MPB Square Lattice Band Structure

This example computes the photonic band structure for a square lattice of dielectric (GaAs) rods in air using MPB (MIT Photonic Bands).

Overview

Photonic crystals with square lattices are fundamental structures for:

• Band gap engineering: Designing photonic band gaps
• Waveguide modes: Defect-based waveguides
• Slow light: Group velocity reduction
• Filters: Wavelength-selective devices

Parameters

K-Point Path

The simulation follows the standard Brillouin zone path:

• Γ (0, 0) → X (0.5, 0) → M (0.5, 0.5) → Γ (0, 0)

Code Structure

from meep import mpb

# Square lattice
geometry_lattice = mp.Lattice(size=mp.Vector3(1, 1))

# GaAs rod
GaAs = mp.Medium(epsilon=11.56)
geometry = [mp.Cylinder(r=0.2, material=GaAs)]

# K-point path: Γ → X → M → Γ
k_points = mp.interpolate(k_interp, [Gamma, X, M, Gamma])

ms = mpb.ModeSolver(
    geometry_lattice=geometry_lattice,
    geometry=geometry,
    k_points=k_points,
    resolution=32,
    num_bands=8,
)

# Compute TE and TM bands
ms.run_te()
ms.run_tm()

Results

The simulation produces:

• TE band structure: Electric field in-plane
• TM band structure: Magnetic field in-plane
• Band gaps: Frequency ranges with no propagating modes

Related Examples

• MPB Triangular Holes - Complete band gap
• MPB Tutorial - Basic MPB usage
• Holey Waveguide Bands - Photonic crystal waveguides