Closed-form approximations for fin-line eigenmodes

The characteristic equations for bilateral, unilateral and antipodal fin lines are formulated in a convenient form for an approximate evaluation. It is shown that the eigenvalues for all higher-order modes can be calculated from closed-form expressions provided that the two lowest eigenvalues are known. Dispersion relations are developed which are equivalent to those for rectangular waveguides. The analysis also comprehends a simple evaluation of the field configurations of all hybrid eigenmodes. The approximate formulas are checked against exact numerical calculations, the agreement being excellent.

Asymptotic eigenvalue distribution functions have been used in physics to approximate the actual frequency distribution of modes in resonant cavities. Certain versions of these formulas have been incorrectly applied to microwave cavity problems in engineering. A brief review of the relevant physics literature is presented along with some of the important results which should be used in engineering calculations. Also presented are the results of experimental measurements (on rectangular cavities), which verify the physical theory at microwave frequencies. Several features of the exact and approximate mode distributions become evident from this study, and these are discussed with respect to microwave cavity design.

In this paper, the numerical steady-state model of mode competition in high power ytterbium-doped fiber amplifiers (YDFA) which considering the distributed photodarkening (PD) loss has been studied and developed for the first time. According to the relationship between PD loss and the upper-state population fraction, the formula of saturated PD loss which can distinguish different modes is established. Based on the rate-equation model considering transverse spatial-hole burning, we calculate the longitudinal distribution and quantitative results of each mode’s PD loss for the first time to the best of our knowledge. The dependence of parameters such as pumping direction, fiber length, and fiber doping composition on YDFA is also investigated and discussed. According to our simulation results, the output power of YDFA is strongly affected by PD loss. Meanwhile, PD increases the loss of higher-order mode (HOM), as well as enhances the ratio between fundamental mode (FM) and HOM. Thus, HOM suppression and improvement of beam quality can be expected within PD effect. In our work, the mode competition of high power YDFA under varying degrees of PD loss has been simulated. Obviously the output power will decrease with increasing the PD loss. However the ratio between FM and HOM has no evident changes with varying the PD loss, which providing guideline on appropriately using PD loss to regulate the mode competition between FM and HOM aiming at effective single-mode output of YDFA.

The first part of this work describes theoretical and experimental studies of Stark-induced three-wave mixing in gaseous NH2D. Application of a dc electric field to a gaseous system destroys the basic inversion symmetry and allows two-photon mixing processes to occur. A theoretical derivation of this effect under conditions of resonantly enhanced non-linearities is given for a three-level system. Calculations are presented for mixing of a CO2 laser with a 4 GHz microwaves in the molecule NH2D, producing single lower sideband radiation. Experimental observation of resonantly enhanced, dc-induced, three-wave mixing in gaseous NH2D is presented. The dependence of this effect on gas pressure, microwave frequency, applied dc field, and microwave power are presented and compared with theoretical predictions. The experiment was done at Hughes Research Laboratories by Abrams and his coworkers. The second part of this work describes the propagation of electromagnetic waves in periodic layered media. The propagation of electromagnetic radiation in periodically stratified media is considered. Media of finite, semi-finite and infinite extent are treated. A diagonalization of the unit cell translation operator is used to obtain exact solutions for the Bloch waves, the dispersion relations, and the band structure of the medium. The theory of electromagnetic Bloch waves in periodic stratified media is then applied to the problems of birefringence, and group velocity in these media. The relevance of periodic media to phase matching in nonlinear mixing experiments-and to laser action in the x-ray region is discussed. New types of guided waves such as Bragg guided waves and optical surface waves are theoretically predicted and experimentally observed.

