Photonic transcendental equation solver using frequency to time mapping

Area of Science:

• Photonics
• Optical Computing
• Computational Mathematics

Background:

• Traditional electronic chips face limitations due to increasing computational and energy demands of AI.
• Photonic processors offer high speed and bandwidth, suitable for complex computations.
• Solving transcendental equations using photonics is an underexplored area.

Purpose of the Study:

• To present a novel photonic design for solving transcendental equations.
• To explore the application of photonic processors beyond traditional computational tasks.
• To enhance the accuracy and efficiency of solving transcendental equations via photonics.

Main Methods:

• A photonic design utilizing a Value-to-graph Mapping method.
• Exploitation of an optical frequency comb and chirped Bragg grating for equation mapping.
• Implementation of a wavelength-division multiplexing (WDM) scheme to improve performance.

Main Results:

• Simulations demonstrated accurate solutions for six representative transcendental equations.
• Single-core accuracies ranged from 91.15% to 96.5%.
• The WDM scheme improved accuracies to between 96.86% and 99.58%.

Conclusions:

• The proposed photonic design offers a viable method for solving transcendental equations.
• The methodology is generalizable for more complex computational problems.
• This work paves the way for advanced photonic computing systems.