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.