Vectorial Method Research Articles

All-optical clock recovery from 40 Gbit/s RZ signal based on microring resonators

A scheme for high-speed clock recovery from return-to-zero (RZ) signal with microring resonators is presented. By using a silicon microring resonator (MRR) for clock extraction and a 3-order nonlinear series-coupled microring resonator (SCMR) for amplitude equalization, clock pulses with amplitude modulation less than 1 dB can be obtained. The proposed scheme is also designed and numerically studied by 3D full vectorial film mode matching method (FMM) and coupled mode theory (CMT). Simulation results show that clock can be recovered at 40 Gbit/s with short rise- and fall- times.

Pump Power Dependence of Four-Wave Mixing Parametric Wavelengths in Normal Dispersion Photonic Crystal Fibers

An experimental study of the wavelength shift of four-wave mixing (FWM) bands as a function of pump power in single-mode photonic crystal fibers pumped at normal dispersion is presented. Three fibers whose zero dispersion wavelength is close to the pump wavelength were investigated. The wavelength shift of the signal and idler bands increases as the pump wavelength offset from the zero dispersion wavelength becomes smaller. A largest shift of 29 and 47 nm for the signal and idler wavelengths, respectively, is reported. Experimental results are compared with theoretical calculations based on a fully vectorial method showing good agreement.

Vector analysis of astigmatic changes after cataract surgery with implantation of a new toric multifocal intraocular lens

To analyze the astigmatic changes after cataract surgery with the implantation of a new toric multifocal intraocular lens (IOL) using the Alpins vector method. Vissum-Instituto de Oftalmológico de Alicante, Alicante, Spain. Prospective case series. After cataract surgery with implantation of an AT Lisa 909M toric multifocal IOL, the visual, refractive, corneal topographic, internal astigmatism, defocus curves, and contrast sensitivity outcomes were evaluated over 6 months. Refractive astigmatic changes (target astigmatism [TIA]; surgically induced astigmatism [SIA]; difference vector; magnitude of error; flattening effect; torque) were analyzed using the Alpins vectorial method. The study enrolled 23 eyes (12 patients). Postoperatively, there was a significant reduction in refractive cylinder (P < .01) with an associated visual improvement for near (P = .03) and distance (P=.01). The magnitude of SIA vector was significantly larger than the TIA 3 months postoperatively (P = .03). The mean magnitude of the difference vector was 0.67 diopter (D) ± 0.51 (SD) at 6 months. The mean magnitude of error remained positive and close to zero over the entire follow-up (P ≥ .19). The mean magnitude of torque vector was 0.49 ± 0.54 D at 6 months. Significant positive correlation was found between the magnitude of torque and the difference vector (r ≥ 0.70, P<.01). The new toric IOL restored distance and near visual function with excellent predictability in eyes with moderate to high corneal astigmatism having cataract surgery.

Vector Analysis of Evolutive Corneal Astigmatic Changes in Keratoconus

To evaluate by vector analysis the corneal astigmatic changes occurring in keratoconic corneas during a 3-year follow-up and to determine the relationship between these changes and other clinical changes. Keratoconic eyes (n = 114) of 75 patients ranging in age from 14 to 70 years were retrospectively reviewed in four different centers. In all cases, a 3-year follow-up was completed after the diagnosis of keratoconus. Visual, refractive, keratometric, aberrometric, internal astigmatism (IA), and pachymetric changes were evaluated during the follow-up. In addition, corneal astigmatic changes were evaluated by examining the following parameters, using a modification of the Alpins vectorial method: evolutive astigmatism (EA) and angle of error (AE). An increase in the magnitude of refractive (P = 0.02) and corneal astigmatism (P = 0.05) was found. The mean magnitude of EA was 1.21 ± 0.97 D at 3 years, with no significant changes at each annual visit (P ≥ 0.52). Mean absolute AE increased significantly by the end of the follow-up (P < 0.01). Absolute AE and the increase in corneal astigmatism were found to correlate at 2 years (r = 0.675, P < 0.01). This correlation became poorer at 3 years (r = 0.352, P = 0.02). The magnitude of the EA was also found to be significantly correlated with central corneal thinning (r = -0.441, P = 0.02). Multiple regression analysis revealed that the magnitude of EA at 3 years correlated significantly with the baseline sphere and IA (R² = 0.86, P < 0.01). Corneal vector astigmatic changes are related to some signs of keratoconus progression and are therefore predictive.

