Group Velocity Difference Research Articles

Supercontinuum generation in an anisotropic microstructure fiber with periodic modulation of hole ellipticity

The supercontinuum generation in an anisotropic microstructure fiber with periodic modulation of hole ellipticity has been numerically simulated. The structure proposed makes it possible to alternate fiber segments with positive and negative differences in group velocities, thus affecting the interaction of pulses with orthogonal polarizations. This configuration makes it possible to effectively control supercontinuum generation. The dynamics of polarized solitons in a microstructure fiber with high nonlinearity is simulated using the modified Schrodinger equation, including the stimulated Raman scattering and higher order dispersion.

Breaking time-resolution limits in pulse radiolysis

Pulse radiolysis, which is a time-resolved stroboscopic method based on ultrashort electron pulse and ultrashort analyzing light, is widely used for the study of the chemical kinetics and radiation primary processes or reactions. Although it has become possible to use femtosecond-pulse electron beam and femtosecond laser light in pulse radiolysis, the resolution is limited by the difference in group velocities of the electrons and the light in sample. In this contribution, we introduce a concept of equivalent velocity spectroscopy (EVS) into pulse radiolysis and demonstrate the methodology experimentally. In EVS, both the electron and the analyzing light pulses precisely overlap at every point in the sample and throughout the propagation time by rotating the electron pulse. The advance allows us to overcome the resolution degradation due to the different group velocity. We also present a method for measuring the rotated angle of the electron pulse and a technique for rotating the electron pulse with a deflecting cavity.

Reduction of Light Signal Pulse Distortion in Cascaded SFG–DFG Wavelength Conversion: Segmented QPM Interleaved by Short Wavelength Cut Filters

Cascaded sum-frequency-generation (SFG) and difference-frequency-generation (DFG) can implement a wavelength conversion between arbitrary combinations of input and output signal wavelengths. By using a tunable wavelength pump light, the output wavelength can be tuned to a desired wavelength. As in many wavelength conversion devices using the nonlinear optical effect, the group velocity difference between light pulses with different wavelength causes a walk-off effect deforming the output pulse shape. Thus, the device length should be kept short to avoid the walk-off effect resulting in limited conversion efficiency. In this report, we propose a method, for quasi-phase matched device, to maintain the pulse shape of the SFG light pulse along the propagation distance. The output DFG light pulse deformation is suppressed and the conversion efficiency can be increased by extending the device length.

Thermalization of incoherent nonlinear waves

The subject of incoherent nonlinear optics received a renewed interest since the first experimental demonstration of incoherent solitons in slowly responding photorefractive crystals. Several theories have been successfully developed to provide a detailed description of the dynamics of incoherent optical solitons. However, such theories leave unanswered the question regarding the long term evolution of a partially incoherent optical field propagating in a nonlinear medium. In analogy with kinetic gas theory, an incoherent optical field evolves, owing to nonlinearity, towards a thermodynamic equilibrium state. Wave turbulence theory describes the essential properties of this irreversible process of thermal wave relaxation to equilibrium. Such irreversible behavior is expressed by a H-theorem of entropy growth, whose origin is analogous to the celebrated Boltzmann’s H-theorem. In this review we analyze the thermalization of incoherent nonlinear optical fields in various circumstances. We shall begin with the simplest case where the optical field is ruled by the scalar NonLinear Schrodinger (NLS) equation. In this case wave thermalization is characterized by a condensation process of the optical field, whose thermodynamic properties are analogous to those of Bose-Einstein condensation, despite the fact that the considered optical wave is completely classical. We then study the thermalization of an ensemble of incoherent fields governed by the vector NLS equation. The influence of the relative intensity of the coupled fields reveals the existence of a process of coherence absorption: The condensation of the optical field is induced by the presence of another small-amplitude field, which absorbs almost all the noise of the system. Such a coherence absorption effect is shown to also occur in thermal quantum Bose gases. The influence of convection (group-velocity difference) on the thermalization process is also analyzed. A set of incoherent wave-packets is shown to irreversibly evolve towards an equilibrium state in which they propagate with an identical group-velocity. This velocity-locking effect has a thermodynamic origin and thus appears as a generic property of a system of incoherent nonlinear waves. The influence of a coherent coupling on wave thermalization leads to an unexpected process of spontaneous polarization of unpolarized incoherent light, without loss of energy. Finally, the influence of higher-order dispersion effects on optical thermalization is responsible for a dramatic spectral broadening phenomenon known as supercontinuum generation. This reveals that supercontinuum generation may be regarded as a consequence of the natural thermalization of an optical field to equilibrium. We finally show that the thermodynamic properties of incoherent nonlinear waves may be analyzed by means of the fundamental T dS equation of thermodynamics.

