Loss and non-linearity saturation effects on the bistability of non-linear distributed feedback structures

We investigate theoretically the effects of optical absorption and saturation of the non-linear index of refraction on the bistability of non-linear distributed feedback structures (NLDFBs). By assuming that the Kerr non-linearity saturates in an exponential fashion, we obtain for the first time closed-form expressions for the so-called self-phase and cross-phase modulation terms. Our investigation shows that both absorption and, in particular, saturation significantly affect the bistable properties of this structure and in many cases eliminate this response completely. In some cases, however, saturation alters the NLDFB's transfer characteristics in a potentially useful manner. We find that weak levels of saturation may increase the contrast ratio between the intensities of the high and low bistable states. At increasing levels of saturation, where bistability is no longer observed, we find regimes where the NLDFB structure could possibly be used for optical amplification. This revised version was published online in November 2006 with corrections to the Cover Date.     

A short and efficient synthesis of (+)-disparlure and its enantiomer

A short and highly efficient approach was applied for the total synthesis of the gypsy moth sex pheromone (+)-disparlure and its enantiomer from isopropylidene D- and L-erythrose, using a common strategy.     

Polarization locking and nonparaxial spatial solitons in media with electronic Kerr nonlinearity

The polarization structure of nonparaxial spatial solitons in a transparent medium with the electronic mechanism of Kerr nonlinearity is studied theoretically. It is demonstrated analytically in the weak nonparaxiality approximation that the regime of polarization locking, in which all the field components have the same propagation constant, is the only stable regime. Estimates of the rate of transition of the initial metastable regime of rotation of the polarization ellipse to the regime of polarization locking are presented. Based on a numerical solution of the nonlinear Maxwell equations, the presence of the nonparaxial regime of polarization locking is confirmed and the main characteristics of the corresponding spatial solitons are obtained.     

A mathematical theory of gravitational collapse

We study the asymptotic behaviour, as the retarded timeu tends to infinity, of the solutions of Einstein's equations in the spherically symmetric case with a massless scalar field as the material model. We prove that when the final Bondi massM ₁ is different from zero, asu , a black hole forms of massM ₁ surrounded by vacuum. We find the rate of decay of the metric functions and the behaviour of the scalar field on the horizon.Research supported in part by National Science Foundation grants MCS-8201599 to the Courant Institute and PHY-8318350 to Syracuse University     

Structure and ultrafast dynamics of liquid water: a quantum mechanics/molecular mechanics molecular dynamics simulations study

A quantum mechanics/molecular mechanics molecular dynamics simulation was performed for liquid water to investigate structural and dynamical properties of this peculiar liquid. The most important region containing a central reference molecule and all nearest surrounding molecules (first coordination shell) was treated by Hartree-Fock (HF), post-Hartree-Fock [second-order Moller-Plesset perturbation theory (MP2)], and hybrid density functional B3LYP [Becke's three parameter functional (B3) with the correlation functional of Lee, Yang, and Parr (LYP)] methods. In addition, another HF-level simulation (2HF) included the full second coordination shell. Site to site interactions between oxygen-oxygen, oxygen-hydrogen, and hydrogen-hydrogen atoms of all ab initio methods were compared to experimental data. The absence of a second peak and the appearance of a shoulder instead in the gO-O graph obtained from the 2HF simulation is notable, as this feature has been observed so far only for pressurized or heated water. Dynamical data show that the 2HF procedure compensates some of the deficiency of the HF one-shell simulation, reducing the difference between correlated (MP2) and HF results. B3LYP apparently leads to too rigid structures and thus to an artificial slow down of the dynamics.     

Reactions of furazano[3,4-b]quinoxalines with phosphorus ylides and an unusual oxidative transformation of the transylidation product

Reactions of furazano[3,4-b]quinoxalines 1 with phosphorus ylides 2 afford the transylidation product 3 and/or 4,9-dihydrofurazano[3,4-b]quinoxalines 4. Oxidation of 3 with phenyliodide bis-trifluoroacetate gave the fused furan derivative 13 in high yield.     

Observation of thermoluminescence induced by fission fragments

Abstract

Thermoluminescence induced in CaF₂ powder by fission fragments emanating from a uranium foil bombarded by fast neutrons has been measured as a function of neutron fluence. A linear relationship between the glow produced and the fast neutron fluence between 5 × 10¹⁰ and 6.5 × 10¹¹ n/cm² has been obtained, thus establishing the feasibility of the use of this method for fast-neutron dosimetry. A limitation of the method is that, if the fissile foil is not separated from the phosphor after irradiation, the TL produced by the α-disintegration of ²³⁸U may eventually mask the fission-induced TL.     

Theory of coupled optical PT-symmetric structures

Starting from Lagrangian principles we develop a formalism suitable for describing coupled optical parity-time symmetric systems.     

Gravitational radiation recoil on anN-body system

The main purpose of this paper is to present a formula of gravitational radiation recoil of an N-body material system.