Soft-lithographical fabrication of three-dimensional photonic crystals in the optical regime

This dissertation describes several projects to realize low-cost and high-quality three-dimensional (3D) microfabrication using non-photolithographic techniques for layer-by-layer photonic crystals. Low-cost, efficient 3D microfabrication is a demanding technique not only for 3D photonic crystals but also for all other scientific areas, since it may create new functionalities beyond the limit of planar structures. We have developed an advanced microtransfer molding technique, called two-polymer microtransfer molding (2P-[mu]TM) that shows an extremely high yield in layer-by-layer microfabrication sufficient to produce highly layered microstructures. The use of two different photo-curable prepolymers, a filler and an adhesive, allows for fabrication of layered microstructures without thin films between layers. Second, we also had to develop an alignment technique. We studied the 1st-order diffracted moiré fringes of transparent multilayered structures comprised of irregularly deformed periodic patterns. We demonstrate the alignment method for the case of layer-by-layer microstructures using soft lithography. The alignment method yields high contrast of fringes even when the materials being aligned have very weak contrasts. The imaging method of diffracted moiré fringes is a versatile visual tool for the microfabrication of transparent deformable microstructures in layer-by-layer fashion. Third, we developed several methods to convert a polymer template to dielectric or metallic structures, for instance, metallic infiltration using electrodeposition, metallic coating using sputter deposition, dielectric infiltration using titania nano-slurry, and dielectric coating using atomic layer deposition of Titania. By several different developed techniques, high quality photonic crystals have been successfully fabricated; however, I will focus on a line of techniques to reach metallic photonic crystals in this dissertation since they are completely characterized at this moment. In addition to the attempts for photonic crystal fabrication, our non-photolithographic technique is applied for other photonic applications such as small optical waveguides whose diameter is comparable to the wavelength of guided light. By 2P-[mu]TM, we achieve low cost, high yield, high fidelity, and tailorable fabrication of small waveguides. Embedded semiconductor quantum-dots and grating couplers are used for efficient internal and external light source, respectively

A Quantum H∗(T)H^*(T)-module via Quasimap Invariants

For $X$ a smooth projective variety, the quantum cohomology ring $QH^*(X)$ is a deformation of the usual cohomology ring $H^*(X)$, where the product structure is modified to incorporate quantum corrections. These correction terms are defined using Gromov-Witten invariants. When $X$ is toric with the geometric quotient description $V /\!/ T$, the cohomology ring $H^*(V /\!/T)$ also has the structure of a quantum $H^*(T)$-module. In this paper, we give a new deformation using quasimap invariants with a light point. This defines $H^*(T)$-module structure on $H^*(X)$ through a modified version of the WDVV equations. Using the Atiyah-Bott localization theorem, we explicitly compute this structure for the Hirzebruch surface of type 2. We conjecture that this new quantum module structure is isomorphic to the natural module structure of the Batyrev ring for a semipositive toric variety