Photonic Systems Support up to 3D Channels, Predictively Bounding Singular Values for Information Capacity

The fundamental limit to how much information a photonic system can carry remains a key question in optical communication and signal processing, and researchers are now offering a new way to calculate this capacity. Paul Virally from Polytechnique Montrêal, Pengning Chao from Massachusetts Institute of Technology, and Alessio Amaolo and Alejandro Rodriguez from Princeton University, alongside Sean Molesky from Polytechnique Montrêal, have developed a method to determine the maximum number of independent channels a photonic system supports. Their approach provides quantifiable upper bounds on channel amplitudes, capturing the complex interplay between different communication pathways within a device, and offers immediate application to calculating crucial metrics like Shannon capacity and Fisher information. This breakthrough enables more accurate design of optical systems, potentially leading to significantly increased data transmission rates and improved signal detection in areas such as waveguides, metasurfaces, and planewave detection.

Scientists have long sought ways to design structures that efficiently manipulate light, but understanding the fundamental limits of these designs has remained a significant challenge. This work establishes quantifiable upper bounds on the singular values of the electromagnetic Green function, a key measure of a system’s ability to channel energy, for any linear photonic structure, no matter how complex. The approach predicts these bounds, revealing inherent tradeoffs between communication channels within a device.

Fundamental Limits of Photonic Information Transfer

Designing efficient photonic structures, such as those used in nanophotonics and metamaterials, requires maximizing their ability to transmit information. Researchers are now pushing beyond traditional design constraints to uncover the fundamental limits of what’s possible. A central tool in this investigation is the T-operator, which describes how a structure responds to electromagnetic waves. The team develops mathematical bounds on the T-operator, defining the maximum achievable performance for any photonic structure. These bounds aren’t just theoretical curiosities; they serve as blueprints for designing optimal devices.

The number of independent ways a structure can be excited, known as degrees of freedom, directly limits its information capacity. The team identifies a set of orthogonal excitations, representing independent ways to encode information within the structure. More orthogonal excitations translate to a higher potential information capacity. Accurate modeling requires accounting for the encoding and decoding processes, captured by the Green’s function. Techniques from randomized matrix theory are employed to efficiently analyze complex structures and approximate crucial matrix decompositions.

By leveraging local conservation laws, such as the conservation of energy and momentum, the researchers derive tighter bounds on the electromagnetic response. They also consider passivity constraints, ensuring the structure doesn’t amplify signals without external power, to create realistic designs. Trace formulas quantify the limits of optical response and heat transfer, while the concept of duality helps to infer structure and optimize designs.

The team proposes an iterative optimization process where designs are refined to approach the theoretical limits defined by the bounds. Optimizing the design within a specific subspace of possible excitations further improves efficiency. Hierarchical mean-field approximations simplify complex interactions, allowing for more manageable calculations. This work has the potential to significantly advance nanophotonics by providing a theoretical framework for designing more efficient and powerful devices. Improved communication systems with higher bandwidth and lower energy consumption are also within reach. Optimized photonic structures could enable more sensitive sensors and higher-resolution imaging systems, potentially inspiring the development of new materials and designs that better harness the power of light.

Applying this framework to three-dimensional volumes spanning multiple wavelengths, the scientists obtained indexed channel bounds relevant to waveguides, metasurfaces, and planewave detection. These results have immediate implications for calculating information-theoretic objectives like Shannon capacity and Fisher information. The findings reveal that while material structuring offers versatility, it cannot overcome fundamental limitations imposed by the underlying physics of scattering. Even in complex designs, features related to the vacuum state persist. The researchers acknowledge that their method’s accuracy, while superior to existing approaches, remains an approximation, and further refinement is possible. Future work could explore the implications of these bounds for specific device designs and investigate the limits of information transfer in increasingly complex electromagnetic systems.