Reduction of light signal pulse distortion in cascaded sum-frequency-generation and difference-frequency-generation wavelength conversion

Cascaded sum-frequency-generation (SFG) and difference-frequency-generation (DFG) can implement a wavelength conversion between arbitrary combinations of input and output signal wavelengths. By using a tunable wavelength pump light, the output wavelength can be tuned to a desired wavelength. As in many wavelength conversion devices using the nonlinear optical effect, the group velocity difference between light pulses with different wavelength causes a walk-off effect deforming the output pulse shape. Thus the device length should be kept short to avoid the walk-off effect resulting in limited conversion efficiency. In this report, we propose a method for a quasi-phase matched (QPM) device to maintain the pulse shape of the SFG light pulse along the propagation distance. The output DFG light pulse deformation is suppressed and the conversion efficiency can be increased by extending the device length.

40-Gbit/s Operation of Ultracompact Photodetector-Integrated Dispersion Compensator Based on One-Dimensional Photonic Crystals

Utilizing large optical group-velocity dependence on wavelength without polarization-mode dependence, we have developed an ultracompact dispersion compensator based on multiple one-dimensional coupled-defect-type photonic crystals. The photonic crystal of the compensator, designed for a 1.55-µm optical communication system, consists of a multilayer thin-film structure and defect layers. The thin-film structure is substrate-free, which enables the compensator to be small, that is, a 1.4-mm-edge cube. To obtain a large group-velocity difference, 60 substrate-free films were stacked to form the compensator. The passband of the compensator is 2 nm, and the group-delay time difference within the band is more than 100 ps. A dispersion-compensator module integrated with a photodetector was fabricated. A 40-Gbit/s non-return-to-zero optical-transmission experiment was carried out with the compensator, demonstrating dispersion-compensation operation over a 10-km standard single-mode fiber, the dispersion of which corresponds to 170 ps/nm.

Dispersion measurement technique based on the self-seeding laser oscillation of a Fabry–Perot laser diode

A simple dispersion measurement technique has been proposed and demonstrated by using the self-seeding laser oscillation of a Fabry–Perot laser diode through an optical closed-loop path. When the multi-mode optical pulses emitted from the laser are re-injected into the laser after traversing a fiber-under-test, a single mode laser oscillation occurs through the closed-loop path due to the group velocity difference between the pulses of different wavelengths. We measured the dispersion parameter of the fiber-under-test from the modulation frequency changes required to induce single-mode laser oscillations through the optical closed-loop path. The maximum measurement error was less than 1.5% for the optical fibers as compared with a commercial instrument.

Conventional and photonic crystal optical fibre for localization sensor

We present theoretical comparison of sesing properties of two kinds of the optical fibre devoted to the localisation sensor. The sensor bases on the group velocity difference of two modes guided in two separated regions of the optical fibre.

Breaking resolution limits in ultrafast electron diffraction and microscopy

Ultrafast electron microscopy and diffraction are powerful techniques for the study of the time-resolved structures of molecules, materials, and biological systems. Central to these approaches is the use of ultrafast coherent electron packets. The electron pulses typically have an energy of 30 keV for diffraction and 100-200 keV for microscopy, corresponding to speeds of 33-70% of the speed of light. Although the spatial resolution can reach the atomic scale, the temporal resolution is limited by the pulse width and by the difference in group velocities of electrons and the light used to initiate the dynamical change. In this contribution, we introduce the concept of tilted optical pulses into diffraction and imaging techniques and demonstrate the methodology experimentally. These advances allow us to reach limits of time resolution down to regimes of a few femtoseconds and, possibly, attoseconds. With tilted pulses, every part of the sample is excited at precisely the same time as when the electrons arrive at the specimen. Here, this approach is demonstrated for the most unfavorable case of ultrafast crystallography. We also present a method for measuring the duration of electron packets by autocorrelating electron pulses in free space and without streaking, and we discuss the potential of tilting the electron pulses themselves for applications in domains involving nuclear and electron motions.

