Lithium niobate on insulator (LNOI) technology is revolutionizing the lithium niobate industry, enabling higher performance, lower cost and entirely new devices and applications. The availability of LNOI wafers has sparked significant interest in the platform for integrated optical applications, as LNOI offers the attractive material properties of lithium niobate, while also offering the stronger optical confinement and a high optical element integration density that has driven the success of more mature silicon and silicon nitride (SiN) photonics platforms. Due to some similarities between LNOI and SiN, established techniques and standards can readily be adapted to the LNOI platform including a significant array of interface approaches, device designs and also heterogeneous integration techniques for laser sources and photodetectors. In this contribution, we review the latest developments in this platform, examine where further development is necessary to achieve more functionalities in LNOI integrated optical circuits and make a few suggestions of interesting applications that could be realized in this platform. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Status and Potential of Lithium Niobate on Insulator (LNOI) for Photonic Integrated Circuits

In this work we review the present status of numerical methods for partial differential equations on vector and parallel computers. A discussion of the relevant aspects of these computers and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial-boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. A brief discussion of application areas utilizing these computers is included.

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Solution of Partial Differential Equations on Vector and Parallel Computers

The authors present a short review of the progress that has occurred during years 1955-91 in both the theoretical and practical characterization of frequency stability of precision frequency sources. The emphasis is on the evolution of ideas and concepts for the characterization of random noise processes in such standards in the time domain and the Fourier frequency domain, rather than a rigorous mathematical treatment of the problem. Numerous references to the mathematical treatments are made. >

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Characterization of frequency stability in precision frequency sources

Accurate knowledge of the velocity dispersion of Lamb modes is important for ultrasonic nondestructive evaluation methods used in detecting and locating flaws in thin plates and in determining their elastic stiffness coefficients. Lamb mode dispersion is also important in the acoustic emission technique for accurately triangulating the location of emissions in thin plates. In this research, the ability to characterize Lamb mode dispersion through a time-frequency analysis (the pseudo Wigner-Ville distribution) was demonstrated. A major advantage of time-frequency methods is the ability to analyze acoustic signals containing multiple propagation modes, which overlap and superimpose in the time domain signal. By combining time-frequency analysis with a broadband acoustic excitation source, the dispersion of multiple Lamb modes over a wide frequency range can be determined from as little as a single measurement. In addition, the technique provides a direct measurement of the group velocity dispersion. The technique was first demonstrated in the analysis of a simulated waveform in an aluminum plate in which the Lamb mode dispersion was well known. Portions of the dispersion curves of the A0, A1, S0, and S2 Lamb modes were obtained from this one waveform. The technique was also applied for the analysis of experimental waveforms from a unidirectional graphite/epoxy composite plate. Measurements were made both along, and perpendicular to the fiber direction. In this case, the signals contained only the lowest order symmetric and antisymmetric modes. A least squares fit of the results from several source to detector distances was used. Theoretical dispersion curves were calculated and are shown to be in good agreement with experimental results.

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Time-Frequency Analysis of the Dispersion of Lamb Modes

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A Bibliography of Publications about the Fortran Programming Language: Part 1: 1956{1980

A comparison was made between two approaches to predict acoustic emission waveforms in thin plates. A normal mode solution method for Mindlin plate theory was used to predict the response of the flexural plate mode to a point source, step-function load, applied on the plate surface. The second approach used a dynamic finite element method to model the problem using equations of motion based on exact linear elasticity. Calculations were made using properties for both isotropic (aluminum) and anisotropic (unidirectional graphite/epoxy composite) materials. For simulations of anisotropic plates, propagation along multiple directions was evaluated. In general, agreement between the two theoretical approaches was good. Discrepancies in the waveforms at longer times were caused by differences in reflections from the lateral plate boundaries. These differences resulted from the fact that the two methods used different boundary conditions. At shorter times in the signals, before reflections, the slight discrepancies in the waveforms were attributed to limitations of Mindlin plate theory, which is an approximate plate theory. The advantages of the finite element method are that it used the exact linear elasticity solutions, and that it can be used to model real source conditions and complicated, finite specimen geometries as well as thick plates. These advantages come at a cost of increased computational difficulty, requiring lengthy calculations on workstations or supercomputers. The Mindlin plat theory solutions, meanwhile, can be quickly generated on personal computers. Specimens with finite geometry can also be modeled. However, only limited simple geometries such as circular or rectangular plates can easily be accommodated with the normal mode solution technique. Likewise, very limited source configurations can be modeled and plate theory is applicable only to thin plates.

