Tanya Malhotra

Basis-neutral Hilbert-space analyzers

Interferometry is one of the central organizing principles of optics. Key to interferometry is the concept of optical delay, which facilitates spectral analysis in terms of time-harmonics. In contrast, when analyzing a beam in a Hilbert space spanned by spatial modes – a critical task for spatial-mode multiplexing and quantum communication – basis-specific principles are invoked that are altogether distinct from that of ‘delay’. Here, we extend the traditional concept of temporal delay to the spatial domain, thereby enabling the analysis of a beam in an arbitrary spatial-mode basis – exemplified using Hermite-Gaussian and radial Laguerre-Gaussian modes. Such generalized delays correspond to optical implementations of fractional transforms; for example, the fractional Hankel transform is the generalized delay associated with the space of Laguerre-Gaussian modes, and an interferometer incorporating such a ‘delay’ obtains modal weights in the associated Hilbert space. By implementing an inherently stable, reconfigurable spatial-light-modulator-based polarization-interferometer, we have constructed a ‘Hilbert-space analyzer’ capable of projecting optical beams onto any modal basis.

Quantum and classical optics–emerging links

Quantum optics and classical optics are linked in ways that are becoming apparent as a result of numerous recent detailed examinations of the relationships that elementary notions of optics have with each other. These elementary notions include interference, polarization, coherence, complementarity and entanglement. All of them are present in both quantum and classical optics. They have historic origins, and at least partly for this reason not all of them have quantitative definitions that are universally accepted. This makes further investigation into their engagement in optics very desirable. We pay particular attention to effects that arise from the mere co-existence of separately identifiable and readily available vector spaces. Exploitation of these vector-space relationships are shown to have unfamiliar theoretical implications and new options for observation. It is our goal to bring emerging quantum–classical links into wider view and to indicate directions in which forthcoming and future work will promote discussion and lead to unified understanding.

Quasinormal mode theory and design of on-chip single photon emitters in photonic crystal coupled-cavity waveguides

Using a quasinormal mode (QNM) theory for open cavity systems, we present detailed calculations and designs of a photonic crystal nanocavity (PCN) side-coupled to a photonic crystal waveguide (PCW) for on-chip single photon source applications. We investigate various cavity-waveguide geometries using an L3 PCN coupled to a W1 PCW, obtaining the quality factors, effective mode volumes, and single photon Purcell factors of the complete loaded cavity-waveguide system as a function of spatial separation between the two. We also show that the quality factor does not monotonically increase with increasing separation between the PCN and PCW, and we identify a particular hole/defect which acts as the key structural parameter in the cavity-waveguide coupling.

Measuring Geometric Phase Without Interferometry

A simple, non-interferometric method for measuring geometric phases of structured-Gaussian beams is presented. By studying the intensity distribution of an occluded beam, the Gouy and Pancharatnam-Berry phases can be determined.

Phase Retrieval in Generalized Two-Path Interferometry

Generalized interferometry is a novel technique that decomposes optical fields into specific transverse basis functions and weighting coefficient magnitudes. To obtain phase, a nonlinear optimization phase retrieval algorithm is developed for use in these systems.

Optical Beam Modal Analysis Via Generalized Two-Path Interferometry

A one dimensional optical implementation of the fractional Fourier Transform (fFT) using programmable lenses is presented. This set-up is used to implement a proof-of-principle experiment demonstrating a spatial mode-sorting Michelson interferometer based on a fFT generalized delay line.

Integrated Nanophotonics for Quantum Photonics Devices

Interferometry with 99% visibility is demonstrated in an integrated nanophotonics device based on photonic crystal circuitry in a GaAs slab. Such a device demonstrates an adaptable and robust platform to implement quantum photonics devices.

Cavity Quantum Electrodynamics with Epitaxial Quantum Dots

We present theoretical and experimental results of quantum photonic devices based on photonics crystals in III-V semiconductors.