Their paper "Large area photonic crystal quantum cascade laser with 5 W surface-emitting power” published in the Optics Express journal explains how they improved their buried heterostructure and buried grating technique through several design tweaks, notably by optimizing current injection using a grid-like overlay electrode.
The large-area PhC-QCL consists of an array of square pillars (over 500 periods in each in-plane dimension), comprising a 2.6μm-thick active region based on a strain-balanced InGaAs/AlInAs structure. One peculiarity of the design is that the top-view shape of each PhC pillar is a square with a missing corner, which the authors explain, creates an asymmetry that enhances the surface power extraction. The empty space of the PhC layer is filled with InP:Fe building the PhC layer with an index contrast between 3.08 (InP) and 3.35 (InGaAs/AlInAs). After growing an InP:Si cladding layer on top, the laser cavity is defined by wet-etching the cladding layer into 1.5x1.5mm square mesas, with SiNx deposited on the boundaries of the mesa to create absorbing boundaries.