ExamplesMeep Examples

Disc Extraction Efficiency

Compute light extraction efficiency from a dielectric disc using near-to-far field

Disc Extraction Efficiency

This example computes the extraction efficiency of dipole emitters in a dielectric disc using cylindrical coordinates and near-to-far field transformation.

Overview

Extraction efficiency is critical for:

  • LEDs: Maximizing light output
  • Single-photon sources: Quantum emitter efficiency
  • Fluorescence: Microscopy and sensing
  • Solar cells: Light trapping (in reverse)

Parameters

ParameterValueDescription
RESOLUTION_UM50Pixels per μm
WAVELENGTH_UM1.0Operating wavelength
N_DISC2.4Disc refractive index
DISC_RADIUS_UM1.2Disc radius
NUM_DIPOLES11Dipole positions

Physical Setup

  1. Dielectric disc: High-index material on substrate
  2. Dipole emitters: Er-polarized at various radial positions
  3. Cylindrical symmetry: Angular modes exp(imφ)
  4. Near-to-far transform: Computes far-field radiation pattern

The extraction efficiency is the fraction of total emitted power that escapes into the upper hemisphere.

Key Concepts

Angular Modes

For a dipole at r > 0, the fields have Fourier components:

  • Sum over m = 0, ±1, ±2, ...
  • Each m requires a separate simulation
  • Convergence when higher m contribute negligibly

LDOS Integration

Total power from LDOS:

P_total = -Re[∫ E·J* dV]

Far-Field Flux

Radiated power from Poynting vector:

P_rad = ∮ S·r̂ r² dΩ

Results

The simulation outputs:

  • Extraction efficiency: η = P_rad / P_total
  • Radiation pattern: Angular distribution
  • Per-dipole contributions: Position-dependent efficiency

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