Embedding matrices in programmable photonic networks with flexible depth and width.

Area of Science:

• Photonics
• Optical Computing
• Integrated Optics

Background:

• Photonic circuit architectures are crucial for advanced computation.
• Current designs often lack flexibility in network depth and width.
• Efficient matrix operations are key for photonic processors.

Purpose of the Study:

• To demonstrate a flexible photonic circuit architecture.
• To establish a method for tailoring network depth and width.
• To show the universal capability of specific photonic layer configurations.

Main Methods:

• Designing programmable photonic circuits with alternating mixing and active layers.
• Developing a mathematical framework for matrix embedding.
• Deriving general relations for network width and depth.

Main Results:

• Alternating layer configurations allow flexible tailoring of network depth and width.
• A mathematical approach embeds target matrices into higher-dimensional representations.
• Two active layers interleaved with passive mixing layers universally implement arbitrary matrix transformations.

Conclusions:

• Programmable photonic circuits offer high flexibility and adaptability.
• The proposed architecture enables scalable photonic matrix processors.
• This approach provides a universal method for photonic matrix operations.