blaze2d 6.0.0

BLAZE - Band-structure LOBPCG Accelerated Zone Eigensolver for 2D Photonic Crystals

BLAZE - Band-structure LOBPCG Accelerated Zone Eigensolver

High-performance 2D photonic crystal band structure solver with Python bindings. Also supports Envelope Approximation (EA) eigenproblems for moiré lattice research.

Installation

pip install blaze2d

Quick Start

Maxwell Mode (Photonic Crystals)

from blaze import BulkDriver

driver = BulkDriver("config.toml")
print(f"Running {driver.job_count} jobs with {driver.solver_type} solver")

# Stream results as they complete
for result in driver.run_streaming():
    bands = result['bands']           # [k_index][band_index] frequencies
    sv = result['sweep_values']       # Current parameter values
    print(f"Job {result['job_index']}: r={sv.get('atom0.radius')}, bands at Γ: {bands[0][:4]}")

# Or collect all results
results, stats = driver.run_collect()
print(f"Completed in {stats['total_time_secs']:.2f}s")

EA Mode (Envelope Approximation)

from blaze import BulkDriver
import numpy as np

driver = BulkDriver("ea_config.toml")

for result in driver.run_streaming():
    eigenvalues = result['eigenvalues']
    eigenvectors = result['eigenvectors']  # List of (N,2) arrays [re, im]
    nx, ny = result['grid_dims']
    
    # Reshape eigenvector to 2D field
    psi = np.array(eigenvectors[0])
    psi_2d = (psi[:, 0] + 1j * psi[:, 1]).reshape((nx, ny))

Configuration Reference

TOML configuration with ordered [[sweeps]] for parameter variations.

Complete Maxwell Example

# Bulk sweep configuration
[bulk]
threads = 8                    # Number of threads (0 = all cores)
verbose = true                 # Print progress
dry_run = false                # Count jobs without running
skip_final_gamma = false       # Copy initial Γ instead of recalculating
disable_band_tracking = false  # Disable eigenvector-based band reordering

[solver]
type = "maxwell"               # "maxwell" or "ea"

# Base values for sweepable parameters
[defaults]
eps_bg = 12.0                  # Background dielectric
resolution = 32                # Grid resolution
polarization = "TM"            # "TM" or "TE"
lattice_type = "square"        # Lattice type

# Geometry definition
[geometry]
eps_bg = 12.0

[geometry.lattice]
type = "square"                # square, rectangular, triangular, hexagonal, oblique
a = 1.0                        # Primary lattice constant
# b = 1.5                      # Required for rectangular/oblique
# angle = 60.0                 # Required for oblique (degrees)

[[geometry.atoms]]
pos = [0.5, 0.5]               # Fractional coordinates [0, 1)
radius = 0.2                   # In units of lattice constant
eps_inside = 1.0               # Dielectric inside atom

# Computational grid
[grid]
nx = 32
ny = 32
lx = 1.0                       # Supercell size
ly = 1.0

# K-path specification
[path]
preset = "square"              # square, rectangular, triangular, hexagonal
segments_per_leg = 10          # Points per segment (default: 8)

# Alternative: explicit k-path (use INSTEAD of preset)
# [path]
# k_path = [[0.0, 0.0], [0.5, 0.0], [0.5, 0.5], [0.0, 0.0]]

# Eigensolver settings
[eigensolver]
n_bands = 8                    # Number of bands
tol = 1e-4                     # Convergence tolerance
max_iter = 200                 # Maximum iterations
block_size = 0                 # LOBPCG block size (0 = auto)
# record_diagnostics = false   # Per-iteration diagnostics

# Dielectric smoothing (MPB-style)
[dielectric.smoothing]
mesh_size = 3                  # Subgrid mesh (1 = disabled, default: 3)
method = "analytic"            # "analytic" (default) or "subgrid"
# interface_tolerance = 1e-6   # Interface detection tolerance

# Parameter sweeps (outer to inner)
[[sweeps]]
parameter = "atom0.radius"
min = 0.15
max = 0.35
step = 0.05

[[sweeps]]
parameter = "polarization"
values = ["TM", "TE"]

# Output configuration
[output]
mode = "full"                  # "full" (one CSV per job) or "selective"
directory = "./results"        # Output directory for full mode
prefix = "job"                 # Filename prefix for full mode
# filename = "results.csv"     # Filename for selective mode
# io_mode = "sync"             # "sync", "batch", or "stream"

# For selective mode
[output.selective]
k_indices = [0, 10, 15]        # K-point indices (0-based)
k_labels = ["Gamma", "X", "M"] # Or use high-symmetry labels
bands = [1, 2, 3, 4]           # Band indices (1-based)

EA Example

[bulk]
threads = 4

[solver]
type = "ea"

[grid]
nx = 64
ny = 64
lx = 10.0
ly = 10.0

[ea]
potential = "data/potential.bin"
mass_inv = "data/mass_inv.bin"
eta = 0.1
domain_size = [10.0, 10.0]
periodic = true

[eigensolver]
n_bands = 12
tol = 1e-4
max_iter = 500

[output]
mode = "full"
directory = "./ea_output"

API Reference

BulkDriver

driver = BulkDriver(config_path: str, threads: int = 0)

Property	Description
job_count	Number of jobs to execute
solver_type	"maxwell" or "ea"

Method	Description
run_streaming()	Iterator yielding results as computed
run_streaming_filtered(k_indices, band_indices)	Filtered streaming (Maxwell only)
run_collect()	Returns (results_list, stats_dict)
dry_run()	Preview job count without executing

Result Dictionary

Common fields:

