Which-path problem for one and two particles with two degrees of freedom and a relation between transverse spatial structure and group velocity of light

Quantum mechanics, optics and indeed any wave theory exhibits the phenomenon of interference. In this thesis we present two problems investigating interference due to indistinguishable alternatives and a mostly unrelated investigation into the free space propagation speed of light pulses in particular spatial modes. In chapter 1 we introduce the basic properties of the electromagnetic field needed for the subsequent chapters. In chapter 2 we review the properties of interference using the beam splitter and the Mach-Zehnder interferometer. In particular we review what happens when one of the paths of the interferometer is marked in some way so that the particle having traversed it contains information as to which path it went down (to be followed up in chapter 3) and we review Hong-Ou-Mandel interference at a beam splitter (to be followed up in chapter 5). In chapter 3 we present the first of the interference problems. This consists of a nested Mach-Zehnder interferometer in which each of the free space propagation segments are weakly marked by mirrors vibrating at different frequencies [1]. The original experiment drew the conclusions that the photons followed disconnected paths. We partition the description of the light in the interferometer according to the number of paths it contains which-way information about and reinterpret the results reported in [1] in terms of the interference of paths spatially connected from source to detector. In chapter 4 we briefly review optical angular momentum, entanglement and spontaneous parametric down conversion. These concepts feed into chapter 5 in which we present the second of the interference problems namely Hong-Ou-Mandel interference with particles possessing two degrees of freedom. We analyse the problem in terms of exchange symmetry for both boson and fermion pairs and show that the particle statistics at a beam splitter can be controlled for suitably chosen states. We propose an experimental test of these ideas using orbital angular momentum entangled photons. In chapter 6 we look at the effect that the transverse spatial structure of the mode that a pulse of light is excited in has on its group velocity. We show that the resulting group velocity is slower than the speed of light in vacuum for plane waves and that this reduction in the group velocity is related to the spread in the wave vectors required to create the transverse spatial structure. We present experimental results of the measurement of this slowing down using Hong-Ou-Mandel interference.

The optical properties of metamaterials

This thesis studies the parametric investigation, polarisation dependence and characterization of fishnet structure at near infrared wavelengths. Detailed simulations are performed to understand the behaviour of the structure at near infrared and optical wavelengths. Simulations are performed to obtain negative refractive index of the fishnet structure formed from nanoimprint lithography (NIL) by taking into account the effect of substrate and polymethyl methacrylate (PMMA) beneath it. Two different structures have been designed and fabricated of varying dimensions using NIL and their resonant wavelength measured in the near infrared at 1.45 µm and 1.88 µm. Simulations suggest that a negative refractive index real part with the magnitude -0.24 is found at 1.53 µm and this decrease to a maximum magnitude of -0.57 at 1.9 µm. The PMMA and suppressed pillars are here responsible for the increasing material losses and limiting the value of negative refractive index. An analytical approach has been suggested to characterise fishnet structures at oblique incidence. The expressions for an absorbing medium are rewritten for an alternative definition of refractive index. The expressions are initially validated for a dielectric slab and a metal film. These results provide the possibility that this proposal may yield a general algorithm for obtaining the complex reflection and transmission coefficients for artificial structures. FDTD simulations have been extensively used in this thesis to understand the optical metamaterials and their characterization.