Liquid Intelligent Metasurfaces Overview

• Liquid Intelligent Metasurfaces are reconfigurable metasurfaces whose response is dynamically tuned via liquid or fluidic mechanisms, enabling precise control of amplitude, phase, and polarization.
• They span diverse implementations—from optical and terahertz liquid crystal systems to wireless platforms with movable liquid elements and fluidic kirigami structures—demonstrating versatile engineering applications.
• Key practical outcomes include full-phase modulation, beam steering, and optimized channel estimation, achieved through integrated control algorithms and external feedback mechanisms.

Liquid Intelligent Metasurface (LIM) denotes a class of reconfigurable metasurfaces in which the local wave response is controlled through a liquid degree of freedom, a liquid-like geometric degree of freedom, or a software-controlled passive surface state that reshapes propagation. In the literature, the term spans liquid-crystal-integrated optical and terahertz metasurfaces, wireless metasurfaces with movable liquid elements, fluid-loaded acoustic interfaces, and fluidic kirigami morphing surfaces. This suggests that LIM is not yet a single fully standardized term, but a family of architectures united by spatially distributed programmability of amplitude, phase, polarization, impedance, geometry, or effective channel response (Moitra et al., 2023, Shen, 22 Jul 2025, He et al., 2019).

1. Terminology and scope

The phrase “Liquid Intelligent Metasurface” is used in multiple, partially overlapping ways. In visible nanophotonics, an electrically tunable reflective TiO$_2$ metasurface embedded in a thin nematic liquid crystal layer is explicitly described as “an excellent example of what can be called a Liquid Intelligent Metasurface (LIM)” because the liquid crystal directly surrounds the nanoresonators and its local orientation is electrically programmed (Moitra et al., 2023). In wireless communications, “Liquid Intelligent Metasurface” can denote a metasurface with movable liquid reflecting elements whose positions $\mathbf{r}_m$ and unit-modulus phase shifts $\theta_m$ are jointly optimized (Shen, 22 Jul 2025). A related but distinct usage appears in “Large Intelligent Metasurface,” where a dense passive array of programmable reflecting elements is controlled by a “smart programmable controller” but has no RF chains or baseband units at the surface itself (He et al., 2019).

In terahertz photonics, a liquid-crystal-integrated reflectarray with independently addressable cells is characterized as “essentially a THz-band LIM prototype based on liquid crystal (LC) as the tunable medium, with fine-grained, per-cell electrical control and algorithmic optimization of the phase profile” (Chen et al., 2023). In mechanics and acoustics, fluid-loaded resonator arrays and fluidic kirigami morphing surfaces are explicitly mapped to LIM ideas because the governing control variable is fluid pressure, fluid loading, or liquid-mediated deformation rather than an electronic phase shifter (Skelton et al., 2017, Kahak et al., 11 Mar 2025).

Literature usage	“Liquid” mechanism	Primary programmable quantity
Optical/THz LC metasurface	Nematic LC around meta-atoms	Phase, polarization, beam direction
Wireless LIM	Movable liquid reflecting elements	Phase shifts and element positions
Large Intelligent Metasurface	Passive programmable reflector array	Reflection phases and on/off states
Fluidic/acoustic LIM	Fluid loading or fluidic morphing	Geometry, impedance, mode conversion

A recurring point of confusion is that “liquid” does not always mean the same physical mechanism. In some papers it is literally a liquid crystal; in others it refers to fluidic or liquid-metal mobility; in still others, especially wireless formulations, the emphasis is on programmable environmental control and passive reflect-beamforming. Likewise, “intelligent” may refer to per-element programmability, to closed-loop optimization, or to both.

2. Unifying physical principles

Across these implementations, LIM behavior can be written as a local-state-dependent scattering or transfer problem. In the reflective visible LC metasurface, the central relation is

$$E_{\text{out}(x,\lambda)} = r(\lambda, V(x))\, e^{i\phi(\lambda, V(x))} E_{\text{in}(x,\lambda)},$$

where the applied voltage pattern $V(x)$ sets a spatially varying reflected phase $\phi$ and reflection amplitude $r$ through LC-controlled resonance tuning (Moitra et al., 2023). In the wireless FAS-LIM model, the combined downlink channel is

$$\mathbf{h}_k^{\mathrm{eff}} = \mathbf{h}_{k}^H + \mathbf{g}_{k}^H \boldsymbol{\Theta} \mathbf{H},$$

so the effective channel depends jointly on BS antenna positions, LIM element positions, and the diagonal phase-shift matrix $\boldsymbol{\Theta}$ (Shen, 22 Jul 2025). In passive large-intelligent-metasurface channel estimation, the block model

$$\mathbf{Y} = \mathbf{G}\big(\mathbf{S} \odot (\mathbf{H}\mathbf{X})\big) + \mathbf{W}$$

makes the same point in a different form: the programmable surface state $\mathbf{r}_m$0 modulates a cascaded propagation operator that must be inferred indirectly because the surface itself has no signal processing capability (He et al., 2019).

