Nonlinear directional coupler in periodically poled lithium niobate

Nonlinear wave propagation was investigated experimentally in coupled waveguides by means of the cascaded nonlinearity in quasi-phase-matched second-harmonic generation. With a specially designed wave-vector-mismatch distribution along the propagation axis, cascading was optimized for low fundamental depletion. High-contrast, ultrafast all-optical switching with switching powers of tens of watts was observed.     

Integrable Equations Arising from Motions of Plane Curves. II

Integrable equations satisfied by the curvature of plane curves or curves on the real line under inextensible motions in some Klein geometries are identified. These include the Euclidean, similarity, and projective geometries on the real line, and restricted conformal, conformal, and projective geometries in the plane. Together with Chou and Qu [Physica D 162 (2002), 9–33], we determine inextensible motions and their associated integrable equations in all Klein geometries in the plane. The relations between several pairs of these geometries provide a natural geometric explanation of the existence of transformations of Miura and Cole-Hopf type.     

Two-dimensional numerical visualization on the interaction of blast waves with obstacles

In this study, the complex phenomena of propagation and interaction of the blast waves impacting on obstacles were visualized and investigated using a numerical method. Three different distances between an immovable wall and a bomb shelter with a square block inside were considered while a blast source is located in front of wall at the same distance from shelter. The transitional shock phenomena were simulated by means of a multi-block mesh system and a flux computational model. Spatial discretization was performed using the Roe’s upwind schemes; time integration was achieved via the second-order explicit Hancock method. Proof of the numerical results indicated that those results were in close agreement with the experimental data obtained for the wedge flow. For the cases proved, the geometries of the reflected wave patterns followed by the incident blast waves crossing the immovable wall and impacting inside of bomb shelters were similar. However the height of wall has a dominating impact on the effect associated with different incident blast waves from the same blast source. Meanwhile, different reflected overpressure-time histories and streamlines were observed and analyzed for the results obtained.     

Single-photon generation from stored excitation in an atomic ensemble

Single photons are generated from an ensemble of cold Cs atoms via the protocol of Duan et al. [Nature (London), ()]]. Conditioned upon an initial detection from field 1 at 852 nm, a photon in field 2 at 894 nm is produced in a controlled fashion from excitation stored within the atomic ensemble. The single-quantum character of field 2 is demonstrated by the violation of a Cauchy-Schwarz inequality, namely w(1(2),1(2)|1(1))=0.24+/-0.05 not > or = 1, where w(1(2),1(2)|1(1)) describes the detection of two events (1(2),1(2)) conditioned upon an initial detection 1(1), with w-->0 for single photons.     

Polarized optical coherence imaging in turbid media by use of a Zeeman laser

A method that uses a Zeeman laser in conjunction with a Glan-Thompson analyzer to image an object in a turbid medium is proposed. A heterodyne signal is generated only when the scattering photons are partially polarized, and the spatial coherence is not seriously degraded after the signal propagates in the turbid medium. A system combining polarization discrimination with optical coherence detection to image the object in a scattering medium is successfully demonstrated. The medium is a solution of polystyrene microspheres measuring 1.072 mum in diameter suspended in distilled water contained in a 10-mm-thick quartz cuvette. The advantages of this optical system, including better selectivity of the weak partially polarized scattering photons and better imaging ability in higher-scattering media, are discussed.     

Error estimates in in covolume methods for elliptic and parabolic problems: A unified approach

In this paper we consider covolume or finite volume element methods for variable coefficient elliptic and parabolic problems on convex smooth domains in the plane. We introduce a general approach for connecting these methods with finite element method analysis. This unified approach is used to prove known convergence results in the norms and new results in the max-norm. For the elliptic problems we demonstrate that the error between the exact solution and the approximate solution in the maximum norm is in the linear element case. Furthermore, the maximum norm error in the gradient is shown to be of first order. Similar results hold for the parabolic problems.