Short chirp pulses in graded-index light guides

We consider the nonlinear process of propagation of a short chirp optical pulse in a light guide in which the refractive index of a fiber material strongly depends on the radial coordinate and weakly depends on the longitudinal coordinates. The chirped and strongly chirped pulses are distinguished by the relationship between the modulation depth and the spectrum width. The chirp-pulse propagation is simulated by a nonlinear wave equation solved asymptotically with respect to the small parameter prescribing the order of magnitude of the pulse amplitude. It is shown that the pulse propagation is three-scale. The phase of high-frequency filling and the field distribution in the fiber cross section are obtained as the eigenvalue and eigenfunction of a singular Sturm-Liouville problem, respectively. On the additional assumption of longitudinal inhomogeneity of the fiber, the general equation for the pulse envelope is reduced to the second Painlevé equation. It is shown that the linear modulation of the carrier frequency is not an independent characteristic of the propagation process, but varies in certain accordance with parameters of the transverse and longitudinal inhomogeneities of the fiber. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 1, pp. 64–71, January 2006.     

Mode-locked lasers and ultrashort light pulses

This article reviews some aspects of the generation of very short optical pulses using mode-locked lasers, with the emphasis laid on pulsed laser systems. Active and passive mode-locking is discussed, and the problem of measuring ultrashort light pulses is considered. A survey of some commonly used sources and techniques for the generation of ultrashort light pulses follows. The paper concludes with a short account of limitations in the generation and propagation of these pulses.     

Calculation of light pulses with chirp in passively mode-locked lasers taking into account the phase memory of absorber and amplifier

Starting from the complete set of Maxwell's equations and density matrix equations for the atomic systems, the change of amplitude and phase of light pulses in passing through absorbing and amplifying samples has been calculated by using certain approximations. It is shown that the phase modulation originates from saturation and phase memory in off-resonance interaction. The use of the simple rate-equation approximations.is only justified if saturation dominates. The full cavity round-trip equation has been established and solved for steady-state pulses under different conditions. For the case of pulses being outside resonance with the media we take into account a linear optical element for intracavity chirp compensation in order to describe the regime, where in experiment the shortest pulses have been found.     

Avoiding temporal distortions in tilted pulses

Tilted femtosecond laser pulses, having an intensity front with an angle to the propagation direction, can be generated by a dispersive element and a lens or mirror for imaging. Here we show that conventional geometries, for example with a grating at Littrow's condition, produce significant temporal distortions over the beam profile. The aberrations are the result of a mismatch between the grating's surface and the object plane of the imaging system. This changes the chirp of the pulses over the beam profile and lengthens the pulses to picoseconds for millimeter-sized beams. The distortions can be avoided by choosing a geometry in which the propagation direction of the tilted pulses is perpendicular to the grating's surface.     

Nonlinear chirp of dispersion-managed return-to-zero pulses

Applying variational methods, we derive a reduced system of equations from the nonlocal equation that governs the average dynamics in dispersion-managed systems. These equations, which apply for any type of return-to-zero pulse, describe the stroboscopic evolution of the pulse parameters and bypass the fast variations inside each dispersion map. In the limit of large map strength we integrate the equations to obtain explicitly formulas for the parameters of a chirped return-to-zero pulse as well as the amount of post-transmission compensation needed to restore the initial pulse width.     

Real-time chirp diagnostic for ultrashort laser pulses

Using a real-time Fourier-transform algorithm, we present a simple technique for measuring the chirp of femtosecond laser pulses. We demonstrate significantly enhanced sensitivity compared with standard autocorrelation measurements.     

Angular magnetoresistance oscillations in bilayers in tilted magnetic fields

Angular magnetoresistance oscillations (AMRO) were originally discovered in organic conductors and then found in many other layered metals. It should be possible to observe AMRO to semiconducting bilayers as well. Here we present an intuitive geometrical interpretation of AMRO as the Aharonov–Bohm interference effect, both in real and momentum spaces, for balanced and imbalanced bilayers. Applications to the experiments with bilayers in tilted magnetic fields in the metallic state are discussed. We speculate that AMRO may be also observed when each layer of the bilayer is in the composite-fermion state.     

Dual-frequency pulses in fiber lasers

We analyze pulse propagation in a soliton fiber laser, modelled by the complex Schrödinger-Ginzburg-Landau equation. It is shown that this equation admits two previously unknown forms of stable stationary solutions. The first of them is a dual-frequency pulse, which propagates as a single unit, but has two symmetric peaks in the spectrum. The second one is a moving pulse, with the asymmetric double-hump spectrum.     

Determination of spectral width and chirp of ultrashort light pulses by analysis of second harmonic beam divergence

It is shown that in the noncollinear second harmonic generation scheme used for ultrashort light pulse duration measurements the divergence of the second harmonic beam is determined by the spectral width and chirp of the pulse. This enables one to measure simultaneously the spectral width, pulse duration, spectral-time product, chirp and its sign for a single pulse in the same device.     

