Nonlinear optical effects in artificial materials

We consider some nonlinear phenomena in metamaterials with negative refractive index properties. Our consideration includes a survey of previously known results as well as identification of the phenomena that are important for applications of this new field. We focus on optical behavior of thin films as well as multi-wave interactions.Comment: 22 pages, no figures. Submitted in book "Nonlinear waves in complex systems: energy flow and geometry

Coherent Amplification of Optical Pulses in Metamaterials

In this paper we theoretically study propagation of steady state ultrashort pulse in dissipative medium. We considered two cases (i) medium consists of lossy metallic nanostructures embedded into a gain material and (ii) the gain material is embedded directly into the nanostructures. We found the shape and velocity of an optical pulse coupled with the polarization wave.Comment: 9 pages, 5 figures, submitted to IEEE Tran

Random polarization dynamics in a resonant optical medium

Random optical-pulse polarization switching along an active optical medium in the $\Lambda$-configuration with spatially disordered occupation numbers of its lower energy sub-level pair is described using the idealized integrable Maxwell-Bloch model. Analytical results describing the light polarization-switching statistics for the single self-induced transparency pulse are compared with statistics obtained from direct Monte-Carlo numerical simulations.Comment: 7 pages, 3 figure

Optical Pulse Dynamics in Active Metamaterials with Positive and Negative Refractive Index

We study numerically the propagation of two-color light pulses through a metamaterial doped with active atoms such that the carrier frequencies of the pulses are in resonance with two atomic transitions in the $\Lambda$ configuration and that one color propagates in the regime of positive refraction and the other in the regime of negative refraction. In such a metamaterial, one resonant color of light propagates with positive and the other with negative group velocity. We investigate nonlinear interaction of these forward- and backward-propagating waves, and find self-trapped waves, counter-propagating radiation waves, and hot spots of medium excitation.Comment: 9 pages, 6 figure

Optical Bistability in Nonlinear Optical Coupler with Negative Index Channel

We discuss a novel kind of nonlinear coupler with one channel filled with a negative index material (NIM). The opposite directionality of the phase velocity and the energy flow in the NIM channel facilitates an effective feedback mechanism that leads to optical bistability and gap soliton formation

Stochastic Pulse Switching in a Degenerate Resonant Optical Medium

Using the idealized integrable Maxwell-Bloch model, we describe random optical-pulse polarization switching along an active optical medium in the Lambda-configuration with disordered occupation numbers of its lower energy sub-level pair. The description combines complete integrability and stochastic dynamics. For the single-soliton pulse, we derive the statistics of the electric-field polarization ellipse at a given point along the medium in closed form. If the average initial population difference of the two lower sub-levels vanishes, we show that the pulse polarization will switch intermittently between the two circular polarizations as it travels along the medium. If this difference does not vanish, the pulse will eventually forever remain in the circular polarization determined by which sub-level is more occupied on average. We also derive the exact expressions for the statistics of the polarization-switching dynamics, such as the probability distribution of the distance between two consecutive switches and the percentage of the distance along the medium the pulse spends in the elliptical polarization of a given orientation in the case of vanishing average initial population difference. We find that the latter distribution is given in terms of the well-known arcsine law

Modeling femtosecond pulse propagation in optical fibers.

Femtosecond pulse propagation in optical fibers requires consideration of higher-order nonlinear effects when implementing the non-linear Schroedinger equation. We show excellent agreement of our model with experimental results both for the temporal and phase features of the pulses. Ultrafast pulse propagation in optical fibers presents a number of challenges given the effect of nonlinearities which become important on such a short time scale. The modeling of femtosecond pulse propagation becomes, consequently, a harder task which has to account for all these effects. In this work, we have included higher order corrections in the non-linear Schroedinger equation and compared the numerical simulation results with experimental data. Our work, besides taking into account the temporal evolution of the pulse, keeps into account also the phase behavior of the electric field, which we compare with experimental results obtained with Frequency Resolved Optical Gating [l]. We also account for self-frequency shift of the pulse and obtain excellent agreement with the experimental results on the Raman shift