Quad-Layer Transmissive Metasurface

• The paper demonstrates a quad-layer metasurface that achieves full 360° phase coverage and >0.8 transmission amplitude, enabling precise deep brain hyperthermia.
• It employs time-reversal phase synthesis by recording the electromagnetic field from a simulated dipole at the tumor site and phase-conjugating the signal for focused energy deposition.
• Experimental validation showed a localized temperature rise of +5°C within 20 minutes and a focal width of approximately 9.5 mm, confirming effective energy delivery and minimal healthy tissue heating.

A quad-layer transmissive metasurface, as experimentally realized for time-reversal microwave hyperthermia, is a four-layer array of square metallic patches separated by dielectric substrates and designed to impose a prescribed transmission-phase distribution on an incident plane wave so that electromagnetic energy refocuses at a deep-seated target inside a head model (Rahmani et al., 17 Sep 2025). In that implementation, the metasurface forms one wall of a semi-cavity, operates near $2\,\mathrm{GHz}$ in simulation and $1.8\,\mathrm{GHz}$ in experiment, and was reported as the first experimental demonstration of metasurface-based time-reversal focusing for deep brain hyperthermia, achieving localized heating while minimizing temperature rise in healthy tissue (Rahmani et al., 17 Sep 2025). More broadly, the device belongs to a wider class of transmissive metasurfaces in which layered architectures are used to control transmitted phase, amplitude, wavelength selectivity, or polarization in free space rather than through guided-wave routing (Horie et al., 2016, Sisler et al., 21 Mar 2026).

1. Structural configuration

In the reported microwave system, the metasurface is configured as a quad-layer array of square metallic patches, each layer separated by RO4003C dielectric substrates for simulations or FR-4 dielectric substrates for experiments (Rahmani et al., 17 Sep 2025). The unit-cell period is $30\,\mathrm{mm}$, described as about $\lambda_0/5$ at $2\,\mathrm{GHz}$, with a metallic patch width $W = 1\,\mathrm{mm}$, an air gap of $13.5\,\mathrm{mm}$, and a variable patch size $L_1$ optimized per unit cell to impart the required phase shift. The substrate thickness is $3\,\mathrm{mm}$ for RO4003C in the simulated design and $1.6\,\mathrm{mm}$ for FR-4 in the experimental realization (Rahmani et al., 17 Sep 2025).

The metasurface does not operate as an isolated sheet. It forms one wall of a semi-cavity whose other three sides and top are metallic Perfect Electric Conductor panels made from aluminum, while the bottom remains open for patient access (Rahmani et al., 17 Sep 2025). This cavity-level arrangement is part of the focusing system rather than a separate enclosure. Within the paper’s formulation, the layer count is not incidental: the quad-layer choice is explicitly tied to the need for full $1.8\,\mathrm{GHz}$0 transmission-phase coverage together with high transmission amplitude.

2. Time-reversal phase synthesis

The design procedure is based on time-reversal focusing. A simulated point source, modeled as a dipole, is placed at the tumor site inside the head model; the electromagnetic field phase is recorded on the metasurface aperture; that field is phase-conjugated; and the metasurface is then designed so that, when illuminated by a plane wave from a distant source, the transmitted wavefront refocuses at the tumor location (Rahmani et al., 17 Sep 2025). The paper expresses the transmission coefficient as

$1.8\,\mathrm{GHz}$1

with

$1.8\,\mathrm{GHz}$2

and states that the angle of $1.8\,\mathrm{GHz}$3 must match the required time-reversal phase at each pixel (Rahmani et al., 17 Sep 2025).

Within that framework, the role of the quad-layer structure is to provide the transmission-phase and transmission-amplitude operating space needed for practical aperture synthesis. Across the full variation of $1.8\,\mathrm{GHz}$4, reported as $1.8\,\mathrm{GHz}$5 to $1.8\,\mathrm{GHz}$6, the transmissive quad-layer unit cell covers the entire $1.8\,\mathrm{GHz}$7-$1.8\,\mathrm{GHz}$8 phase range with $1.8\,\mathrm{GHz}$9 amplitude at the frequency of interest (Rahmani et al., 17 Sep 2025). The same paper contrasts this with single- or dual-layer metasurfaces, stating that the quad-layer structure enables extended phase manipulation range, reduced phase quantization error by allowing smaller patch-size increments and smoother $30\,\mathrm{mm}$0 phase curves, and high transmission essential for maximizing energy delivery to the focal spot.

