Optimization of structural parameters of colloidal photonic crystals for wide pseudo-bandgaps

The stopband characteristics of colloidal photonic crystals (PhCs) with a non-close-packed arrangement have not been fully analyzed and reported in the literature for deducing the optimum values of the dielectric constant and packing fraction of the colloids suitable for applications. We study these aspects here specifically in the Γ-$L$ and Γ-$X$ directions which are the most accessible directions in the experimental studies on self-assembled crystals. It is observed that in both these directions, the packing fraction that gives the maximum and minimum stopband widths will decrease with increase in the dielectric constant of the colloidal spheres relative to that of the background material. In the Γ-$L$ direction, the width of the stopband approaches zero twice while varying the packing fraction of PhCs with large values of relative dielectric constant. The PhC with a relative dielectric constant of 4 will possess a comparatively wide pseudo bandgap in both Γ-$L$ and Γ-$X$ directions at its optimum packing fraction. The influence of the packing fraction on the stopband characteristics of finite thickness PhCs is also studied by calculating the reflection spectrum. Optimizing the packing fraction is crucial for further applications. As an example, the effect of the packing fraction on the group velocity and thus on the emission enhancement for the modes near the first order band edge in active PhCs is discussed in order to highlight its relevance in designing devices based on optical amplification, low-threshold band edge lasing and non-linear optical effects. (paper)