Group Velocity Difference Research Articles

Broadband amplification of ultraviolet laser pulses

Broadband amplification of laser pulses at 400 nm is demonstrated with a maximum gain of 3550 using non-collinear optical parametric amplification. Without depleting the pump, the spectral gain was found to be almost flat along the available 17-nm-wide spectrum of the signal pulse. It is also shown that the group velocity difference between the signal and pump pulses eventually results in an even broader amplified spectrum. The extension of this technique to other UV wavelengths can also be accomplished, so that femtosecond laser pulses between 300–400 nm can be directly amplified.

Bandwidth control of long-period grating-based mode converters in few-mode fibers

Control of the group-velocity differences between two distinct modes in a few-mode fiber can be used to define the spectral characteristics of long-period gratings written in them. Using this effect, we report the demonstration of strong mode conversion (>99%) with long-period fiber gratings over what is believed to be a record bandwidth of 63 nm. These novel spectra are obtained from gratings written in specially designed few-mode fibers in which the grating phase-matching condition is satisfied over a large spectral range. We show that the bandwidths of such mode converters can be tailored by suitably altering the design of the few-mode fibers. The polarization-dependent coupling for the mode converters varies by less than 0.004% over the entire spectrum.

Equivalent Medium Parameters for Numerical Modeling in Media with Near-Surface Low Velocities

We have developed a methodology to discretize an isotropic velocity model with low velocities near the free surface for full waveform numerical modeling. The method modifies the near-surface minimum velocity in a given (original) model by replacing parts of the model with equivalent medium parameters (EMP). The discretized model (with EMP) has a higher minimum velocity and minimizes the difference between the seismograms evaluated for the original model and the model with EMP. The method is suitable for studies requiring full waveform numerical modeling with a limited frequency range (such as a finite-difference full waveform modeling in a sedimentary basin). The discretized model with EMP is set to match locally surface-wave velocities evaluated in the original model over the frequency range of interest. The difference in group velocity calculated for the original vertical profile and the vertical profile with EMP provides an estimate of the error due to the modification of the original model.

Multichannel pulse dynamics in a stabilized Ginzburg-Landau system

We study the stability and interactions of chirped solitary pulses in a system of nonlinearly coupled cubic Ginzburg-Landau (CGL) equations with a group-velocity mismatch between them, where each CGL equation is stabilized by linearly coupling it to an additional linear dissipative equation. In the context of nonlinear fiber optics, the model describes transmission and collisions of pulses at different wavelengths in a dual-core fiber, in which the active core is furnished with bandwidth-limited gain, while the other, passive (lossy) one is necessary for stabilization of the solitary pulses. Complete and incomplete collisions of pulses in two channels in the cases of anomalous and normal dispersion in the active core are analyzed by means of perturbation theory and direct numerical simulations. It is demonstrated that the model may readily support fully stable pulses whose collisions are quasielastic, provided that the group-velocity difference between the two channels exceeds a critical value. In the case of quasielastic collisions, the temporal shift of pulses, predicted by the analytical approach, is in semiquantitative agreement with direct numerical results in the case of anomalous dispersion (in the opposite case, the perturbation theory does not apply). We also consider a simultaneous collision between pulses in three channels, concluding that this collision remains quasielastic, and the pulses remain completely stable. Thus, the model may be a starting point for the design of a stabilized wavelength-division-multiplexed transmission system.

Study of spatial–temporal characteristics of optical fiber based on ultrashort-pulse interferometry

We demonstrate a method for reconstruction of the modal intensity distribution of light at the output of an optical fiber. Spatial modes of the optical fiber are separated in time as a result of differences in group velocity and are detected experimentally by observation of the interference of the modal field distribution with the time-gating reference field. The detected interference patterns of the modal fields are analyzed, providing the spatial impulse response of the fiber. We also use interferometric correlation to determine the spatiotemporal characteristics of the fiber modes, such as pulse width, linear chirp, and group velocity, for each mode.

The impact of group velocity on frequency-hopping optical code division multiple access system

In this paper, we develop a systematic method that employs transfer function considering encoder, fiber channel, and decoder to analyze the frequency-hopping (FH) optical code-division multiple-access (OCDMA) system. We analyze the FH-OCDMA system when both single-mode fiber and dispersion-shifted fiber are employed as the transmission medium. The difference of group velocities affects system performance more seriously than dispersion effect does. The results show that single-mode fiber is not proper for a FH-OCDMA system, even if the transmission length is no more than 1 km. The dispersion-shifted fiber is suitable for a FH-OCDMA system, especially in an access network. We also propose an optical device to compensate the group velocities.

Probing Slow Polariton Propagation by Bipolaritons

Using a Four-Wave-Mixing (FWM) experiment in backward-scattering geometry the coherent dynamics of the quadrupole polarization associated with excitonic molecules is studied in bulk CdSe. By analyzing the FWM signal at negative delay times and exploiting the large differences in group velocities of the propagating polaritons, a picosecond dephasing time is found for the bipolariton. By comparison of the measured dephasing time with the calculated radiative lifetime of the bipolariton, the validity of the bipolariton representation is verified for excitonic molecules in CdSe at low temperatures.

