Photon Design’s FDTD software OmniSim can be used to model Photonic Crystals lasers.
- GUI for Photonic Crystal structures
- Band Solver
- FDTD
- Active-FDTD for modeling gain
- Import gain spectra from HAROLD
OmniSim’s Active FDTD
OmniSim can run Active FDTD simulations to simulate gain.
There are two gain models to choose from:
The Static Gain Model (Simple)- Saturable gain model
- Gain as a function of intensity
- Simple to use
- Gain as a function of carrier density
- Uses gain curves from data or imported from Harold
PCSEL - Static Gain Model
In this example we will use the Static Gain model to simulate a photonic crystal surface emitting laser (PCSEL) and reproduce the results given in [1].
A laser cavity is created by introducing a defect in a 2D photonic crystal of air holes in a thin membrane of active InP material.
The photonic crystal has a lattice constant of 365 nm and a hole diameter of 175 nm; the InP membrane is 280nm thick and surrounded by air on both sides.
[1] W. H. P. Pernice, F. P. Payne and D. F. G. Gallagher, J. of Light. Tech., 25, 9, pp. 2306-2314 (2007)
First, the resonant frequency is determined using a standard FDTD calculation without including gain. The cavity is excited by a 1uW pulse, centered on 1.25um wavelength, then results are measured from T=50fs.
Left: Flux in the cavity shows the resonant wavelength is 1.248um.
Right: Intensity vs Time in the cavity shows that the light decays exponentially, as expected in absence of gain.
Next, to prepare for an Active-FDTD simulation, an active material is defined using the parameters below in the Material Database.
Next, to prepare for an Active-FDTD simulation, an active material is defined using the parameters below in the Material Database.
The above gain function is defined as a Lorentzian curve centred on 1.24um, with a width of 500nm and an amplitude of 10000 cm-1. “GAIN_EPS” defines the gain saturation coefficient of 2.1e-15 cm3.
The Active-FDTD simulation will now include the saturable gain in the time-domain simulation.
Left: Hy field of resonant mode in the cavity.
Right: Intensity vs Time in the cavity (log scale). The saturation of the power is quite clear and occurs from 500fs onwards.
Flux vs Wavelength of the laser mode shows a single peak at 1.246um with a very narrow linewidth of the order of 1nm.
Left: Linear scale
Right: Log scale
A sensor is placed above the InP membrane to calculate the farfield of the radiation emitted at the resonant wavelength.
The farfield shows that the single cavity does not provide a highly directional beam.
The output beam has a horizontal semi-angle of 55 degrees and a vertical semi-angle of 27 degrees.
Now, consider a PCSEL in the same membrane that consists of an array of seven cavities.
The dominant peak for the 7-cavity PCSEL is located at 1.231um. This resonance has a linewidth of the order of 0.3nm.
The farfield (right) of this laser mode shows a much narrower profile than for the single cavity.
Horizontal semi-angle: 22 degrees. Vertical semi-angle: 12 degrees.
PCSEL - Dynamic Gain Model
Instead of using a material with static gain definition, OmniSim Active FDTD also has a Dynamic Gain Model.
- User provides gain curves, either from experiment or simulated using Harold (or other laser simulator
- Rate equation model of carriers including spontaneous recombination, stimulated recombination, injection current.
- Wide-Band Gain model, with automatic fitting to a set of gain curves (g(l) at a set of different carrier densities).
- Convergence Acceleration – Usually spontaneous lifetime is too long to model in FDTD. Convergence Acceleration converges to the steady state more quickly.
HAROLD can generate an effective material model for OMNISIM’s Active-FDTD Calculation
