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CST – Computer Simulation Technology

Simulation of Photonic Crystal Cavities

This article demonstrates how properties of the resonant modes of photonic crystal (PhC) point defect cavities are obtained from transient solver simulations using CST MICROWAVE STUDIO® (CST MWS). In this example a single point defect in a triangular lattice of air holes in a high refractive index slab is used. Properties of particular interest are: the resonance frequency, intrinsic Q factor and field distribution of the resonant modes. The cavity is excited using discrete ports, and the spectral features are recorded with point probes. The Q factor is determined from the energy decay rate and using auto regressive (AR) filtering. 2D and 3D field monitors record the field distributions.

As shown in Figure 1, the point defect is surrounded by eight hexagonal layers of air holes arranged in a triangular lattice geometry, with a lattice constant a = 410 nm and hole radius r = 0.35a. The innermost holes have a reduced radius of r1 = 0.26a, and have been shifted outward to tangentially match the outer lattice. The slab is a dielectric material with refractive index n = 3.5 and thickness d = 220 nm....

Figure 1: Left: Geometry of the single point defect in a triangular lattice of air holes and the boundary conditions. Right: Detail of the cavity geometry with reduced innermost holes and the discrete port used for excitation

The cavity is excited by a discrete current port at its center (excitation frequency range 200 - 210 THz). The number of frequency samples is set to 10001 and the simulation is aborted after simulating 10 pulse widths. The boundary conditions are open in all directions. The simulation volume is reduced by one half by introducing a magnetic symmetry plane at the center of the slab plane (TE polarization). The choice of the other two symmetry planes depends on the expected symmetry properties of the resonator mode. The total simulation volume comprises 600.000 mesh cells. To record the field spectrum, field probes are positioned within the cavity where the field is expected to have its maximum values.

This structure is highly resonant and hence the energy decays very slowly (left hand part of Figure 2). To avoid an excessive computation time the simulation is aborted prematurely after simulating the equivalent of 10 excitation pulse width. The resulting probe spectrum is then AR filtered to eliminate truncation errors from the Fourier transform of the signal (right hand part of Figure 2). Using the full width half maximum the quality factor of this cavity is 2.1 x 104 and the resonance frequency is located at 204.51 THz.

Figure 2: Left: Energy decay of a PhC cavity simulation with Q = 21,000. Right: H-field probe spectrum before and after AR filtering

The mode field pattern is best recorded using either time or frequency field monitors, which give the same result (see Figure 3). The frequency monitor needs to be set exactly at the resonance frequency, but this is usually not known before the simulation. Hence this method does require two simulation runs, but produces very accurate phase information. The time monitor is set to record the field starting at a time when the source is switched off and the non-resonant effects have vanished.

Figure 3: Magnetic field distribution of the PhC defect dipole mode at the center slab plane recorded using a frequency monitor tuned to the resonant frequency (left) or a time monitor after the excitation pulse (right). Both methods yield similar results

This article showed how PhC cavities with high Q factors can be excited and evaluated using CST MWS. The Q factor and resonance frequency are obtained from AR filtered probe spectra, while the resonant mode field distribution can be recorded either by time or frequency field monitors.

Courtesy of: Hamburg University of Technology (TUHH) Institute for Optical and Electronic Materials

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