Three control mechanisms recur. The first is liquid-mediated dielectric tuning, exemplified by nematic LC director rotation around optical or THz resonators. The second is liquid-mediated geometric tuning, exemplified by physically movable reflecting elements in wireless LIM and by fluidic kirigami cells whose out-of-plane deformation $\mathbf{r}_m$1 is set by a single global pressure input $\mathbf{r}_m$2 but differs from cell to cell because of geometry (Shen, 22 Jul 2025, Kahak et al., 11 Mar 2025). The third is fluid–wave coupling, exemplified by fluid-loaded elastic plates where resonator arrays alter the dispersion relation

$\mathbf{r}_m$3

thereby enabling rainbow trapping and mode conversion between surface and bulk waves (Skelton et al., 2017).

This suggests a useful unifying abstraction: a LIM is a metasurface whose local constitutive response is not fixed after fabrication, but instead depends on a controllable liquid or liquid-like state variable that can be spatially distributed and, in many cases, updated through feedback.

3. Optical and terahertz realizations

In visible nanophotonics, a representative LIM is the reflective TiO$\mathbf{r}_m$4 metasurface SLM operating near 650–665 nm. The device uses TiO$\mathbf{r}_m$5 nanodisks of thickness $\mathbf{r}_m$6 nm, designed diameter $\mathbf{r}_m$7 nm, and periodicity $\mathbf{r}_m$8 nm above a $\mathbf{r}_m$9 nm SiO$\theta_m$0 spacer and a $\theta_m$1 nm Al reflector. A commercial nematic LC fills the space around the resonators; the designed LC thickness is $\theta_m$2 nm and the realized thickness is $\theta_m$3 nm. Ninety-six individually addressable Al electrodes, each $\theta_m$4 wide with $\theta_m$5 pitch, tune the LC orientation and shift the metasurface resonance by about $\theta_m$6 nm experimentally. The structure yields continuous phase modulation close to a full $\theta_m$7–$\theta_m$8 range, with an experimental phase modulation depth of about $\theta_m$9 within $$E_{\text{out}(x,\lambda)} = r(\lambda, V(x))\, e^{i\phi(\lambda, V(x))} E_{\text{in}(x,\lambda)},$$0 V at reflectance $$E_{\text{out}(x,\lambda)} = r(\lambda, V(x))\, e^{i\phi(\lambda, V(x))} E_{\text{in}(x,\lambda)},$$1, a threshold around $$E_{\text{out}(x,\lambda)} = r(\lambda, V(x))\, e^{i\phi(\lambda, V(x))} E_{\text{in}(x,\lambda)},$$2 V, and saturation around $$E_{\text{out}(x,\lambda)} = r(\lambda, V(x))\, e^{i\phi(\lambda, V(x))} E_{\text{in}(x,\lambda)},$$3 V. Beam steering was demonstrated with field of view up to $$E_{\text{out}(x,\lambda)} = r(\lambda, V(x))\, e^{i\phi(\lambda, V(x))} E_{\text{in}(x,\lambda)},$$4 for a 3-pixel supercell and diffraction efficiencies increasing from $$E_{\text{out}(x,\lambda)} = r(\lambda, V(x))\, e^{i\phi(\lambda, V(x))} E_{\text{in}(x,\lambda)},$$5 for 3P to $$E_{\text{out}(x,\lambda)} = r(\lambda, V(x))\, e^{i\phi(\lambda, V(x))} E_{\text{in}(x,\lambda)},$$6 for 12P (Moitra et al., 2023).

