Design and characterisation of nanostructured gradient index lenses.

Abstract

The design and characterisation of nanostructured gradient index lenses is investigated in this thesis. Nanostructured gradient index materials achieve their refractive index pro le by creating a pattern with feature sizes of =5 and smaller from two glasses with di erent refractive indices. These structures are fabricated by the stack-anddraw technology generally used for photonic crystal bres. The rigorous theoretical analysis is performed with the Fourier modal method or the nite di erence time domain algorithm. A comprehensive introduction of the Fourier modal method for one and two dimensional gratings is given. Due to the inherit periodicity of the Fourier modal method, an algorithm to calculate the transmitted eld of isolated non-periodic lamellar gratings is developed and tested experimentally with a multi layer lens grating in the microwave regime. Furthermore, the eld stitching method for the analysis of large two dimensional gratings with very small feature sizes is developed. The numerical performance is tested with a di ractive element consisting of 32 32 pixels and shown to reduce the required memory as well as the computation time by more than an order of magnitude in certain con gurations. Considerations of symmetries in the grating structure are also included in the derivation of the eld stitching method. The e ective medium theory for nanostructured gradient index materials is introduced which allows to describe nanostructured materials with the equations for standard gradient index lenses. The stack-and-draw fabrication process is described including the choice of glass types, assembly and drawing of the preforms. For the design of the required binary pattern, the simulated annealing algorithm is used in conjunction with the e ective medium theory. In order to provide experimental evidence of the simulations, two lenses were assembled from PTFE rods with a diameter of 6mm and characterised in the microwave regime at = 3 cm. It is shown that with this wavelength to feature size ratio, the nanostructured gradient index lenses can have properties nearly identical to conventional gradient index lenses. Finally, a spherical and an elliptical nanostructured microlens are characterised in the optical regime. On the elliptical microlens, phase and intensity measurements are performed and compared to simulations obtained with the Fourier modal method.