Fig. 1 (a), Photonic crystal dispersion curves calculated by 2D Plane wave expansion, several complete bandgaps are observed (semi-transparent gray shadows, e.g. PBG1 and PBG2). Blue dashed lines indicate the light light. Red dashed circle locates the two slow light band-edge states of interest (Γ2, Γ3). The pillar filling factor (ff) is 40%. (b), Sketch of the surface emitting lasing scheme at the band-edges (Γ2, Γ3). The pillar height is about 15 µm and the lattice constant range is between 32 and 40 µm. (c), Left: Side view SEM image of PhC pillar after dry etching. Top right: Top view SEM image of holes-on-pillars (HOP) device. Bottom right: Top view SEM image of holes-on-BCB (HOB) device. (d), Top panel, extraction modal Q on the Γ3 state as a function of the extractor size. Bottom panel, eigenfrequency on the Γ3 state as a function of the extractor size. The holes-on-pillars (HOP) scheme always has a larger impact on the band structure than the holes-on-BCB (HOB) scheme.

Fig. 2 Elliptical pillar photonic crystal degeneracy lifting. (a) Left, PhC dispersion of circular pillar around PBG2 calculated along k-vector direction of K-Γ-M. E_z field maps of each band-edges (Γ2 and Γ3) are shown as inserts. A schematic drawing of the lattice is inserted with circular pillar configuration. Right, lasing spectra of such circular pillar-PhC laser at a = 40 μm, the zoom region show the multimode behavior at the quasi-degenerated band-edge. (b) Left, PhC dispersion of elliptical pillars calculated along k-vector direction of K-Γ-M. Elliptical pillars are designed with x/y ratio of 0.8, and rotated with 30° angle respective to the horizontal direction. A schematic drawing of the lattice is inserted with elliptical pillar configuration. The degeneracy of the Γ2 and Γ3 band-edge states is lifted. The splitting is about Δu = 0.0224 in reduced energy, which corresponds to a broad frequency bandwidth of 168 GHz at lattice constant a = 40 μm. Right, lasing spectra of such elliptical pillar PhC lasers at a = 36 μm and a = 38 μm. For a = 36 μm, two sharp peaks were observed whose splitting energy is in good agreement with the calculated value Δu = 0.0224 between Γ2 and Γ 3 states. The multimode behavior is due to the gain bandwidth wide enough to overlap with both states. For a = 38 μm, single mode was observed as the gain bandwidth overlaps with only one of the two states (Γ3). The elliptical pillar structure has 6-fold degenerated M points, they split in two groups: a 2-fold of M points, and 4-fold of M* points.

Fig. 3 Light–current–voltage (LIV) a circular pillar type photonic-crystal laser with lattice constant a = 40 μm, with extractor scheme of Holes-on-BCB. The maximum power collected from the top of the device exceeds 31 mW.

Fig. 4 Light–current–voltage (LIV) and spectral characterizations of elliptical pillar type photonic crystal quantum cascade lasers. (a) and (b), Light–current–voltage (LIV) characteristics as a function of temperature for the two type of extractors. The maximum power collected from the top of the devices are 18.2 mW and 13.4 mW, for holes on pillars and holes on BCB extraction schemes, respectively. The maximum operating temperature for both devices is 120 K, which is the same as the standard FP ridge lasers (embedded with BCB) fabricated on the same batch with the same material. (c) and (d), Dispersion curves and lasing spectra of elliptical pillar-type photonic-crystal lasers at lattice constant a = 32 µm, with holes on pillars and holes on BCB configurations, as shown insert SEM images for (c) and (d), respectively. The intense line at u = 0.35 correspond to lasing at a M3* point.