, transport, and topological properties of photonic, electronic, and hybrid light-matter systems. Detailed theoretical and experimental investigations have revealed a wide array of quantum-geometric phenomena in surface polariton systems, ranging from quantized spin Hall effects to tunable band flattening and ultrastrong light-matter coupling regimes.

1. Theoretical Foundations of Surface Polaritons

Surface polaritons emerge at the interface of media with contrasting dielectric properties. Classical surface plasmon polaritons (SPPs) are found at metal–dielectric interfaces and are governed by the electromagnetic boundary conditions dictating their dispersion and confinement. The general condition for the existence of lossless surface polaritons is determined by the complex permittivities of the two media ($\varepsilon_1,\;\varepsilon_2$), which, when expressed in polar form $\varepsilon_{j} = \varepsilon_{mj}e^{i\alpha_{j}}$, yield the canonical SPP dispersion: $$\beta(\omega) = k_0 \sqrt{ \frac{\varepsilon_1\varepsilon_2}{\varepsilon_1 + \varepsilon_2} }$$ with lossless propagation when

$$\varepsilon_{m1}\sin\alpha_2 + \varepsilon_{m2}\sin\alpha_1 = 0 \,,\quad \varepsilon_{m1}\cos\alpha_2 + \varepsilon_{m2}\cos\alpha_1 \geq 0$$

These generalize the well-known criterion $$\text{Re}\,\varepsilon_1\cdot\text{Re}\,\varepsilon_2<0$$ for SPPs at metal-dielectric interfaces to regimes involving gain or sign-switches in the imaginary parts of $\varepsilon_j$, thus supporting a broad class of “generalized surface polaritons” (Xu et al., 2016, Maurer et al., 16 Jan 2026). These modes underpin modern nanoplasmonics, nano-optics, and the development of hybrid quantum-photonic devices.

2. Quantum-Geometric Tensor: Metric and Berry Curvature

The quantum geometric tensor (QGT) $T_{ij}(k)$ for a Bloch band $|u_{n,k}\rangle$ is defined as: $T_{ij}(k) = g_{ij}(k) + \frac{i}{2}F_{ij}(k)$ where $g_{ij}(k)$ is the (real, symmetric) quantum metric—the infinitesimal distance in Hilbert space between neighboring Bloch states—and $\varepsilon_{j} = \varepsilon_{mj}e^{i\alpha_{j}}$0 is the (imaginary, antisymmetric) Berry curvature, representing a “fictitious magnetic field” in momentum space. Explicitly,

$\varepsilon_{j} = \varepsilon_{mj}e^{i\alpha_{j}}$1

$\varepsilon_{j} = \varepsilon_{mj}e^{i\alpha_{j}}$2

In polaritonic lattices, the QGT structure encodes both conventional topological phenomena and more subtle local band geometry effects, impacting optical selection rules, nonlinear responses, and transport characteristics (Cuerda et al., 2023, Walicki et al., 2024).

3. Surface Polaritons in Quantum and Non-Hermitian Regimes

Quantum descriptions of SPPs and related surface polaritons utilize a Power–Zienau–Woolley Hamiltonian, treating the quantized electronic oscillator (bulk plasmon mode) and its coupling to the photonic continuum: $\varepsilon_{j} = \varepsilon_{mj}e^{i\alpha_{j}}$3 with nonperturbative interaction terms giving rise to geometry- and environment-dependent renormalization of the plasma frequency and thereby the polariton dispersion: $\varepsilon_{j} = \varepsilon_{mj}e^{i\alpha_{j}}$4 where the $\varepsilon_{j} = \varepsilon_{mj}e^{i\alpha_{j}}$5 “depolarization parameter” is fixed by interface or nanoparticle geometry and local dielectric environment. Even in simple configurations, the light–matter coupling $\varepsilon_{j} = \varepsilon_{mj}e^{i\alpha_{j}}$6 is large ($\varepsilon_{j} = \varepsilon_{mj}e^{i\alpha_{j}}$7) and the system is generically in the ultrastrong coupling regime, leading to ground-state quantum fluctuations tunable by geometry and dielectric choice (Maurer et al., 16 Jan 2026).

Non-Hermitian physics, arising from radiative or ohmic loss, breaks conventional time-reversal symmetry and fundamentally modifies the quantum geometric structure of SPP bands. Specifically, losses induce a nonzero Berry curvature even in trivial lattice geometries, as captured by the imaginary antisymmetric part $\varepsilon_{j} = \varepsilon_{mj}e^{i\alpha_{j}}$8 in the QGT, and can be mapped through numerical or analytic approaches (T-matrix, Hopfield diagonalization) (Cuerda et al., 2023).

4. Quantum-Geometric Coupling in Surface Polaritonic Lattices

In periodic arrays of plasmonic nanoparticles, collective photonic–plasmonic bands, known as surface lattice resonances (SLRs), are characterized by polarization-dependent pseudospin degrees of freedom. TE–TM band splitting and pseudospin–orbit coupling enable the emergence of sharply localized quantum metric peaks at symmetry points (zone diagonals), while loss-induced non-Hermitian Berry curvature can yield local anomalous group-velocity corrections—observable as transverse drifts in the wavepacket propagation.

The non-orthogonality of Bloch states with neighboring quasi-momenta (finite $\varepsilon_{j} = \varepsilon_{mj}e^{i\alpha_{j}}$9) enhances nonlinear light–matter interactions, Purcell factors, and photonic responses in regions with large metric, while engineered losses (Ω″) can locally steer SLR transport without requiring external magnetic fields (Cuerda et al., 2023). Flat-band systems coupled to surface polaritons show optically accessible transitions enabled by nontrivial quantum metric, even for zero group velocity, and surface-polariton-driven Floquet engineering can actively tune bandwidth, band curvature, and enable topological transitions (Walicki et al., 2024).

