Propagation Of Short Pulses Research Articles

Supercontinuum generation in submicrometer diameter silica fibers

Silica nanowires provide strong mode confinement in a cylindrical silica-core/air-cladding geometry and serve a model system for studying nonlinear propagation of short optical pulses inside fibers. We report on the fiber diameter dependence of the supercontinuum generated by femtosecond laser pulses in silica fiber tapers with average diameters in the range of 200 nm to 1200 nm. We observe a strong diameter-dependence of the spectral broadening, which can be attributed to the fiber's diameter-dependent dispersion and nonlinearity. The short interaction length (less than 20 mm) and the low energy threshold for supercontinuum generation (about 1 nJ) make tapered fibers with diameters between 400 nm and 800 nm an ideal source of coherent white-light source in nanophotonics.

Near-field imaging of nonlinear pulse propagation in planar silica waveguides

A simplified near-field scanning optical microscope is employed to image the propagation of short laser pulses in planar silica waveguides, in the anomalous dispersion regime, under varying conditions of input beam power and width. Our results show a complex evolution of the transverse intensity profiles of the beam when there is a pronounced difference between the input diffraction and dispersion lengths. Numerical simulations confirm that these complex spatial dynamics are intimately related to the temporal and spectral evolution of the pulse.

Least-squares support vector machines modelization for time-resolved spectroscopy

By use of time-resolved spectroscopy it is possible to separate light scattering effects from chemical absorption effects in samples. In the study of propagation of short light pulses in turbid samples the reduced scattering coefficient and the absorption coefficient are usually obtained by fitting diffusion or Monte Carlo models to the measured data by use of numerical optimization techniques. In this study we propose a prediction model obtained with a semiparametric modeling technique: the least-squares support vector machines. The main advantage of this technique is that it uses theoretical time dispersion curves during the calibration step. Predictions can then be performed by use of data measured on different kinds of sample, such as apples.

On highly convergent 2D acoustic and elastic wave propagation models

AbstractThe presented approach for reducing the phase and group errors in short wavelength pulses propagation modelling is based upon modal error minimization. A computational model is built of component substructures (CS) the matrices of which are obtained by modal synthesis. The necessary modal properties of CS are established by solving the cumulative modal error minimization problem for a sample domain the exact modal frequencies of which are known theoretically. Earlier the approach has been demonstrated to work well in 1D case. In this work the results for 2D rectangular meshes describing elastic and/or acoustic wave propagation have been obtained. As a result, models having up to 80% of modal frequencies with an error less than 2% can be obtained by using the optimized component substructures. Though the synthesized mass matrices are non‐diagonal, the obtained dynamic models are able to simulate short transient waves and wave pulses propagating in elastic or acoustic environments by using only a few nodal points per pulse length. Copyright © 2005 John Wiley & Sons, Ltd.

Statistical description of short pulses in long optical fibers: effects of nonlocality

We present a statistical description of the propagation of short pulses in long optical fibers, taking into account the Kerr and nonlocal nonlinearities on an equal footing. We use the Wigner approach on the modified nonlinear Schrödinger equation to obtain a wave kinetic equation and a nonlinear dispersion relation. The latter shows that the optical pulse decoherence reduces the growth rate of the modulational instability and thereby contributes to the nonlinear stability of the pulses in long optical fibers. It is also found that the interaction between spectral broadening and nonlocality tends to extend the instability region.

Ultrashort rectangular optical pulse generation by nonlinear directional couplers

We numerically demonstrate the generation of femtosecond rectangular optical pulses by nonlinear directional couplers. Single and cascaded coupler structures are investigated and the conditions for generating a rectangular pulse are presented. It is shown that under realizable conditions, femtosecond rectangular-like pulse can be generated in a second-order cascaded NLDC with 5 mm half-beat length and picosecond ideal rectangular pulse can be achieved in a third-order cascaded NLDC. With respect to the short pulse propagation, the influence of intermodal and third-order dispersions are included in the numerical analysis.

