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.

Stability analysis of polarization attraction in optical fibers

The nonlinear cross-polarization interaction among two intense counterpropagating beams in a span of lossless randomly birefringent telecom optical fiber may lead to the attraction an initially polarization scrambled signal towards wave with a well-defined state of polarization at the fiber output. By exploiting exact analytical solutions of the nonlinear polarization coupling process we carry out a linear stability study which reveals that temporally stable stationary solutions are only obtained whenever the output signal polarization is nearly orthogonal to the input pump polarization. Moreover, we predict that polarization attraction is acting in full strength whenever equally intense signal and pump waves are used

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

Optical turbulence in fiber lasers

We analyse the nonlinear stage of modulation instability in passively mode locked fiber lasers leading to chaotic or noise-like emission. We present the phase transition diagram among different regimes of chaotic emission in terms of the key cavity parameters: amplitude or phase turbulence, and spatio-temporal intermittency

Spatiotemporal chaos and order in fiber lasers

We introduce a model that permits the unified description of the emergence of different regimes of complex temporal structures in noise-like or quasi-CW fiber lasers. The model is based on the vector Ginzburg-Landau equation that also permits to reproduce the experimentally observed polarization antiphase behavior and the synchronization of spatiotemporal turbulence into polarizations domain wall solitons

Mitigation of Nonlinear and PMD Impairments by Bit-Synchronous Polarization Scrambling

Our statistical study by the importance sampling method shows that a significant performance improvement may be achieved by bit-synchronous polarization scrambling in the presence of polarization mode dispersion and fiber nonlinearity in dispersion managed, single-channel, or wavelength- division- multiplexed NRZ 10 Gbit/s fiber optic transmission systems

Analytical method for designing dispersion-managed fiber systems

This paper was published in Optics Letters and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/abstract.cfm?URI=ol-26-20-1544. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.Peer reviewedPublisher PD

Silicon Raman Polarizer

We theoretically investigate the polarization properties of Raman amplifiers based on silicon-on-insulator waveguides, and show that it is possible to realize a waveguide Raman polarizer. The Raman polarizer is a special type of Raman amplifier with the property of producing an amplified and highly repolarized beam when it is fed by a relatively weak and unpolarized signal