Förster resonance energy transfer (FRET) is a near-field, non-radiative energy transfer mechanism between a donor and an acceptor molecule. In the visible spectrum, FRET is crucial for processes within 3-20nm, impacting solar energy harvesting, organic lighting, single-molecule biophysics, and biosensing. While the control of spontaneous emission from a single quantum emitter via the photonic environment is well-understood, controlling FRET between two emitters through the environment remains less clear. Previous research presents varied and sometimes contradictory findings regarding the effects of the photonic environment, particularly regarding the influence of surface plasmons, on FRET. Some studies report enhancement, others no effect, and some even quenching. The effect is particularly unclear in the intermediate near-field regime (between λ/100 and λ/2), where direct measurements in optics are difficult beyond 15nm. This study aims to address the open questions about surface plasmon effects on FRET in this near-field range by leveraging the precise control offered by microwave experiments.

The literature on the influence of the photonic environment on FRET is extensive and complex. For very short dipole-dipole separations (R < λ/100), the FRET rate is largely unaffected by the environment. At larger separations (far-field, R exceeding several wavelengths), the presence of propagating surface plasmons or waveguide modes can significantly enhance FRET. However, this falls outside the typical near-field FRET regime characterized by a 1/R⁶ distance dependence. The near-field regime (λ/100 < R < λ/2) shows the most contradictory results. Theoretical work suggests that in absorption-less and dispersion-less media, FRET rates are independent of the local density of optical states (LDOS). However, the impact of surface plasmons in real metals remains unsettled, with experiments showing enhancement, no change, or quenching depending on the system studied. The challenges of precisely controlling emitter positions and orientations in optical experiments further complicate the matter. Previous work has used techniques such as optical topological transitions in metamaterials to demonstrate energy transfer, but the understanding of surface plasmon effects in the near field remains an active area of research.

This study uses microwave experiments to overcome the limitations of optical FRET experiments in investigating the near-field regime. A metasurface designed to support surface waves analogous to surface plasmons in optics was fabricated. The metasurface consists of a square lattice of miniaturized crossed slots etched into a copper sheet, placed on an FR-4 substrate. The design supports Transverse Magnetic (TM)-polarized surface waves. The dispersion curve of the first propagating mode was validated using numerical simulations (CST Microwave Studio 2019). Near-field probing (Langer EMV-Technik MFA 01) was employed to map the magnetic field in the vertical plane, confirming the excitation of surface waves by both parallel and perpendicular electric dipoles. A vector network analyzer (Anritsu model MS2036C) was used to measure scattering parameters (S12 for two dipoles, S22 without the acceptor) in the presence of the metasurface and in homogeneous space. The LDOS enhancement was calculated using the input impedance of the dipole in both scenarios, and FRET rate enhancement was determined by comparing the S12 parameters. A programmable 3D positioning system with sub-mm accuracy allowed for precise control of dipole separation and height above the metasurface. The experiments were conducted in the frequency range of 4-4.5 GHz, with results scaled in units of k0R to ensure relevance to the optical domain. A perfect electric conductor (PEC) served as a control for comparison. Numerical simulations were performed to corroborate experimental results. The dipoles used in both the simulations and experiments were 10mm long and 2mm wide, with a 2mm gap between branches. Their resonant frequency was outside the experimental frequency range.

The experiments confirmed the excitation of surface waves by the metasurface, absent in the PEC control. LDOS measurements showed enhancement for both dipole orientations when the metasurface was used, agreeing well with numerical simulations. This enhancement was particularly pronounced at short distances (k0z < 1). FRET measurements revealed significant enhancement (above 10x) for both dipole orientations at short distances (k0z < 1) with the metasurface, contrasting sharply with the PEC control. For the PEC, FRET was quenched for the parallel orientation and showed a theoretical enhancement of up to 4x for the perpendicular orientation (not fully measurable experimentally). In the metasurface case, the observed FRET enhancements were highest in the near-field, where the surface waves strongly influence the energy transfer. Analyzing FRET rate versus LDOS enhancements revealed a linear correlation for the metasurface but not for the PEC, clearly indicating the key role of surface waves in mediating FRET. Oscillations in FRET enhancement were observed as the acceptor was moved away from the donor (at larger separations), corresponding to the nodes of the surface wave. The oscillations were also observed in the simulations.

The results definitively demonstrate the significant role of surface waves in enhancing near-field FRET. The clear contrast between the metasurface and PEC results, along with the linear correlation between FRET and LDOS enhancement in the presence of the metasurface, supports the conclusion that surface waves create new dipole-dipole coupling pathways. The study extends the understanding of FRET beyond the commonly investigated deeply subwavelength and far-field regimes, providing insight into the complex interplay between surface waves, LDOS, and FRET in the near-field. This work directly addresses the long-standing debate on the relationship between FRET and LDOS, clarifying the specific role of surface waves in enhancing both. The microwave analogy provides a valuable experimental tool to investigate a range of near-field distances not readily accessible in optical experiments.

This study provides the first clear experimental evidence of the strong influence of surface waves on near-field FRET. The comparison with a PEC control and the observed linear relationship between FRET and LDOS enhancements in the presence of the metasurface highlight the crucial role of surface waves. The microwave approach enabled exploration of the near-field regime, providing insights valuable for optimizing near-field energy transfer applications. Future work could focus on extending this approach to different metasurface designs and exploring optical implementations of these concepts for light-harvesting, quantum information, and biomolecular imaging.

The experiments were conducted in the microwave regime, which might not perfectly mimic all aspects of optical FRET. The finite size of the dipole antennas limited the minimum achievable distance to the metasurface, particularly for perpendicular orientations. While numerical simulations corroborated experimental findings, slight discrepancies between experimental and simulated resonant frequencies exist, likely due to limitations in the metasurface fabrication. The study focuses on a specific metasurface design, and the results might not be directly generalizable to all types of surface wave structures.