Compensation for higher order mode coupling between inclined coupling slots and radiating slots in planar slotted waveguide arrays

Summary form only given. Geometric simplicity, efficiency and polarization purity make slot antenna arrays ideal solutions for many radar, communications and navigation applications, especially when high power, light weight and limited scan volume are priorities. Resonant arrays of longitudinal slots have a slot spacing of one-half guide wavelength at the design frequency, so that the slots are located at the standing wave peaks. Planar arrays are implemented using a number of rectangular waveguides (branch line guides), arranged side-by-side, while waveguides main lines located behind and at right angles to the branch lines excite the radiating waveguides via centered-inclined coupling slots. Planar slotted waveguide arrays radiate broadside beams and all radiators are designed to be in phase.

Nonlinear mode coupling of surface acoustic waves on an isotropic solid

The nonlinear mode coupling between two co-directional quasi-harmonic Rayleigh surface waves on an isotropic solid is analysed using the method of multiple scales. This procedure yields a system of six semi-linear hyperbolic partial differential equations with the same principal part governing the slow variations in the (complex) amplitudes of the two fundamental, the two second harmonic and the two combination frequency waves at the second stage of the perturbation expansion. A numerical solution of these equations for excitation by monochromatic signals at two arbitrary frequencies, indicates that there is a continuous transfer of energy back and forth among the fundamental, second harmonic and combination frequency waves due to mode coupling. The mode coupling tends to be more pronounced as the frequencies of the interacting waves approach each other.

Mode-coupling glass transition in a fluid confined by a periodic potential

We show that a fluid under strong spatially periodic confinement displays a glass transition within mode-coupling theory at a much lower density than the corresponding bulk system. We use fluctuating hydrodynamics, with confinement imposed through a periodic potential whose wavelength plays an important role in our treatment. To make the calculation tractable we implement a detailed calculation in one dimension. Although we do not expect simple 1d fluids to show a glass transition, our results are indicative of the behavior expected in higher dimensions. In a certain region of parameter space we observe a three-step relaxation reported recently in computer simulations [S. H. Krishnan, Ph.D. thesis, Indian Institute of Science (2005); Kim et al., Eur. Phys. J. Special Topics 189, 135 (2010)] and a glass-glass transition. We compare our results to those of Krakoviack [Phys. Rev. E 75, 031503 (2007)] and Lang et al. [Phys. Rev. Lett. 105, 125701 (2010)].

Anomalous power law decay in solvation dynamics of DNA: a mode coupling theory analysis of ion contribution

Several time dependent fluorescence Stokes shift (TDFSS) experiments have reported a slow power law decay in the hydration dynamics of a DNA molecule. Such a power law has neither been observed in computer simulations nor in some other TDFSS experiments. Here we observe that a slow decay may originate from collective ion contribution because in experiments DNA is immersed in a buffer solution, and also from groove bound water and lastly from DNA dynamics itself. In this work we first express the solvation time correlation function in terms of dynamic structure factors of the solution. We use mode coupling theory to calculate analytically the time dependence of collective ionic contribution. A power law decay in seen to originate from an interplay between long-range probe-ion direct correlation function and ion-ion dynamic structure factor. Although the power law decay is reminiscent of Debye-Falkenhagen effect, yet solvation dynamics is dominated by ion atmosphere relaxation times at longer length scales (small wave number) than in electrolyte friction. We further discuss why this power law may not originate from water motions which have been computed by molecular dynamics simulations. Finally, we propose several experiments to check the prediction of the present theoretical work.

Mode coupling theory analysis of electrolyte solutions: Time dependent diffusion, intermediate scattering function, and ion solvation dynamics

