XPM-induced pulse compression in birefringent dispersion decreasing fiber

The pulse compression induced by cross-phase modulation in birefringent dispersion decreasing fiber is discussed theoretically by solving the coupled Schrodinger equations which include the contribution of the high-order non-linear effects, and third-order dispersion. In particular, it is found that a high quality compressed signal pulse can be obtained by a pump pulse of low intense through the technique. The dependence of optimum compression on the non-linear factor N, time delay tau(d) and the dispersive ratio f is also discussed in detail. (c) 2005 Elsevier B.V. All rights reserved.

Stability of parametrically excited differential equations

Sufficient stability criteria for classes of parametrically excited differential equations are developed and applied to example problems of a dynamical nature.

Stability requirements are presented in terms of 1) the modulus of the amplitude of the parametric terms, 2) the modulus of the integral of the parametric terms and 3) the modulus of the derivative of the parametric terms.

The methods employed to show stability are Liapunov’s Direct Method and the Gronwall Lemma. The type of stability is generally referred to as asymptotic stability in the sense of Liapunov.

The results indicate that if the equation of the system with the parametric terms set equal to zero exhibits stability and possesses bounded operators, then the system will be stable under sufficiently small modulus of the parametric terms or sufficiently small modulus of the integral of the parametric terms (high frequency). On the other hand, if the equation of the system exhibits individual stability for all values that the parameter assumes in the time interval, then the actual system will be stable under sufficiently small modulus of the derivative of the parametric terms (slowly varying).

Fetntosecond pulse shaping with space-to-time conversion based on planar optics

We propose a novel structure of planar optical configuration for implementation of the space-to-time conversion for femtosecond pulse shaping. The previous apparatuses of femtosecond pulse shaping are 4f Fourier-transforming type system that is usually large, expensive, difficult to align. The planar integration of free-space optical systems on solid substrates is an optical module with the attractive advantages of compact, reliable and robust. This apparatus is analyzed in details and the design of the particular lens for femtosecond pulse shaping based on planar optics is presented. (c) 2006 Elsevier GmbH. All rights reserved.

Miniature pulse compressor of deep-etched gratings

We propose a miniature pulse compressor that can be used to compensate the group velocity dispersion that is produced by a commercial femtosecond laser cavity. The compressor is composed of two identical highly efficient deep-etched transmissive gratings. Compared with prism pairs, highly efficient deep-etched transmissive grating pairs are lightweight and small. With an optimized groove depth and a duty cycle, 98% diffraction efficiency of the -1 transmissive order can be achieved at a wavelength of 800 nm under Littrow conditions. The deep-etched gratings are fabricated in fused silica by inductively coupled plasma etching. With a pair of the fabricated gratings, the input positively chirped 73.9 fs pulses are neatly compressed into the nearly Fourier transform-limited 43.2 fs pulses. The miniature deep-etched grating-based pulse compressor should be of interest for practical applications. (c) 2008 Optical Society of America

Bragg diffraction of multilayer volume holographic gratings under ultrashort laser pulse readout

The multilayer coupled wave theory is extended to systematically investigate the diffraction properties of multilayer volume holographic gratings (MVHGs) under ultrashort laser pulse readout. Solutions for the diffracted and transmitted intensities, diffraction efficiency, and the grating bandwidth are obtained in transmission MVHGs. It is shown that the diffraction characteristics depend not only on the input pulse duration but also on the number and thickness of grating layers and the gaps between holographic layers. This analysis can be implemented as a useful tool to aid with the design of multilayer volume grating-based devices employed in optical communications, pulse shaping, and processing. (C) 2008 Optical Society of America

DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION (SCALAR THEORY) .1. STATIC TRANSMISSION CASE

Static optical transmission is restudied by postulation of the optical path as the proper element in a three-dimensional Riemannian manifold (no torsion); this postulation can be applied to describe the light-medium interactive system. On the basis of the postulation, the behaviors of light transmitting through the medium with refractive index n are investigated, the investigation covering the realms of both geometrical optics and wave optics. The wave equation of light in static transmission is studied modally, the postulation being employed to derive the exact form of the optical field equation in a medium (in which the light is viewed as a single-component field). Correspondingly, the relationships concerning the conservation of optical fluid and the dynamic properties are given, and some simple applications of the theories mentioned are presented.

DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION (SCALAR THEORY) .2. TIME-DEPENDENT TRANSMISSION THEORY

By generalization of the methods presented in Part I of the study [J. Opt. Soc. Am. A 12, 600 (1994)] to the four-dimensional (4D) Riemannian manifold case, the time-dependent behavior of light transmitting in a medium is investigated theoretically by the geodesic equation and curvature in a 4D manifold. In addition, the field equation is restudied, and the 4D conserved current of the optical fluid and its conservation equation are derived and applied to deduce the time-dependent general refractive index. On this basis the forces acting on the fluid are dynamically analyzed and the self-consistency analysis is given.

Effects of the frequency chirp on the fields of a chirped Gaussian pulse passing through a hard-edged aperture

Based on the Huygens-Fresnel diffraction integral and Fourier transform, propagation expression of a chirped Gaussian pulse passing through a hard-edged aperture is derived. Intensity distributions of the pulse with different frequency chirp in the near-field and far-field are analyzed in detail by numerical calculations. In the near-field, amplitudes of the intensity peaks generated by the modulation of the hard-edged aperture decrease with increasing the frequency chirp, which results in the improving of the beam uniformity. A physical explanation for the smoothing effect brought by increasing the frequency chirp is given. The smoothing effect is achieved not only in the pulse with Gaussian transverse profile but also in the pulse with Hermite-Gaussian transverse profile when the frequency chirp increases. (C) 2005 Elsevier B.V. All rights reserved.

Influence of the chirp on the intensity distributions of an apertured pulse

Starting from the Huygens-Fresnel diffraction integral and the Fourier transform, the propagation expression of a chirped pulse passing through a hard-edged aperture is derived. Using the obtained expression, the intensity distributions of the pulse with different chirp in the near and far fields are analyzed in detail. Due to the modulation of the aperture, many intensity peaks emerge in the intensity distributions of the chirped pulse in the near field. However, the amplitudes of the intensity peaks decrease on increasing the chirp, which results in the smoothing effect in the intensity distributions. The beam smoothing brought by increasing the chirp is explained physically. Also, it is found that the radius of the intensity distribution of the chirped pulse decreases when the chirp increases in the far field. (c) 2005 Elsevier GmbH. All rights reserved.

Temporal-space-transforming pulse-shaping system with a knife-edge apparatus for a high-energy laser facility

For the first time to our knowledge, in a high-energy laser facility with an output energy of 454.37 J, by using a temporal-space-transforming pulse-shaping system with our own design of a knife-edge apparatus, we obtained a quasi-square laser pulse. (c) 2005 Optical Society of America.