Key	Type	Description
job_index	int	Job number (completion order)
result_type	str	"maxwell", "ea", or "ea_hamiltonian"
params	dict	Full configuration snapshot
sweep_values	dict	Current sweep parameter values
sweep_order	str	Parseable string "param1=val1|param2=val2"
num_bands	int	Number of bands computed

Maxwell fields:

Key	Type	Description
k_path	list	K-points as (kx, ky) tuples (fractional coordinates)
distances	list	Cumulative path distance (for x-axis plotting)
bands	list	2D array [k_index][band_index] (ω/2π normalized)
num_k_points	int	Number of k-points

EA fields:

Key	Type	Description
eigenvalues	list	Sorted eigenvalues
eigenvectors	list	Each as (N, 2) array [re, im]
grid_dims	list	[nx, ny] for reshaping
converged	bool	Solver convergence status
n_iterations	int	Number of iterations used
num_eigenvalues	int	Number of eigenvalues

EA Hamiltonian fields (result_type = "ea_hamiltonian"):

Key	Type	Description
k0	tuple	Carrier momentum (kx, ky)
registry	tuple	Registry point (Rx, Ry)
n_retained	int	Number of retained bands
n_remote	int	Number of remote bands
eigenvalues	list	All n_total eigenvalues
velocity_matrices	dict	{"x": [...], "y": [...]} complex (re, im) tuples
w_matrices	dict	{"xx": [...], "xy": [...], ...} second derivatives
mass_tensor_inv	dict	{"xx": [...], ...} Löwdin-corrected inverse mass
r_derivative_matrices	dict	Optional {"x": [...], "y": [...]}
metric_derivative_matrices	dict	Optional {"x": [...], "y": [...]} for ∂B/∂R
berry_connection_matrices	dict	Optional {"x": [...], "y": [...]} retained-space Berry blocks
born_huang	list	Optional Born–Huang potential matrix; for TM this is the generalized metric-compatible geometric potential
slow_coefficient_potential	list	Optional TE-only slow-coefficient matrix U_sc
overlap_matrix	list	Optional overlap matrix
polarization	str	"TE" or "TM"

EAExtractor (Direct Python API)

from blaze import EAExtractor

result = EAExtractor.extract(
    lattice_vectors=[[1.0, 0.0], [0.0, 1.0]],
    atoms=[{"pos": [0.0, 0.0], "radius": 0.2, "eps_inside": 1.0}],
    eps_bg=12.0,
    k0=[0.0, 0.0],
    polarization="TE",
    resolution=32,
    n_retained=4,
    n_remote=8,
)

eigenvalues = result["eigenvalues"]
mass_inv_xx = result["mass_tensor_inv_xx"]  # list of (re, im) tuples

Stats Dictionary (from run_collect)

Key	Type	Description
total_jobs	int	Total jobs executed
total_time_secs	float	Wall-clock time
jobs_per_second	float	Throughput

Sweep Parameters

Parameter	Format	Description
eps_bg	range	Background dielectric constant
resolution	range	Grid resolution (nx=ny)
polarization	values	["TM", "TE"]
lattice_type	values	["square", "rectangular", "triangular", "hexagonal"]
atomN.radius	range	Atom N radius (N = 0, 1, 2, ...)
atomN.pos_x	range	Atom N x-position
atomN.pos_y	range	Atom N y-position
atomN.eps_inside	range	Atom N dielectric

Range format: { min = 0.1, max = 0.5, step = 0.1 }

Values format: ["value1", "value2"]

K-Path Presets

Preset	Path	Description
square	Γ → X → M → Γ	Square lattice
rectangular	Γ → X → S → Y → Γ	Rectangular lattice
triangular	Γ → M → K → Γ	Triangular lattice
hexagonal	Γ → M → K → Γ	Hexagonal lattice (same as triangular)

Band Data Interpretation

Frequencies are normalized: ω_norm = ωa/(2πc)

Convert to physical frequency:

a = 500e-9  # lattice constant in meters
c = 3e8     # speed of light
f_Hz = omega_norm * c / a

Plotting Example

import matplotlib.pyplot as plt
from blaze import BulkDriver

driver = BulkDriver("sweep.toml")

for result in driver.run_streaming():
    distances = result['distances']
    for band_idx in range(result['num_bands']):
        band = [result['bands'][k][band_idx] for k in range(result['num_k_points'])]
        plt.plot(distances, band)
    plt.xlabel('k-path')
    plt.ylabel('ω (normalized)')
    plt.title(f"Job {result['job_index']}")
    plt.show()

Filtered Streaming

For large sweeps, use server-side filtering to reduce memory:

# Stream only high-symmetry points and first 4 bands
for result in driver.run_streaming_filtered(
    k_indices=[0, 10, 15],      # Γ, X, M (0-based)
    band_indices=[0, 1, 2, 3]   # First 4 bands (0-based)
):
    assert result['num_k_points'] == 3
    assert result['num_bands'] == 4

Note: Filtering only applies to Maxwell results. EA results pass through unchanged.

EA Input Data Format

EA mode requires binary input files (raw f64, little-endian, row-major):

• Potential: Nx × Ny values
• Mass inverse: Nx × Ny × 4 values [m_xx, m_xy, m_yx, m_yy]
• Group velocity (optional): Nx × Ny × 2 values [vg_x, vg_y]

import numpy as np

nx, ny = 64, 64
Lx, Ly = 10.0, 10.0
X, Y = np.meshgrid(np.linspace(0, Lx, nx), np.linspace(0, Ly, ny))

V = 0.1 * (np.cos(2*np.pi*X/Lx) + np.cos(2*np.pi*Y/Ly))
V.astype(np.float64).tofile('potential.bin')

License

MIT