Blaze's research core computes TE and TM bands for circular inclusions in positive scalar dielectrics, runs parameter sweeps, and projects Maxwell operators. Native and browser execution share a configuration format. MPB comparisons and convergence metadata provide the baseline for further work.

Start with rotations and reflections that preserve the sampled crystal. Equivalent wavevectors can then share a solve. Symmetry sectors and real-valued representations offer further reductions where the material and discretization allow them.

Independent geometry jobs currently start afresh in Blaze. MPB's standard run also resets fields, although explicit reuse is possible.^[2] Blaze already reuses fields along k-paths and accepts native warm-start inputs. The planned step is automatic reuse between configurations: correct the old subspace for the new material and check its residual. Published methods for tracking Maxwell modes as geometry changes provide a starting point.^[3]

Keep this website up-to-date with the theory, implementation reasoning, and reproducible measurements. Profile setup, FFTs, orthogonalization, allocations, and memory. Compare total runtime at equal accuracy, with configurations, hardware, and tolerances reported alongside the results.

Add polygons, composite shapes, and imported dielectric grids, with clear overlap rules and accurate material-interface sampling. Initially retain positive scalar permittivity. Tensor materials, loss, and dispersion would need separate extensions to the physical formulation.

Tune the existing block eigensolver, preconditioning, memory layout, and precision choices. Then add calculations near a chosen frequency, a capability MPB already offers. Evaluate alternative algorithms against difficult or clustered bands, with the same residual accuracy and requested band coverage.

Extend operator workflows with geometry and material derivatives. Minkov and colleagues demonstrated photonic-crystal inverse design through automatic differentiation.^[5] Blaze needs derivatives consistent with its discrete operators, including careful treatment of interfaces and degenerate modes.

Begin with equivalent examples, geometry conversion, and a scoped Python adapter. Match units, field normalization, metadata, and required exports such as HDF5. Broader Python or Scheme compatibility can follow as tested workflows expand.

Keep FFTs, material operations, preconditioning, and block algebra on the device throughout a solve. Jin and Xie report over 40× average acceleration for their 3D finite-difference solver using CuPy on an RTX 4090 D against a NumPy CPU implementation.^[6] Blaze's plane-wave solver needs its own measurements.

Extend to lossless periodic 3D crystals with vector fields, 3D FFTs, and material sampling. The scalar TE/TM split no longer applies: enforce transverse fields and handle the curl operator's null space, with a larger memory budget.

Periodic 3D geometry

Coupled vector fields

Guided-mode expansion uses the modes of an unpatterned waveguide as a reduced basis for efficient slab band calculations, combining periodicity in the plane with vertical confinement. Legume implements this for photonic crystal slabs.^[8] A similar extension could expose slab bands, fields, and radiative losses, within the method's basis and perturbative radiation approximations.