<p>We use continuous seismic data from permanent and temporary, broadband and short-period stations that were operating during 2001 and 2008 to investigate the subsurface velocity structure of the Tongariro Volcanic Centre (TgVC) of New Zealand, particularly the highly active but poorly understood Ruapehu and Tongariro Volcanoes. Stacks of cross-correlation of two concurrent ambient noise seismograms can be used to estimate the interstation Green's Function, i.e., the impulse response of the earth between the two receivers. The Green's Functions are used to retrieve the dispersion relation (frequency-dependent velocity) of surface waves at different periods, which reflects the shear-wave velocity structure in the Fresnel volume of the propagating surface waves. Several studies have used dispersion measurements from ambient noise cross-correlations to investigate the shallow subsurface shear-wave velocity structure of active volcanoes around the world. Most use vertical components to retrieve the Rayleigh waves, but it is becoming increasingly common to use the horizontal seismogram components in addition to the vertical, giving further constraints to Rayleigh-wave measurements and introducing data relating to Love waves. We compute 1,048,968 daily cross-correlations for 955 viable station pairs across the two periods, including all nine-components of the cross-correlation tensor where possible. These daily functions are then stacked into 7458 full-stacks, of which we make group velocity dispersion measurements for 2641 RR-, RZ-, TT-, ZR- and ZZ-component stacks. Cross-correlation quality varies across the networks, with some station pairs possibly contaminated with timing errors. We observe both the fundamental and rst higher-order modes within our database of dispersion measurements. However, correctly identifying the mode of some measurements is challenging as the range of group velocities measured reflects both presence of multiple modes and heterogeneity of the local velocity structure. We assign modes to over 1900 measurements, of which we consider 1373 to be high quality. We invert fundamental mode Rayleigh- and Love-wave dispersion curves independently and jointly for one dimensional shear-wave velocity profiles at Ruapehu and Tongariro Volcanoes, using dispersion measurements from two individual station pairs and average dispersion curves from measurements within specifi c areas on/around the volcanoes. Our Ruapehu profiles show little velocity variation with depth, suggesting that volcanic edifice is made of material that is compacting and being hydrothermally altered with depth. At Tongariro, we observe larger increases in velocity with depth, which we interpret as different layers within Tongariro's volcanic system. Slow shear-wave velocities, on the order of 1-2 km/s, are consistent with both P-wave velocities from existing velocity pro files of areas within the TgVC, and the observations of worldwide studies of shallow volcanic systems that used ambient noise cross-correlation. A persistent observation across the majority of our dispersion measurements is that group velocities of the fundamental mode Love-wave group velocity measurements are slower than those of fundamental mode Rayleigh-waves, particularly in the frequency range of 0.25-1 Hz. Similarly, first higher-order mode Love-wave group velocities are slower than first higher-mode Rayleigh-wave velocities. This is inconsistent with the differences between synthetic dispersion curves that were calculated using isotropic, layered velocity models appropriate for Ruapehu and Tongariro. We think the Love-Rayleigh discrepancy is due to structures such as dykes or cracks in the vertical plane having greater influence than horizontal layering on surface-wave propagation. However, several measurements where Love-wave group velocities are faster than Rayleigh-wave group velocities suggests that in some places horizontal layering is the stronger influence. We also observe that the differences between the Love- and Rayleigh-wave dispersion curves vary with the azimuth of the interstation path across Ruapehu and Tongariro Volcanoes. Some significant differences between Rayleigh-wave velocities of measurements with different interstation orientations are also observed, as are differences between Love-wave velocities. This suggests a component of azimuthal anisotropy within the volcanic structures, which coupled with the radial anistropy makes the shear-wave velocity structures of Ruapehu and Tongariro Volcanoes anisotropic with orthorhombic symmetry. We suggest that further work to determine three-dimensional structure should include provisions for anisotropy with orthorhombic or lower symmetry.</p>

In this paper, we present a new and efficient technique for the exact reconstruction of large mode area (LMA) higher order mode (HOM) optical fibers by using arbitrary shape HOM electric field profiles. One known strategy to achieve LMAs for high power optical applications is by using optical fibers supporting multimode operation, and engineering these fibers such that they operate on just a single transverse mode. Although the fundamental mode is preferred in most circumstances, there is an increasing interest in operating on a single HOM instead since these can have interesting dispersion characteristics and also significantly higher ability to scale mode areas. An issue with the use of HOMs in high power applications is that often they demonstrate regions of high field intensity across the core. This leads to problems with optical damage at lower values of effective area than might otherwise be expected. In order to avoid this problem, we offer designs of optical fibers supporting mode-flattened HOM electric fields. We develop a new inverse transmission line technique for calculating directly and accurately the refractive index profiles of such fibers from knowledge of the desired HOM electric field. We demonstrate this algorithm with a number of example reconstructions of LMA HOM optical fibers supporting prescribed mode-flattened electric field profiles with ultralarge effective mode areas We expect such fiber designs to be useful in the mitigation of nonlinear effects and in thermal and damage management.