Parametric amplification and up-conversion of optical image in coupled nonlinear optical processes

We develop quantum theory of process of the parametric optical image amplification at high-frequency pumping which is accompanied by up - conversion one. Such interactions can be implemented by two coupled three-frequency optical processes. The theory developed takes into account the diffraction effect and the difference of group velocities of interacting waves. The expressions for mean photon numbers and noise figures of the interacting waves are obtained and the dependence of these parameters on the interaction length are examined.

Gain Properties of multi-wavelength time division multiplexed Raman amplifier

We report gain properties of the multi-wavelength pulsed Raman pump. Based on fiber dispersion property, we obtain the group velocity difference between pump pulses which imposes the upper limit of pulse repetition rate beyond which pump-to-pump interaction occurs. The pump-to-pump interaction can be severe when pump instantaneous power is high due to small duty cycle. However, bigger duty cycle imposes much lower limit to the pulse repetition rate. Therefore, an optimized level of duty cycle is required. In addition, shorter pump wavelength separation helps to increase the upper limit of pulse repetition rate. Ultimately this will improve the noise performance of TDM Raman amplifier.

Pulse compression in a silver gallium sulfide, midinfrared, synchronously pumped optical parametric oscillator

We present experiments and numerical modeling of optical-pulse compression in a silver gallium sulfide, synchronously pumped optical parametric oscillator. In the experiments, 10 ps pump pulses from a pulsed Nd:YAG laser interacted in the parametric oscillator to generate infrared output pulses as short as 500 fs, yielding over 20-fold compression. Parametric conversion and pulse compression were studied by numerical simulation of the nonlinear wave equations and found to be in excellent agreement. The compression mechanism is related to group-velocity walkoff in the nonlinear interaction. Dispersion measurements and simulations of pulse compression in the wavelength range of 2.5-4.0 µm indicate that compression is inversely related to the signal-idler group-velocity difference. Although compression requires group-velocity walkoff between the pump and signal waves, the compression is most strongly controlled by the mismatch between the signal and idler group velocities.

Sonar detection performance prediction of a moving source in an uncertain environment

This paper addresses the problem of passive sonar detection of a moving acoustic source when both the signal spatial wavefront and background noise field are uncertain. The classic sonar equation is derived for a stationary source-receiver geometry and known environment. For dynamic scenarios, however, array gain (AG) and transmission loss (TL) can fluctuate in time and frequency over the integration time and bandwidth used. This is caused by signal multipath group and phase velocity differences at the receiver array. Moreover, for adaptive methods, noise covariance matrix snapshot support is often limited. This paper presents methods for estimating TL and AG under these conditions from a moving source of opportunity. These estimates are then used to predict adaptive detection performance. Results for probability of detection versus signal-to-noise ratio using real horizontal array data from the Swellex-96 experiment are shown to compare favorably with theoretically predicted detection performance. [Work supported by ONR.]

Ultrafast Single-Shot Optical Oscilloscope based on Time-to-Space Conversion due to Temporal and Spatial Walk-Off Effects in Nonlinear Mixing Crystal

A simple method for single-shot sub-picosecond optical pulse diagnostics has been demonstrated by imaging the time evolution of the optical mixing onto the beam cross section of the sum-frequency wave when the interrogating pulse passes over the tested pulse in the mixing crystal as a result of the combined effect of group-velocity difference and walk-off beam propagation. A high linearity of the time-to-space projection is deduced from the process solely dependent upon the spatial uniformity of the refractive indices. A snap profile of the accidental coincidence between asynchronous pulses from separate mode-locked lasers has been detected, which demonstrates the single-shot ability.

Pulse collisions in the stretched-pulse fiber laser.

We report the observation of a new regime of operation in the stretched-pulse fiber laser in which two groups of bound pulses travel in the cavity at different velocities. The pulse groups collide periodically and remain apparently unaltered after the collisions. The observed group-velocity difference is shown to exhibit a strong dependence on the time interval between the pulses in each bound state.

Minimization of the pulse's timing jitter in a dispersion-compensated WDM system

We address the problem of the collision-induced crosstalk between pulses in a dispersion-compensated WDM system composed of a periodic array of cells that include two or three fiber segments. Both the cross- and self-phase-modulation nonlinearities are taken into account. A semi-analytical approximation and direct simulations are used to calculate the frequency shift (FS) of colliding pulses, and to search for conditions which provide for minima of the FS and the temporal shift (TS), including the most promising possibility of minimizing both shifts simultaneously. Semi-analytical results, obtained by means of the perturbation theory, are in qualitative agreement with the numerical findings, especially in regimes near the optimum. In searching for the FS and TS minima, we investigate the effect of changing the initial width and chirp of the pulse, position of the amplifier within the dispersion–compensation period, group-velocity difference between the channels, allocation of the group-velocity-dispersion (GVD) inside the cell, and the average GVD. We conclude that a more sophisticated dispersion–compensation map, with three different local values of GVD, may be significantly more efficient than the one based on two different segments. A global FS minimum, with respect to the variation of all the parameters, is found.

