Photonic Crystal VCSEL

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

A 3D model of the VCSEL is shown  here in the FDTD Solutions layout editor. The 2D triangular lattice PC cavity with emission opening, as created by the simulation object library, is shown etched into the top mirror to a depth of 2 microns.  Analysis of the modal structure supported by the combined photonic crystal/DBR cavity is conducted through excitation via a broadband, dipole source located within the laser cavity.

3D model of photonic crystal enhanced VCSEL drawn in FDTD Solutions
Three dimensional FDTD Solutions model of a photonic crystal enhanced VCSEL. A point dipole source is used to excite the device.

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

By conducting an FFT-based analysis of the cavity time response, the resonant frequeny of the cavity can be obtained.  After determining the resonant frequency of the VCSEL cavity, the mode profiles are calculated using apodized frequency domain monitors which are configured to extract the CW response of the VCSEL device at the resonant frequency of interest.

Cross-sectional refractive index distribution of VCSEL
A vertical cross-sectional view of the refractive index profile through the VCSEL structure.
Cross-section of intensity profile of PC-VCSEL cavity mode
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.

Lateral index and frequency profile measurement monitors can be used to measure the refractive index profile in the lateral plane, and the corresponding spatial intensity distribution as confined by the photonic crystal structure.

Planar refractive index distribution of PC-VCSEL
A planar view of the refractive index of the photonic crystal cavity etched into the surface of the VCSEL.
pc vcselmode xyzoom60
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.

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

Using the built-in fully vectorial near-to-far field transformation functions in FDTD Solutions, the near field just above the top surface of the VCSEL can be converted into a far field radiation profile.  The polar plot below shows the multi-lobed far field structure introduced by the photonic crystal patterning, and the relative intensity of those lobes and their propagation angle in the far field.

Farfield intensity distribution for PC-VCSEL cavity mode (plot scale in dB)
Most of the light emanates from the VCSEL at normal incidence within a cone of  approximately 5 degrees FWHM.  The peak intensity of the other lobes is ~-20dB relative to the main lobe.