At terahertz frequencies, an ultrathin LC-integrated reflectarray at $$E_{\text{out}(x,\lambda)} = r(\lambda, V(x))\, e^{i\phi(\lambda, V(x))} E_{\text{in}(x,\lambda)},$$7 THz provides a complementary LIM embodiment. The structure is a metal–insulator–metal configuration with a patterned Au patch array, a $$E_{\text{out}(x,\lambda)} = r(\lambda, V(x))\, e^{i\phi(\lambda, V(x))} E_{\text{in}(x,\lambda)},$$8 LC layer, and a continuous Au ground plane on Si. The metasurface has 80 independently addressable meta-atoms across a $$E_{\text{out}(x,\lambda)} = r(\lambda, V(x))\, e^{i\phi(\lambda, V(x))} E_{\text{in}(x,\lambda)},$$9 cm aperture and is driven by an FPGA with a $V(x)$0 kHz AC square wave from $V(x)$1 to $V(x)$2 V$V(x)$3. At $V(x)$4 THz it achieves approximately $V(x)$5 measured continuous phase tuning, a record-large $V(x)$6 field of view, a peak gain of $V(x)$7 dBi, and maximum steering efficiency of about $V(x)$8. It also supports multiple beams with adjustable directions and adjustable power ratios. The measured rise and fall times are $V(x)$9 ms and $\phi$0 ms, respectively, and the total power consumption for 80 cells is $\phi$1 mW (Chen et al., 2023).

A third optical realization is the optically addressable transmissive LC metasurface SLM designed for high-power near-infrared operation. It embeds a TiO$\phi$2 nanopillar metasurface resonant in the $\phi$3–$\phi$4 nm range within a thin $\phi$5 LC layer and replaces conventional pixel electrodes with a photoactive BSO top contact addressed by patterned $\phi$6 nm light. The active area is $\phi$7 mm$\phi$8. The device demonstrates $\phi$9 linear polarization rotation in reconfigurable patterns with overall transmittance $r$0, resolves $r$1 features in projected patterns, and exhibits switching times of $r$2 ms on and $r$3 ms off for the LC–metasurface cell (Sisler et al., 21 Mar 2026).

These optical and THz results clarify a central point about LIM operation in photonics: the dominant tuning mechanism is not simply propagation phase through a thick liquid layer. Instead, thin liquid layers are used to perturb high-confinement resonant meta-atoms, converting small refractive-index changes into large phase, polarization, or diffraction changes.

4. Wireless and communication-theoretic formulations

In wireless systems, LIM is often formulated as a passive programmable surface embedded into the channel model. For large-intelligent-metasurface-assisted massive MIMO, the base station–surface and surface–user channels are $r$4 and $r$5, while each surface element has on/off state $r$6 and phase $r$7. The key technical difficulty is that the surface only passively reflects incident waves and has no signal processing capability, so the receiver only observes a bilinear cascaded channel. The paper introduces a two-stage “Joint Bilinear Factorization and Matrix Completion (JBF-MC)” framework consisting of sparse bilinear factorization via BiG-AMP followed by low-rank matrix completion via Riemannian gradient. In the reported simulations, $r$8, $r$9, $$\mathbf{h}_k^{\mathrm{eff}} = \mathbf{h}_{k}^H + \mathbf{g}_{k}^H \boldsymbol{\Theta} \mathbf{H},$$0, $$\mathbf{h}_k^{\mathrm{eff}} = \mathbf{h}_{k}^H + \mathbf{g}_{k}^H \boldsymbol{\Theta} \mathbf{H},$$1, and $$\mathbf{h}_k^{\mathrm{eff}} = \mathbf{h}_{k}^H + \mathbf{g}_{k}^H \boldsymbol{\Theta} \mathbf{H},$$2; JBF-MC outperforms K-SVD and SPAMS in estimating $$\mathbf{h}_k^{\mathrm{eff}} = \mathbf{h}_{k}^H + \mathbf{g}_{k}^H \boldsymbol{\Theta} \mathbf{H},$$3, while RGrad outperforms IHT and IST for recovering $$\mathbf{h}_k^{\mathrm{eff}} = \mathbf{h}_{k}^H + \mathbf{g}_{k}^H \boldsymbol{\Theta} \mathbf{H},$$4 (He et al., 2019).

A more explicit “liquid” wireless formulation appears in the FAS-LIM architecture, where both the base station and the metasurface are spatially reconfigurable. The LIM consists of $$\mathbf{h}_k^{\mathrm{eff}} = \mathbf{h}_{k}^H + \mathbf{g}_{k}^H \boldsymbol{\Theta} \mathbf{H},$$5 liquid reflecting elements, each with position $$\mathbf{h}_k^{\mathrm{eff}} = \mathbf{h}_{k}^H + \mathbf{g}_{k}^H \boldsymbol{\Theta} \mathbf{H},$$6 and unit-modulus phase shift $$\mathbf{h}_k^{\mathrm{eff}} = \mathbf{h}_{k}^H + \mathbf{g}_{k}^H \boldsymbol{\Theta} \mathbf{H},$$7, constrained by minimum-spacing and aperture constraints. The base station employs $$\mathbf{h}_k^{\mathrm{eff}} = \mathbf{h}_{k}^H + \mathbf{g}_{k}^H \boldsymbol{\Theta} \mathbf{H},$$8 fluid antennas with positions $$\mathbf{h}_k^{\mathrm{eff}} = \mathbf{h}_{k}^H + \mathbf{g}_{k}^H \boldsymbol{\Theta} \mathbf{H},$$9. The optimization objective is the downlink sum rate

