We undertake a comprehensive study of the inverse square root dependence of spatial resolution on the saturation factor in stimulated emission depletion (STED) microscopy and generalize it to account for various focal depletion patterns. We used an experimental platform featuring a high quality depletion pattern which results in operation close to the optimal optical performance. Its superior image brightness and uniform effective resolution <25 nm are evidenced by imaging both isolated and self-organized convectively assembled fluorescent beads. For relevant saturation values, the generalized square-root law is shown to predict the practical resolution with high accuracy.

Manipulation of the distribution of phonons ini a solid is important for both basic science and applications ranging from heat management to reduction of noise in electronic circuits and creating materials with superior acoustic and acousto-optical properties. This thesis explores hypersonic phononic crystals as means to achieve control over high frequency acoustic phonons. An integrated approach to fabrication, measurement and analysis of hypersonic phononic crystals with band gaps in the GHz range is presented.First, the phonon dispersion relation for one dimensional polymeric phononic crystals fabricated by coextrusion of a large number of poly(methylmethacrylate)/poly(carbonate) and poly(methylmethacrylate)/poly(ethylene terephthalate) bilayer pairs is investigated as a function of a lattice constant and composition using Brillouin light scattering and numerical simulations. This set of relatively simple multilayer structures represents an excellent platform to gain a basic understanding of phononic band gap phenomena. In addition, their in-plane phonon dispersion is used to extract information about the elastic constants and glass transition temperatures of individual nanolayers in a periodic multilayer arrangement. Next, two dimensional epoxy/air phononic crystals fabricated in a photoresist using interference lithography are studied. These structures are 2D single crystalline, enabling direction-resolved measurements of their phonon dispersion relation. with performance characteristics that can be adjusted dynamically during operation. The investigations described in this thesis demonstrate both theoretically and experimentally that 1D, 2D and 3D periodic submicron structures have complex phonon dispersion relations at GHz frequencies. As a result, these crystals can be used to manipulate the flow of random thermal phonons as well as externally generated acoustic waves resulting in novel acoustic and thermal properties.

Interference lithography (IL) holds the promise of fabricating large‐area, defect‐free 3D structures on the submicrometer scale both rapidly and cheaply. A stationary spatial variation of intensity is created by the interference of two or more beams of light. The pattern that emerges out of the intensity distribution is transferred to a light sensitive medium, such as a photoresist, and after development yields a 3D bicontinuous photoresist/air structure. Importantly, by a proper choice of beam parameters one can control the geometrical elements and volume fraction of the structures. This article provides an overview of the fabrication of 3D structures via IL (e.g., the formation of interference patterns, their dependence on beam parameters and several requirements for the photoresist) and highlights some of our recent efforts in the applications of these 3D structures in photonic crystals, phononic crystals and as microframes, and for the synthesis of highly non spherical polymer particles. Our discussion concludes with perspectives on the future directions in which this technique could be pursued.

We show how to fabricate three basic photonic crystal structures with simple cubic, fcc, and bcc translational symmetry by interference lithography. The structures are fabricable by the interference of beams launched from the same half space. The simple cubic structure is size scalable while the structure with fcc translational symmetry possesses two band gaps. Both these structures are experimentally realized.