Gregory L. Wojcik

A study of second harmonic generation by focused medical transducer pulses

Second harmonic imaging systems transmit relatively low frequency pulses, e.g., 2.5 MHz, and image the frequency-doubled second harmonic generated by acoustic nonlinearity. Imaging the second rather than the first harmonic eliminates significant wavefront aberration and attenuation on the forward path, narrows the beam, and suppresses sidelobes. This technique is used successfully in commercial medical imaging systems and may become dominant in the near future. However, system optimization requires a better understanding of second harmonic generation by focused ultrasound pulses in tissue. Data and simulations are presented quantifying aberration and second harmonic generation by two-dimensional ultrasound beams in realistic tissue models. A pseudo-spectral solver is used to achieve very high accuracy over long paths through lossy, nonlinear abdominal wall and liver.

Pseudospectral methods for large-scale bioacoustic models

Large-scale simulations of ultrasonic waves in heterogeneous tissue models are useful in biomedical R&D for imaging and therapeutics. The scale of bioacoustic models is hundreds of wavelengths. Typical 2D wave solvers are not practical at this scale, and 3D is out of the question, because of numerical errors and/or computer limits. To achieve much higher performance we use the periodic pseudospectral (PS) method, where spatial derivatives are calculated from FFTs over Cartesian grids. With a 4th order explicit time integrator, the PS method yields the necessary accuracy and efficiency. However, the domain must be periodic. We show how to circumvent this intrinsic limitation with Berengers perfectly matched layer (PML) on the boundaries. High accuracy, computational efficiency, and parallelism are demonstrated and a large-scale bioacoustic model is calculated. Generalizations of the method are described, including attenuation and nonlinearity.

Time-domain models of MUT array cross-talk in silicon substrates

Micromachined ultrasonic transducer (MUT) arrays are topical because, among other opportunities, they may supplant piezoelectric arrays in ultrasound medical imaging. However, imaging system companies need to explore performance and design issues thoroughly before making a serious commitment to these silicon-based electrostatic devices. To this end, a fully nonlinear, 3D MUT virtual prototyping capability was recently added to PZFlex. It is described here and applied to medical-type arrays. Simple representations of MUT plate vibration, including acoustic loading and radiation, are presented. Array cross-talk through the surface structure and silicon substrate is quantified using large-scale models. Additionally, an intuitive 1D electromechanical MUT model is developed for modeling and design guidance.

Theoretical and Experimental Particle Size Response of Wafer Surface Scanners

The particle size response of wafer surface scanners is experimentally and theoretically studied. The basis for the theoretical predictions is the angular relative-intensity distributions obtained by three different methods: a numerical solution of Maxwells electromagnetic wave equations for a polystyrene latex (PSL) sphere on a silicon surface, and two approximate models that superimpose the Mie scattering from the sphere and the Fresnel reflection at the wafer surface. The predicted scattered intensities are averaged over the geometry of the collection optics to yield the theoretical size responses that are compared with the experimental results. The experimental size response calibrations of the Tencor Surfscan models 4000 and 5500 are obtained by using uniformly deposited monodisperse PSL spheres on a bare silicon wafer. There is good agreement between the experimental data and the size response obtained from numerical solutions of Maxwells equations. Compared to these numerical results, the two app...

Laser alignment modeling using rigorous numerical simulations

This paper describes a three-dimensional computer modeling technique for alignment system simulation, and some example calculations. The technique has been developed to address issues of alignment and overlay accuracy for future generation VLSI technology. The analytical basis is a general finite element electromagnetic wave propagation code, EMFlex, that rigorously simulates light scattering from the 3-D alignment mark. Using the Nikon Laser Step Alignment (LSA) system as a model instrument, the overlay error and signal shape are simulated. Examples of an idealized asymmetric metal mark are studied. Preliminary results suggest that the rigorous simulations are substantially different from the one-dimensional Fresnel approximations that have been used previously.