Comparative Analysis of Clinical Outcomes Obtained With a New Diffractive Multifocal Toric Intraocular Lens Implanted Through Two Types of Corneal Incision

To analyze and compare the clinical outcomes obtained after cataract surgery with the implantation of a new multifocal toric intraocular lens (IOL) using two different types of corneal incision. Retrospective study including 64 eyes of 35 patients who underwent surgery with implantation of the AT LISA 909M multifocal toric IOL (Carl Zeiss Meditec) in 2 different ophthalmologic centers using different criteria for corneal incision size: sub-1.8 mm (micro-incision surgery [MICS] group) and 2.2 mm (mini-incision group). Visual, refractive, and corneal topographic outcomes were evaluated during 6-month follow-up. Additionally, refractive astigmatic changes were analyzed using the Alpins vectorial method. Significant reductions of refractive sphere and cylinder were observed postoperatively (P<.03), with associated visual improvements for near and distance (P<.01) in both groups. Mean postoperative magnitudes of difference vector, torque, and magnitude of error in the overall sample were 0.52±0.36 diopters (D), 0.36 ± 0.36 D, and 0.08 ± 0.38 D, respectively. A mean overcorrection of 4% in refractive astigmatism was found. Mean angle of error was 0.37± 5.50° and -4.51±13.16° for the MICS and mini-incision groups, respectively (P=.09). Significant positive correlations were found between the magnitudes of torque and difference vector (r=0.78, P<.01) as well as between the magnitude of torque and absolute angle of error (r=0.76, P<.01). Implantation of the AT LISA toric IOL using corneal incisions <2.2 mm provides excellent predictability for astigmatic correction.

Vector analysis of astigmatic changes after cataract surgery with toric intraocular lens implantation

To analyze the astigmatic changes after cataract surgery with toric intraocular lens (IOL) implantation and determine the relationship between these changes and the final visual outcomes. Vissum-Instituto de Oftalmológico de Alicante, Alicante, Spain. Prospective case series. This study comprised eyes with visually significant cataract that had surgery with Acrysof toric IOL implantation. Refractive, corneal topography, internal astigmatism, and contrast sensitivity outcomes were evaluated over 6 months. The Alpins vectorial method was used to analyze the target (TIA) and surgically (SIA) induced astigmatism, difference vector, magnitude of error, flattening effect, and torque. The study enrolled 27 eyes (21 patients). Postoperatively, there was a significant reduction in refractive cylinder (P < .01) with an associated visual improvement (P < .01). The magnitude of the SIA vector was significantly lower than the TIA 1 month and 6 months after surgery (P < .01). The mean magnitude of the difference vector was 0.91 diopter (D) ± 0.45 (SD) at 6 months, with no significant differences between postoperative visits (p > 0.19). The mean magnitude of torque vector was 0.59 ± 0.42 D at 6 months. There was a significant negative correlation between refractive cylinder and the magnitude of torque (r ≤ -0.54, P < .01) and the difference vector (r = -0.98, P < .01). The toric IOL restored distance visual function in eyes with cataract and significant corneal astigmatism, although there was a small trend toward undercorrection related to misalignment of treatment. No author has a financial or proprietary interest in any material or method mentioned.

Novel ECG markers for ventricular repolarization: Is the QT interval obsolete?

Novel ECG markers for ventricular repolarization: Is the QT interval obsolete?

