Multifractal Photonic Membranes for Random Lasing Devices

Random lasers are at the center of an intense research activity due to their ease of fabrication and robustness combined with small-size (micron-scale) of the order of the lasing wavelength as well as their unique characteristics that include low-spatial coherence, lack of directionality, and bio-compatibility. In particular, non-resonant random laser devices rely on uncorrelated random fluctuations of the dielectric environment that give rise to traditional photon diffusion. On the other hand, anomalous light transport phenomena with significantly slower dynamics, or sub-diffusive transport, occur in engineered random media with correlated disorder, providing opportunities to further enhance optical amplification and reduce device footprints. In this talk, we present our work on the design and fabrication of active photonic membranes with multifractal structural correlations and we characterize their optical emission properties using leaky-mode and photoluminescence spectroscopy.<br/>Photonic multifractals are heterogeneous optical media with complex spatial fluctuations at multiple length scales characterized by a rich spectrum of local scaling exponents, i.e., a multifractal spectrum. Differently from well-known fractal structures, which possess only one global scaling quantified by a single fractal dimension, multifractals feature a continuous distribution of generalized fractal dimensions and can be considered as “intertwined sets" of self-similar structures. While the optical properties of fractal structures are well-understood, photon transport and light emission in multifractals remain fundamentally open problems. Here, we discuss photonic structures with tailored multi-scale correlations generated by iterative and multiplicative cascades of random fields. Localization and transport properties are explored and optimized using rigorous multi-particle Mie theory in combination with efficient tight-binding models. Based on this approach, using electron beam lithography and high-quality deep reactive ion etching, we demonstrate multifractal nano-hole arrays in both passive (a-Si:H, Si₃N₄) and active (ZnO) photonic membrane geometries. We report on the characterization of the optical and structural properties of each membrane structure with variable angle spectroscopic ellipsometry (VASE), photoluminescence spectroscopy, x-ray diffraction measurements, scanning electron microscope imaging(SEM) and atomic force microscopy.