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We investigate analytically, numerically, and experimentally the modulational instability in a layered, cubically nonlinear (Kerr) optical medium that consists of alternating layers of glass and air. We model this setting using a nonlinear Schrödinger (NLS) equation with a piecewise constant nonlinearity coefficient and conduct a theoretical analysis of its linear stability, obtaining a Kronig-Penney equation whose forbidden bands correspond to the modulationally unstable regimes. We find very good quantitative agreement between the theoretical analysis of the Kronig-Penney equation, numerical simulations of the NLS equation, and the experimental results for the modulational instability. Because of the periodicity in the evolution variable arising from the layered medium, we find multiple instability regions rather than just the one that would occur in uniform media.

We have studied the large-scale beam breakup and filamentation of femtosecond pulses in a Kerr medium. We have experimentally monitored the formation of stable light filaments, conical emission, and interactions between filaments. Three major stages lead to the formation of stable light filaments: First the beam breaks up into a pattern of connected lines (constellation), then filaments form on the constellations, and finally the filaments release a fraction of their energy through conical emission. We observed a phase transition to a faster filamentation rate at the onset of conical emission. We attribute this to the interaction of conical emissions with the constellation which creates additional filaments. Numerical simulations show good agreement with the experimental results.

We present experimental results on the transverse modulation instability of an elliptical beam propagating in a bulk nonlinear Kerr medium, and the formation and self-organization of spatial solitons. We have observed the emergence of order, self organization and a transition to an unstable state. Order emerges through the formation of spatial solitons in a periodic array. If the initial period of the array is unstable the solitons will tend to self-organize into a larger (more stable) period. Finally the system transitions to a disordered state where most of the solitons disappear and the beam profile becomes unstable to small changes in the input energy.

This paper studies the propagation of femtosecond pulses in a Kerr medium both experimentally and numerically. This work also investigates the similarities between the propagation of light pulses in a Kerr medium and the evolution of fluid dynamical systems, and proposes the use of an optical system to simulate fluid dynamics.

The paper reports on the generation of spatial solitons with carbon disulfide (CS_2) as the nonlinear material, which has a critical power of 190 kW for the laser wavelength of 800 nm. A 150-femtosecond pulse with a maximum energy of 1 mJ is also used. Each pulse from the laser is split into pump and probe pulses. The pump pulse is focused into a line (using a cylindrical lens) at the entrance face of a 10 mm glass cell filled with CS_2.

We have observed the filamentation of optical pulses in carbon disulfide(CS2) using femtosecond time-resolved optical polarigraphy(FTOP). A pump-probe setup is used to capture the propagation of a 150 femtosecond laser pulse in CS2. The probe pulse propagates in a direction perpendicular to the pump. The high intensity of the pump pulse causes a transient index change in the material through the Kerr effect. The induced birefringence is proportional to the intensity of the pump and can be captured by monitoring the polarization of the probe. The probe pulse is imaged on a CCD camera to recover the intensity profile of the pump pulse. We have used this technique to observe the spatial evolution of the pulse as a function of power and propagation distance. Initially, the pulse propagation causes a coarse redistribution of the intensity. The beam then breaks up into stable light filaments which propagate for several millimeters, and finally the beam profile becomes unstable to small fluctuations in the input power.

We present a holographic recording technique with 150 femtosecond time resolution. This technique allows us to capture either a single hologram with fine spatial resolution (4 micrometers), or a time-sequence of multiple holograms with reduced spatial resolution in a single-shot experiment, while preserving amplitude and phase information. The time resolution and the frame rate are limited only by the duration of the laser pulses. The holograms are recorded on a CCD camera and digitally reconstructed. We have used the technique to study the nonlinear propagation of high energy femtosecond pulses through liquids. We have observed dramatic differences in the pulse propagation characteristics depending on the strength of the nonlinear coefficient of the material and it's time response. The fine spatial resolution allows us to zoom in and visualize the spatial profile of the pulses breaking up into multiple filaments while the phase recovered from the holograms helps us identify the nonlinear index changes in the material. We have measured both positive and negative index changes. Very fast positive index changes are generally attributable to the Kerr nonlinearity. The negative index changes can be caused by electron plasma generated by multiphoton absorption.

We report on a holographic probing technique that allows for measurement of free-electron distribution with fine spatial detail. Plasma is generated by focusing a femtosecond pulse in air. We also demonstrate the capability of the holographic technique of capturing the time evolution of the plasma-generation process.

We report on holographic recording of nanosecond events on a conventional CCD camera. Three frames of an air-discharge event, with resolution of 5.9 ns and frame interval of 12 ns, are recorded in a single CCD frame. Each individual frame is reconstructed by digital filtering of the CCD frame, since successively recorded holograms are centered at different carrier frequencies in the spatial frequency domain.

In this paper we report on a holographic method used to record fast events in the nanosecond time scale. Several frames of the expansion of shock waves in air and in a polymer sample are recorded holographically in a single shot experiment, using a pulse train generated with a single pulse from a Q-switched Nd:YAG laser. The time resolution is limited by the laser pulse width, which is 5.9 ns. The different frames are recorded on the holographic material using angle multiplexing. Two cavities are used to generate the signal and reference pulses at different angles. We also present a method in which the recording material is replaced by a CCD camera. In this method the holograms are recorded directly on the CCD and digitally reconstructed. The holograms are recorded on a single frame of the CCD camera and then digitally separated and reconstructed.