Photonic Crystal VCSEL simulations using FDTD Solutions

In order for vertical-cavity surface-emitting lasers (VCSELs) to be used in high performance optical communication systems, typically high power, stable, single mode operation is required. Recently, such robust lateral mode control has been demonstrated using two-dimensional photonic crystal (2D PC) patterns etched approximately halfway into the top DBR of the VCSEL.

Here we consider a novel PC-VCSEL design described by Yakouchi et al., (Appl. Phys. Lett., Vol. 82, (2003) p.3608) and calculate the mode profile and farfield radiation pattern for the device.

Step 1. Create the FDTD Solutions model of PC-VCSEL

3D model of photonic crystal enhanced VCSEL drawn in FDTD Solutions.

A 3D model of the VCSEL is shown  here in the FDTD Solutions layout editor with the high (low) index material of the DBR mirrors drawn as blue (green) and the active layer as red. The 2D triangular lattice PC is shown etched into the top mirror to a depth of 2 microns. • The simulation region (orange) is reduced by a factor 4 using symmetry to approximately 10x10x9 microns . • A point dipole source, (not shown) is used to excite the device. • Monitors, shown in yellow, are used to determine the desired near-field profiles and provide the data necessary to calculate the farfield radiation pattern for the VCSEL.

Step 2. Calculate the modal profiles of PC-VCSEL in 3D

After determining the resonant frequency of the VCSEL cavity, the mode profiles are calculated using apodized frequency domain monitors.

The left plot shows a cross-sectional view of the refractive index profile through the VCSEL, while the right plot shows the corresponding mode intensity profile. The DBR mirrors create a standing wave like profile in the z direction while the photonic crystal provides confinement in the lateral direction.

Cross-sectional refractive index distribution of VCSEL

Cross-section of intensity profile of PC-VCSEL cavity mode

Here the left plot shows a planar view of the refractive index of the photonic crystal cavity, and the right plot shows the near field modal intensity at the top (exit) surface of the DBR mirror. The intricate intensity distribution in the near field is due to the photonic crystal patterning.

Planar refractive index distribution of PC-VCSEL

Planar intensity profile at surface of PC-VCSEL

Step 3. Determine the farfield radiation pattern of the PC-VCSEL

Farfield intensity distribution for PC-VCSEL cavity mode (plot scale in dB).

Using the built-in EM toolbox functions in FDTD Solutions to post-process the nearfield data shown above, the farfield radiation pattern for the PC-VCSEL may easily be determined. • Most of the light emanates at normal incidence within a cone of  approximately 5 degrees FWHM. • One can see a small fraction of the light is diffracted in symmetric directions at an angle approximately 30 degrees from normal due to the photonic crystal pattern used. The peak intensity in these directions is only ~-20dB.

Step 4. Examine the effect of the photonic crystal pattern on the Q-factor of VCSEL cavity

Time signal showing decay of PC VCSEL cavity mode. The linear slope of the amplitude (plot on a logscale) determines the Q-factor.

The time domain data provided by FDTD Solutions allows for direct calculation of the decay of the electromagnetic fields  inside the resonator cavity as plotted left on a logarithmic scale. From this data, therefore, the Q-factor of the PC-VCSEL may be determined.   • The Q-factor is found to be ~20000 • By performing a similar calculation with no photonic crystal pattern, the Q-factor for the unpatterned resonator is ~80000 indicating that, in this case, the photonic crystal pattern reduces the resonator Q by a factor of 4.

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