Analysis of the four wave mixing effect (FWM) in a dispersion decreasing fiber (DDF) for a WDM system

We did a numerical investigation of the propagation of short light pulses in the region of 1.55 μm and the conversion efficiency (CE) for the four wave mixing generation (FWM) of ordinary and dispersion decreasing fibers for use in wavelength division multiplexing (WDM) systems. Our simulations studies three different profiles, linear, hyperbolic, and constant. One conclude that for all the profiles there is decrease of the conversion efficiency with the increase in the channel separation. The hyperbolic profile present a higher efficiency of around 1000 above in magnitude compared with the others profiles at 0.2 nm of channel separation. We calculate the conversion efficiency versus the fiber length for the three profiles. The conversion efficiency for the hyperbolic profile is higher when compared to the constant and linear profiles. The other interesting point of the hyperbolic profile is that the increase of the CE in the beginning of the fiber does not show any oscillation in the CE value ( log η ), which was observed for the constant and linear profiles. For all the profiles there is an increase of the conversion efficiency with the increase of the pump power. The compression factor C i for the generated FWM signal at ω 3 was measured along the DDF's and the constant profile fibers. One can conclude that with the use of decreasing dispersion profile (DDF) fibers one can have a control of the (CE) conversion efficiency and the compression factor of the four wave mixing (FWM) generation in WDM systems.

Extraction of /spl epsiv//sub r/(f) and tan/spl delta/(f) for printed circuit board insulators up to 30 GHz using the short-pulse propagation technique

In this paper, the self-consistent, frequency-dependent dielectric constant epsivr(f) and dielectric loss tandelta(f) of several materials are determined over the range 2 to 30 GHz using a short-pulse propagation technique and an iterative extraction based on a rational function expansion. The simple measurement technique is performed in the time domain on representative printed circuit board wiring. Broadband, fully causal transmission-line models based on these results are generated up to 50 GHz for card wiring using low loss materials including BT, Nelco N4000-13, and Nelco N4000-13SI. Simulation and modeling results highlight the need for the accurate frequency-dependent dielectric loss extraction. Signal propagation based on these results shows very good agreement with measured step and pulse time-domain excitations and provides validation of the measurement and model generation technique

The Impact of Out-of-Band Crosstalk on Optical Communication Link Performances

In modern long-haul optical system operating at high bit rates, besides combined influence of nonlinear and dispersive effects, it is of great importance to take into consideration the influence of crosstalk on optical pulse propagation. This paper deals with the so-called out-of-band crosstalk and its influence on propagation of short optical pulses through nonlinear dispersive single-mode optical fiber (SMF).

Dynamical behavior of ultrashort pulse laser in para-nitroaniline molecules

The electronic structures and dipole moments of para- nitroaniline molecule are calculated by use of density functional theory at ab initio level. We then inve stigate theoretically the interaction between the ultrashort pulse laser and the para-nitroaniline molecule medium by solving the full Maxwell-Bloch equations. The effects of permanent dipole moments on the pulse reshaping, the spectrum com ponents, and the evolutions of energy state populations are discussed in detail. The results show that the standing slowly varying envelope and the rotating-wav e approximations fail to give a good description for the propagation of an ultra short pulse in the molecule medium. Furthermore, the dipole moments of the molec ule make the propagation deviate from the area theorem further and make the pul se split more quickly. When the pulse with the excitation energy of the charge-t ransfer state propagates in the para-nitroaniline molecule medium, the second-ha rmonic spectral component appears obviously and becomes stronger as the propagat ing distance increases, which displays the high two-photon absorption properties of the molecule.