$\boldsymbol{\Theta}$0

subject to transmit-power, unit-modulus, spacing, and aperture constraints. The solution uses alternating optimization together with successive convex approximation and the penalty convex-concave procedure. In the reported setup, $\boldsymbol{\Theta}$1, $\boldsymbol{\Theta}$2, $\boldsymbol{\Theta}$3, $\boldsymbol{\Theta}$4 dBm, $\boldsymbol{\Theta}$5 m$\boldsymbol{\Theta}$6, and the algorithm converges in about 6 iterations. The fully optimized FAS-LIM yields the highest sum-rate among the benchmarks, while incorporating NLoS spatial correlation produces about $\boldsymbol{\Theta}$7 rate loss (Shen, 22 Jul 2025).

This literature also clarifies a frequent misconception. In wireless LIM, “liquid” need not denote a liquid crystal or fluid dielectric around each meta-atom. It may instead denote physically movable reflecting elements, fluid antennas, or a highly reconfigurable passive aperture whose geometry and phase states are jointly controlled. The unifying object is not the material composition alone, but the programmable propagation operator.

5. Fluid-loaded, fluidic, and morphing-wave LIMs

Outside optics and RF communications, LIM concepts appear in fluid-loaded and fluidic metasurfaces whose primary control variable is geometry. A fluid-loaded elastic plate carrying a periodic array of resonators in water provides one such case. The system comprises an aluminium plate of thickness $\boldsymbol{\Theta}$8 m, water with $\boldsymbol{\Theta}$9 kg/m$$\mathbf{Y} = \mathbf{G}\big(\mathbf{S} \odot (\mathbf{H}\mathbf{X})\big) + \mathbf{W}$$0 and $$\mathbf{Y} = \mathbf{G}\big(\mathbf{S} \odot (\mathbf{H}\mathbf{X})\big) + \mathbf{W}$$1 m/s, and resonators spaced by $$\mathbf{Y} = \mathbf{G}\big(\mathbf{S} \odot (\mathbf{H}\mathbf{X})\big) + \mathbf{W}$$2 m. The periodic dispersion relation

$$\mathbf{Y} = \mathbf{G}\big(\mathbf{S} \odot (\mathbf{H}\mathbf{X})\big) + \mathbf{W}$$3

supports a subsonic surface wave coupled to the fluid. By grading the resonator mass from $$\mathbf{Y} = \mathbf{G}\big(\mathbf{S} \odot (\mathbf{H}\mathbf{X})\big) + \mathbf{W}$$4 kg to $$\mathbf{Y} = \mathbf{G}\big(\mathbf{S} \odot (\mathbf{H}\mathbf{X})\big) + \mathbf{W}$$5 kg over 120 resonators, the metasurface produces either rainbow trapping or mode conversion. At $$\mathbf{Y} = \mathbf{G}\big(\mathbf{S} \odot (\mathbf{H}\mathbf{X})\big) + \mathbf{W}$$6 Hz, a mass-increasing ramp traps the surface wave around $$\mathbf{Y} = \mathbf{G}\big(\mathbf{S} \odot (\mathbf{H}\mathbf{X})\big) + \mathbf{W}$$7 m with strong resonator displacement, whereas a mass-decreasing ramp converts the surface wave into a bulk acoustic beam in the fluid (Skelton et al., 2017).

A different fluidic realization is the high-precision fluidic kirigami metasurface, where the outer wall of a fluid-filled chamber is patterned into heterogeneous unit cells and actuated by a single global pressure input $$\mathbf{Y} = \mathbf{G}\big(\mathbf{S} \odot (\mathbf{H}\mathbf{X})\big) + \mathbf{W}$$8. In the ultrasonic holographic lens, square-cut kirigami cells of size $$\mathbf{Y} = \mathbf{G}\big(\mathbf{S} \odot (\mathbf{H}\mathbf{X})\big) + \mathbf{W}$$9 mm are inverse-designed from a target thickness map generated by the iterative angular spectrum approach. The demonstrated lens operates at $\mathbf{r}_m$00 kHz, uses 52 cells, and achieves displacement error below $\mathbf{r}_m$01 mm, with tunable $\mathbf{r}_m$02 from $\mathbf{r}_m$03 to $\mathbf{r}_m$04 mm at $\mathbf{r}_m$05 kPa. In the haptic interface, circular-cut kirigami cells are designed to produce a $\mathbf{r}_m$06–$\mathbf{r}_m$07 N force range and $\mathbf{r}_m$08–$\mathbf{r}_m$09 mm displacement range under pneumatic actuation, with a constant contact area and high-resolution output force (Kahak et al., 11 Mar 2025).

