Ultrafast non-linear optical properties of Ge20As25Se55 chalcogenide films

The non-resonant third-order non-linear optical properties of amorphous Ge20As25Se55 films were studied experimentally by the method of the femtosecond optical heterodyne detection of optical Kerr effect. The real and imaginary parts of complex third-order optical non-linearity could be effectively separated and their values and signs could be also determined, which were 6.6 x 10(-12) and -2.4 x 10(-12) esu, respectively. Amorphous Ge20As25Se55 films showed a very fast response in the range of 200 fs under ultrafast excitation. The ultrafast response and large third-order non-linearity are attributed to the ultrafast distortion of the electron orbitals surrounding the average positions of the nucleus of Ge, As and Se atoms. The high third-order susceptibility and a fast response time of amorphous Ge20As25Se55 films makes it a promising material for application in advanced techniques especially in optical switching. (c) 2005 Elsevier B.V. All rights reserved.

Non-resonant third-order non-linear optical properties of amorphous GeSe2 film

The real and imaginary parts of third-order susceptibility of amorphous GeSe2 film were measured by the method of the femtosecond optical heterodyne detection of optical Kerr effect at 805 nm with the 80 fs ultra fast pulses. The results indicated that the values of real and imaginary parts were 8.8 x 10(-12) esu and -3.0 x 10(-12) esu, respectively. An amorphous GeSe2 film also showed a very fast response within 200 fs. The ultra fast response and large third-order non-linearity are attributed to the ultra fast distortion of the electron orbits surrounding the average positions of the nucleus of Ge and Se atoms. (c) 2005 Elsevier B.V. All rights reserved.

Coincidence point theorems in quasi-metric spaces without assuming the mixed monotone property and consequences in G-metric spaces

In this paper, we present some coincidence point theorems in the setting of quasi-metric spaces that can be applied to operators which not necessarily have the mixed monotone property. As a consequence, we particularize our results to the field of metric spaces, partially ordered metric spaces and G-metric spaces, obtaining some very recent results. Finally, we show how to use our main theorems to obtain coupled, tripled, quadrupled and multidimensional coincidence point results.

Results on proximal and generalized weak proximal contractions including the case of iteration-dependent range sets

This paper presents some further results on proximal and asymptotic proximal contractions and on a class of generalized weak proximal contractions in metric spaces. The generalizations are stated for non-self-mappings of the forms for and , or , subject to and , such that converges uniformly to T, and the distances are iteration-dependent, where , , and are non-empty subsets of X, for , where is a metric space, provided that the set-theoretic limit of the sequences of closed sets and exist as and that the countable infinite unions of the closed sets are closed. The convergence of the sequences in the domain and the image sets of the non-self-mapping, as well as the existence and uniqueness of the best proximity points, are also investigated if the metric space is complete. Two application examples are also given, being concerned, respectively, with the solutions through pseudo-inverses of both compatible and incompatible linear algebraic systems and with the parametrical

Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces

The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.