A self-consistent mode coupling theory (MCT) with microscopic inputs of equilibrium pair correlation functions is developed to analyze electrolyte dynamics. We apply the theory to calculate concentration dependence of (i) time dependent ion diffusion, (ii) intermediate scattering function of the constituent ions, and (iii) ion solvation dynamics in electrolyte solution. Brownian dynamics with implicit water molecules and molecular dynamics method with explicit water are used to check the theoretical predictions. The time dependence of ionic self-diffusion coefficient and the corresponding intermediate scattering function evaluated from our MCT approach show quantitative agreement with early experimental and present Brownian dynamic simulation results. With increasing concentration, the dispersion of electrolyte friction is found to occur at increasingly higher frequency, due to the faster relaxation of the ion atmosphere. The wave number dependence of intermediate scattering function, F(k, t), exhibits markedly different relaxation dynamics at different length scales. At small wave numbers, we find the emergence of a step-like relaxation, indicating the presence of both fast and slow time scales in the system. Such behavior allows an intriguing analogy with temperature dependent relaxation dynamics of supercooled liquids. We find that solvation dynamics of a tagged ion exhibits a power law decay at long times-the decay can also be fitted to a stretched exponential form. The emergence of the power law in solvation dynamics has been tested by carrying out long Brownian dynamics simulations with varying ionic concentrations. The solvation time correlation and ion-ion intermediate scattering function indeed exhibit highly interesting, non-trivial dynamical behavior at intermediate to longer times that require further experimental and theoretical studies. (c) 2015 AIP Publishing LLC.

Nonlinear mode coupling and internal resonances in MoS2 nanoelectromechanical system

Atomically thin two dimensional (2D) layered materials have emerged as a new class of material for nanoelectromechanical systems (NEMS) due to their extraordinary mechanical properties and ultralow mass density. Among them, graphene has been the material of choice for nanomechanical resonator. However, recent interest in 2D chalcogenide compounds has also spurred research in using materials such as MoS2 for the NEMS applications. As the dimensions of devices fabricated using these materials shrink down to atomically thin membrane, strain and nonlinear effects have become important. A clear understanding of the nonlinear effects and the ability to manipulate them is essential for next generation sensors. Here, we report on all electrical actuation and detection of few-layer MoS2 resonator. The ability to electrically detect multiple modes and actuate the modes deep into the nonlinear regime enables us to probe the nonlinear coupling between various vibrational modes. The modal coupling in our device is strong enough to detect three distinct internal resonances. (C) 2015 AIP Publishing LLC.

Mode coupling and vertical radiation loss for whispering-gallery modes in 3-D microcavities

The characteristics of whispering-gallery modes (WGMs) in 3-D cylindrical, square, and triangular microcavities with vertical optical confinement of semiconductors are numerically investigated by the finite-difference time-domain (FDTD) technique. For a microcylinder with a vertical refractive index 3.17/3.4/3.17 and a center layer thickness 0.2 mu m, Q-factors of transverse electric (TE) WGMs around wavelength 1550 nm are smaller than 10(3), as the radius R < 4 mu m and reach the orders of 10(4) and 10(6) as R = 5 and 6 mu m, respectively. However, the Q-factor of transverse magnetic (TM) WGMs at wavelength 1.659 mu m reaches 7.5 x 10(5) as R = 1 mu m. The mode coupling between the WGMs and vertical radiation modes in the cladding layer results in vertical radiation loss for the WGMs. In the microcylinder, the mode wavelength of TM WGM is larger than the cutoff wavelength of the vertical radiation mode with the same mode numbers, so TM WGMs cannot couple with the vertical radiation mode and have high Q-factor. In contrast, TE WGMs can couple with the corresponding vertical radiation mode in the 3-D microcylinder as R < 5 mu m. However, the mode wavelength of the TE WGM approaches (is larger than) the cutoff wavelength of the corresponding radiation modes at R = 5 mu m (6 mu m), so TE WGMs have high Q-factors in such microcylinders too. The results show that a critical lateral size is required for obtaining high, Q-factor TE WGMs in the 3-D microcylinder. For 3-D square and triangular microcavities, we also find that the Q-factor of TM WGM is larger than that of TE WGM.