NON UNIFORM GRATING COUPLERS FOR COUPLING OF GAUSSIAN BEAMS TO COMPACT WAVEGUIDES

Coupling to compact waveguides can have improved efficiency with use of a grating with non uniform teeth. A combined numerical and mathematical technique for designing this coupler and Finite Element Method results is presented. This paper is a preprint of the final paper which was published in the Integrated Photonics Research Technical Digest, Optical Society of America, 1994 * Currently at Integrated Photonic Systems, Inc. P.O. Box 717, Clarksburg, NJ 08510, (609) 259-1654, e-mail: lcw@intphsys.com NON UNIFORM GRATING COUPLERS FOR COUPLING OF GAUSSIAN BEAMS TO COMPACT WAVEGUIDES Lawrence C. West, Charles Roberts, and Jason Dunkel AT&T Bell Laboratories, Room 4G518, Holmdel, NJ 07733 (908) 949-8715 and Gregory Wojcik, John Mould, Jr., Weidlinger Associates, 4410 El Camino Real, Los Altos, CA 94022 (415) 949-3010 INTRODUCTION: The beams that emit from lasers are typically have a Gaussian spatial profile. Yet the field profile that emits from a uniform grating is one of a decaying exponential[1]. This fundamental mismatch prevents high efficiency (> 90%) coupling of light into compact waveguides. This limitation has been supported by the difficulty of making high precision waveguide gratings in the near infrared on semiconductor surfaces, especially when non-uniform. However, improved lithography techniques and use of practical devices in the mid-IR overcome these limitations. We discuss a method for understanding and designing grating couplers that may emit beam profiles other than a decaying exponential. Special attention is given to the Gaussian beam profile because of its importance to the laser community and it’s minimum diffraction spread. The basic technique is to vary the tooth width along the grating coupler so as to project the desired beam image. THE DESIGN METHOD: We use a numerical Finite Element Method[2] to measure the complex amplitude reflection, transmission, and scattered power coefficients for a single mode waveguide for various tooth depths, widths, and geometries. A single mode is injected into a waveguide and scattered off a single tooth within the waveguide. The resultant complex reflection and transmission coefficients into the single mode are measured. The energy difference of these and the original beam is assumed to be the scattered power. A table of these coefficients versus tooth parameters is created. For fabrication simplicity, we typically constrain ourselves to a constant depth tooth so the grating can be fabricated with a single mask and single etch. But actual lithography results, such as a change in etch hole profile for smaller teeth, can and should be taken into account by a substitution of those teeth with their respective coefficients. Figure 1: Geometry of scattering problem solved per tooth. The grating itself will be made of an ensemble of the individual teeth. The tooth spacing will remain roughly constant (this is not a chirped grating) but the tooth size will change. The spacing between teeth can be adjusted to correct for phase changes under the teeth so as to maintain a flat phase profile in the scattered beam, but this is a small percentage of the overall spacing. These Input Reflection Transmission Scattered Power GaAs Substrate Ge Waveguide tooth 0.6 m 1.75 m n = 4.0 n = 3.27 = 10.0 m 0 w reflection and transmission coefficients are calculated by subtracting the original mode as if there were no tooth and taking the remainder as a change in transmission or reflection caused by the tooth. Shown here is a chart of the coefficients for the tooth of Figure 1 with a 0.477 mm deep tooth. Of particular interest is the scattered power versus tooth width. Since the period of the grating is 3.0 micrometers to match the phase period of the waveguide mode, the maximum tooth size is 3.0 micrometers, at which point the waveguide is a smaller unconfined material. The scattered power is almost linear in tooth width with a proportionality of α. The reflection coefficient is almost a constant. We use these assumptions to derive a simple analytic form for the scattered light. A simple first order derivation of the desired tooth width can be found by assuming the grating is efficient, so that the power remaining in the grating is that which has not been scattered yet. Since the desired scattered power is proportional to the product of remaining power in the guide and the tooth width with constant α, we have the n’th tooth has a size of w p e e dz n z z z z z zc = ∫ α 2 0 2

Dielectric and mechanical absorption mechanisms for time and frequency domain transducer modeling

In all practical transduction systems-such as biomedical imaging arrays, underwater sonar systems or piezoelectric actuators and transformers, electromechanical losses impact overall system performance. Adverse effects of these losses include heat generation, sub-optimal electrical matching, and reduced operational efficiency. Consequently, it is imperative to fully understand the implications of loss mechanisms and incorporate them properly in numerical and analytical models. In this paper, time-domain electromechanical absorption mechanisms are studied in terms of their physical mechanisms and frequency-domain counterparts. We examine the mechanical and dielectric losses of some common piezoelectric materials and discuss some of the issues that arise in attempting to measure and model them.

Computer modeling of diced matching layers

We describe 2D/3D model studies of resonance and radiation characteristics of diced matching layers for ultrasound transducers. Calculations are done with PZFlex, a time-domain, finite element, electromechanical code. Continuous, thin film, quarter-wave matching layers have, of course, been used routinely at optical interfaces for most of this century. A similar approach is often vital to achieving the acoustic performance required of ultrasound imaging transducers. However, the ultrasound problem is complicated by lateral propagation in the layer and crosstalk between transducer elements. This necessitates dicing the continuous layer into discrete resonators on the piezoelectric element(s), whence, crosstalk is minimized, but sometimes at the expense of anomalous local modes and compromised radiation patterns. To better understand multi-dimensional diced matching layer dynamics, a single, solid piezoceramic element and a multi-element composite are modeled. We examine beam pressure and mode shapes and include comparisons with experimental composite data and a coupled-mode design curve.

Nonlinear pulse calculations and data in water and a tissue mimic

Nonlinear propagation is recognized as an important aspect of ultrasonic medical imaging. In particular, rigorous estimates of tissue bioeffects must include it. Regulatory standards rely on measurements in water to estimate effects in lossy tissue, but nonlinearity confuses the relationship. To help clarify the connection the authors complement laboratory hydrophone data with computer simulations of acoustic pulses in water and a tofu tissue mimic. A 2.25 MHz focused disk transducer is used instead of a rectangular medical array to facilitate modeling with a 2D pseudospectral solver that includes causal attenuation, inhomogeneity, multiple reflections, nonlinearity, and shock smoothing. Pressure scans near the transducer characterize the source and drive the wave solver. Measured and calculated nonlinear acoustic fields are compared over a 6 cm range in water and behind tofu cylinders. In the absence of high drive data the authors rely on nonlinear simulations to contrast water and tofu results, in anticipation of derating studies.

Some image modeling issues for I-line, 5X phase-shifting masks

The current image-theoretical basis for phase shifting masks (PSMs) relies on the scalar and Kirchhoff approximations, which neglect vector wave and edge diffraction effects around the mask. In this paper we use EMFlex finite element modeling to quantify vector diffraction effects, and show a method for modeling broadband illumination using the codes transient (optical pulse) capability and the Fourier transform in time. Simulations indicate that: the Kirchhoff approximation applied to etched quartz PSMs can lead to unacceptable errors due to a dark boundary layer on the quartz sidewall; diffraction produces relatively strong vector wave fields near feature edges but their contribution to the lithographic image is negligible; and the paraxial partial coherence approximation is generally valid for 4x or 5x projection systems. We discuss examples illustrating needs for better PSM metrology and phase measurements.