Schematic diagram of polariton diffusions under real frequency and complex complex frequency excitation. While polariton waves at real frequencies have a limited propagation distance, combining propagation waves from different real frequencies based on complex occurrence frequencies can achieve almost lossless propagation. Credit: University of Hong Kong
A research group, led by Professor Shuang Zhang, interim head of the Department of Physics at the University of Hong Kong (HKU), and Professor Cheng Dai from the National Center for Nanoscience and Technology in China, has provided a solution to a common problem. In the world of nanophotonics – the study of light on a very small scale.
Their findings were recently published in a prestigious academic journal Nature materials, Propose a synthetic complex frequency wave (CFW) approach to address optical loss in polariton propagation. These findings offer practical solutions such as more efficient light-based devices for faster and more compact data storage and processing in devices such as computer chips and data storage devices, and improve Accuracy In sensors, imaging technologies and security systems.
Surface plasmon polaritons and phonon polaritons offer advantages such as efficient energy storage, local field enhancement, and high sensitivities, taking advantage of their ability to confine light to small scales. However, their practical applications are hampered by the issue of ohmic loss, which causes energy to be dissipated when interacting with natural materials.
Hyperbolic phonon polariton and elliptical phonon polariton propagation on α-MoO3 film. (a) AFM of the antenna mounted on the α-MoO3 film. (b) Real frequency measurements of the hyperbolic polariton at different real frequencies. (c) Complex frequency scaling provides very long-distance propagation behavior. (d) AFM of two different spaced gold antennas. (e) Amplitude and real part of measurements at real frequency f=990cm-1. (f) Amplitude and real part of measurements at complex frequency f=(990-2i)cm-1. (Figures adapted from Nature Materials, 2024). Credit: University of Hong Kong
Over the past three decades, this limitation has hampered progress in nanophotonics for sensing, superior imaging, and nanophotonic circuits. Overcoming ohmic loss would dramatically enhance device performance, enabling advances in sensor technology, high-resolution imaging, and advanced nanocircuits.
Professor Shuang Zhang, corresponding author of the paper, explained the focus of the research: “To address the challenge of sight loss in key applications, we put forward a practical solution. By using a new synthetic complex wave excitation, we can achieve virtual gain and counteract the intrinsic loss of the polariton system. To validate this approach, we applied it to a phonon polariton propagation system and observed a significant improvement in polariton propagation.
We demonstrated our approach by performing experiments with phonon polariton materials, such as hBN and MoO3, in the optical frequency range. “As expected, we obtained an almost lossless propagation distance consistent with our theoretical expectations,” added Dr. Fuxin Guan, first author of the paper and a postdoctoral fellow at the Department of Physics at the University of Hong Kong.
A multi-frequency approach to overcome optical loss
In this research, the team developed a new multi-frequency approach to address energy loss in polariton propagation. They used a special type of wave called “complex frequency waves” to achieve virtual gain and loss compensation in the optical system. While a normal wave maintains a constant amplitude or intensity over time, a complex frequency wave exhibits both oscillation and amplification simultaneously. This property allows a more comprehensive representation of wave behavior and enables compensation for energy loss.
1D polariton propagation (from left to right) using optical frequency hBN film. (a) True frequency images show a clear decay field profile in the propagation direction. (b) Complex frequency measurements provide almost non-dissipative propagation behaviour. (Figures adapted from Nature Materials, 2024) Source: University of Hong Kong
While frequency is usually viewed as a real number, it can also have an imaginary part. This imaginary part tells us how the wave becomes stronger or weaker over time. Waves with a complex frequency characterized by a negative (positive) imaginary part that decays (amplifies) with time. However, performing our measurements directly under complex frequency wave excitation in optics is challenging because it requires complex time-gated measurements. To overcome this, the researchers used a Fourier transform mathematical tool to split the complex frequency wave (CFW) into multiple components with individual frequencies.
Just like when you're cooking and need a specific, hard-to-find ingredient, the researchers used a similar idea. They break down complex frequency waves into simpler components, such as using substitute ingredients in a recipe. Each component represents a different aspect of the wave. It's like preparing a delicious dish using substitute ingredients to get the desired flavour. By measuring these components at different frequencies and combining the data, they reconstructed the behavior of the system illuminated by the complex frequency wave. This helped them understand and compensate for energy loss. This approach greatly simplifies the practical implementation of CFWs in various applications, including polariton diffusion and ultrathin imaging. By performing optical measurements at different real frequencies with a fixed time interval, it becomes possible to construct the optical response of the system at a complex frequency. This is achieved by mathematically combining optical responses obtained at different real frequencies.
This work provided a practical solution to address the long-standing problem of optical loss in nanophotonics, said Professor Qing Dai, National Center for Nanoscience and Technology and another author of the paper. He highlighted the importance of the complex frequency method, noting that it can be easily applied to various other applications such as molecular sensing and nanoscale integrated circuits. He further stressed that “this method is remarkable and universally applicable, as it can also be used to address losses in other wave systems, including sound waves, elastic waves and quantum waves, thus enhancing imaging quality to unprecedented levels.”
Reference: “Compensating polariton propagation losses through complex frequency excitation” by Fuxin Guan, Xiangdong Guo, Shu Zhang, Kebo Zeng, Yue Hu, Chenchen Wu, Shaobo Zhou, Yuanjiang Xiang, Xiaoxia Yang, Qing Dai, Shuang Zhang, 8 January. 2024, Nature materials.
doi: 10.1038/s41563-023-01787-8
This work was supported by the New Cornerstone Science Foundation and the Hong Kong Research Grants Council.
