A recent review article published in the journal Science highlights how modern optical sciences are increasingly leveraging the principles of non-Hermitian physics, resonant phenomena, and metamaterials to break traditional boundaries of wave control. These emerging strategies go beyond the constraints of passive, lossy materials and traditional monochromatic excitation, opening new possibilities in imaging, sensing, energy harvesting, and information processing.
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Background
The core principles of optics have traditionally been rooted in wave propagation, scattering, and interference. In particular, classical optics focuses on how monochromatic light interacts with materials, where effects like diffraction, refraction, and scattering set the fundamental limits on resolution and efficiency. A well-known example is the diffraction limit, which restricts the spatial resolution achievable with conventional lenses and microscopy techniques.
At the same time, challenges such as material losses, thermoviscous dissipation, and fabrication imperfections continue to compromise the performance and accuracy of optical systems, especially at the nanoscale where light-matter interactions become significantly stronger. To address these hurdles, researchers have turned to innovations like super-resolution imaging, metamaterials, and plasmonic structures.
While these approaches have made notable progress, they often come with trade-offs. Increased system complexity can introduce additional losses, and conventional design strategies typically remain constrained by the limitations of passive materials.
Studies Highlighted in the Review
The review highlights several pivotal studies that demonstrate how complex-frequency techniques are reshaping what’s possible in optical systems. A central theme is the manipulation of scattering phenomena to exceed classical limits. One notable example is superscattering, where subwavelength nanostructures are engineered to scatter light with intensities beyond what passive systems typically allow. This is achieved through complex-frequency excitations, generated via methods like postprocessing and Fourier synthesis, which enable access to regimes of virtual gain.
Unlike actual gain, virtual gain doesn’t amplify power in the traditional sense. Instead, it exploits the complex frequency domain to emulate gain effects, compensating for material losses and boosting the quality factors of resonant modes. This results in improved resolution in imaging and enhanced sensitivity in optical sensing.
In the realm of super-resolution imaging, techniques such as ptychography have been adapted to make use of complex-frequency excitation. These approaches recover high-spatial-frequency components that would normally be lost due to the diffraction limit. By synthesizing complex fields through iterative algorithms and postprocessing, researchers can simulate gain-loss compensation, enabling fine control over waveforms. This allows the design of resonant structures with precisely engineered singularities, such as perfect absorption or lasing at designated complex frequencies, unlocking highly efficient light-matter interactions in compact optical devices.
The review also discusses how complex-frequency excitation enhances optical sensing. Here, virtual gain supports sustained resonance in platforms like biosensors by effectively increasing the decay length of polaritons and other coupled modes. This translates into higher sensitivity, as the signal remains tightly confined within the sensing volume, despite the presence of intrinsic material losses.
Another key area of exploration involves overcoming long-standing physical limits, such as the Rozanov bound, which links absorber thickness to bandwidth. By introducing complex-frequency design principles, researchers are beginning to challenge and, in some cases, surpass these fundamental constraints.
Discussion
The article reflects on the profound implications of utilizing complex-frequency excitations within optics. By extending the transfer functions of optical systems into the complex plane, researchers can engineer wave phenomena with an unprecedented degree of control. This includes manipulating the spectral singularities (poles and zeros) that correspond to resonances, perfect absorption, or lasing. Such control mechanisms facilitate the design of devices with enhanced resolution, sensitivity, and energy efficiency, often surpassing fundamental passive limits. Significantly, the virtual gain effect allows for effective loss mitigation and amplification of resonant fields, without relying on traditional active gain media, which are often limited by noise, thermal instability, and other performance challenges.
The authors discuss how non-Hermitian physics, particularly the strategic placement of EPs and the utilization of PT-symmetry, provides a versatile toolkit for reconfiguring light-matter interactions. These phenomena confer robustness against fabrication imperfections and environmental perturbations, making them attractive for practical applications. The review emphasizes that although many of these effects have been demonstrated successfully in acoustics, microwave, and plasmonic regimes, translating them into the optical domain presents ongoing challenges. These include controlling ultrafast temporal dynamics, managing fabrication tolerances at the nanoscale, and integrating complex-frequency control schemes into scalable devices.
The intricate relationship between complex frequencies and nonlinear interactions in optics also emerges as a promising avenue. Nonlinear resonators, combined with virtual gain mechanisms, could lead to the realization of phenomena such as single-photon memories, nonreciprocal devices, and dynamic reconfiguration of wavefronts. Moreover, employing complex-frequency excitations opens pathways toward overcoming the Rozanov bound, which constrains the trade-off between absorber thickness and operational bandwidth.
Conclusion
The review concludes by underscoring the significant potential of complex-frequency excitation techniques to advance optical science. Looking forward, it outlines key directions for future research. Among the priorities are developing scalable and stable platforms that can support real-time complex-frequency control, as well as extending these methods into nonlinear and quantum regimes. Integrating complex-frequency concepts into practical, device-level applications is another critical step.
The creation of complex-radiation sources and the application of these techniques in broader areas, such as quantum optics and energy harvesting, are also highlighted as promising avenues. These developments could translate recent theoretical advances into impactful, real-world technologies.
Journal Reference
Kim S., et al. (2025). Complex-frequency excitations in photonics and wave physics. Science, 387, eado4128. DOI: 10.1126/science.ado4128, https://www.science.org/doi/full/10.1126/science.ado4128