Critical Behavior of Light

Light is shown to exhibit critical and tricritical behavior in passive mode-locked lasers with externally injected pulses. It is a first and unique example of critical phenomena in a one-dimensional many body light-mode system. The phase diagrams consist of regimes with continuous wave, driven para-pulses, spontaneous pulses via mode condensation, and heterogeneous pulses, separated by phase transition lines which terminate with critical or tricritical points. Enhanced nongaussian fluctuations and collective dynamics are observed at the critical and tricritical points, showing a mode system analog of the critical opalescence phenomenon. The critical exponents are calculated and shown to comply with the mean field theory, which is rigorous in the light system.Comment: RevTex, 5 pages, 3 figure

Hydraulic flow through a channel contraction: multiple steady states

We have investigated shallow water flows through a channel with a contraction by experimental and theoretical means. The horizontal channel consists of a sluice gate and an upstream channel of constant width $b_0$ ending in a linear contraction of minimum width $b_c$. Experimentally, we observe upstream steady and moving bores/shocks, and oblique waves in the contraction, as single and multiple steady states, as well as a steady reservoir with a complex hydraulic jump in the contraction occurring in a small section of the $b_c/b_0$ and Froude number parameter plane. One-dimensional hydraulic theory provides a comprehensive leading-order approximation, in which a turbulent frictional parametrization is used to achieve quantitative agreement. An analytical and numerical analysis is given for two-dimensional supercritical shallow water flows. It shows that the one-dimensional hydraulic analysis for inviscid flows away from hydraulic jumps holds surprisingly well, even though the two-dimensional oblique hydraulic jump patterns can show large variations across the contraction channel

Exact solutions to chaotic and stochastic systems

We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time-series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.Comment: 31 pages, 18 figures (.eps). To appear in Chaos, March 200

Experimental Implementation of Optical Clockwork without Carrier-Envelope Phase Control

We demonstrate an optical clockwork without camer-envelope phase control using sum-frequency generation between a CW optical parametric oscillator at 3.39 μm and a modelocked Tisapphire laser with dominant spectral peaks at 834 and 670 nm

Optical Clockwork without Carrier-Envelope Phase Control

We demonstrate optical clockwork without carrier-envelope phase control using sum-frequency generation between a cw optical parametric oscillator at 3.39 μm and a mode-locked Ti:sapphire laser with dominant spectral peaks at 834 nm and 670 nm

Demultiplexing of 80-Gb/s Pulse-Position Modulated Data With an Ultrafast Nonlinear Interferometer

Abstract-Pulse-position modulation may be used to reduce patterning effects arising from gain saturation in all-optical switches employing semiconductor optical amplifiers. We present a novel technique for return-to-zero pulse-position modulation of data suitable for use in optical time-division-multiplexed (OTDM) networks. We demonstrate two methods for all-optical demultiplexing of a pulse-position modulated data stream using an ultrafast nonlinear interferometer. Errorfree operation is obtained for demultiplexing from OTDM data rates as high as 80 Gb/s with control pulse energies of 25 fJ