We consider the approximate solution of the initial value problem du du , .. . . _ = _ „(*,0) = »(*), by a dissipative Galerkin method. When v is taken to have a jump discontinuity at zero, that discontinuity will propagate along x + t = 0, in the true solution u. Estimates in L^ and Lx of the pollution effects of the discontinuity are found. These estimates show those effects to decay exponent...

We study adiabatic transformation in optical waveguides with discrete translational symmetry. We calculate the reflection and transmission coefficient for a structure consisting of a slab waveguide that is adiabatically transformed into a photonic crystal waveguide and then back into a slab waveguide. The calculation yields high transmission over a wide frequency range of the photonic crystal w...

Twisted hollow waveguides with noncircular cross sections may be considered as slow-wave structures. In a twisted waveguide, propagating radio frequency (rf) waveguide modes can have phase velocities slower than those of similar modes in a straight waveguide. This property is interesting since a twisted waveguide basically has a uniform cross section along the propagation direction. In such a w...

Waveguide array lenses are waveguide arrays that focus light incident on all waveguides at the input side into a small number of waveguides at the output side. Ideal waveguide array lenses provide complete (100%) power concentration of incident light into a single waveguide. While of great interest for several applications, ideal waveguide array lenses have not been demonstrated for practical a...

We present the experimental observation of a spatial vector soliton formed by counterpropagation of coherent optical fields. This is to our knowledge the first observation of a vector soliton in which the induced waveguide (potential) is periodic in the propagation direction. This vector soliton induces a waveguide and a thick grating within the waveguide, which can be used as a tunable optical...

The vast majority of work on waveguide-coupled resonators focuses on decreasing losses in the waveguide and coupling region. Here we present fully integrated resonators based on an ultralow-loss Si3N4 waveguide platform. By tailoring the directional coupler excitation to the resonators, we are able to achieve lower loss singlemode coupling to multimode waveguide widths compared to straight bus ...

In epidemiology, the regression discontinuity design has received increasing attention recently and might be an alternative to randomized controlled trials (RCTs) to evaluate treatment effects. In regression discontinuity, treatment is assigned above a certain threshold of an assignment variable for which the treatment effect is adjusted in the analysis. We performed simulations and a validatio...

Background Cerebral electrical activity in extremely preterm infants is affected by various factors including blood gas and circulatory parameters. Objective To investigate whether continuously measured invasive mean arterial blood pressure (BP) is associated with electroencephalographic (EEG) discontinuity in extremely preterm infants. Study design This prospective observational study exam...

We proposed an asymmetric hybrid plasmonic waveguide which is placed on a substrate for practical applications by introducing an asymmetry into a symmetric hybrid plasmonic waveguide. The guiding properties of the asymmetric hybrid plasmonic waveguide are investigated using finite element method. The results show that, with proper waveguide sizes, the proposed waveguide can eliminate the influe...

Apodized photonic crystal (PC) waveguide gratings are proposed to suppress sidelobes which appear in reflection spectra of usual PC waveguide gratings. By using specific functions (Gauss and Gauss-cosine functions) for the longitudinal refractive index distribution, it is possible to suppress sidelobes in the reflection spectra of PC waveguide gratings efficiently. The apodization is realized b...