λλ: A Programming Language for Silicon Photonics

We present λλ1, a programming language for silicon photonics. λλ uses a linear type system to encode the physical constraints of optics, rejecting unrealizable programs at compile time. The compiler lowers well-typed programs to a graph-based intermediate representation, then solves a constrained embedding problem to map these graphs onto arbitrary silicon photonic switch targets while minimizing signal loss. We validate λλ on a commercial photonic switch, demonstrating correct operation for circuit switching, time-varying rotor switching and analog in-network computation. Across various hardware targets and programs, the λλ compiler scales to silicon photonic switches with over 100,000 programmable elements and handles switch programs with 128 input-output pairs. Finally, we develop a synthesizer to automatically generate λλ programs from high-level specifications, allowing users to program photonic hardware without reasoning about optical primitives.