3. Electromagnetic and thermal performance metrics

The principal electromagnetic absorption metric is the power loss density

$30\,\mathrm{mm}$1

which quantifies absorbed electromagnetic energy in tissue (Rahmani et al., 17 Sep 2025). Focusing quality is assessed through $30\,\mathrm{mm}$2, defined in the paper as the ratio of the maximum healthy-tissue power loss to the mean within the tumor; lower values indicate better localization and less unwanted heating of healthy tissue (Rahmani et al., 17 Sep 2025). Reported simulated values are $30\,\mathrm{mm}$3 for the ideal time-reversal phase case and $30\,\mathrm{mm}$4 for the quad-layer metasurface with quantization. For the spherical head model, the paper reports $30\,\mathrm{mm}$5, described there as safe and highly localized focus (Rahmani et al., 17 Sep 2025).

Thermal validation is coupled to electromagnetic simulation through the Pennes’ bio-heat equation,

$30\,\mathrm{mm}$6

where $30\,\mathrm{mm}$7 is derived from the electromagnetic field (Rahmani et al., 17 Sep 2025). In the reported simulation, the tumor reaches at least $30\,\mathrm{mm}$8 within $30\,\mathrm{mm}$9 minutes of irradiation while surrounding tissue remains around $\lambda_0/5$0. The same study states that power loss maps and phase profiles confirm tight spatial focus and minimal hot spots outside the tumor (Rahmani et al., 17 Sep 2025).

These results are significant because they separate two related design objectives: maximizing transmission through the aperture and localizing deposition within tissue. The quad-layer architecture is presented not simply as a transmission-enhancement scheme, but as a means of preserving aperture-level phase fidelity sufficiently well that the thermal hotspot remains spatially confined after propagation through a heterogeneous head model.

4. Fabrication and experimental validation

The metasurface was fabricated by etching or soldering square metallic patches of precisely simulated lengths onto FR-4 substrates, followed by layer-by-layer assembly (Rahmani et al., 17 Sep 2025). Aluminum foil of $\lambda_0/5$1 thickness was used for the external cavity walls because its skin depth at $\lambda_0/5$2 was described as negligible. The head phantom was prepared using a Bruggeman-mixed recipe of distilled water, canola oil, and gelatin powder, tailored to match brain tissue permittivity $\lambda_0/5$3, conductivity $\lambda_0/5$4, and thermal capacity (Rahmani et al., 17 Sep 2025).

The experimental excitation used a standard gain horn antenna, identified as ETS 3160-03, placed $\lambda_0/5$5 from the metasurface to approximate plane-wave illumination (Rahmani et al., 17 Sep 2025). The frequency was shifted from $\lambda_0/5$6 in simulation to $\lambda_0/5$7 in experiment for equipment compatibility. Initial and post-heating temperature profiles were measured with a Testo 872 thermal camera after $\lambda_0/5$8 minutes of continuous microwave irradiation, with the phantom positioned so that the artificial tumor coincided with the simulated focus point. The paper reports a total free-space path loss of $\lambda_0/5$9 and a substrate transmission loss of $2\,\mathrm{GHz}$0 (Rahmani et al., 17 Sep 2025).

The measured temperature rise at the focus or tumor site was $2\,\mathrm{GHz}$1 after $2\,\mathrm{GHz}$2 minutes, from $2\,\mathrm{GHz}$3 to $2\,\mathrm{GHz}$4, while the surrounding tissue increase was limited to $2\,\mathrm{GHz}$5 (Rahmani et al., 17 Sep 2025). The reported hot-spot full width at half maximum was approximately $2\,\mathrm{GHz}$6–$2\,\mathrm{GHz}$7, matching the focusing simulation. The paper attributes minor degradation in $2\,\mathrm{GHz}$8 and focal tightness relative to the ideal phase-conjugated case to fabrication and phase quantization, while still describing the localization as superior to typical metasurfaces (Rahmani et al., 17 Sep 2025).

5. Relation to other transmissive metasurface architectures

The quad-layer microwave design is part of a broader family of transmissive metasurface systems that use layered stacks to control transmitted fields in free space, but the physical mechanisms differ substantially across spectral regimes (Horie et al., 2016, Sisler et al., 21 Mar 2026).