The most explicitly self-organized optical-liquid realization is the thin-liquid-film metasurface formed by optical interference, thermocapillary or solutocapillary stresses, and surface-tension-driven deformation. In that framework, interfering surface plasmon polaritons or slab waveguide modes write a periodic relief $\mathbf{r}_m$10 into a thin liquid dielectric film, and the resulting liquid lattice feeds back into the optical modes through a nonlocal complex Ginzburg–Landau equation. The paper shows that these optical liquid lattices have tunable symmetry, support phase transition and tuning of topological properties, allow the formation, destruction, and motion of Dirac points in $\mathbf{r}_m$11-space, and support extremely low lasing threshold relative to solid dielectric films (Rubin et al., 2019).

Taken together, these results show that LIM need not be restricted to electronically addressed resonant pixels. It also includes wave-controlled liquids, pressure-morphing surfaces, and fluid-loaded resonant interfaces where the “meta” response is encoded in a reconfigurable geometry or hydrodynamic state.

6. Control architectures, optimization, and open questions

The “intelligence” in LIM is most often realized as a control layer above the physical surface. In the visible reflective LC metasurface, voltage profiles for beam steering are optimized numerically in real time using a Python API, angle-resolved optical feedback, a cost function based on intensity in a target angular and wavelength window, and the DIRECT-L and COBYLA algorithms (Moitra et al., 2023). In the THz LC metasurface, single- and multi-beam patterns are refined by SPGD, a measurement-driven optimization loop that adjusts voltages based on a figure of merit defined from received amplitudes at target angles (Chen et al., 2023). In RF 3D sensing, MetaSensing formulates a cross-entropy minimization problem over metasurface beamformer patterns and a sensing network, then uses deep reinforcement learning to jointly compute the optimal beamformer patterns and the mapping of received signals to voxel occupancies (Hu et al., 2020). More recent programmable-surface control work pushes this further by mapping pilot observations directly to metasurface and precoder configurations with a frozen GPT-2 backbone, projection layers, attention blocks, and physically constrained output heads, achieving shorter training time and faster inference than GNN and DRL baselines in the reported RIMSA setting (Huang et al., 18 Aug 2025).

This broader literature also sharpens the distinction between programmability and full autonomy. Intelligent metasurfaces with continuously tunable local surface impedance were defined early on as structures that perform multiple tunable functions and whose desired response is controlled by a computer influencing the individual electromagnetic properties of each inclusion (Liu et al., 2018). Full-duplex wireless work similarly characterizes intelligent metasurfaces as dynamic, ultra-compact, multi-functional and programmable structures, with controllability governed through dc bias and occasionally RF modulation (Taravati et al., 2021). In that sense, many current LIMs are “intelligent” because they are software-addressable and optimization-driven, not because the decision logic is embedded in the liquid itself.

Several limitations recur across embodiments. Optical LC LIMs remain polarization-dependent and resonance-band-limited, and may exhibit residual crosstalk, LC nonuniformity near nanostructures, or anomalous high-voltage phase behavior (Moitra et al., 2023). THz LC devices offer wide field of view and low power but have sub-second switching time (Chen et al., 2023). Optically addressed transmissive LC metasurfaces improve high-power compatibility yet still depend on LC anchoring, photoconductor response, and multiphysics co-design (Sisler et al., 21 Mar 2026). Wireless LIMs face a fundamental passive-surface bottleneck in cascaded channel estimation and inherit non-convex optimization problems with diagonal ambiguities and training-overhead trade-offs (He et al., 2019). Fluidic and kirigami LIMs provide large geometric tunability but are constrained by fabrication resolution, mechanical nonlinearities, and slower actuation scales (Kahak et al., 11 Mar 2025).

A plausible synthesis is that LIM has evolved into an umbrella term for metasurfaces whose reconfigurability is mediated by liquids, fluidic motion, or liquid-like spatial mobility, and whose useful operation depends on an external optimization or feedback layer. The field’s central research direction is therefore not merely new liquid materials, but the co-design of liquid physics, meta-atom or structural geometry, and control algorithms so that the surface becomes a programmable wave operator rather than a static boundary.