Figure 1

(a) Top-view SEM of a ZnO PhCS. The inset shows structural Fourier transform from the digitized SEM. Long-range periodicity is reflected in the six maxima at the positions corresponding to the perfect lattice. (b) Difference between the digitized SEM of real sample and the perfect honeycomb lattice reveals the structural disorder.Reuse & Permissions

Figure 2

(a) $k_{\parallel }$ distributions of the highest-$Q_{\mathrm{tot}}$ modes at one pixel beneath the slab-substrate interface. The thin (thick) dashed curve represents the mode found in the disorderless system ($N=24$) with (without) an artificial defect. The corresponding solid curves are representative examples of the highest-$Q_{\mathrm{tot}}$ modes in these systems with position disorder ($\delta x=10\mathrm{nm}$). The vertical line marks the substrate light-cone boundary. The inset is a schematic sketch of the simulated structure. (b) Squares and circles represent $⟨Q_{\parallel }/Q_{\perp }⟩$, averaged over 300 random realizations of $N=24$ system with and without the artificial defect, versus disorder strength $\delta x$.Reuse & Permissions

Figure 3

(a) $⟨1/Q_{\mathrm{tot}}⟩$ for the highest-$Q_{\mathrm{tot}}$ modes found numerically in PhCS depicted in the inset of Fig. 2a. The average is taken over an ensemble of 300 random realizations. The squares and triangles represent the results for $\delta x=5\mathrm{nm}$ and 15 nm, respectively. Circles correspond to the disorderless system. Dotted, solid, and dashed lines are $N^{-\alpha }$ fits with $\alpha =2.7$, 2.3, and 1.9, respectively. (b) Ensemble-averaged incident pump pulse energy at the lasing threshold, measured in the samples of $a=115\mathrm{nm}$ (squares) and $a=118\mathrm{nm}$ (triangles), versus the pattern size. The data are fitted with the power law dependence as in (a) with $\alpha =2.5$ (solid line) and 1.7 (dashed line). (c) Intensity profile of the highest-quality mode found numerically in a 2D disordered hexagonal array of air holes in the dielectric with refractive index $n=1.55$. The pattern size is $5\times 5\mu \mathrm{m}$, lattice constant $a=186\mathrm{nm}$, and the hole radius $R=65\mathrm{nm}$. The wavelength of the mode is 393 nm. It is located at the dielectric band edge, and the electric field is concentrated inside the dielectric. (d) Measured intensity distribution of the lasing mode in a ZnO PhCS with $a=115\mathrm{nm}$ and $R=0.25a$. Dashed box outlines the boundary of the $8\times 8\mu \mathrm{m}$ pattern.Reuse & Permissions

Figure 4

(a) Experimentally measured incident pump pulse energy at the lasing threshold (averaged over five to ten samples) as a function of lattice constant $a$. (b) The circles are the measured mean wavelength of lasing modes, the error bar depicts the range of lasing wavelengths. The solid curve represents the wavelength of the calculated dielectric band edge ${\lambda }_d$ in ZnO PhCS as a function of $a$. The shade of the background qualitatively describes the position and width of ZnO gain spectrum.Reuse & Permissions