Z-scan theory based on a diffraction model

Based on Fresnel-Mrchhoff diffraction theory, a diffraction model of nonlinear optical media interacting with a Gaussian beam has been set up that can interpret the Z-scan phenomenon in a new way. This theory not only is consistent with the conventional Z-scan theory for a small nonlinear phase shift but also can be used for larger nonlinear phase shifts. Numerical computations indicate that the shape of the Z-scan curve is greatly affected by the value of the nonlinear phase shift. The symmetric dispersionlike Z-scan curve is valid only for small nonlinear p base shifts (\Deltaphi(0)\ < pi), but, with increasingly larger nonlinear phase shifts, the valley of the transmittance is severely suppressed and the peak is greatly enhanced. The power output through the aperture will oscillate with increasing nonlinear phase shift caused by the input laser power. The aperture transmittance will attenuate and saturate with increasing Kerr constant. (C) 2003 Optical Society of America.

Nonlinear copropagation of two optical pulses of different frequencies in photonic crystal fibers

A theoretical investigation of the nonlinear copropagation of two optical pulses of different frequencies in a photonic crystal fiber is presented. Different phenomena are observed depending on whether the wavelength of the signal pulse is located in the normal or the anomalous dispersion region. In particular, it is found that the phenomenon of pulse trapping occurs when the signal wavelength is located in the normal dispersion region while the pump wavelength is located in the anomalous dispersion region. The signal pulse suffers cross-phase modulation by the Raman shifted soliton pulse and it is trapped and copropagates with the Raman soliton pulse along the fiber. As the input peak power of the pump pulse is increased, the red-shift of the Raman soliton is considerably enhanced with the simultaneous further blue-shift of the trapped pulse to satisfy the condition of group velocity matching.

Fast Locking and High Accurate Current Matching Phase-Locked Loop

In this paper, a charge-pump based phase-locked loop (CPLL) that can achieve fast locking and tiny deviation is proposed and analyzed. A lock-aid circuit is added to achieve fast locking of the CPLL. Besides, a novel differential charge pump which has good current matching characteristics and a PFD with delay cell has been used in this PLL. The proposed PILL circuit is designed based on the 0.35um 2P4M CMOS process with 3.3V/5V supply voltage. HSPICE simulation shows that the lock time of the proposed CPLL can be reduced by over 72% in comparison to the conventional PILL and its charge pump sink and source current mismatch is only 0.008%.

Non-Gravitational Effects with Density-Matching in Evaluating the Influence of Sedimentation on Colloidal Coagulation

The method of density matching between the solid and liquid phases is often adopted to effectively eliminate the effect of sedimentation of suspensions in studies on dynamic behaviour of a colloidal system. However, the associated changes in the solvent composition may bring side effects to the properties investigated and therefore might lead to a faulty conclusion if the relevant correction is not made. To illustrate the importance of this side effect, we present an example of the sedimentation influence on the coagulation rate of suspensions of 2 μm (diameter) polystyrene. The liquid mixtures, in the proper proportions of water (H2O), deuterium oxide (D2O) and methanol (MeOH) as the liquid phase, density-matched and unmatched experiments are performed. Besides the influence of viscosity, the presence of methanol in solvent media, used to enhance the sedimentation effect, causes significant changes (reduction) in rapid coagulation rates compared to that in pure water. Without the relevant corrections for those non-gravitational factors it seems that gravitational sedimentation would retard the coagulation. The magnitude of the contribution from the non-gravitational factor is quantitatively determined, making the relevant correction possible. After necessary corrections for all factors, our experiments show that the influence of the sedimentation on coagulation rates at the initial stage of the coagulation is not observable.

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Evolution induced catastrophe in a nonlinear dynamical model of material failure

In order to study the failure of disordered materials, the ensemble evolution of a nonlinear chain model was examined by using a stochastic slice sampling method. The following results were obtained. (1) Sample-specific behavior, i.e. evolutions are different from sample to sample in some cases under the same macroscopic conditions, is observed for various load-sharing rules except in the globally mean field theory. The evolution according to the cluster load-sharing rule, which reflects the interaction between broken clusters, cannot be predicted by a simple criterion from the initial damage pattern and even then is most complicated. (2) A binary failure probability, its transitional region, where globally stable (GS) modes and evolution-induced catastrophic (EIC) modes coexist, and the corresponding scaling laws are fundamental to the failure. There is a sensitive zone in the vicinity of the boundary between the GS and EIC regions in phase space, where a slight stochastic increment in damage can trigger a radical transition from GS to EIC. (3) The distribution of strength is obtained from the binary failure probability. This, like sample-specificity, originates from a trans-scale sensitivity linking meso-scopic and macroscopic phenomena. (4) Strong fluctuations in stress distribution different from that of GS modes may be assumed as a precursor of evolution-induced catastrophe (EIC).