5. Hybrid Quantum-Strong Coupling Architectures

Surface polaritons enable hybridization with diverse quantum systems: quantum dots, Rydberg ensembles, 2D materials, and atomic lattices. Representative architectures and their quantum-geometric features include:

Platform	Quantum-Geometric Phenomena	Key Metrics/Mechanisms
Metal/QD interface	Rabi splitting, tunable SPP–exciton coupling	$$\beta(\omega) = k_0 \sqrt{ \frac{\varepsilon_1\varepsilon_2}{\varepsilon_1 + \varepsilon_2} }$$0 (Bludov et al., 2011)
Plasmonic lattice	Finite quantum metric, nonzero loss-induced Berry curvature	TE–TM splitting, pseudospin–orbit coupling (Cuerda et al., 2023)
Phonon–polariton grating (SiC)	Superradiant coupling, normal-mode splitting	$$\beta(\omega) = k_0 \sqrt{ \frac{\varepsilon_1\varepsilon_2}{\varepsilon_1 + \varepsilon_2} }$$1 with pillar density $$\beta(\omega) = k_0 \sqrt{ \frac{\varepsilon_1\varepsilon_2}{\varepsilon_1 + \varepsilon_2} }$$2 (Gubbin et al., 2015)
Rydberg–SPhP	Collective coupling $$\beta(\omega) = k_0 \sqrt{ \frac{\varepsilon_1\varepsilon_2}{\varepsilon_1 + \varepsilon_2} }$$3; >100 MHz Rabi splitting	Strong geometric anisotropy, mode volume scaling (Sheng et al., 2016)

Hybrid structures frequently exploit the deep-subwavelength field confinement and high momentum of surface polaritons to significantly enhance light–matter coupling, bandwidth, and selection-rule tunability. In plasmonic platforms, the resulting polariton–exciton or polariton–atom couplings are orders of magnitude larger than in free-space, enabling robust strong- and ultrastrong-coupling regimes with clear quantum-geometric signatures.

6. Quantum-Geometric Photocurrents and Momentum-Selective Probing

Surface polaritons carrying finite in-plane momentum $$\beta(\omega) = k_0 \sqrt{ \frac{\varepsilon_1\varepsilon_2}{\varepsilon_1 + \varepsilon_2} }$$4 (the so-called “polariton drag” effect) unlock quantum-geometric photocurrent responses in otherwise forbidden symmetry contexts. In high-symmetry (e.g., $$\beta(\omega) = k_0 \sqrt{ \frac{\varepsilon_1\varepsilon_2}{\varepsilon_1 + \varepsilon_2} }$$5, $$\beta(\omega) = k_0 \sqrt{ \frac{\varepsilon_1\varepsilon_2}{\varepsilon_1 + \varepsilon_2} }$$6) systems, polaritonic fields couple to electronic bands via the interband quantum-geometric tensor, generating shift- and injection-type currents dependent on Berry connection and metric tensor, respectively: $$\beta(\omega) = k_0 \sqrt{ \frac{\varepsilon_1\varepsilon_2}{\varepsilon_1 + \varepsilon_2} }$$7 The polariton-selective photoexcitation (PSP) regime emerges when only narrow momentum arcs at the Fermi surface are photoexcited, providing direct probes of band quantum geometry and enabling momentum-resolved quantum-geometry spectroscopy (Xiong et al., 2021).

7. Topological and Spin-Orbit Phenomena in Surface Polaritons

Surface polaritons universally exhibit spin–momentum locking, where the electric field spin is locked orthogonally to momentum, giving rise to photonic quantum spin Hall effects. The quantized spin Hall coefficient $$\beta(\omega) = k_0 \sqrt{ \frac{\varepsilon_1\varepsilon_2}{\varepsilon_1 + \varepsilon_2} }$$8 serves as a topological invariant (first Chern number) for these surface bands. The system supports topological phase transitions—for example, across PT-symmetry boundaries in complex permittivity space, where the chirality of spin winding flips discontinuously (Xu et al., 2016).

These fundamental quantum-geometric invariants are tightly linked with observable Berry phases and can be manipulated via interface design, gain/loss engineering, and mode selection.

8. Applications and Perspectives

Surface polaritons coupled to quantum geometry underpin a broad set of applications in nanophotonics and quantum technologies:

• Topological routing and robust transport: Enabled by quantized spin Hall responses and Berry curvature engineering.
• Quantum-geometry-enhanced nonlinear optics: Quantum metric-driven enhancement of light–matter coupling, spontaneous emission, and nonreciprocal responses.
• Strong- and ultrastrong-coupling devices: Tunable polaritonic hybrids with QD, atomic, or SMM systems, enabling Rabi splittings significantly exceeding dissipation rates.
• Quantum and topological metamaterials: Manipulation of spin–momentum coupling and Berry curvature for nonreciprocal, chiral, and protected edge states.
• Momentum-resolved quantum-geometry spectroscopy: Direct mapping of band geometry in otherwise “dark” materials using polariton-drag photocurrents and selective excitation protocols.

The fusion of surface polaritons and quantum-geometric coupling opens a path toward on-chip, tunable, robust quantum-optic functionalities and the realization of nontrivial band-geometry–driven phenomena well beyond the reach of traditional free-space photonics or electronic condensed-matter platforms (Xu et al., 2016, Maurer et al., 16 Jan 2026, Cuerda et al., 2023, Walicki et al., 2024, Xiong et al., 2021, Bludov et al., 2011, Gubbin et al., 2015, Sheng et al., 2016).