Evaluation of refractive index approximations used for modedetermination in multiple quantum well slab waveguides

Approximations commonly used to determine the effective indexes of the guided modes of optical waveguides formed using multiple quantum well (MQW) materials are compared to the exact solutions in the slab waveguide model. Modeling the quantum well region as a single homogeneous layer with an average index of refraction is shown to produce results in close agreement with exact values of the effective index. A geometrically weighted average of the indexes provides the most accurate approximation for typical values of index and layer thickness of GaAs-Al_xGa_1-xAs quantum well waveguides     

The road to chaos by time-asymmetric Hebbian learning in recurrent neural networks

This letter aims at studying the impact of iterative Hebbian learning algorithms on the recurrent neural network's underlying dynamics. First, an iterative supervised learning algorithm is discussed. An essential improvement of this algorithm consists of indexing the attractor information items by means of external stimuli rather than by using only initial conditions, as Hopfield originally proposed. Modifying the stimuli mainly results in a change of the entire internal dynamics, leading to an enlargement of the set of attractors and potential memory bags. The impact of the learning on the network's dynamics is the following: the more information to be stored as limit cycle attractors of the neural network, the more chaos prevails as the background dynamical regime of the network. In fact, the background chaos spreads widely and adopts a very unstructured shape similar to white noise. Next, we introduce a new form of supervised learning that is more plausible from a biological point of view: the network has to learn to react to an external stimulus by cycling through a sequence that is no longer specified a priori. Based on its spontaneous dynamics, the network decides "on its own" the dynamical patterns to be associated with the stimuli. Compared with classical supervised learning, huge enhancements in storing capacity and computational cost have been observed. Moreover, this new form of supervised learning, by being more "respectful" of the network intrinsic dynamics, maintains much more structure in the obtained chaos. It is still possible to observe the traces of the learned attractors in the chaotic regime. This complex but still very informative regime is referred to as "frustrated chaos."     

A constructive algorithm to solve "convex recursive deletion" (CoRD) classification problems via two-layer perceptron networks.

A sufficient condition that a region be classifiable by a two-layer feedforward neural net (a two-layer perceptron) using threshold activation functions is that either it be a convex polytope or that intersected with the complement of a convex polytope in its interior, or that intersected with the complement of a convex polytope in its interior or... recursively. These have been called convex recursive deletion (CoRD) regions. We give a simple algorithm for finding the weights and thresholds in both layers for a feedforward net that implements such a region. The results of this work help in understanding the relationship between the decision region of a perceptron and its corresponding geometry in input space. Our construction extends in a simple way to the case that the decision region is the disjoint union of CoRD regions (requiring three layers). Therefore this work also helps in understanding how many neurons are needed in the second layer of a general three-layer network. In the event that the decision region of a network is known and is the union of CoRD regions, our results enable the calculation of the weights and thresholds of the implementing network directly and rapidly without the need for thousands of backpropagation iterations.     

Exact modal analysis and optimization of N×N×1 cascadedwaveguide structures with multimode guiding sections

Cascaded multimode interference waveguide devices are analyzed to predict their switching properties. The results obtained using an exact modal analysis of an infinite slab model of these structures are compared to those found using simple approximations. Using this model, design parameters for both 2×2×1 and 8×8×1 switching structures are optimized; robustness of the numerical optimization algorithm is discussed. Sensitivity of device transmission performance to lengths and widths of each of the multimode regions, phase shifts in the interconnect regions, and wavelength are presented for the optimized devices. The deviations of the multimode region lengths found using simple approximations from those found by optimizing the model are also presented     

Three-dimensional phase step profilometry with a multicore optical fiber

This paper demonstrates the feasibility of using phase stepping and a multicore optical fiber to calculate an object's depth profile. An interference pattern is projected by an optical fiber onto the object. The distorted interference pattern containing the object information is captured by a CCD camera and processed using a phase step interferometry method. The phase step method is less computationally intensive compared to two-dimensional Fourier transform profilometry and provides more accuracy when measuring objects of high frequency spatial variations.     

Four digital algorithms for activation detection from unipolarepicardial electrograms

The reproducibility of activation detection by each of four algorithms used to calculate maximum derivatives was tested on two sequential paced beats of right ventricular unipolar epicardial electrograms which represented either local activation of the right ventricle alone or synchronous activation of both ventricles. The methods were evaluated by comparing the shape of the two beats aligned on their selected activation times, i.e., the time at which the maximum negative deflection occurred, the differences in activation intervals for the two beats, and the effect on the activation time of superimposing distant events on local activation. The 17-point second-order data fit algorithm performed slightly better than the first-order difference, three-point Lagrange derivative, and five-point second-order data fit algorithms except that activation time selection by the 17-point technique was slightly, but significantly, delayed by the superposition of distant potentials. The 17-point second-order data fit technique is therefore recommended for use in detecting activation unless computation time is a major consideration. In that case, the five-point second-order data fit technique, which uses only four data values for each computation, can be used with only slight decreases in accuracy.     

Generalized switching properties of three-guide circular fiberarrays using coupled-mode analysis

A numerical method that utilizes coupled-mode theory to examine the switching properties of arrays formed by three fibers arranged in a circular configuration is developed. An error function that depends on the difference between the desired output conditions and those obtained for a given set of coupling and detuning coefficients is defined. To determine the values of these coefficients for a particular switching operation, the error function is minimized by varying the coupling and detuning coefficients. Results are presented for configurations that switch a signal from one fiber to another, equally split the power from a single input guide into two fibers at the output, and divide the power from a single input guide equally among all three output guides     

An optimality criteria-based method for the simultaneous optimization of the structural design and placement of piezoelectric actuators

Structural and Multidisciplinary Optimization - This work provides an optimality criteria-based method for the simultaneous optimization of the structural design and optimal placement of...     

Two-Photon Lithography of Platinum-Porphyrin Oxygen Sensors

Oxygen sensing structures were generated by two-photon microfabrication. By copolymerizing metalloporphyrins with a two-photon (2P) photo-initiated polymer, oxygen sensors were patterned into complex 3-D shapes. The sensors were generated on the interior walls of small bore capillaries to allow for controlled concentrations of oxygenated water and cell-rich media to be pumped through their local environment. Phosphorescence lifetime of the patterns were acquired at known levels of O₂ as a standard for measuring the respiration rate of a tiny population of bacterial cells. In addition, we report that the inclusion of the Pt-Porphyrin significantly reduces the 2P polymerization threshold. Fabricating near the inferred polymerization threshold, 3-D structures as small as 50 nm were observed in both the Pt-Porphyrin enhanced and the pure photopolymerizable monomers