We address the design and performance issues of 640-nm range GaInP-AlGaInP laser diodes based on a longitudinal photonic bandgap crystal (PBC). The all-epitaxial design is based on selective filtering of high-order modes and allows extending of the fundamental mode over a PBC waveguide achieving very large vertical modal spot size. At the same time the robustness of the narrow far-field vertical beam divergence is remarkably high with respect to layer thickness variations. Optimal design ensures that all high-order optical modes show high absolute values of leakage loss (> 30 cm/sup -1/), which are order (orders) of magnitude higher than the leakage loss for the fundamental mode. This PBC-induced resonant tunneling effect for high-order modes leads to preferential excitation of the fundamental mode and the high-order modes are not excited even at the highest injection current densities. Broad-area (100 /spl mu/m) devices show vertical beam divergence of 8' (full-width at half-maximum) and lateral beam divergence of 7'-8'. The far-field pattern is circular shaped and stable upon an increase in injection current. Differential quantum efficiency is as high as 85 %. Maximum pulsed total optical output power is 20 W for 100-tim-wide stripe lasers with uncoated fac.

Fluid-Structure Coupling Effects on the Dynamic Response of Pump-Turbine Guide Vanes

This report studies the dispersive wave propagation in the transversely isotropic (6 mm) piezoelectromagnetic (PEM) plate when the mechanical, electrical, and magnetic boundary conditions for both the upper and lower free surfaces of the plate are as follows: the mechanically free, electrically open, and magnetically open surfaces. This study follows some original results obtained in book. The fundamental modes’ dispersion relations are graphically shown for the following well-known PEM composite materials: BaTiO3–CoFe2O4 and PZT-5H–Terfenol-D. It is natural that for large values of the nondimensional parameter kd (k is the wave number and d is the plate half-thickness), the velocities of both the fundamental modes approach the surface shear-horizontal wave called the piezomagnetic exchange surface Melkumyan wave. It is well known that plate waves are usually utilized in the nondestructive testing and evaluation, for instance, in the airspace industry. Also, PEM materials are used as smart ones in various technical devices such as dispersive wave delay lines, (biochemi)sensors, lab-on-a-chip, etc.

State-of-the-art data analysis tools have to deal with high-dimensional data. Fortunately, the inherent dimensionality of data is often much smaller, as it has an internal structure limiting its degrees of freedom. In most cases, this structure can be approximated using a graph, i.e, a set of nodes connected by edges. Based on this idea, graphs have been largely used in semi-supervised and unsupervised learning. The canonical assumption when incorporating a graph prior is to assume that the signal is smooth with respect to the graph, i.e, that connected pieces of data have similar values. Nevertheless, this hypothesis is insufficient to characterize more complex relations between the data and its structure, the graph. To this end, the field of Graph Signal Processing (GSP) extends the graph smoothness hypothesis to a more general assumption. Its key idea is to think of the signal as a sum of harmonic modes, which are obtained from the eigen-decomposition of the Laplacian, an operator representing the second order derivative. Thus, the essence of GSP resides in the Fourier transform defined by the projection on the Laplacian eigenvectors basis, which allows us to filter graph signals. However, GSP suffers from a counterintuitive irregularity. Contrarily to the classical Fourier basis, the graph Laplacian eigenvectors are not spreading uniformly on the vertex set and can be highly concentrated in a region of the graph. This non-uniformity results in a lack of any intuitive translation operator and consequently poses challenges to generalize some of the classical signal processing theory, e.g., stationarity, uncertainty principles, or sampling. In this thesis, we answer these difficulties by accepting that each node is unique and should be treated specially according to its surrounding structure. This is achieved using an operator called localization that shifts a kernel defined in the spectral domain around a specific node while adapting to the local graph structure. In the first part of the thesis, we focus on harmonic analysis in GSP. We start by making use of the norm of localized kernels to capture the spectral local features of the graph vertices. To illustrate the relevance of this analysis we then introduce structural clustering, an algorithm that groups nodes according to the role they play in the graph. Then, we bound the vertex-frequency concentration of graph filter banks atoms. Because of the irregular structure of graphs, we construct a local uncertainty principle that is, again, driven by the norm of a localized kernel. In the second part of the thesis, we tackle GSP problems from a machine learning perspective. We use the localization operator to extend the notion of stationarity to graph signals. It consists of a graph signal probabilistic framework allowing us to optimally solve inverse problems. Finally, we show how the graph total variation can be used in semi-supervised learning and prove its consistency with respect to the underlying graph manifold.

