Introduction
A high-performance solver for photonic crystals, and the research that made it necessary.
What is Blaze2D
Blaze2D is a plane-wave eigensolver for two-dimensional photonic crystals, written in Rust. It computes photonic band structures, the frequencies at which light is allowed to propagate through a periodic dielectric, faster than MIT Photonic Bands (MPB) , the field’s reference solver, while matching its accuracy. Just as importantly, it exposes the full eigenvector-level data that downstream theory needs, not only the eigenfrequencies.
What it solves
A photonic crystal is a periodic arrangement of dielectric material. Its band structure tells you which frequencies of light can travel through it, and in which directions: the optical analogue of the electronic band structure of a semiconductor.
Blaze obtains the right-hand panel from the left by solving the photonic master equation, an eigenvalue problem for the magnetic field in a medium with dielectric function :
In two dimensions this separates into two scalar polarizations (TE and TM) and reduces to a Hermitian eigenproblem that Blaze solves in reciprocal space. Everything else the solver does is in service of this one equation, evaluated quickly and accurately, many thousands of times.
Why Blaze exists
Blaze was not built to win a benchmark. It was built because a master’s thesis needed it.
That thesis develops a new theoretical framework for photonic moiré crystals: what emerges when two photonic crystals are overlaid with a small relative twist. The framework turns an otherwise intractable problem into a dense sweep over thousands of local crystal configurations, and it needs the full Bloch eigenvectors at each one: band energies, group velocities, effective masses, Berry connections. No existing solver delivered both properties at once: MPB is fast and accurate but does not expose this data; the tools that do expose it are far too slow for thousands of solves.
So the solver and the theory were built together.
→ Why Blaze2D exists: photonic moiré crystals
Engineered for the hardware
The speedup is not one trick; it comes from treating the solver as a hardware problem.
Blaze runs a mixed-precision (f32/f64) LOBPCG eigensolver on a cache-aware,
memory-bandwidth-conscious architecture: memory layouts, FFT scheduling, and the
eigensolver inner loop are all tuned to the cache and bandwidth limits of the target
machine, and entire solve jobs are parallelized rather than individual operations. The
result is a ~95% reduction in memory footprint and roughly a 3× speedup over MPB,
with reference accuracy preserved.
This is the part worth reading closely → Architecture · Technical Report
Where Blaze is today, and where it’s going
Blaze is a production-quality CPU solver, cross-validated against an independent finite-difference (FDFD) solver that is itself checked against MPB. You can run it without installing anything: the engine compiles to WebAssembly, so the Examples are live and runnable in the browser, and the Workbench computes band structures and parameter sweeps interactively: serious exploration with no code and no install.
The goal is for Blaze to become a faithful drop-in replacement for MPB in two dimensions first, and a strict superset wherever operator-level data extraction reaches physics MPB cannot. Several optimizations remain on the table, with symmetry reduction, parameter warm-starts across sweeps, and further memory-layout improvements among them.
See the Roadmap and Optimization Potential for what comes next.