Nonlinear propagation of ultraslow pulses in media with electromagnetically induced transparency

The nonlinear behavior of a probe pulse propagating in a medium with electromagnetically induced transparency is studied both numerically and analytically. A new type of nonlinear wave equation is proposed in which the noninstantaneous response of nonlinear polarization is treated properly. The resulting nonlinear behavior of the propagating probe pulse is shown to be fundamentally different from that predicted by the simple nonlinear Schrodinger-like wave equation that considers only instantaneous Kerr nonlinearity. (c) 2005 Optical Society of America.

Quantum interference effects of two coherent population trapping states on the atomic spectral lines of a F-e=0 -> F-g=1 transition

We investigate the fluorescence spectrum in a nearly degenerate atomic system of a F-e = 0 -> F-g = 1 transition by analytically solving Schrodinger equations. An ultranarrow fluorescence spectral line in between the two coherent population trapping windows has been found. Our analytic solutions clearly show the origin of the ultranarrow spectral line. Due to quantum interference effects between two coherent population trapping states, the width and intensity of the central spectral line can be controlled by an external magnetic field. Such an effect may be used to detect a magnetic field.

FUZZY SOLID SETS FOR MATHEMATICAL MORPHOLOGY AND OPTICAL IMPLEMENTATION

Fuzzy sets in the subject space are transformed to fuzzy solid sets in an increased object space on the basis of the development of the local umbra concept. Further, a counting transform is defined for reconstructing the fuzzy sets from the fuzzy solid sets, and the dilation and erosion operators in mathematical morphology are redefined in the fuzzy solid-set space. The algebraic structures of fuzzy solid sets can lead not only to fuzzy logic but also to arithmetic operations. Thus a fuzzy solid-set image algebra of two image transforms and five set operators is defined that can formulate binary and gray-scale morphological image-processing functions consisting of dilation, erosion, intersection, union, complement, addition, subtraction, and reflection in a unified form. A cellular set-logic array architecture is suggested for executing this image algebra. The optical implementation of the architecture, based on area coding of gray-scale values, is demonstrated. (C) 1995 Optical Society of America

Fuzzy inferring mathematical morphology and optical implementation

Fuzzification is introduced into gray-scale mathematical morphology by using two-input one-output fuzzy rule-based inference systems. The fuzzy inferring dilation or erosion is defined from the approximate reasoning of the two consequences of a dilation or an erosion and an extended rank-order operation. The fuzzy inference systems with numbers of rules and fuzzy membership functions are further reduced to a simple fuzzy system formulated by only an exponential two-input one-output function. Such a one-function fuzzy inference system is able to approach complex fuzzy inference systems by using two specified parameters within it-a proportion to characterize the fuzzy degree and an exponent to depict the nonlinearity in the inferring. The proposed fuzzy inferring morphological operators tend to keep the object details comparable to the structuring element and to smooth the conventional morphological operations. Based on digital area coding of a gray-scale image, incoherently optical correlation for neighboring connection, and optical thresholding for rank-order operations, a fuzzy inference system can be realized optically in parallel. (C) 1996 Society of Photo-Optical Instrumentation Engineers.

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.