Complex-frequency excitations in photonics and wave physics.

Closed, lossless optical cavities are characterized by a Hamiltonian that obeys Hermiticity, resulting in strictly real-valued resonance frequencies. By contrast, non-Hermitian wave systems are characterized by Hamiltonians with poles and zeros at complex frequencies, whose control through precise engineering of material loss and gain can lead to exotic scattering phenomena. Notably, excitation signals that oscillate at complex-valued frequencies can mimic the emergence of gain and loss, facilitating access to these non-Hermitian responses without material modifications. These findings have been advancing the fundamental understanding of wave-matter interactions and are enabling breakthroughs in metamaterials, imaging, sensing, and computing. This Review examines theoretical advances and experimental discoveries in this emerging field, demonstrating how tailored time-domain excitations offer new opportunities for wave manipulation and control. Editor's summary: Light interactions with linear resonant systems can be modeled in the frequency domain, assuming ideal monochromatic excitations with infinite oscillation time at real frequencies. Kim et al. reviewed recent developments in the field of complex frequency excitations in photonics and in other fields of physics governed by wave equations. In this excitation scheme, the signal pulses exponentially grow or decrease in amplitude over time. This dynamical behavior allows passive systems to mimic the emergence of gain and loss, facilitating access to non-Hermitian responses without specific material modifications and leading to exotic optical effects. Applicable to wave systems in general, such complex excitations can be applied to developments in metamaterials, optical computing, sensing, and image processing. —Ian S. Osborne BACKGROUND: Customizing how a system responds to external stimuli is essential for a wide range of wave-based technologies, such as photonics, acoustics, elastodynamics, radiofrequency engineering, and quantum optics. This response involves the intricate dynamics of wave interactions with matter, leading to reflection, absorption, diffraction, and scattering of waves, altering their momentum and energy flow. In turn, these principles underpin a multitude of wave phenomena and technologies, from the reflection of light and the echo of sound to the intricate behavior observed in photonic systems. In most settings, these phenomena are limited by fundamental system properties such as passivity, linearity, and time-reversal symmetry, imposing constraints on bandwidth, efficiency, and other performance metrics. Recent efforts to overcome these limitations involve the use of material gain; tailored responses in systems characterized by nonconservative interactions with their environment; time modulation, amplification, and lasing; and nonreciprocal materials. Although these strategies show promise, they often introduce unwanted challenges, such as increased complexity, reduced ease of integration, high costs, and footprint requirements. ADVANCES: In recent years, excitations that oscillate at complex-valued frequency have transitioned from being merely analytical and numerical tools to model photonic systems to becoming a viable route to experimentally access exotic wave responses. By utilizing excitation signals with tailored waveforms whose amplitudes grow or decay exponentially in time, researchers have been able to effectively mimic the effect of gain and loss in passive systems without modifying their material properties. This advancement has led to experimental demonstrations of phenomena previously thought unattainable in passive systems. Notable examples include compensating losses in metamaterials, enhanced sensing, parity-time symmetry transitions without the need for active elements, and generation of optical pulling forces without specially designed spatial field gradients. These breakthroughs have also unlocked new capabilities, such as the manipulation of light for super-resolution imaging and real-time control over light-matter interactions and critical coupling of optical cavities, as well as phenomena that mimic the presence of material gain in passive systems. By bridging theoretical concepts with experimental implementations, these advances demonstrate the feasibility of accessing non-Hermitian responses in passive linear systems. This enables new possibilities for wave-based technologies without the need for complex materials and the downsides of active elements. OUTLOOK: The recent progress in the use of complex frequencies and their associated wave-matter interactions offers metamaterials and wave control new opportunities, particularly in the context of non-Hermitian wave phenomena. In optics and photonics, these tools offer opportunities to dramatically alter how light interacts with matter in a highly dynamic and tunable fashion, enabling enhanced control over light emission and transport. This paves the way for observing non-Hermitian and topological wave phenomena without relying on complex non-Hermitian materials, which are challenging to realize. By applying this excitation approach to well-established platforms, it becomes possible to exploit the interplay of effective gain and loss encoded in the temporal waveform of the excitation to create new functionalities and enhance the performance of modern technologies. For instance, in optical communications, sensing, and computing, the ability to manipulate waves by using complex-frequency excitations may lead to more efficient and adaptable systems. Future research directions include developing more efficient methods for generating complex-frequency excitations, integrating these techniques into existing technologies, and exploring their applications across various fields. Emerging platforms such as metasurfaces, polaritonic materials, optomechanical systems, and topological insulators provide unexplored opportunities to investigate the effects of complex-frequency excitations in systems with inherently large nonlinearities, naturally strong light-matter interactions, and intrinsic robustness. Tailored effective gain and loss driven by the excitation waveform in these systems opens the potential for a substantial shift in the study, application, and control of wave-matter interactions across many physical domains. By bridging theoretical advancements with practical implementations, we anticipate that complex-frequency excitations may become crucial for future technological innovations, impacting fields beyond photonics and wave physics, such as quantum computing, biomedical engineering and sensing, imaging, and energy harvesting. Complex-frequency excitations in various wave physics settings.: Exotic wave phenomena available across optics, radiofrequency (RF), elastodynamics, mid-infrared (mid-IR), acoustics, and quantum wave systems, leveraging complex-frequency excitations to enhance modern technologies. [ABSTRACT FROM AUTHOR]