Enhancement of third harmonic generation by wave vector mismatch to counter phase-modulation

Recent experimental developments in material sciences have generated hope that it will be possible to devise optical media where the difference in group velocity between the fundamental and third harmonic may be strongly suppressed. Under these circumstances both pulses would travel together over a long distance. This would lead to an enhancement of the generation process, and hence strong focusing and/or using ultra-short pulses might not be crucial. If the perfect phase matching condition is assumed, the only remaining mechanisms to decrease efficiency are self and cross phase modulation. Here we suggest that, instead of exactly matching wave vectors, we admit a small mismatch and show how it can be tailored to compensate for the cross phase modulation of the third harmonic by the fundamental during the generation process. This is very beneficial for the efficiency of third harmonic generation, even increasing it by a factor of two or more.

Optimization of the split-step fourier method in modeling optical-fiber communications systems

We studied the efficiency of different implementations of the split-step Fourier method for solving the nonlinear Schro/spl uml/dinger equation that employ different step-size selection criteria. We compared the performance of the different implementations for a variety of pulse formats and systems, including higher order solitons, collisions of soliton pulses, a single-channel periodically stationary dispersion-managed soliton system, and chirped return to zero systems with single and multiple channels. We introduce a globally third-order accurate split-step scheme, in which a bound on the local error is used to select the step size. In many cases, this method is the most efficient when compared with commonly used step-size selection criteria, and it is robust for a wide range of systems providing a system-independent rule for choosing the step sizes. We find that a step-size selection method based on limiting the nonlinear phase rotation of each step is not efficient for many optical-fiber transmission systems, although it works well for solitons. We also tested a method that uses a logarithmic step-size distribution to bound the amount of spurious four-wave mixing. This method is as efficient as other second-order schemes in the single-channel dispersion-managed soliton system, while it is not efficient in other cases including multichannel simulations. We find that in most cases, the simple approach in which the step size is held constant is the least efficient of all the methods. Finally, we implemented a method in which the step size is inversely proportional to the largest group velocity difference between channels. This scheme performs best in multichannel optical communications systems for the values of accuracy typically required in most transmission simulations.

Coherence properties of the parametric three-wave interaction driven from an incoherent pump.

We consider the basic problem of the parametric generation process from an incoherent pump wave. The analysis of the degenerate configuration of the two-wave interaction reveals that the mutual convection (i.e., group-velocity difference) between the incoherent pump and the signal (i.e., the daughter wave) may quench their parametric interaction, so that the gain experienced by the signal may become arbitrarily small. Conversely, in the absence of convection, the incoherent pump efficiently amplifies the signal wave, although this amplification process cannot lead to the generation of a coherent signal. However, in the case of nondegenerate three-wave interaction, we show the existence of a convection-induced phase-locking mechanism in which the incoherence of the pump is absorbed by the idler wave allowing the signal wave to grow efficiently with a high degree of coherence. We calculate explicitly the autocorrelation function of the generated signal in this regime of coherent-incoherent interaction. The analysis reveals that, owing to the convection-induced averaging process that accompanies the phase-locking mechanism, the degree of coherence of the signal increases as the degree of coherence of the pump decreases. We establish the experimental conditions that would allow for the observation of the transition between the incoherent and the coherent regimes of the three-wave parametric interaction.

Solitons in a three-wave system with intrinsic linear mixing and walkoff

A modification of the usual Type-II second-harmonic-generation model is proposed, which includes two additional features: linear conversion and walkoff (group-velocity difference) between two components of the fundamental-frequency (FF) wave. Physical interpretations of the model are possible in both temporal and spatial domains. In the absence of the intrinsic walkoff, the linear mixing makes real soliton solutions stable or unstable, depending on the relative sign of the two FF components. Unstable solitons spontaneously re-arrange themselves into stable ones. Fundamental solitons change their shape (in particular, they develop chirp) but remain stable if the intrinsic walkoff is included. In addition, quasi-stable double-humped solitary waves are found in the latter case.