Tailoring hybrid glyco-nanolayers composed of chitohexaose and cellohexaose for cell culture applications

Hybrid glyco-nanolayers of two oligosaccharides with controlled surface sugar density were prepared on a gold surface by self-assembly chemisorption of chitohexaose and cellohexaose as bioactive carbohydrate and molecular spacer, respectively, whose reducing ends were site-selectively modified with thiosemicarbazide (TSC). Quartz crystal microbalance analysis and X-ray photoelectron spectroscopy suggested successful formation of self-assembled nanolayers consisting of chitohexaose–TSC and cellohexaose–TSC with various molar ratios. Human hepatocellular carcinoma cells which recognize an N-acetylglucosamine residue efficiently adhered to the hybrid nanolayers. The cells formed multicellular spheroids on nanolayers with particular molar ratios of the oligosaccharides. Relatively high enzymatic activity for the deethoxylation of ethoxyresorufinviacytochrome P450 1A1 was observed for the as-formed spheroids. The experimental data indicate that the surface density of bioactive chitohexaose, tailored by variation of the relative proportions of chitohexaose and cellohexaose, was a key factor in cell adhesion efficiency, morphological variation and some cellular responses, possibly due to carbohydrate–protein interactions. Architectural design of carbohydrate-based hybrid nanolayers via the vectorial chain immobilization method is expected to provide a new concept for the functional development of glyco-decorated biointerfaces.

Development of a Special Two-Dimensional Fingerprint for the Quality Evaluation of Euonymus Alatu by HPLC with Diode Array Detector Coupled with Chemiluminescence Detection

A special two-dimensional fingerprint developed by a hyphenated method, HPLC–DAD coupled with flow injection analysis and chemiluminescence detection (HPLC–DAD–FIA–CL), was applied to evaluate the quality of Euonymus alatu. Chromatographic fingerprint and active characteristics of Euonymus alatu from different habitats were investigated by HPLC–DAD–FIA–CL method. The similarity of two-dimensional fingerprint obtained by a vectorial angle method was used to evaluate the quality of Euonymus alatu. The results suggested that the two-dimensional fingerprint could reveal more objective conclusions for the quality of Euonymus alatu, and might be helpful to improve the quality control ability of herbal medicines.

A Nonlinear Switch Based on Irregular Structures and Nonuniformity in Doped Photonic Crystal Fibers

We propose a novel nonlinear switch-based on the irregularity in a three-core-doped photonic crystal fiber (PCF). We numerically investigate the proposed structure, which consists of air holes arranged in a triangular lattice around two defects separated by a single Er-Yb doped core. Its switching operation is based on the gain change in the doped core due to the nonuniformity and irregular structure around it. It is shown that by adjusting the gain in the doped core, the light is entirely transferred from the central core to the upper and lower ones. We have employed the full vectorial finite-element method and the finite-difference time domain to investigate and optimize the optical modes, nonlinear parameter, and gain effects on the switching operation. It is found that an optimum gain is essential to allow either a periodic exchange of the light between the upper and lower cores or independent core propagation. Possible nonuniformity in the hole diameters and irregularity problems of the proposed PCF design during the fabrication process have been predicted. The waveguide dispersion with respect to the doped central core region has been thoroughly investigated.

Semivectorial method based on effective index for VCSEL analysis

A combination of the plane-wave expansion method with the effective-index approximation is presented, which allows vectorial properties of electromagnetic field in three-dimensional structures to be considered. I formulate mathematical equations that are the basis of this combined approach, and then I show the simulation of the optical properties of oxide-confined vertical-cavity surface-emitting lasers (VCSELs). The results are compared with the ones obtained with the classical effective-index method and with the fully vectorial plane-wave admittance method. Next the semivectorial properties of the new model are utilized to analyze a birefringent VCSEL structure.