Investigation of mode coupling in a microdisk resonator for realizing directional emission

Mode coupling between the whispering-gallery modes (WGMs) is numerically investigated for a two-dimensional microdisk resonator with an output waveguide. The equilateral-polygonal shaped mode patterns can be constructed by mode coupling in the microdisk, and the coupled modes can still keep high quality factors (Q factors). For a microdisk with a diameter of 4.5 mu m and a refractive index of 3.2 connected to a 0.6-mu m-wide output waveguide, the coupled mode at the wavelength of 1490 nm has a Q factor in the order of 10(4), which is ten times larger than those of the uncoupled WGMs, and the output efficiency defined as the ratio of the energy flux confined in the output waveguide to the total radiation energy flux is about 0.65. The mode coupling can be used to realize high efficiency directional-emission microdisk lasers. (C) 2009 Optical Society of America

Mode coupling between first- and second-order whispering-gallery modes in coupled microdisks

The mode characteristics for two coupled microdisks are investigated by the finite-difference time-domain technique. In the two coupled micodisks, mode coupling between the same order whispering-gallery modes (WGMs) results in coupled WGMs with split mode wavelengths. The numerical results show that the split mode wavelengths of the coupled first- and second-order WGMs can have a crossing point in some cases, which can induce anticrossing mode coupling between them and greatly reduce the mode Q factor of the coupled first-order WGMs. The time variation of mode field pattern shows the transformation between the coupled first- and second-order WGMs. (C) 2007 Optical Society of America

Mode analysis and Q-factor enhancement due to mode coupling in rectangular resonators

Modes in rectangular resonators are analyzed and classified according to symmetry properties, and quality factor (Q-factor) enhancement due to mode coupling is observed. In the analysis, mode numbers p and q are used to denote the number of wave nodes in the direction of two orthogonal sides. The even and odd mode numbers correspond to symmetric and antisymmetric field distribution relative to the midlines of sides, respectively. Thus, the modes in a rectangle resonator can be divided into four classes according to the parity of p and q. Mode coupling between modes of different classes is forbidden; however, anti-crossing mode coupling between the modes in the same class exists and results in new modes due to the combination of the coupled modes. One of the combined modes has very low power loss and high Q-factor based on far-field emission of the analytical field distribution, which agrees well with the numerical results of the finite-difference time-domain (FDTD) simulation. Both the analytical and FDTD results show that the Q-factors of the high Q-factor combined modes are over one order larger than those of the original modes. Furthermore, the general condition required to achieve high-Q modes in the rectangular resonator is given based on the analytical solution.

Finite-difference time-domain analysis of deformed square cavity filters with a traveling-wave-like filtering response by mode coupling

An add-drop filter based on a perfect square resonator can realize a maximum of only 25% power dropping because the confined modes are standing-wave modes. By means of mode coupling between two modes with inverse symmetry properties, a traveling-wave-like filtering response is obtained in a two-dimensional single square cavity filter with cut or circular corners by finite-difference time-domain simulation. The optimized deformation parameters for an add-drop filter can be accurately predicted as the overlapping point of the two coupling modes in an isolated deformed square cavity. More than 80% power dropping can be obtained in a deformed square cavity filter with a side length of 3.01 mu m. The free spectral region is decided by the mode spacing between modes, with the sum of the mode indices differing by 1. (c) 2007 Optical Society of America.

Distributed mode coupling in microring channel drop filters

The authors present the observation of wide transmission dips in a microring channel drop filter by two-dimensional finite-difference time-domain simulation. The authors show that distributed mode coupling between the input waveguide and the resonator results in the oscillations of the coupling efficiency and the envelope of transmission spectra with wavelength. The critical coupling as the light just passing through the coupling region is important for optimizing related devices. If the width of the input waveguide is different from that of the ring resonator, the phenomenon can be greatly reduced. (c) 2006 American Institute of Physics.

Mode-coupling analysis of three-dimensional microdisk resonators by the finite-difference time-domain technique

Quality factor enhancement due to mode coupling is observed in a three-dimensional microdisk resonator. The microdisk, which is vertically sandwiched between air and a substrate, with a radius of 1 mu m, a thickness of 0.2 mu m, and a refractive index of 3.4, is considered in a finite-difference time-domain (FDTD) numerical simulation. The mode quality factor of the fundamental mode HE71 decreases with an increase of the refractive index of the substrate, n(sub), from 2.0 to 3.17. However, the mode quality factor of the first-order mode HE72 reaches a peak value at n(sub) = 2.7 because of the mode coupling between the fundamental and the first-order modes. The variation of mode field distributions due to the mode coupling is also observed. This mechanism may be used to realize high-quality-factor modes in microdisks with high-refractive-index substrates. (c) 2006 Optical Society of America.