A physical meaning of the higher-order Landau mode is proposed from the theoretical calculation of the dispersion relation. When the plasma is composed of two electron temperatures, the dispersion relation of the two-temperature mode (the modified fundamental Landau mode) suddenly merges into one of the next higher-order Landau modes in the region ω/ω p <1 (ω p : electron plasma frequency) as the temperature of the small high energy tail in the velocity distribution increases.

The on-chip detection of fluorescent light is essential for many bioanalytical and life-science related applications. Here, the optofluidic light cage consisting of a sparse array of micrometer encircling a hollow core represents an innovative concept, particularly for on-chip waveguide-based spectroscopy. In the present work, we demonstrate the potential of the optofluidic light cage concept in the context of integrated on-chip fluorescence spectroscopy. Specifically, we show that fluorescent light from a dye-doped aqueous solution generated in the core of a nanoprinted dual-ring light cage can be efficiently captured and guided to the waveguide ports. Notably, the fluorescence collection occurs predominantly in the fundamental mode, a property that distinguishes it from evanescent field-based waveguide detection schemes that favor collection in higher-order modes. Through exploiting the flexibility of waveguide design and 3D nanoprinting, both excitation and emission have been localized in the high transmission domains of the fundamental core mode. Fast diffusion, detection limits comparable to bulk measurements, and the potential of this approach in terms of device integration were demonstrated. Together with previous results on absorption spectroscopy, the achievements presented here suggest that the optofluidic light cage concept defines a novel photonic platform for integrated on-chip spectroscopic devices and real-time sensors compatible with both the fiber circuitry and microfluidics. Applications in areas such as bioanalytics and environmental sciences are conceivable, while more sophisticated applications such as nanoparticle tracking analysis and integrated Raman spectroscopy could be envisioned.

A W-band multi-beam traveling-wave tube (TWT) based on sine slow-wave structure is designed. The cold bandwidths of the fundamental and higher-order modes in the slow-wave circuit are analyzed using HFSS software. Through reasonable structural design, the fundamental mode and low-order mode are suppressed. The beam-wave interaction capability of the multi-beam TWT is analyzed based on the high-order mode transmission design. At the voltage of 11.7 kV, the current density of the sheet electron beam is 96 A/cm2 which can be produced by the non-convergent electron gun, and the output power is over 150 W in the operating frequency 90 GHz-100 GHz.

The stable operation of the high-order mode multibeam extended-interaction oscillator (EIO) with coaxial structure can effectively overcome the size limitation of the fundamental mode operating circuit at high frequency. The research on the transverse mode shows that the high-order TM31 mode can establish a stronger axial electric field than the fundamental TM01 mode in a large size coaxial cavity. Although the design of a coaxial extended interaction cavity is straightforward, the operating stability is greatly affected by the mode competition. Based on the interaction characteristic between the multiple beams and the multigap cavity operating in the high-order mode, this article proposes a simplified analysis method based on the equivalent circuit theory to study the high-frequency characteristics of the complex structure. The space-charge wave theory is combined with the dispersion curve to analyze the stability of the five-gap coaxial EIO operating in the TM31 mode. Finally, the particle-in-cell (PIC) simulation has obtained a TM31 mode EIO operating at 35.3 GHz with an output power of 290.3 kW. The device uses six beams with a total current of 25.8 A (evenly divided among six beams) at a voltage of 51 kV. The design provides a promising approach for making a stable high-power RF circuit applied in high-frequency EIOs.

Optimal suppression of higher-order modes (HOMs) in hollow-core antiresonant fibers comprising a single ring of thin-walled capillaries was previously studied, and can be achieved when the condition on the capillary-tocore diameter ratio is satisfied (d/D ≈ 0.68). Here we report on the conditions for maximizing the leakage losses of HOMs in hollow-core nested antiresonant node-less fibers, while preserving low confinement loss for the fundamental mode. Using an analytical model based on coupled capillary waveguides, as well as full-vector finite element modeling, we show that optimal d/D value leading to high leakage losses of HOMs, is strongly correlated to the size of nested capillaries. We also show that extremely high value of degree of HOM suppression (∼1200) at the resonant coupling is almost unchanged on a wide range of nested capillary diameter dN ested values. These results thus suggest the possibility of designing antiresonant fibers with nested elements, which show optimal guiding performances in terms of the HOM loss compared to that of the fundamental mode, for clearly defined paired values of the ratios dN ested/d and d/D. These can also tend towards a single-mode behavior only when the dimensionless parameter dN ested/d is less than 0.30, with identical wall thicknesses for all of the capillaries.