Paper	Structure	Reported function
(Rahmani et al., 17 Sep 2025)	Quad-layer array of square metallic patches with RO4003C or FR-4 substrates in a semi-cavity	Time-reversal focusing for deep brain microwave hyperthermia
(Horie et al., 2016)	DBR-metasurface-DBR planar filter array with low loss dielectric metasurface layers sandwiched between two distributed Bragg reflectors	Optical bandpass filters with spatially varying center wavelengths
(Sisler et al., 21 Mar 2026)	TiO$2\,\mathrm{GHz}$9 metasurface embedded in a thin LC layer with a BSO photoactive top contact	Optically addressable transmissive SLM with $W = 1\,\mathrm{mm}$0 linear polarization rotation

In the optical filter array of (Horie et al., 2016), each filter pixel is composed of a bottom distributed Bragg reflector, an SU-8 polymer cavity layer, a dielectric metasurface layer of amorphous silicon nano-posts embedded in SU-8, and a top distributed Bragg reflector. There, the metasurface functions as a phase-shifting element inside a Fabry-Pérot resonator, allowing center wavelength control by changing only the in-plane geometry of the sandwiched metasurfaces. The reported operating range is $W = 1\,\mathrm{mm}$1 to $W = 1\,\mathrm{mm}$2, corresponding to $W = 1\,\mathrm{mm}$3 and $W = 1\,\mathrm{mm}$4, with experimentally measured quality factors larger than $W = 1\,\mathrm{mm}$5 (Horie et al., 2016).

In the optically addressable liquid-crystal transmissive SLM of (Sisler et al., 21 Mar 2026), the device stack comprises a sapphire substrate with ITO, a SiO$W = 1\,\mathrm{mm}$6 layer, a TiO$W = 1\,\mathrm{mm}$7 metasurface, a thin E7 liquid crystal layer of about $W = 1\,\mathrm{mm}$8, an alignment layer, and a photoactive BSO top contact. That device is described as fully transmissive and all-dielectric, with the BSO illuminated by a patterned $W = 1\,\mathrm{mm}$9 laser to create a transient electrical contact that switches the LC locally. The reported outcome is $13.5\,\mathrm{mm}$0 linear polarization rotation in reconfigurable patterns across a $13.5\,\mathrm{mm}$1 active area with overall transmittance of $13.5\,\mathrm{mm}$2 (Sisler et al., 21 Mar 2026).

Taken together, these examples show that “transmissive metasurface” does not denote a single material platform or a single function. It can refer to metallic microwave transmitarrays for time-reversal focusing, dielectric phase-shifting layers inside DBR-defined optical resonators, or all-dielectric LC-integrated modulators for high-power transmitted light (Rahmani et al., 17 Sep 2025, Horie et al., 2016, Sisler et al., 21 Mar 2026).

6. Interpretation, design trade-offs, and recurring misconceptions

A recurrent misconception is that additional metasurface layers are primarily a structural complication that inevitably increase loss. The reported microwave study points in a different direction: the quad-layer architecture was selected because it enables full $13.5\,\mathrm{mm}$3 transmission-phase coverage with $13.5\,\mathrm{mm}$4 amplitude, reduced phase quantization error, and smoother $13.5\,\mathrm{mm}$5 phase curves than single- or dual-layer alternatives (Rahmani et al., 17 Sep 2025). This suggests that, in this context, layer count is being used to enlarge the accessible phase-amplitude design space rather than merely to stack resonant sheets.

Another misconception is that transmissive metasurfaces are intrinsically tied to one fabrication philosophy. The microwave hyperthermia demonstrator uses square metallic patches and aluminum PEC walls (Rahmani et al., 17 Sep 2025), the optical filter array uses low loss dielectric metasurface layers sandwiched between two DBRs (Horie et al., 2016), and the LC SLM uses an all-dielectric TiO$13.5\,\mathrm{mm}$6-LC-BSO stack specifically to avoid lossy metallic layers in the optical path (Sisler et al., 21 Mar 2026). The diversity of these implementations indicates that “transmissive” describes the operational mode of field control more directly than it specifies materials.

A further point concerns free-space operation. The DBR-metasurface-DBR optical filter array was explicitly described as free-space coupled and requiring no waveguides, with potential for direct integration on top of photodetector arrays for on-chip high-resolution spectrometers (Horie et al., 2016). The microwave hyperthermia system likewise relies on plane-wave-like illumination from a horn antenna at a standoff distance of $13.5\,\mathrm{mm}$7, rather than guided delivery through a conformal feed network (Rahmani et al., 17 Sep 2025). This suggests that transmissive metasurfaces occupy a distinct position relative to guided photonic or microwave filtering schemes: they reshape fields across an aperture while preserving through-propagation.

The principal limitation explicitly identified in the quad-layer hyperthermia study is the departure from the ideal time-reversal phase case caused by fabrication and phase quantization, which degrades the figure of merit and focal tightness (Rahmani et al., 17 Sep 2025). Even so, the same study reports patient-specific customization for different tumor locations as an advantage of the smooth phase tuning facilitated by the quad-layer design. Within the evidence presented, the central technical problem is therefore not whether transmission can be achieved, but how accurately the transmitted phase profile can reproduce the prescribed time-reversed field under practical fabrication constraints.