Self-action of short pulses in nonhomogeneous graded-index light guides

The weak nonlinear process of propagation of short pulses in graded-index light guides that are weakly inhomogeneous in the longitudinal direction and slightly bent is investigated by means of a consistent asymptotic method. The process as a whole is proved to be three-scale in respect to a small parameter related to the magnitude of nonlinearity. The phase of the most rapid process and transverse distribution of the wave field are expressed explicitly in terms of a certain Sturm-Liouville problem. For a pulse envelope the nonlinear Schrödinger equation is derived, its coefficients depending on the longitudinal coordinate. The existence of a guaranteed interval of conservation of concentration of the pulse envelope is ascertained. For a class of very smooth inhomogeneities formulae are obtained describing the variation of the amplitude and width of the pulse during propagation.     

Angular chirp and tilted light pulses in CPA lasers

We investigate analytically and experimentally various aspects of the angular chirp of ultrashort laser pulses. This type of chirp is easily produced by slight misalignment of standard pulse stretcher and/or compressor setups. Angular chirp leads to tilted pulse fronts in the near field and to a strong reduction of intensity in the focus. The effect is rather difficult to observe with standard diagnostic techniques. We present a method that is based on interferometric field autocorrelation and allows us to measure the angular chirp reliably. Suggestions on how to avoid this effect are outlined as well.     

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.     

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.     

Optically induced mode conversion in graded-index fibers using ultra-short laser pulses

We propose the use of graded-index few-mode fibers for mode conversion by long-period gratings (LPG) transiently written by ultrashort laser pulses using the optical Kerr effect. The mode interaction is studied by numerically solving the multi-mode coupled nonlinear Schrödinger equations. We present highly efficient conversion of the LP₀₁- into the LP₁₁-mode preserving the pulse shape in contrast to previous results in step-index fibers. Furthermore, mode conversion using different wavelengths for inducing and probing the LPG is shown. Due to the flat phase-matching curve of the examined modes in the graded-index fiber, mode conversion can be observed for probe center wavelengths of 1,100 nm up to 1,800 nm with a write beam centered around 1,030 nm. Therefore, a complete separation of the probe from the write beam should be possible as well as the application of optically induced guided-mode conversion for all-optical modulation across a broad wavelength range.     

Transverse light guides in microstructured optical fibers

A novel class of microstructured optical fiber coupler is introduced that operates by resonant, rather than proximity, energy transfer by means of transverse light guides built into a fiber cross section. Such a design permits significant spatial separation between interacting fibers, which, in turn, eliminates intercore cross talk owing to proximity coupling. A controllable energy transfer between the cores is then achieved by localized and highly directional transmission through a transverse light guide. The main advantage of this coupling scheme is its inherent scalability, as one can integrate additional fiber cores into the existing fiber cross section simply by placing the cores far enough from the existing optical circuitry to prevent proximity cross talk and then making the necessary intercore connections with transverse light wires, in direct analogy with on-chip electronics integration.     

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.     

Driving light pulses with light in two-level media

A two-level medium, described by the Maxwell-Bloch system, is engraved by establishing a standing cavity wave with a linearly polarized electromagnetic field that drives the medium on both ends. A light pulse, polarized along the other direction, then scatters the medium and couples to the cavity standing wave by means of the population inversion density variations. We demonstrate that control of the applied amplitudes of the grating field allows one to stop the light pulse and to make it move backward (eventually to drive it freely). A simplified limit model of the Maxwell-Bloch system with variable boundary driving is obtained as a discrete nonlinear Schr?dinger equation with tunable external potential. It reproduces qualitatively the dynamics of the driven light pulse.     

Ultralocalized superluminal light pulses

We consider a sophisticated localized light wave—the so-called focused X wave which possesses a strong exponential localization in its waist region and propagates faster than the speed of light in a vacuum or in a linear medium. We show how this wave—until now considered in the literature as a mathematical object only—could be generated in reality by making use of cylindrical diffraction gratings.     

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) .     

Design of wideband graded-index antireflection coatings at oblique light incidence

We suggest a design method of graded-refractive-index (GRIN) antireflection (AR) coating for s-polarized or p-polarized light at off-normal incidence. The spectrum characteristic of the designed antireflection coating with a quintic effective refractive-index profile for a given state of polarization has been discussed. In addition, the genetic algorithm was used to optimize the refractive index profile of the GRIN antireflection for reducing the mean reflectance of s- and p-polarizations. The average reflectance loss was reduced to only 0.04% by applying optimized GRIN AR coatings onto BK7 glass over the wavelength range from 400 to 800 nm at the incident angle of θ₀ =70°.     

Transform-limited spectral compression by self-phase modulation of amplitude-shaped pulses with negative chirp

Spectral compression by self-phase modulation of amplitude- and phase-shaped pulses is demonstrated as superior compared to pulses that have only been phase shaped. We synthesize linearly negatively chirped parabolic pulses, which we send through a nonlinear photonic crystal fiber, in which self-phase modulation compresses the spectrum of the pulses to within 20% of the Fourier transform limit.     

Design of wideband graded-index antireflection coatings at oblique light incidence

We suggest a design method of graded-refractive-index (GRIN) antireflection (AR) coating for s-polarized or ppolarized light at off-normal incidence.The spectrum characteristic of the designed antireflection coating with a quintic effective refractive-index profile for a given state of polarization has been discussed.In addition,the genetic algorithm was used to optimize the refractive index profile of the GRIN antireflection for reducing the mean reflectance of s-and p-polarizations.The average reflectance loss was reduced to only 0.04% by applying optimized GRIN AR coatings onto BK7 glass over the wavelength range from 400 to 800 nm at the incident angle of θ 0=70°.     

Propagation of femtosecond light pulses

Femtosecond transform limited light pulse propagation in vacuum is described in scalar approximation of diffraction theory. Evolution of the spatial and temporal characteristics of the pulse are presented.     

Photorefractive deceleration of light pulses

We theoretically study the effect of light deceleration in photorefractive nonlinear media. This includes consideration of different types of the photorefractive nonlinear response, different wave interaction schemes, and an analysis of the influence of the input parameters, such as the input temporal pulse width and the coupling strength, on the output pulse characteristics: the time delay, the propagation velocity, the amplification factor, and the output width. We show that photorefractive light deceleration has numerous advantages over other known techniques. It works already at low intensities, at room temperature, and within wide spectral ranges and offers a vast variety of handles for manipulating light pulses. An analogy with the light deceleration method based on the quantum effect of electromagnetically induced transparency in ultracold resonant gases is also considered. The text was submitted by the authors in English.     

Divergence and aperture angle of conical light guides

Relations derived for the angle of divergence and the aperture of hollow metallic or dielectric cones may not directly be assigned to dielectric core/cladding light guides. The accurate results for the angle of aperture and divergence are stated here under consideration of the total internal reflection at the junction of the core to the surroundings. Furthermore the full angle of the conical element, the geometrical length and the varying diameters, the refractive indices and non-axial ray entrance are considered. All derivations are made by means of geometrical optics for meridional rays.     

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.