Nonlinear X-wave formation and conical emission at different powers of a femtosecond laser pulse in water

Nonlinear X-wave formation at different pulse powers in water is simulated using the standard model of nonlinear Schrodinger equation (NLSE). It is shown that in near field X-shape originally emerges from the interplay between radial diffraction and optical Kerr effect. At relatively low power group-velocity dispersion (GVD) arrests the collapse and leads to pulse splitting on axis. With high enough power, multi-photon ionization (NIPI) and multi-photon absorption (MPA) play great importance in arresting the collapse. The tailing part of pulse is first defocused by MPI and then refocuses. Pulse splitting on axis is a manifestation of this process. Double X-wave forms when the split sub-pulses are self-focusing. In the far field, the character of the central X structure of conical emission (CE) is directly related to the single or double X-shape in the near field. (c) 2007 Elsevier B.V. All rights reserved.

Observing the fractional Fourier transform by free-space Fresnel diffraction

The fractional Fourier transform of an object can be observed in the free-space Fresnel diffraction pattern of the object. (C) 1997 Optical Society of America

Scaled fractional Fourier transform and its optical implementation

The scaled fractional Fourier transform is suggested and is implemented optically by one lens for different values of phi and output scale. In addition, physically it relates the FRT with the general lens transform-the optical diffraction between two asymmetrically positioned planes before and after a lens. (C) 1997 Optical Society of America.

Extended fractional Fourier transforms

The concept of an extended fractional Fourier transform (FRT) is suggested. Previous PBT's and complex FRT's are only its subclasses. Then, through this concept and its method, we explain the physical meaning of any optical Fresnel diffraction through a lens: It is just an extended FRT; a lens-cascaded system can equivalently be simplified to a simple analyzer of the FRT; the two-independent-parameter FRT of an object illuminated with a plane wave can be readily implemented by a lens of arbitrary focal length; when cascading, the Function of each lens unit and the relationship between the adjacent ones are clear and simple; and more parameters and fewer restrictions on cascading make the optical design easy. (C) 1997 Optical Society of America.

Near-field hexagonal array illumination based on fractional Talbot effect

Hexagonal array is a basic structure widely exists in nature and adopted by optoclectronic device. A phase plate based on the fractional Talbot effect that converts a single expanded laser beam into a regular hexagonal array of uniformly illuminated apertures with virtually 100% efficiency is presented. The uniform hexagonal array illumination with a fill factor of 1/12 is demonstrated by the computer simulation. (C) 2006 Elsevier GmbH. All rights reserved.

A Novel 0.72-6.2GHz Continuously-Tunable Delta Sigma Fractional-N Frequency Synthesizer

This paper presents a wideband Delta Sigma-based fractional-N synthesizer with three integrated quadrature VCOs for multiple-input multiple-output (MIMO) wireless communication applications. It continuously covers a wide range frequency from 0.72GHz to 6.2GHz that is suitable for multiple communication standards. The synthesizer is designed in 0.13-um RE CMOS process. The dual clock full differential multi-modulus divide (MMD) with low power consumption can operate over 9GHz under the worst condition. In the whole range frequency from 0.72GHz to 6.2GHz, the maximal tuning range of the QVCOs reaches 33.09% and their phase noise is -119d8/Hz similar to 124d8/Hz @1MHz. Its current is less than 12mA at a 1.2V voltage supply when it operates at the highest frequency of 6.2GHz.

Determination of fractional energy loss of waves in nearshore waters using an improved high-order Boussinesq-type model

Fractional energy losses of waves due to wave breaking when passing over a submerged bar are studied systematically using a modified numerical code that is based on the high-order Boussinesq-type equations. The model is first tested by the additional experimental data, and the model's capability of simulating the wave transformation over both gentle slope and steep slope is demonstrated. Then, the model's breaking index is replaced and tested. The new breaking index, which is optimized from the several breaking indices, is not sensitive to the spatial grid length and includes the bottom slopes. Numerical tests show that the modified model with the new breaking index is more stable and efficient for the shallow-water wave breaking. Finally, the modified model is used to study the fractional energy losses for the regular waves propagating and breaking over a submerged bar. Our results have revealed that how the nonlinearity and the dispersion of the incident waves as well as the dimensionless bar height (normalized by water depth) dominate the fractional energy losses. It is also found that the bar slope (limited to gentle slopes that less than 1:10) and the dimensionless bar length (normalized by incident wave length) have negligible effects on the fractional energy losses.

A HYBRID METHOD OF FRACTIONAL STEPS WITH PREDICTOR-CORRECTOR DIFFERENCE-PSEUDOSPECTRUM FOR NUMERICAL-SOLUTION OF THE CONVECTION-DOMINATED FLOW PROBLEMS

A fractional-step method of predictor-corrector difference-pseudospectrum with unconditional L(2)-stability and exponential convergence is presented. The stability and convergence of this method is strictly proved mathematically for a nonlinear convection-dominated flow. The error estimation is given and the superiority of this method is verified by numerical test.