Due to the strong light-matter interactions, coupled plasmonic systems have broad applications in such areas as light manipulation, optical sensing, optical imaging, and optoelectronic devices. However, the inherent dissipation of materials and radiation dissipation of resonant structures limit the strength, service life, and propagation distance of coupled plasmonics, weakening the coupling signals and reducing the sensitivity and other performance of coupled plasmon devices. One possible solution is to add optical gain materials into the systems to compensate for the dissipation, but the utilization of gain materials is still limited because of the introduction of noise and instability. Another possibility is to employ complex frequency waves as light sources. It has been theoretically demonstrated that complex frequency waves with temporal attenuation can restore information losses. Unfortunately, producing complex frequency waves in real optical systems still faces significant challenges and has not been yielded experimentally. Currently, a novel method for synthesizing complex frequency waves has been proposed to be successfully applied to super-resolution imaging and highly sensitive biosensing. Therefore, we adopt this method to compensate for the dissipation of coupled plasmonic systems, thereby enhancing their resonance signals and avoiding experimental challenges. We hope that our study can benefit the development of coupled plasmonic systems for various potential applications.

We employ a periodic plasmonic structure composed of two perpendicular silver rods as an example to investigate the mechanism behind the attenuation of coupled resonance in coupled plasmonic systems. The structure is simulated by the finite-difference time-domain (FDTD) method using CST Studio Suite software. In the simulation, a plane wave with different polarization angles (45°, 90°, and 135°) is normally incident onto the structure with the periodic boundary to obtain the transmission coefficients, with the permittivity of silver described by the Drude model. Furthermore, we combine the Lorentz polarization model with temporal coupled-mode theory to analyze the interaction of plasmonic modes.

The simulation results (Fig. 1) show that under an incident wave whose polarization angle equals 45° (135°) , the eigenmode of the plasmonic structure appears at 290 THz (310 THz) with no conversion of orthogonal polarization. Subsequently, a wave with 90° polarization can simultaneously excite the two eigenmodes and generate the coupled signal of the structure. Theoretical analysis shows that the strength of the coupled plasmonic signals depends on the frequency difference and the dissipation of the eigenmodes. Under the relatively small frequency difference and large dissipation, the two coupled new modes will have a large broadening and high overlap in the spectra, causing the coupled valley in the center to be weakened and shallowed. The Lorentz polarization model shows that complex frequency waves with temporal attenuation can enhance the weakened signals by reducing the dissipation of the eigenmodes. Based on Fourier transform analysis, the linear responses excited by complex frequency waves can be synthesized by the coherent combination of multiple real frequency responses. The calculation results (Fig. 3) show that synthesized complex frequency waves with different virtual gains can gradually enhance the coupled signals, where the coupled valley in the spectral line becomes increasingly deeper. Additionally, the synthesized complex frequency wave method is also effective for different coupling strengths (distance adjustment between silver rods). Even if the original signal is difficult to distinguish, this method can also restore it to the split state.

We study the dissipation in coupled plasmonic systems based on numerical simulations using CST Studio Suite software and theoretical analysis that incorporates the Lorentz polarization model and temporal coupled modes theory. Meanwhile, we explain the formation mechanism of coupled plasmonic signals and identify their limiting factors. Our findings suggest that under small coupling strength, larger dissipation of plasmonic systems will significantly hamper their coupled resonance. Then, we analyze the influence of complex frequency wave excitation on coupled plasmonic systems, and the results indicate that complex frequency waves with temporal attenuation can compensate for the dissipation of the system and restore the weak signal. To avoid the experimental difficulties of complex frequency waves in real optical systems, we employ a new method for synthesizing complex frequency responses via real frequency waves to calculate the transmission spectrum of the coupled plasmonic structure excited by complex frequency waves. Our results demonstrate that the proposed method can compensate for the dissipation of the coupled plasmonic structure in different conditions, significantly enhancing the coupled signals with almost no additional cost. The findings provide a practical and general method for solving the long-standing dissipation of coupled plasmonic systems, facilitating further applications of coupled plasmonic systems such as optical imaging, spectroscopy technology, and optical sensing.