Spectral window engineering for synthetic wave compensation of plasmonic loss

Abstract: Synthetic complex-frequency excitations have emerged as a powerful tool for loss compensation and resolution enhancement. We show that, ideally, these excitations allow for the complete offsetting of intrinsic damping over long evolution times, governed by a universal inverse-time scaling law for residual damping under Nth-order synthetic illumination. However, in realistic experimental settings, the achievable virtual gain is fundamentally restricted by the finite spectral measurement range, which introduces unwanted temporal artifacts and disrupts this ideal scaling. We demonstrate that the conventional rectangular spectral window creates a slowly decaying temporal kernel (1/t) that leaks unwanted early-time signals into the late-time regime, thereby masking the targeted response. To mitigate this constraint, we introduce a Hann-window filtering technique that yields a faster decaying temporal kernel (1/t)^3. This simple spectral engineering dramatically suppresses spurious contributions and extends the usable lifetime of the synthetic waveform. Experimental validation using coupled plasmonic resonators demonstrates that Hann-window filtering improves the loss-offsetting efficiency by nearly a factor of three compared with the standard rectangular window. Our results reveal the fundamental temporal limits of synthetic complex-frequency waves and provide a practical strategy to achieve long-lived, high-SNR loss compensation in nanophotonic systems.