Long-distance radiative excitation transfer between quantum dots in disordered photonic crystal waveguides

We theoretically investigate the magnitude and range of the photon-mediated interaction between two quantum dots embedded in a photonic crystal waveguide, including fabrication disorder both in the crystal and in the dot positioning. We find that disorder-induced light localization has a drastic effect on the excitation transfer rate - as compared to an ideal structure - and that this rate varies widely among different disorder configurations. Nevertheless, we also find that significant rates of 50 micro-eV at a range of 10 micro-meters can be achieved in realistic systems.Comment: 5 pages, 3 figure

Haldane Quantum Hall Effect for Light in a Dynamically Modulated Array of Resonators

Topological insulators have attracted abundant attention for a variety of reasons -- notably, the possibility for lossless energy transport through edge states `protected' against disorder. Topological effects like the Quantum Hall state can be induced through a gauge field, which is however hard to create in practice, especially for charge-neutral particles. One way to induce an effective gauge potential is through a dynamic, time-periodic modulation of the lattice confining such particles. In this way, the Haldane Quantum Hall effect was recently observed in a cold atom system. Here, we show how this same effect can be induced for light confined to a lattice of identical optical resonators, using an on-site modulation of the resonant frequencies. We further demonstrate the existence of one-directional edge states immune to back-scattering losses, and discuss the possibilities for a practical implementation, which would enable slow-light devices of unprecedented quality

Radiative coupling of quantum dots in photonic crystal structures

We derive a general formalism to model the polariton states resulting from the radiation-matter interaction between an arbitrary number of excitonic transitions in semiconductor quantum dots and photon modes in a photonic crystal structure in which the quantum dots are embedded. The Maxwell equations, including the linear nonlocal susceptibility of the exciton transitions in the quantum dots, are cast into an eigenvalue problem, which can be applied to any structure whose photon modes can be computed with reliable accuracy, and in addition naturally allows for disorder effects to be taken into account. We compute realistic photon modes using Bloch-mode expansion. As example systems, we study typical InGaAs quantum dots in a GaAs photonic crystal structures -- an $Ln$ cavity or a $\mathit{W1}$ waveguide. For a single dot, we reproduce known analytical results, while for the two dot case, we study the radiative excitation transfer mechanism and characterize its strength, the dependence on the detuning between quantum dot and photon modes, and the dependence on inter-dot distance. We find in particular that the inter-dot radiative coupling strength can reach $100 \mu{eV}$ in a short cavity, and its decay with distance in longer cavities and waveguides is determined by the group velocity of the exchanged photons and their radiative lifetime. We also show that, for an $Ln$ cavity of increasing length, the radiative excitation transfer mechanism is subject to a crossover from a regime where a single photon mode is dominating, to a multi-mode regime -- occurring around $\mathit{n}$ = 150 for the system under study.Comment: 17 pages, 12 figure

Exact solution to the steady-state dynamics of a periodically-modulated resonator

We provide an analytic solution to the coupled-mode equations describing the steady-state of a single periodically-modulated optical resonator driven by a monochromatic input. The phenomenology of this system was qualitatively understood only in the adiabatic limit, i.e. for low modulation speed. However, both in and out of this regime, we find highly non-trivial effects for specific parameters of the modulation. For example, we show complete suppression of the transmission even with zero detuning between the input and the static resonator frequency. We also demonstrate the possibility for complete, lossless frequency conversion of the input into the side-band frequencies, as well as for optimizing the transmitted signal towards a given target temporal waveform. The analytic results are validated by first-principle simulations

Numerical study and optimization of photonic crystals

Photonic crystals (PhCs) are engineered nanostructures that enable an extraordinary control over the flow of light. These structures can be fabricated out of common semiconductors, are compatible with existing industrial fabrication technologies, and are expected to play a major role in future devices integrating photonic circuits - e.g. for telecommunications or in future quantum technologies. In this thesis, we explore a wide range of properties of the most common class of PhCs, formed by a lattice of circular holes in a semiconductor slab. To compute the electromagnetic eigenmodes of a given structure, we use fast mode-expansion methods, which are presented in detail here. The first application consists in a detailed analysis of the effects of fabrication disorder on the PhC structures. It is by now well-known that disorder is in many cases the limiting factor in device performance. Here, we shed more light on its effects, by statistically comparing various designs for PhC cavities with a high quality factor, and by analyzing the effect of irregular hole shapes on a PhC waveguide. The second application presented here stems from the fact that PhCs are in fact tremendously flexible, and their features are determined by a large number of controllable parameters. This is on one hand a great advantage, but on the other a great challenge when it comes to finding the optimal device for a given application. To face this challenge, we have developed an automated optimization procedure, using a global optimization algorithm for the exploration of an insightfully selected parameter space. This was applied to various devices of interest, and inevitably resulted in a vast improvement of their qualities. Specifically, we demonstrate various high-Q cavity designs, and a slow-light coupled-cavity waveguide with extraordinary features. We also present several experimental confirmations of the validity of our designs. Finally, we discuss two domains in which PhCs (and our optimization procedure) can be expected to play a major role. The first one is integrating quantum dots with the goal of long-range, photon-assisted dot-dot coupling, with implications for quantum information processing. We develop a semi-classical formalism, and analyze the magnitude and attenuation length of this coupling in large PhC cavities, as well as in a waveguide. The second outlook is in the field of topological photonics. We describe an array of resonators, in which an effective gauge field for photons can be induced through an appropriate time-periodic modulation of the resonant frequencies. This results in a Quantum Hall effect for light, and, in a finite system, one-directional edge states immune to fabrication disorder are predicted. We discuss the possibilities for a practical implementation, for which a PhC slab is among the most promising platforms

A Photonic Crystal Slab Laplace Differentiator

We introduce an implementation of a Laplace differentiator based on a photonic crystal slab that operates at transmission mode. We show that the Laplace differentiator can be implemented provided that the guided resonances near the $\Gamma$ point exhibit an isotropic band structure. Such a device may facilitate nanophotonics-based optical analog computing for image processing.Comment: Primary text 6 pages, 5 figures; Supplementary material 5 pages, 3 figure