High-order virtual gain for optical loss compensation in plasmonic metamaterials

Metamaterials exhibit extraordinary properties yet suffer from pronounced wave dissipation, particularly in optical imaging and sensing systems. Recent advances leveraging complex frequency wave excitations with virtual gain effect, synthesized by multi-monochromatic waves, offer promising solutions for optical loss compensation. However, this approach faces limitations in extreme loss scenarios. The complex frequency wave requires sufficient virtual gain, i.e., temporal attenuation, to offset material loss, inevitably triggering rapid signal decay to zero before reaching a quasi-static state. To address this challenge, we introduce synthetic waves of high-order virtual gain to slow down the decay rate while preserving the loss compensation efficiency. We experimentally demonstrate 20-fold noise suppression in plasmonic resonance systems compared to conventional complex frequency excitations. This approach exhibits broad applicability across diverse fields, including imaging, biosensing, and integrated photonic signal processing.