Dual pumped microresonator frequency combs

A study is made of the nonlinear dynamics of dual pumped microresonator Kerr frequency combs described by a driven and damped nonlinear Schr\"odinger equation, with an additional degree of freedom in the form of the modulation frequency. A truncated four wave model is derived for the pump modes and the dominant sideband pair which is found to be able to describe much of the essential dynamical behaviour of the full equation. The stability of stationary states within the four wave model is investigated and numerical simulations are made to demonstrate that a large range of solutions, including cavity solitons, are possible beyond previously considered low intensity patterns.Comment: 7 pages, 9 figures, submitted to Phys. Rev.

Dynamics of the Modulational Instability in Microresonator Frequency Combs

A study is made of frequency comb generation described by the driven and damped nonlinear Schr\"odinger equation on a finite interval. It is shown that frequency comb generation can be interpreted as a modulational instability of the continuous wave pump mode, and a linear stability analysis, taking into account the cavity boundary conditions, is performed. Further, a truncated three-wave model is derived, which allows one to gain additional insight into the dynamical behaviour of the comb generation. This formalism describes the pump mode and the most unstable sideband and is found to connect the coupled mode theory with the conventional theory of modulational instability. An in-depth analysis is done of the nonlinear three-wave model. It is demonstrated that stable frequency comb states can be interpreted as attractive fixed points of a dynamical system. The possibility of soft and hard excitation states in both the normal and the anomalous dispersion regime is discussed. Investigations are made of bistable comb states, and the dependence of the final state on the way the comb has been generated. The analytical predictions are verified by means of direct comparison with numerical simulations of the full equation and the agreement is discussed.Comment: 9 pages, 6 figures, submitted to Phys. Rev.

Modulational instability of nonlinear polarization mode coupling in microresonators

We investigate frequency comb generation in the presence of polarization effects induced by nonlinear mode coupling in microresonator devices. A set of coupled temporal Lugiato-Lefever equations are derived to model the propagation dynamics, and an in-depth study is made of the modulational instability of their multistable homogeneous steady-state solutions. It is shown that new kinds of instabilities can occur for co-propagating fields that interact through nonlinear cross-phase modulation. These instabilities display properties that differ from their scalar counterpart, and are shown to result in the generation of new types of incoherently coupled frequency comb states.Comment: 8 pages, 7 figure

On the numerical simulation of Kerr frequency combs using coupled mode equations

It is demonstrated that Kerr frequency comb generation described by coupled mode equations can be numerically simulated using Fast Fourier Transform methods. This allows broadband frequency combs spanning a full octave to be efficiently simulated using standard algorithms, resulting in orders of magnitude improvements in the computation time.Comment: 3 pages, 1 figure, submitted to Optics Communication

Is Dark Matter made up of Massive Quark Objects?

We suggest that dark matter is made up of massive quark objects that have survived from the Big Bang, representing the ground state of ``baryonic'' matter. Hence, there was no overall phase transition of the original quark matter, but only a split-up into smaller objects. We speculate that normal hadronic matter comes about through enforced phase transitions when such objects merge or collide, which also gives rise to the cosmic gamma-ray bursts.Comment: 8 pages Latex, no figures; to be published in the Proceedings of Dark '98, Heidelberg, July 199

Distributed Interior-point Method for Loosely Coupled Problems

In this paper, we put forth distributed algorithms for solving loosely coupled unconstrained and constrained optimization problems. Such problems are usually solved using algorithms that are based on a combination of decomposition and first order methods. These algorithms are commonly very slow and require many iterations to converge. In order to alleviate this issue, we propose algorithms that combine the Newton and interior-point methods with proximal splitting methods for solving such problems. Particularly, the algorithm for solving unconstrained loosely coupled problems, is based on Newton's method and utilizes proximal splitting to distribute the computations for calculating the Newton step at each iteration. A combination of this algorithm and the interior-point method is then used to introduce a distributed algorithm for solving constrained loosely coupled problems. We also provide guidelines on how to implement the proposed methods efficiently and briefly discuss the properties of the resulting solutions.Comment: Submitted to the 19th IFAC World Congress 201

Quantum Hall Physics - hierarchies and CFT techniques

The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past thirty years, has generated many groundbreaking new ideas and concepts. Very early on it was realized that the zoo of emerging states of matter would need to be understood in a systematic manner. The first attempts to do this, by Haldane and Halperin, set an agenda for further work which has continued to this day. Since that time the idea of hierarchies of quasiparticles condensing to form new states has been a pillar of our understanding of fractional quantum Hall physics. In the thirty years that have passed since then, a number of new directions of thought have advanced our understanding of fractional quantum Hall states, and have extended it in new and unexpected ways. Among these directions is the extensive use of topological quantum field theories and conformal field theories, the application of the ideas of composite bosons and fermions, and the study of nonabelian quantum Hall liquids. This article aims to present a comprehensive overview of this field, including the most recent developments.Comment: added section on experimental status, 59 pages+references, 3 figure

Higgs Pain? Take a Preon!

The Higgs mechanism is the favourite cure for the main problem with electroweak unification, namely how to reconcile a gauge theory with the need for massive gauge bosons. This problem does not exist in preon models for quark and lepton substructure with composite $Z^0$ and $W$s, which, consequently, also avoid all other theoretical complications and paradoxes with the Higgs mechanism. We present a new, minimal preon model, which explains the family structure, and predicts several new, heavy quarks, leptons and vector bosons. Our preons obey a phenomenological supersymmetry, but without so-called squarks and sleptons, since this SUSY is effective only on the composite scale.Comment: The preon contents of some quarks and leptons have been changed in order to achieve a more consistent scheme. A few new comments have been added. 13 pages, LaTeX, no figures. To be published in Proc. of the Meeting on 'The Fundamental Structure of Matter' and 'Tests of the Electroweak Symmetry Breaking', Ouranoupolis, Greece, May 199

Preon Trinity

We present a new minimal model for the substructure of all known quarks, leptons and weak gauge bosons, based on only three fundamental and stable spin-1/2 preons. As a consequence, we predict three new quarks, three new leptons, and six new vector bosons. One of the new quarks has charge $-4e/3$. The model explains the apparent conservation of three lepton numbers, as well as the so-called Cabibbo-mixing of the $d$ and $s$ quarks, and predicts electromagnetic decays or oscillations between the neutrinos $\bar{\nu}_{\mu}$ ($\nu_{\mu}$) and $\nu_e$ ($\bar{\nu}_e$). Other neutrino oscillations, as well as rarer quark mixings and CP violation can come about due to a small quantum-mechanical mixing of two of the preons in the quark and lepton wave functions.Comment: 5 pages, Latex, no figure