Propagation of Radar Pulses from a Horizontal Dipole in Variable Dielectric Ground: A Numerical Approach

We numerically investigate the propagation of radar type short pulses from a horizontal dipole in the presence of some simple models of inhomogeneous ground with a flat surface. We use 3-dimensional (3-D) pseudospectral time domain (PSTD) and 2-D finite difference time domain forward modeling to determine the range and azimuth dependence of electric field components and to simulate events in a moveout profile. The models are: (i) a uniform half space with either high or low conductivity; (ii) a vertical dielectric wedge; (iii) a surface thin layer with a monocline wedge overlaid on the dielectric half space. Our homogeneous results agree with the analytical solutions, and more clearly show the significant vertical electric field component, which occurs for all models. The incorporation of an anomalous dielectric quadrant does not affect the air wave and only complicates ground wave propagation near the boundary. Modeling of a monocline dielectric wedge shows predictable subsurface reflections and refractions, some of which are highly dispersive events, depending on the direction of propagation. We present two field examples that appear to demonstrate some of our findings. We conclude that air waves make suitable references for moveout profiles regardless of dielectric complications, and that our results provide some insight into the interpretation of unique events seen in moveout profiles.

Propagation of short pulses in an active nonlinear two-core optical fiber

The switching dynamics of short pulses in an active nonlinear two-core fiber coupler is investigated theoretically. The analysis takes into account the effects of coupling-coefficient dispersion, gain bandwidth, and gain saturation. In particular, we demonstrate that the pulse breakup effect due to coupling-coefficient dispersion can be suppressed by limiting the bandwidth of the linear gain, whether gain saturation is considered or not.

Highly convergent dynamic models obtained by modal synthesis with application to short wave pulse propagation

AbstractA general approach for obtaining the matrices of a substructure ensuring minimum modal frequency errors of the whole structure is presented. The mass and stiffness matrices of a small component domain of selected dimension are obtained by applying the modal synthesis of a limited number of close‐to‐exact modes such that after assembling a larger joined domain model the modal convergence rate of the latter should be as high as possible. The goal is achieved by formulating the minimization problem for the penalty‐type target function representing the cumulative relative modal frequency error of the joined sample domain and by applying the gradient descent minimization method. After the optimum matrices of a component domain are obtained, they can be used in any structure as higher‐order elements or super‐elements. The well‐known generalized mass matrices obtained as a weighted sum of lumped and consistent components can be treated as a special case of the presented approach. The obtained dynamic models are used for modelling short transient waves and wave pulses propagating in elastic or acoustic environments by using a only a few nodal points per pulse length. Copyright © 2004 John Wiley & Sons, Ltd.

Propagation of intense short laser pulses in a gas of atomic clusters

We present a model and numerical simulations for the propagation of intense short laser pulses in gases of atomic clusters. As the pulse propagates through the clusters, they absorb energy, expand and explode. The clustered gas thus acts as a medium with time dependent effective dielectric constant. A self-consistent model for the cluster expansion and the laser pulse propagation is developed. Self-focusing of the laser pulse, coupling of laser energy to clusters and the evolution of the pulse spectrum are studied for a laser-cluster system with typical laboratory parameters.

Long-distance propagation of intense short laser pulse in air

Long-distance propagation of intense laser pulse in air is reconsidered analytically by generalizing the analogy between the laser spotsize and the orbit of a classical particle. It is shown that multiphoton ionization introduces unique features to the laser-air interaction, thereby enabling the long-distance behavior. Several interesting characteristics of the latter are pointed out.

Femtosecond dynamics of active semiconductor waveguides: microscopic analysis and experimental investigations

We present theoretical and experimental results of nonlinear amplification and propagation of short optical pulses in Fabry–Perot semiconductor lasers. The theoretical description is based on spatially resolved Maxwell–Bloch–Langevin equations that take into account the spatially varying light-field dynamics including counterpropagation, diffraction, self-focusing, and the microscopic carrier dynamics including carrier heating and carrier relaxation. Femtosecond pump–probe measurements using upconversion and femtosecond-resolved pump–probe measurements and frequency-resolved optical gating on a Fabry–Perot laser allow a combined analysis of the transmitted pulses in real time and the spectral domain. The experimental results are compared with the microscopically calculated gain and index distributions, pulse shapes, and optical spectra. In order to assess the full potential of semiconductor lasers and amplifiers, a quantitative measurement and understanding of amplitude and phase dynamics is required. The computer simulations of the ultrashort dynamics of semiconductor waveguides with optical injection of light pulses provide insight into the dynamic spectral gain and index changes responsible for frequency drifts and self-phase modulation, visualization of propagation effects, and a time- and frequency-resolved analysis of the amplified light pulses.