Generation of a pure phase-modulated pulse by the cascading effect: a theoretical approach

New techniques to produce spatiotemporal phase modulation without the use of electro-optic devices are proposed and discussed. By using the nonlinear second-order effect in crystal it is possible to change the amplitude modulation of a pump wave into the phase of a signal wave. To that end, we propose the use of a well-known cascading configuration for which the phase mismatch is high. Analytical results of spatial and temporal incoherent phase modulation are developed with the correlation function formalisms. Furthermore, highly accurate expansions of signal phase and intensity are derived. The effects of group-velocity difference, group-velocity dispersion, and diffraction on the change of amplitude into phase modulation are studied. Finally, an experimental demonstration of a KDP crystal with a sinusoidal pump modulation that creates sinusoidal phase modulation is proposed.

Optical fiber for dispersion addressing

This letter presents a fully distributed forward propagating system, suitable for use with microbend sensors. The principle relies on selected mode launch in specially designed multimode fiber where a short pulse is launched into the fundamental mode. In the presence of microbend disturbance located down the sensing fiber, light couples from the fundamental to higher-order modes that propagate at different group velocity than the fundamental mode. The position of the disturbance is determined by the time delay between the pulse carried by the fundamental mode and by the pulse carried by higher-order modes. The group velocity difference is maximized by proper construction of the refractive index profile of the proposed fiber. Experimentally produced fibers exhibited difference of group velocities in ranges over 1%. This allows for easy reconstruction of position and amplitude of microbend deformations located down the sensing fiber.

On the Different Types of Superposed Solitonic Solutions In a Birefringent Optical Fibre

We have analysed the form of superposed solitonic femto-second pulses propagating in a birefringent optical fibre where the difference in polarisation dispersions and the difference in group velocities are taken into account. Here Hirota's approach is used to study the general structure of solitonic states. The graphical structure of these solutions are shown for specific material properties. On the other hand superposition of two kinds of solitary pulses are seen to propagate in a special situation when dispersion coefficients of two polarisations are assumed to be identical.

Numerical models of broad-bandwidth nanosecond optical parametric oscillators

We present three new methods for modeling broad-bandwidth, nanosecond optical parametric oscillators in the plane-wave approximation. Each accounts for the group-velocity differences that determine the operating linewidth of unseeded optical parametric oscillators, and each allows the signal and the idler waves to develop from quantum noise. The first two methods are based on split-step integration methods in which nonlinear mixing and propagation are calculated separately on alternate steps. One method relies on Fourier transforming the fields between t and ω to handle propagation, with mixing integrated over a Δz step; the other transforms between z and kz in the propagation step, with mixing integrated over Δt. The third method is based on expansion of the three optical fields in terms of their respective longitudinal empty cavity modes, taking into account the cavity boundary conditions. Equations describing the time development of the mode amplitudes are solved to yield the time dependence of the three output fields. These models exclude diffraction and group-velocity dispersion but can be readily extended to include them.

Analytical Expression for the Reduction of XPM-Induced Crosstalk by Walk-Off

Wavelength division multiplexing (WDM) is an attractive scheme to increase the capacity of the already installed optical links. However, the effect of cross-phase modulation (XPM) causes nonlinear crosstalk in intensity modulated direct detection WDM systems based on dispersive fibers and thus could limit the total number of channels that such a system can support. On the other hand, the interference among channels decreases due to the so-called walk-off with growing difference in group velocity and channel spacing, respectively. Considering the propagation of Gaussian pulses, a formula which describes analytically this diminution as a function of the differential group delay is derived. Since the data signals transmitted in different channels are statistically independent XPM induces random-like intensity fluctuations. The theoretical results for their variance are verified by means of simulations. For comparison purposes, the variance of intensity fluctuations induced by pulses with edges steeper than those of a Gaussian pulse is calculated numerically.

Variational approach for walking solitons in birefringent fibres

We use the variational method to obtain approximate analytical expressions for the stationary pulse-like solutions in birefringent fibres when differences in both phase velocities and group velocities between the two components and rapidly oscillating terms are taken into account. After checking the validity of the approximation, we study how the soliton pulse shape depends on its velocity and nonlinear propagation constant. By numerically solving the propagation equation we have found that most of these stationary solutions are stable.