Nonlinear second-harmonic pulse compression with tilted pulses

We demonstrate that the group velocities of interacting pulses can be adjusted by pulse tilting to optimize second-harmonic pulse compression for a variety of nonlinear crystals and wavelengths. As an experimental proof we present results of ninefold compression of 1.3-ps Nd:glass laser pulses in beta -barium borate crystal.     

Analysis of chirp characteristics of DFB lasers and integrated laser-modulators

A new method of analyzing the chirp characteristics of directly modulated lasers and integrated laser-modulators is presented in this paper. Phase-circuit has been introduced into the circuit model of distributed feedback (DFB) lasers in the analysis. Therefore, the chirp characteristics of the device can be obtained by simulating the modified circuit model. The simulation results agree well with the published data. Furthermore, this modified model is combined with the circuit model of electroabsorption (EA) modulators to simulate the chirp characteristics of the monolithic integration of a DFB laser and an EA modulator. The simulation is focused on the dependence of the frequency chirp of the integrated device on the isolation resistance between laser and modulator. Much lower chirp can be seen in the integrated lightwave source compared to the directly modulated laser.     

High order dispersion control for femtosecond CPA lasers

Taking advantage of the temperature dependence of the refractive index, an arrangement is proposed for thermal control of dispersion of a chirped pulse amplification (CPA) laser. A glass slab, inserted into the Fourier plane of a stretcher or a compressor, having a spatially varying temperature profile across the beam ensures continuous variation of the spectral phase shift of the pulses. Model calculations are carried out to investigate the feasibility of the arrangement. As a demonstration, simple temperature profiles are created which compensate for the material dispersion of the thermal slab. In a proof of principle experiment it is proved that changes of spectral phase of femtosecond pulses follow the spatially varying temperature profile of a BK7 slab inserted into the compressor of a CPA system. Such a thermal slab is lossless, has a large spectral range, introduces no pixellation and exhibits a high damage threshold. Since it is easy to build into either the stretcher or the compressor of existing CPA lasers, it may become a promising candidate for high order dispersion compensation of high-power femtosecond laser systems. PACS 42.65.Re; 42.79.-e; 42.60.By     

Amplitude and chirp characterization of high-power laser pulses in the 5-fs regime

Frequency-resolved optical gating (FROG) based on second-harmonic generation has been demonstrated to be capable of high-fidelity measurement of the electric-field envelope and of the temporal evolution of the instantaneous carrier frequency of 0.1-TW 5-fs pulses without the need for any correction for systematic experimental errors. At a 1-kHz repetition rate, pulse energies of a few microjoules are sufficient for reliable FROG characterization of pulses with durations down to the single-cycle regime. The results obtained reveal that carefully designed hollow-fiber chirped-mirror compressors are able to deliver high-power sub-10-fs pulses with a smooth Gaussianlike leading edge that has an intensity contrast of approximately 10(-2) .     

Ultrashort pulses from semiconductor diode lasers

Careful design of mounting structures and drive-circuit parameters is essential to obtain very short pulse-lengths with high peak powers from semiconductor diode lasers. We have developed a diode laser model using a coupled rate equation approach to predict operating regimes producing ultrashort output pulses. The model has been refined through comparison with experiment, and a 10 ps source, designed on the basis of this model, has been implemented.     

Picosecond pulses from mode-locked dye lasers

Picosecond pulses have been generated in laser pumped (15 psec) and flashlamp pumped (6 psec) mode-locked dye lasers. Two-photon fluorescence and streak camera measurements are described.     

Mode-locked pulses of homogeneous gain lasers

We discuss a number of errors in a recent paper by Piche and Belanger concerned with an approximate solution to an integral equation satisfied by mode-locked pulses of a homogeneous gain laser. An alternative method of solution which is, in principle, exact is presented.     

Angular dispersion of femtosecond pulses in a Gaussian beam

The angular dispersion of spatially Gaussian laser pulses, unlike for plane waves, changes with the distance between the disperser and the observer and between the beam waist and the disperser. The formula that is derived is experimentally verified by use of a high-precision measurement technique. Because the angular dispersion of a Gaussian beam is substantially different from that of a plane wave after the same disperser, the phenomenon may be of special interest for short-pulsed laser systems, for which alignment of the stretcher-compressor system for zero residual angular dispersion is essential.     

Optimization design of chirp managed lasers by integral layer-peeling method

The chirp managed laser (CML) mainly includes a directly modulated laser followed by an optical spectrum reshaper (OSR) filter. In this paper, an integral layer-peeling method has been applied to synthesize the OSR filter with the desired reflection spectrum, which breaks the trade-off between the filter bandwidth and the filter slope steepness inherently existing in the FP etalon based filter, and hence greatly facilitates the optimization design of the OSR for a better transmission performance of a CML. Using this approach, we have, respectively, investigated the optimization design of the OSR filter in terms of the edge slope and the 3 dB bandwidth in the CML modulated at 10 and 25 Gb/s, through studying their transmission performances over the standard single-mode fiber. With the optimum design of OSR, the longest transmission distances at which the power penalty is 1 dB at a bit error rate of 10^?12 are 135 and 18 km for the 10 and 25 Gb/s CML, respectively.