Photonic transcendental equation solver using frequency to time mapping.

The growing computational and energy demands of artificial intelligence and large-scale models are pushing traditional electronic chips to their limits. Photonic processors, offering high speed, large bandwidth, and multi-dimensional operation, present a promising alternative to break through the limits of Moore's Law, and have already been applied to matrix multiplication, differentiation, and integration operations. However, its application in solving transcendental equations, which represent a critical type of computational problem, remains largely unexplored. This paper presents a photonic design capable of solving transcendental equations using a Value-to-graph Mapping method. The proposed scheme exploits an optical frequency comb and a chirped Bragg grating to map equations into the optical domain. To validate the proposed method, we evaluated six representative transcendental equations through simulations, achieving single-core solution accuracies of 91.15%, 93.48%, 93.31%, 96.4%, 96.5%, and 95.5%, respectively. To enhance the solving performance, we further introduced a wavelength-division multiplexing (WDM) scheme, which fully capitalizes on the comb bandwidth for more precise waveform mapping. With the WDM scheme, the corresponding solution accuracies were improved to 99.58%, 96.86%, 98.6%, 98.4%, 98.6%, and 97.2%, respectively. This approach enables solutions to certain transcendental equations within predefined domains. The underlying methodology is generalizable and can be extended to tackle more complex computational tasks, thereby paving the way for sophisticated photonic computing systems.