Experimental evidence of Förster energy transfer enhancement in the near field through engineered metamaterial surface waves

The study addresses how engineered surface waves (plasmon-like modes) influence near-field Förster resonance energy transfer (FRET) between two dipoles. While spontaneous emission control via the local density of optical states (LDOS) is well established for single emitters, prior reports on environmental control of FRET have yielded contradictory outcomes (enhancement, no effect, or quenching). Deep subwavelength separations (R < λ/100) generally show little modification, and far-field regimes (R ≫ λ) can show strong coupling via propagating surface plasmons or waveguides but correspond to radiative transfer rather than near-field FRET. The intermediate near-field regime (λ/100 to λ/2) remains insufficiently explored experimentally in optics due to positioning/orientation challenges and limited measurable donor–acceptor separations (>~15 nm). The authors use a microwave platform to precisely control geometry and emulate optical surface plasmons with a metasurface supporting surface waves. They investigate whether such surface waves can enhance near-field FRET, how this compares to a perfect electric conductor (PEC) mirror, and how FRET relates to LDOS in realistic, lossy, dispersive environments.

Prior work established photonic environment control of spontaneous emission via LDOS and reported varied effects on FRET: enhancements near cavities, nanoparticles, nanoantennas, and nanostructures; negligible effects or lack of correlation with LDOS in lossless, weakly dispersive media; and quenching near certain metallic environments. Long-range energy transfer mediated by surface plasmons and waveguides has been observed in the far field, while deeply subwavelength separations show minimal environmental influence. Theoretical analyses (e.g., Wubs & Vos) predict FRET rate independence from LDOS in absorption-less, dispersion-less media, whereas more recent theory (Cortes & Jacob) provides figures of merit for engineering FRET considering realistic losses/dispersion. Experimental challenges in optics (precise control of donor–acceptor position/orientation beyond ~15 nm) have limited direct probing of the near-field regime between λ/100 and λ/2. Metamaterial/topological transitions have demonstrated modified energy transfer at optical frequencies, but a definitive experimental clarification of surface plasmon influence on near-field FRET remained open.

- Platform and frequency scaling: Experiments performed at 4–4.5 GHz with results expressed in normalized parameters k0R = 2πR/λ and k0z = 2πz/λ to provide scalable insights for optics. - Metasurface: Inductive (aperture-type) frequency-selective surface made by etching miniaturized crossed slots in a 20 µm copper film on FR-4 (εr = 4.9 + 0.1i). Unit cell dimensions: period a = 8 mm, substrate thickness h = 1.9 mm, slot widths w1 = 7 mm, w2 = 5 mm, w3 = 0.5 mm. The metasurface supports TM-polarized plasmon-like surface waves below ~4.5 GHz with a Bloch-type mode exhibiting near-field hot spots. - Reference: A flat copper plate used as a PEC mirror benchmark with available analytical Green’s function solutions for LDOS/FRET near a planar boundary. - Dipoles and positioning: Electrically small electric dipoles (total length 10 mm, width 2 mm, gap 2 mm), driven via coaxial feeds. A programmable 3D translation system (sub-mm accuracy ~λ/60) adjusts donor/acceptor heights z and separations R while maintaining orientations (parallel or perpendicular to the surface). - Field mapping: Near-field microprobe measurements (Langer EMV-Technik MFA 01) mapped magnetic field components to verify surface-wave excitation for both dipole orientations; comparison made against simulations and PEC case. - S-parameter measurements: Donor and acceptor connected to a vector network analyzer (Anritsu MS2036C). Measured S22 (single dipole, no acceptor) to derive LDOS enhancement via input impedance, and S12 (two dipoles) to derive FRET rate enhancement as the ratio |S12|^2 relative to homogeneous space. VNA calibrated over bandwidth, cables included. For very low signals in perpendicular orientation, a spatialized electric field probe (MVG SAR PROBE SN 17/21 EP353) was used. - Computation of metrics: LDOS enhancement obtained from the real part of input impedance derived from S22; FRET rate enhancement computed from |S12|^2 normalized to free-space |S12^0|^2 (equivalently, mutual impedance ratio). Measurements repeated for varying z (at fixed R) and varying R (at fixed z) for both orientations. - Numerical simulations: Full-size metasurface model (25×25 unit cells, 200×200 mm^2) in CST Microwave Studio 2019. Eigenmode solver used for dispersion; transient solver used to obtain scattering parameters for LDOS and FRET enhancements. Simulations included dipole feeds via discrete ports. - Operating points and constraints: Fixed R = λ/7 (k0R = 0.9) for height scans; height fixed at z = λ/14 (k0z = 0.47, parallel) and z = λ/10 (k0z = 0.6, perpendicular) for R scans, limited by dipole size. Frequencies of peak LDOS near metasurface: ~4.23 GHz (parallel) and ~3.98 GHz (perpendicular) in experiments; simulations at ~4.32 GHz and ~4.22 GHz, respectively.

