Characterizing randomness in photonic glasses using autocorrelation functions of two-dimensional images

We have developed a simple method to quantify randomness in photonic glasses in relation to the ideal random limit, using autocorrelation functions obtained from two-dimensional images. In our case, the photonic glasses consist of randomly packed silica microspheres which serve as a model system representing isotropic random media. Conventional methods of characterizing randomness in photonic materials often entail technical complexities, such as chemical functionalization, three-dimensional rendering, and particle tracking. Our method circumvents these difficulties based on a mathematical relation that we derive between the autocorrelation function and the radial distribution function. This relation enables us to find the autocorrelation function in the ideal random limit. The autocorrelation function of experimentally fabricated photonic glasses is then obtained from images of a single cross-sectional plane and directly compared to that of the ideal limit. The comparison shows that the autocorrelation function of real structures deviates only slightly from the ideal limit. We find that the deviation can be explained in part by the microsphere polydispersity. Our general method would be useful in characterizing a large class of photonic random media, encompassing biological materials, radiative cooling coatings, and random lasing photonic glasses.