Localized surface plasmon resonance of dielectrically-coated gold nanoparticle arrays

In this thesis, I study the localized surface plasmon resonance phenomenon in dielectrically coated, closely-spaced gold nanoparticles. I examine the effect of a dielectric coating (that models the sensing of a biomolecular analyte layer) on the optical absorption of these particles. The extinction spectra and the electric field around the particles are calculated. The particles are chosen to be either spheres or hemispheres to be representative of solution phase (3D) or surface (2D) experiments. Calculations are based on the Discrete Dipole Approximation method. In particular, I study the effect of a dielectric coating on the localized surface plasmon spectra around clusters of coated gold nanohemispheres. Based on this study, I propose a new sensing mechanism for detecting biomolecules attached onto a linear array of closely-spaced gold nanohemispheres immobilized on a waveguide surface

State transfer based on classical nonseparability

We present a state transfer protocol that is mathematically equivalent to quantum teleportation, but uses classical nonseparability instead of quantum entanglement. In our implementation we take advantage of nonseparability among three parties: orbital angular momentum (OAM), polarization, and the radial degrees of freedom of a beam of light. We demonstrate the transfer of arbitrary OAM states, in the subspace spanned by any two OAM states, to the polarization of the same beam

Wigner distribution of twisted photons

We present the first experimental characterization of the azimuthal Wigner distribution of a photon. Our protocol fully characterizes the transverse structure of a photon in conjugate bases of orbital angular momentum (OAM) and azimuthal angle (ANG). We provide a test of our protocol by characterizing pure superpositions and incoherent mixtures of OAM modes in a seven-dimensional space. The time required for performing measurements in our scheme scales only linearly with the dimension size of the state under investigation. This time scaling makes our technique suitable for quantum information applications involving a large number of OAM states

Hanbury Brown and Twiss Interferometry with Twisted Light

The rich physics exhibited by random optical wave fields permitted Hanbury Brown and Twiss to unveil fundamental aspects of light. Furthermore, it has been recognized that optical vortices are ubiquitous in random light and that the phase distribution around these optical singularities inprints a spectrum of orbital angular momentum onto a light field. We demonstrate that random fluctuations of light give rise to the formation of correlations in the orbital angular momentum components and angular positions of pseudothermal light. The presence of these correlations is manisfested through distinct interference structures in the orbital angular momentum-mode distribution of random light. These novel forms of interference correspond to the azimuthal analog of the Hanbury Brown and Twiss effect. This family of effects can be of fundamental importance in applications where entanglement is not required and where correlations in angular position and orbital angular momentum suffice. We also suggest that the azimuthal Hanbury Brown and Twiss effect can be useful in the exploration of novel phenomena in other branches of physics and astrophysics.Comment: Science Advance

Direct measurement of the quantum density matrix in the basis of azimuthal angle

We theoretically propose and experimentally demonstrate a method for directly measuring the density matrix of an unknown quantum system in the basis of azimuthal angle. We apply our method for characterizing 7-dimensional pure and mixed superpositions of orbital-angular-momentum modes

Compressive direct measurement of the quantum wave function

The direct measurement of a complex wave function has been recently realized by using weak values. In this Letter, we introduce a method that exploits sparsity for the compressive measurement of the transverse spatial wave function of photons. The procedure involves weak measurements of random projection operators in the spatial domain followed by postselection in the momentum basis. Using this method, we experimentally measure a 192-dimensional state with a fidelity of 90% using only 25 percent of the total required measurements. Furthermore, we demonstrate the measurement of a 19200-dimensional state, a task that would require an unfeasibly large acquiring time with the standard direct measurement technique. © 2014 American Physical Society

Sorting photons by radial quantum number

The Laguerre-Gaussian (LG) modes constitute a complete basis set for representing the transverse structure of a {paraxial} photon field in free space. Earlier workers have shown how to construct a device for sorting a photon according to its azimuthal LG mode index, which describes the orbital angular momentum (OAM) carried by the field. In this paper we propose and demonstrate a mode sorter based on the fractional Fourier transform (FRFT) to efficiently decompose the optical field according to its radial profile. We experimentally characterize the performance of our implementation by separating individual radial modes as well as superposition states. The reported scheme can, in principle, achieve unit efficiency and thus can be suitable for applications that involve quantum states of light. This approach can be readily combined with existing OAM mode sorters to provide a complete characterization of the transverse profile of the optical field

Measurement of the radial mode spectrum of photons through a phase-retrieval method

We propose and demonstrate a simple and easy-to-implement projective-measurement protocol to determine the radial index 'p' of a Laguerre-Gaussian (LGlp) mode. Our method entails converting any specified high-order LG0p mode into a near-Gaussian distribution that matches the fundamental mode of a single-mode fiber (SMF) through the use of two phase-screens (unitary transformations) obtained by applying a phase-retrieval algorithm. The unitary transformations preserve the orthogonality of modes and guarantee that our protocol can, in principle, be free of crosstalk. We measure the coupling efficiency of the transformed radial modes to the SMF for different pairs of phase-screens. Because of the universality of phase-retrieval methods, we believe that our protocol provides an efficient way of fully characterizing the radial spatial profile of an optical field