- Surface-wave excitation: Near-field maps show fields bound to the metasurface for both dipole orientations, confirming excitation of plasmon-like surface waves. No such surface-bound fields observed with PEC, matching simulations. - LDOS vs height: For PEC, LDOS near the surface follows image-dipole interference: parallel orientation shows LDOS suppression near z → 0; perpendicular shows ~2× enhancement at very small z, in agreement with Green’s function theory. For the metasurface, LDOS is clearly enhanced for both orientations at k0z < 1 (z ≲ λ/6), evidencing additional decay channels via surface waves; enhancement decays rapidly with z. - FRET vs height (R fixed at λ/7, k0R = 0.9): For PEC, FRET mirrors image-dipole behavior: parallel orientation quenched at small z; perpendicular orientation theoretically up to ~4× very close to the mirror, though not reached experimentally due to minimum z constraint. For the metasurface, strong near-field FRET enhancements >10× for both orientations at k0z < 1, demonstrating that surface waves open new coupling routes. - FRET vs separation R (z fixed): With metasurface, pronounced FRET enhancement occurs for 0.7 ≲ k0R ≲ 2.5 (R ≈ λ/9 to λ/3). Oscillations in enhancement vs R (period ~0.7 in k0R) are observed and reproduced by simulations, attributed to discrete unit cell periodicity (8 mm). Finite dipole size averages out some oscillation contrast but preserves the overall trend. For PEC, at large k0R > 2 the FRET rate tends toward radiative behavior of the donor: parallel case quenched (destructive interference), perpendicular ~4× (constructive). - FRET–LDOS relationship: For PEC (lossless, weakly dispersive), experiments show no correlation between FRET and LDOS for the perpendicular orientation, confirming theory for absorption-less media. For the metasurface, an approximately linear relationship between FRET and LDOS is observed for both orientations, indicating that surface waves jointly enhance donor field (Green’s function) at both donor and acceptor positions. - Regime specificity: At very small separations (k0R < 0.3), FRET remains essentially unchanged relative to free space even if LDOS is altered, whereas at intermediate separations (k0R ~ 1) metasurface waves dominate energy transfer. - Agreement and metrics: Experimental trends show excellent agreement with numerical predictions for both LDOS and FRET across z and R scans. Peak LDOS frequencies differ between measurement and simulation by amounts consistent with ~±4% fabrication tolerances. Technical noise floors (VNA ~3×10^-4; probe ~1×10^-9 V) are below data magnitudes (e.g., S21 down to ~5×10^-3; perpendicular probe signals down to ~3×10^-8 V).

The findings demonstrate that engineered surface waves on a metasurface substantially modify near-field dipole–dipole interactions by providing additional, efficient coupling pathways that are absent for PEC mirrors. This results in significant LDOS increases near the surface and commensurate FRET enhancements in the near-field regime, particularly for intermediate separations (k0R ≈ 0.7–2.5). The approximate linear FRET–LDOS relationship observed with the metasurface underscores the central role of surface modes that enhance the donor’s Green’s function both at the source (LDOS) and at the acceptor location (FRET). In contrast, for lossless, weakly dispersive planar mirrors (PEC) FRET and LDOS decouple, in line with theory. These results reconcile prior contradictory observations by highlighting material loss/dispersion and the presence of surface waves as key determinants of whether FRET correlates with LDOS. The microwave platform enables precise control of geometry and scaling to optical conditions, providing clear guidance that in realistic plasmonic systems surface-wave engineering can boost near-field energy transfer, whereas cavity-like systems without strong surface waves need not show a direct FRET–LDOS link. The discrete metasurface periodically modulates coupling as R varies, explaining observed oscillations and indicating that unit-cell design can tune spatial ranges and strengths of energy transfer.

The work provides experimental and numerical evidence that surface waves supported by an engineered metasurface strongly enhance both LDOS and near-field FRET, with enhancements >10× at k0z < 1 and pronounced gains for intermediate donor–acceptor separations (k0R ≈ 0.7–2.5). Comparison with a PEC mirror isolates the qualitative role of surface waves and nonradiative losses, confirming a near-linear FRET–LDOS relationship when surface modes dominate, and no such correlation for lossless planar mirrors. The microwave-analogy methodology overcomes positioning/orientation constraints that limit optical experiments and enables systematic exploration of the near-field regime (λ/20–λ/2). These insights pave the way to metasurface designs that engineer surface-wave propagation to control dipole–dipole energy transfer across photonics, microwaves, and acoustics, with potential impact on photovoltaics, quantum information, and biophysics. Future work could extend to optical implementations with nanoscale fabrication, explore different metasurface symmetries and losses to optimize FRET bandwidth and range, and integrate donor–acceptor ensembles for many-body interaction studies.

- Geometric constraints: Finite dipole size limited the minimum achievable height z, especially for the perpendicular orientation, preventing experimental access to the theoretically predicted ~4× FRET enhancement near PEC at very small z. - Fabrication tolerances: ~±4% uncertainty in metasurface unit-cell dimensions likely caused shifts between simulated and measured resonance frequencies and sensitivities to dipole placement relative to the unit cell. - Sensitivity to setup: Measurements are highly sensitive to the exact positions/orientations of dipoles and cables; finite dipole extent averages spatial field variations, reducing visibility of oscillations. - Measurement domain: Results obtained in the microwave regime and scaled via k0R and k0z; while physically relevant to optics, direct optical demonstrations remain experimentally challenging. - Statistics: Direct measurements without statistical or systematic error analysis; however, reported technical errors are small compared to signal levels and do not affect the main conclusions.