Numerical developments for short-pulsed Near Infra-Red laser spectroscopy. Part I: direct treatment

This two part study is devoted to the numerical treatment of short-pulsed laser near infra-red spectroscopy. The overall goal is to address the possibility of numerical inverse treatment based on a recently developed direct model to solve the transient radiative transfer equation. This model has been constructed in order to incorporate the last improvements in short-pulsed laser interaction with semi-transparent media and combine a discrete ordinates computing of the implicit source term appearing in the radiative transfer equation with an explicit treatment of the transport of the light intensity using advection schemes, a method encountered in reactive flow dynamics. The incident collimated beam is analytically solved through Bouger–Beer–Lambert extinction law. In this first part, the direct model is extended to fully non-homogeneous materials and tested with two different spatial schemes in order to be adapted to the inversion methods presented in the following second part. As a first point, fundamental methods and schemes used in the direct model are presented. Then, tests are conducted by comparison with numerical simulations given as references. In a third and last part, multi-dimensional extensions of the code are provided. This allows presentation of numerical results of short pulses propagation in 1, 2 and 3D homogeneous and non-homogeneous materials given some parametrical studies on medium properties and pulse shape. For comparison, an integral method adapted to non-homogeneous media irradiated by a pulsed laser beam is also developed for the 3D case.

Propagation of ultra-short optical pulses in cubic nonlinear media

We derive a partial differential equation that approximates solutions of Maxwell’s equations describing the propagation of ultra-short optical pulses in nonlinear media and which extends the prior analysis of Alterman and Rauch [Phys. Lett. A 264 (2000) 390; Diffractive nonlinear geometric optics for short pulses, Preprint, 2002]. We discuss (non-rigorously) conditions under which this approximation should be valid, but the main contributions of this paper are: (1) an emphasis on the fact that the model equation for short pulse propagation may depend on the details of the optical susceptibility in the wavelength regime under consideration, (2) a numerical comparison of solutions of this model equation with solutions of the full nonlinear partial differential equation, (3) a local well-posedness result for the model equation and (4) a proof that in contrast to the nonlinear Schrödinger equation, which models slowly varying wavetrains, this equation has no smooth pulse solutions which propagate with fixed shape and speed.

Possible Origin of Ultralow-Frequency Whistlers

The sonographic analysis of records of ultralow-frequency emissions recorded by the induction magnetometer at the Mirnyi observatory (Antarctica) in 1981–1985 has revealed the presence of a special class of signals in the frequency band 0.25–5 Hz having a characteristic dispersion reminiscent of the dynamic spectra of LHR-whistlers observed in the VLF band. The ULF whistlers are observed, as a rule, at morning and evening hours of local time at moderate values of the Kp-index (0 < Kp < 4). The analysis of the frequency–time behavior of observed signals shows that the canalized propagation of short broadband pulses as magnetosonic waves in the layered medium, for example, in the magnetospheric current sheet can serve as a possible cause of the dispersion. Such sporadic phenomena on the magnetopause as microreconnections or FTE-events may be sources of these pulses.

Measurement of the moments of the relaxation time spectrum of a liquid by pulsed acoustic spectroscopy

On the basis of theoretical results describing the propagation of short acoustic pulses in relaxation media, the temporal characteristics of a signal that carry the information on the first five moments of the relaxation time spectrum (RTS) are determined. The measurement of these characteristics forms the basis of the proposed variant of pulsed acoustic spectroscopy of relaxation media. An experimental setup was developed in which short acoustic pulses were excited by a neodymium glass laser. Test measurements of RTS moments for an acetic acid, the liquid with a single relaxation time, are carried out.