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
| Parameter | Value | Description |
|---|---|---|
RESOLUTION_UM | 50 | Pixels per μm |
WAVELENGTH_UM | 1.0 | Operating wavelength |
N_DISC | 2.4 | Disc refractive index |
DISC_RADIUS_UM | 1.2 | Disc radius |
NUM_DIPOLES | 11 | Dipole positions |
Physical Setup
- Dielectric disc: High-index material on substrate
- Dipole emitters: Er-polarized at various radial positions
- Cylindrical symmetry: Angular modes exp(imφ)
- 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 dΩResults
The simulation outputs:
- Extraction efficiency: η = P_rad / P_total
- Radiation pattern: Angular distribution
- Per-dipole contributions: Position-dependent efficiency
Related Examples
- Antenna Radiation - Far-field patterns
- Metal Cavity LDOS - LDOS calculations
- Zone Plate - Near-to-far transforms