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Finite Element and Plate Theory Modeling of Acoustic Emission Waveforms

The requirements for dynamic finite-element modeling of the source dynamics and wave propagation of buried acoustic-emission point sources were examined. Maximum permissible source and cell sizes for point sources were determined as a function of the minimum wavelength for frequencies of interest These wavelengths were calculated from the source rise-times. For both buried monopoles and dipoles, finite-element predictions for both plates and half-spaces were compared with published results obtained from other approaches. The modeled signals were evaluated from the epicenter to a distance of 15 plate thicknesses for plates with a thickness of s 25 mm. The finite-element method provided accurate results and a practical means to analyze \ finite specimens, unlike most alternate approaches.

Modeling of buried monopole and dipole sources of acoustic emission with a finite element technique

We have developed a rigorous phenomenological model for analyzing rare-earth doped waveguide lasers. The model is based on time-dependent laser rate equations for an arbitrary rare-earth-doped laser host with multiple energy levels. The rate equations are coupled with the laser signal and pump photon flux equations that have time-dependent boundary conditions. The formulation results in a large and stiff set of transcendental and coupled differential equations that are solved using finite difference discretization and the method of lines. Solutions for the laser signal power, pump power, and populations of ion energy levels as functions of space and time are obtained for waveguide lasers. We have used the model to predict the CW characteristics and Q-switched performance of waveguide lasers in lithium niobate pumped by a 980-nm source. Our analysis shows that hole burning can occur in erbium-doped lithium niobate lasers because of the intensity variation across guided transverse modes. We have predicted that Q-switch pulse peak powers can exceed 1 kW with pulsewidths less than 1 ns. Moreover, we have compared the CW and Q-switched performance of 980-nm pumped waveguide lasers and 1480 nm pumped waveguide lasers. An analysis of the effects of host- and fabrication-dependent parameters on CW 980-nm pumped lasers is included. These parameters include cooperative upconversion, excited state absorption, doping concentration, excess waveguide loss, cavity length, and mirror reflectance values. We demonstrate good quantitative agreement with waveguide laser experimental data obtained in our laboratory and with results from the literature.

Time-dependent modeling of erbium-doped waveguide lasers in lithium niobate pumped at 980 and 1480 nm

The capability of a three-dimensional dynamic finite element method for predicting far-field acoustic emission signals in thin plates of finite lateral extent, including their reflections from the plate edges, was investigated. A lead break (Hsu-Neilsen) source to simulate AE was modeled and used in the experimental measurements. For the thin plate studied, the signals were primarily composed of the lowest order symmetric (S0) and antisymmetric (A0) Lamb modes. Experimental waveforms were detected with an absolutely calibrated, wideband, conical element transducer. The conditions of lead fractures both on the surface of the plate as well as on the edge of the plate were investigated. Surface lead breaks preferentially generate the A0 mode while edge lead breaks generate the S0 mode. Reflections of developed plate waves from both normal and oblique incidence angles were evaluated. Particularly interesting for the case of the lead break on the plate edge were S0 waves produced by the interaction of a Rayleigh wave with the plate corner and by a bulk shear wave mode converting at the side edge. The Rayleigh wave, in this case, propagated along the specimen edge. For all cases considered, the experimental measurements were in good agreement with the predictions of the finite element model.

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Reflections of AE Waves in Finite Plates: Finite Element Modeling and Experimental Measurements

We have performed a study to validate a three-dimensional dynamic finite element code for calculating expected dynamic displacement fields in the far field from various types of acoustic emission sources. This work uses several approaches to complete the validation and to determine values for key parameters so that acoustic emission sources can be modeled. These parameters include the cell size, source diameter, and source rise time. Laboratory experiments using pencil-lead breaks on a large 25.4 mm thick steel plate were used to validate the three-dimensional code. Lead breaks were carried out both on the top surface of the plate and at various depths along one edge. Using a calibrated, wideband displacement sensor, the experimental out-of-plane displacements versus time were quantitatively compared to calculated displacements at distances of up to 366 mm from the source. In addition, certain interesting cases were examined with the code.

John M. Gary

Papers

Finite Element and Plate Theory Modeling of Acoustic Emission Waveforms

Modeling of buried monopole and dipole sources of acoustic emission with a finite element technique

Time-dependent modeling of erbium-doped waveguide lasers in lithium niobate pumped at 980 and 1480 nm

Reflections of AE Waves in Finite Plates: Finite Element Modeling and Experimental Measurements

Far-field acoustic emission waves by three-dimensional finite element modeling of pencil-lead breaks on a thick plate