Femtosecond soliton pulses in birefringent optical fibers

We consider femtosecond soliton-pulse propagation in a birefringent optical fiber where rapidly oscillating terms, the difference in polarization dispersions, and the difference in group velocities of the two polarization components have to be taken into account. We demonstrate the existence of a novel class of linearly polarized soliton states (with the linear polarization ranging from 0 to 2π). We also find the elliptically polarized soliton states, which do not appear to be acceptable to the coupled nonlinear Schrödinger equations describing the pulse evolution in the birefringent fiber when the different dispersions between the two polarizations are ignored and the group-velocity difference is taken into account. More importantly, the corresponding stability analysis reveals that within certain operating regions the fast soliton can be stable and the slow soliton can be unstable, whereas in the others the fast soliton is unstable and the slow soliton is stable, in contrast to those reported earlier by neglecting different polarization dispersions. On the other hand, both the linearly polarized soliton states and the elliptically polarized soliton states are found to be unstable. This indicates that for high-capacity coherent soliton communication in the femtosecond regime, the pulse must be launched along either the slow or the fast axis of a practical polarization-maintaining fiber. Finally, the potential applications of weakly unstable linearly polarized soliton states for ultrafast soliton switching are discussed.

Surface-wave propagation across the Mexican Volcanic Belt and the origin of the long-period seismic-wave amplification in the Valley of Mexico

A network of nine broad-band seismographs was operated from March to May 1994 to study the propagation of seismic waves across the Mexican Volcanic Belt (MVB) in the region of the Valley of Mexico. Analysis of the data from the network reveals an amplification of seismic waves in a wide period band al the stations situated in the southern part of the MVB. The group velocities of the fundamental mode of the Rayleigh wave in the period range 2–13 s are found to be lower in the southern part of the MVB than in its northern part and in the region south of the MVB. The inversion of dispersion curves shows that the difference in group velocities is due to the presence of a superficial low-velocity layer (with an average S-wave velocity of 1.7 km s-1 and an average thickness of 2 km) beneath the southern part of the MVB. This low-velocity zone is associated with the region of active volcanism. Numerical simulations show that this superficial low-velocity layer causes a regional amplification of 8–10 s period signals, which is of the same order as the amplification measured from the data. This layer also increases the signal duration significantly because of the dispersion of the surface waves. These results confirm the hypothesis of Singh et al. (1995), who suggested that the regional amplification observed in the Valley of Mexico is due to the anomalously low shear-wave velocity of the shallow volcanic rocks in the southern MVB

Resonance Thirring solitons in type II second-harmonic generation

It is shown that second-harmonic generation in a grating allows one to cancel the group-velocity difference between two polarization components at fundamental by means of nonlinearly induced phase shifts. This occurs when a new type of cascading soliton propagates on resonance.

Bright and dark simultons in second-harmonic generation

A symbiotic pair of dark (second-harmonic) and bright (fundamental frequency) solitons sustain each other and travel locked in second-harmonic generation dominated by group-velocity difference or spatial walk-off. The conditions of existence of the soliton pair are determined, and its stability in the presence of dispersion is discussed.

Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals

The effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals are numerically revealed. These calculations treat the transverse-mode profile and the temporal pulse shape of the interaction pulses simultaneously. Combining calculations with experimental results, the values of a second-order nonlinear coefficient and two-photon absorption coefficient at 0.6 μm are obtained as d24=4.2 pm/V and 0.35 pm/W, respectively. Due to the back-conversion, the maximum conversion efficiency with a 5-mm-length crystal is limited to about 10%. This is because the beam diameter and the pulse duration of the signal and idler fields become small in the propagation and interaction with the pump field cannot take place at the entire portion of the pump field. The calculation results also indicate that 280 fs output pulses are obtained from a 1 ps pump pulse by the pulse narrowing effect. It is also clarified that the back-conversion causes depression and splitting of the transverse mode and walk-off plays an important role in the transformation of the transverse-mode profile. The depression and splitting can be suppressed by using a short-length crystal or decreasing pump intensity.

Simultaneous source panging and bottom geoacoustic inversion using shallow water, broadband dispersion of fin whale calls

Beamformed time series of fin whale calls from the North Atlantic recently have been obtained. Spectrograms of these recordings have an unusual appearance—three to four downsweeping clicks occur in rapid succession, almost as if the whale was stuttering. These arrivals can be explained in terms of the differences in group velocity between the lowest‐order modes that propagate in the shallow water (about 350 m) waveguide. By matching predicted spectrograms calculated from a shallow water waveguide model with actual spectrograms, estimates of both the range of the whale and the compressional wave velocity in the ocean bottom are obtained. The approach makes various assumptions, including that the whale emits a signal with a downsweep rate of 25 Hz per second. However, known deviations from the assumptions can be incorporated into the modeling. The results have several implications such as that whale signals may provide loud, broadband, tomographic sources of opportunity for determining oceanographic/geophysical properties, and that some differences in whale call recordings from different populations of the same species may be caused by propagation effects. Might whales take advantage of propagation‐induced distortions in order to learn something about the ocean medium? [Work partially supported by ONR.]

Stationary solitonlike pulses in birefringent optical fibers.

We study pulse propagation in birefringent fibers when differences in both phase velocities and group velocities between the two components are taken into account. We have found that both slow and fast linearly polarized solitons are unstable when the group velocity difference is high enough, and that a two-parameter family of coupled soliton states appears in this regime.