Optimization of high-order harmonic by genetic algorithm for the chirp and phase of few-cycle pulses

The brightness of a particular harmonic order is optimized for the chirp and initial phase of the laser pulse by genetic algorithm. The influences of the chirp and initial phase of the excitation pulse on the harmonic spectra are discussed in terms of the semi-classical model including the propagation effects. The results indicate that the harmonic intensity and cutoff have strong dependence on the chirp of the laser pulse, but slightly on its initial phase. The high-order harmonics can be enhanced by the optimal laser pulse and its cutoff can be tuned by optimization of the chirp and initial phase of the laser pulse.

Accurate determination of the absolute phase and temporal-pulse phase of few-cycle laser pulses

A Fourier analysis method is used to accurately determine not only the absolute phase but also the temporal-pulse phase of an isolated few-cycle (chirped) laser pulse. This method is independent of the pulse shape and can fully characterize the light wave even though only a few samples per optical cycle are available. It paves the way for investigating the absolute phase-dependent extreme nonlinear optics, and the evolutions of the absolute phase and the temporal-pulse phase of few-cycle laser pulses.

Tunneling-induced large cross-phase modulation in an asymmetric quantum well

We propose an asymmetric double AlGaAs/GaAs quantum well structure with a common continuum to generate a large cross-phase modulation (XPM). It is found, owing to resonant tunneling, that a large XPM can be achieved with vanishing linear and two-photon absorptions. (c) 2007 Optical Society of America.

Phase-step calibration technique based on a two-run-times-two-frame phase-shift method

A novel phase-step calibration technique is presented on the basis of a two-run-times-two-frame phase-shift method. First the symmetry factor M is defined to describe the distribution property of the distorted phase due to phase-shifter miscalibration; then the phase-step calibration technique, in which two sets of two interferograms with a straight fringe pattern are recorded and the phase step is obtained by calculating M of the wrapped phase map, is developed. With this technique, a good mirror is required, but no uniform illumination is needed and no complex mathematical operation is involved. This technique can be carried out in situ and is applicable to any phase shifter, whether linear or nonlinear. (c) 2006 Optical Society of America.

Control of polarization signal distortion by frequency domain phase conjugation in optical fiber systems

Optical frequency domain phase conjugation (FDPC) is based on phase conjugation of spectrum of an input signal. It is equivalent to the phase conjugation and the time reversal of the temporal envelope of an input signal. The use of FDPC to control polarization signal distortion in birefringent optical fiber systems is proposed. Evolution of polarization signals in the system using midway FDPC is analyzed theoretically and simulated numerically. It is shown that the distortion of polarization signals can be controlled effectively by FDPC. The impairments due to dispersion and nonlinear effects can be suppressed simultaneously.

Analysis of beam-quality degradation in nonlinear frequency conversion

Based on the ripple transfers of electric-field amplitude and phase in frequency tripling, simple formulas are derived for the harmonic laser's beam-quality factor M-3omega(2), with an arbitrary fundamental incidence to ideal nonlinear crystals. Whereas the harmonic beam's quality is generally degraded, the beam's divergence is similar to that of the fundamental after nonlinear frequency conversion. For practical crystals with periodic surface ripples that are caused by their machining, a multiorder diffractive model is presented with which the focusing properties of harmonic beams can be studied. Predictions of the theories are shown to be in excellent agreement with full numerical simulations. (C) 2002 Optical Society of America.

Super-resolution scanning laser microscopy with a third-order optical nonlinear thin film

In a configuration of optical far-field scanning microscopy, super-resolution achieved by inserting a third-order optical nonlinear thin film is demonstrated and analyzed in terms of the frequency response function. Without the thin film the microscopy is diffraction limited; thus, subwavelength features cannot be resolved. With the nonlinear thin film inserted, the resolution is dramatically improved and thus the microscopy resolves features significantly smaller than the smallest spacing allowed by the diffraction limit. A theoretical model is established and the device is analyzed for the frequency response function. The results show that the frequency response function exceeds the cutoff spatial frequency of the microscopy defined by the laser wavelength and the numerical aperture of the convergent lens. The main contribution to the improvement of the cutoff spatial frequency is from the phase change induced by the complex transmission of the nonlinear thin film. Experimental results are presented and are shown to be consistent with the results of theoretical simulations.