Space-angle distribution of the reflected charged particles adjusted for spin calculations

The efficiency of the proposed method of solution for the spin-considered highly anisotropic multiple scattering problem is based, following optics, upon the admission that the complete solution of the vectorial transport equation boundary problem is the superposition of the anisotropic and smooth parts, calculated separately. We use a vectorial small angle modification of the spherical harmonics method to evaluate the anisotropic part and the vectorial discrete ordinates method to obtain a smooth one. Some calculation examples for reflected radiation are given.

Modelling and Analysis of Modal Behaviour in SOI Slot Waveguides

Mode behaviour for SOI slot waveguides is modelled and analysed using a numerical full vectorial method based on the film mode matching method (MMM). Only the quasi-TE mode is investigated. Waveguide heights and slot widths, as well as silicon widths are properly chosen with respect to the single mode behaviour in the slot region. Comparison between the effective index method and our side loss method shows that our single mode condition is creditable. The optical power confinement in slot region for the quasi-TE mode is also studied and presented. We demonstrate that the maximum achievable optical power confinement Pslot and the maximum normalized average optical intensity Islot are 42% and 26μm-2, respectively.

Glycoproteomics of Implantation.

Our limited understanding of the processes underlying steroid hormonal control of human endometrial receptivity is largely due to the lack of an informative model. Mouse embryos implant on human Ishikawa cells in a steroid- and substrate- dependent manner. In order to identify molecular mediators we have combined transcriptomics, bioinformatics and glycoproteomics. An informatics filter of transcriptomic data focussed on glyco-genes expressed in both the model system and normal endometrium during secretory phase identified 140 candidates of which 19 were integral to the plasma membrane, 64 were glycosyl transferases, 12 were calcium-related and 5 were lectins or lectin-related. Of these only 7 showed >2 fold increase in secretory over proliferative phase endometrium. One of these expressed only during secretory phase is a glycosyl transferase with a role in cycle-dependent mucin glycosylation. Several adhesion-related genes emerged; most lacked evidence of hormonal regulation at mRNA level, suggesting that local signalling interactions between the uterine epithelium and the embryo may be important in regulating attachment. An efficient vectorial method was used for the biotinylation of apically-displayed glycoproteins in confluent epithelial layers. Labelled components were affinity-selected and then subjected to a proteomic protocol, leading to the identification of approximately 30 membrane species, only half previously known as endometrial cell surface glycoproteins. Several candidates so far tested immunochemically are confirmed at the apical epithelial surface. Experiments are in progress to analyse their function in implantation in vitro.

Exactness of simplified scalar optical approaches in modelling a threshold operation of possible nitride vertical‐cavity surface‐emitting diode lasers

AbstractModern small‐size vertical‐cavity surface‐emitting diode lasers (VCSELs) require principally fully vectorial optical modelling because their cavity sizes are of the order of the wavelength of emitted radiation. However, much simpler scalar approaches are often surprisingly exact even beyond the limits of their confirmed validity. Therefore, in the present paper, reasonable limits of an application of simplified scalar optical approaches (instead of more exact but also much more involved and time‐consuming rigorous vectorial ones) are determined to model threshold operation of possible nitride VCSELs equipped with tunnel junctions with the aid of a comparison of results of the scalar effective frequency method with those obtained using the fully vectorial three‐dimensional plane wave admittance method. Both these optical methods have been found to give usually quite close results for the fundamental transverse mode. Larger discrepancies between the results of both approaches have been found for first‐order transverse modes (and even larger are expected for higher‐order ones) and for larger (or very small) active regions. Some structural modifications of nitride VCSELs, which may enable their low‐threshold single‐fundamental‐mode room‐temperature continuous‐wave operation, are proposed. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Effective index method for all-solid photonic bandgap fibres

An effective index method is proposed for all-solid photonic bandgap fibres, where the effective cladding index is taken to be that of the lower edge of the bandgaps. The weak-guidance approximation allows the effective indices of both the fibre cladding and the defect modes to be calculated analytically. Comparison with a vectorial plane wave method shows that good accuracy is obtained.

