Coupled-mode theory for periodic side-coupled microcavity and photonic crystal structures

We use a phenomenological Hamiltonian approach to derive a set of coupled mode equations that describe light propagation in waveguides that are periodically side-coupled to microcavities. The structure exhibits both Bragg gap and (polariton like) resonator gap in the dispersion relation. The origin and physical significance of the two types of gaps are discussed. The coupled-mode equations derived from the effective field formalism are valid deep within the Bragg gaps and resonator gaps.Comment: 13 pages, 6 figure

Nonlinear and Quantum Optics with Whispering Gallery Resonators

Optical Whispering Gallery Modes (WGMs) derive their name from a famous acoustic phenomenon of guiding a wave by a curved boundary observed nearly a century ago. This phenomenon has a rather general nature, equally applicable to sound and all other waves. It enables resonators of unique properties attractive both in science and engineering. Very high quality factors of optical WGM resonators persisting in a wide wavelength range spanning from radio frequencies to ultraviolet light, their small mode volume, and tunable in- and out- coupling make them exceptionally efficient for nonlinear optical applications. Nonlinear optics facilitates interaction of photons with each other and with other physical systems, and is of prime importance in quantum optics. In this paper we review numerous applications of WGM resonators in nonlinear and quantum optics. We outline the current areas of interest, summarize progress, highlight difficulties, and discuss possible future development trends in these areas.Comment: This is a review paper with 615 references, submitted to J. Op

Feasibility of UV lasing without inversion in mercury vapor

We investigate the feasibility of UV lasing without inversion at a wavelength of $253.7$ nm utilizing interacting dark resonances in mercury vapor. Our theoretical analysis starts with radiation damped optical Bloch equations for all relevant 13 atomic levels. These master equations are generalized by considering technical phase noise of the driving lasers. From the Doppler broadened complex susceptibility we obtain the stationary output power from semiclassical laser theory. The finite overlap of the driving Gaussian laser beams defines an ellipsoidal inhomogeneous gain distribution. Therefore, we evaluate the intra-cavity field inside a ring laser self-consistently with Fourier optics. This analysis confirms the feasibility of UV lasing and reveals its dependence on experimental parameters.Comment: changes were made according to reviewer comments (accepted for publication in JOSA B

Quantum Dynamics of Kerr Optical Frequency Combs below and above Threshold: Spontaneous Four-Wave-Mixing, Entanglement and Squeezed States of Light

In this article, we use quantum Langevin equations to provide a theoretical understanding of the non-classical behavior of Kerr optical frequency combs when pumped below and above threshold. In the configuration where the system is under threshold, the pump field is the unique oscillating mode inside the resonator, and triggers the phenomenon of spontaneous four-wave mixing, where two photons from the pump are symmetrically up- and down-converted in the Fourier domain. This phenomenon can only be understood and analyzed from a fully quantum perspective as a consequence of the coupling between the field of the central (pumped) mode and the vacuum fluctuations of the various sidemodes. We analytically calculate the power spectra of the spontaneous emission noise, and we show that these spectra can be either single- or double peaked depending on the parameters of the system. We also calculate as well the overall spontaneous noise power per sidemode, and propose simplified analytical expressions for some particular cases. In the configuration where the system is pumped above threshold, we investigate the phenomena of quantum correlations and multimode squeezed states of light that can occur in the Kerr frequency combs originating from stimulated four-wave mixing. We show that for all stationary spatio-temporal patterns, the side-modes that are symmetrical relatively to the pumped mode in the frequency domain display quantum correlations that can lead to squeezed states of light. We also explicitly determine the phase quadratures leading to photon entanglement, and analytically calculate their quantum noise spectra. We finally discuss the relevance of Kerr combs for quantum information systems at optical telecommunication wavelengths, below and above threshold.Comment: 27 pages, 11 figure

Modal analysis of semiconductor lasers with nonplanar mirrors

We present a formalism for analyzing laser resonators which possess nonplanar mirrors and lateral waveguiding [e.g., an unstable resonator semiconductor laser (URSL)]. The electric field is expanded in lateral modes of the complex-index waveguide and is required to reproduce itself after, one roundtrip of the cavity. We show how the waveguide modes, their gain and loss, and hence the criterion for truncation of the infinite set of modes can be derived from the Green's function of the one-dimensional eigenvalue equation for the waveguide. Examples are presented for three cases of interest - a purely gain-guided URSL, an index-guided URSL, and a gain-guided tilted-mirror resonator. We compare theoretical calculations to previous experiments

Utilising optical Kerr microresonators for polarisation control, logic gates, and quantum optics applications

When high intensities of light are focused inside of a medium, strange effects occur. Light can self-interact. It can be slowed down based on how bright it is, it can be made to go in one direction but not the other, and it can even be made to c change colour. It is hard to imagine how the world would look if these were effects that we experienced in our everyday lives. Fortunately, it takes a significant amount of effort to make the conditions right for such events to occur, specifically, with high optical intensities required. This thesis details some of these efforts. In this work, I present some applications of Kerr microresonantor based nonlinear and quantum optics. Microresonators are minute devices that can be integrated in photonic circuits. They trap and guide light on a repeating path, with each roundtrip leading to an increase in intensity until nonlinear effects start to occur. I start by explaining how such resonators work, are fabricated, and how nonlinear effects can manifest. Next, an all-optical polarisation controller is introduced, in which the nonlinear splitting of otherwise degenerate polarisation modes is employed. This device could find application in integrated photonic circuits that require fast response times. A similar effect, but this time for counter-propagating light, is then used to demonstrate an all-optical, universal logic gate. Interestingly, a set of such logic gates could be used for the on-chip routing of optical signals to provide low-latency communications for telecoms and distributed computing. Finally, the quantum nature of these nonlinearities is explored, first with the calculation of multi-modal entanglement metrics before then discussing work that is progressing towards a single-photon source. These phenomena show promise for integration into future quantum technologies, in particular in secure quantum communications and for state generation for quantum information processing.Open Acces

Simulation of continuous-wave solid-state laser resonators using field tracing and a fully vectorial fox-li algorithm

In this PHD thesis the scalar Fox and Li algorithm for the dominant transversal resonator eigenmode calculation is generalized to a fully vectorial field tracing concept. Therefore Fox and Li’s scalar integral equation is reformulated to a set of coupled operator equations. The introduction of a field tracing round trip operator concept shows that, in principle, any modeling technique which can be formulated to operate for electromagnetic fields can be used to simulate light propagation through the different subdomains of the resonator. This allows a flexible, fast, and accurate simulation of the fully vectorial dominant transversal resonator eigenmode. Several examples are presented to demonstrate the flexibility and accuracy of the field tracing approach

Topological Photonics

Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.Comment: 87 pages, 30 figures, published versio