Comparison of Exactness of Scalar and Vectorial Optical Methods Used to Model a VCSEL Operation

In the paper, a comparison between results of the optical scalar and vectorial optical methods, using the scalar effective frequency method and the vectorial method of lines, respectively, as their typical examples, applied for simulating an operation of vertical-cavity surface-emitting diode lasers (VCSELs) is presented. Both optical approaches has been applied to simulate an operation of the standard 1.3-mum GaAs-based oxide-confined GaInAsN double quantum-well VCSEL, but comparison conclusions seem to be more general and concerns all VCSELs. Validity limits of the simplified scalar approach have been determined by comparing its approximate results with more exact ones obtained with the aid of the accurate vectorial model. The scalar model has been found to be quite exact in the case of a determination of the wavelength of emitted radiation, whereas its exactness in the lasing threshold analysis is much worse, especially in the case of higher order modes, smaller aperture diameters and/or weak radial optical guidance. Our analysis leads also to more general designing conclusions concerning the optimal position and the thickness of the oxide layer assuring, respectively, the stable single mode operation and the lowest threshold gain

A full vectorial contrast source inversion scheme for three-dimensional acoustic imaging of both compressibility and density profiles

Imaging the two acoustic medium parameters density and compressibility requires the use of both the acoustic pressure and velocity wave fields, described via integral equations. Imaging is based on solving for the unknown medium parameters using known measured scattered wave fields, and it is difficult to solve this ill-posed inverse problem directly using a conjugate gradient inversion scheme. Here, a contrast source inversion method is used in which the contrast sources, defined via the product of changes in compressibility and density with the pressure and velocity wave fields, respectively, are computed iteratively. After each update of the contrast sources, an update of the medium parameters is obtained. Total variation as multiplicative regularization is used to minimize blurring in the reconstructed contrasts. The method successfully reconstructed three-dimensional contrast profiles based on changes in both density and compressibility, using synthetic data both with and without 50% white noise. The results were compared with imaging based only on the pressure wave field, where speed of sound profiles were solely based on changes in compressibility. It was found that the results improved significantly by using the full vectorial method when changes in speed of sound depended on changes in both compressibility and density.

How exact are simplified scalar approaches to optical fields in oxide-confined stripe-geometry diode lasers?

AbstractOptical model, scalar or vectorial one, describing behaviour of an optical field within a diode-laser cavity, is one of the most important parts of modelling of a diode-laser operation. As compared to more accurate vectorial optical approaches, scalar ones are known to be less exact but simultaneously they need much less computation time. Besides, they have been sometimes found to be surprisingly exact even beyond their confirmed range of validity. Therefore, in this paper, real validity limits of their application have been determined by comparing their simplified results with more exact results obtained with the aid of vectorial models. The analysis comprises a comparison of an application of the most popular scalar approach to optical properties of diode lasers, i.e., the effective index method, and the vectorial method of lines for the standard 1.3-µm GaAs-based stripe-geometry diode laser. The scalar model has been found to be quite exact in the case of a determination of the effective refractive index, i.e., the wavelength of emitted radiation, whereas its exactness in the lasing threshold analysis is much worse, especially in the case of higher-order modes. Our analysis is concluded with a determination of the regions where both models give satisfactorily close results.

Kepler's Problem in Rotating Reference FramesPart I: Prime Integrals, Vectorial Regularization

This paper studies the Keplerian motion in rotating reference frames based on tensorial orthogonal and skew-symmetric maps. By using a time-regularization vectorial method, an exact solution to Keplerian noninertial motion is offered. A qualitative and quantitative comprehensive study is made. The paper generalizes the approaches to the inertial Keplerian motion presented by Levi-Civita and Kustaanheimo-Stiefel. A Sundman-like vectorial regularization is introduced to eliminate the singularity occurring in the attraction center. It transforms the strong nonlinear initial value problem with variable coefficients that describes the Keplerian motion in a noninertial reference frame into a linear one, with constant coefficients. A direct application to this approach is satellite relative dynamics.