Symmetric hyperbolic systems include many physically relevant systems of partial differential equations (PDEs) such as Maxwell’s equations, the elastic wave equations and the acoustic equations [28]. In this paper we extend the Gaussian beam method to efficiently compute the high frequency solutions to such systems with polarized waves, in which the dispersion matrix of the hyperbolic system ha...

We study the maximum temperature rise induced by a rotating or dithering Gaussian laser beam on a semi-infinite body. An analytical solution is obtained by solving the transient three-dimensional heat equation in a semi-infinite domain with insulating surface. The effect of rotating or dithering frequency on maximum temperature rise is quantitatively investigated for stainless steel and carbon ...

In this letter, we explore the possibilities of generating diffraction-free caustics over a predetermined range. For the first time we demonstrate the possibility to generate diffraction-free caustic beams. Caustic beams are a topic of increased interest over the past few years. Diffraction-free caustics may find applications in situations where large depth of field and uniform axial energy dis...

We adopt the frozen Gaussian approximation (FGA) for modeling seismic waves. The method belongs to the category of ray-based beam methods. It decomposes seismic wavefield into a set of Gaussian functions and propagates these Gaussian functions along appropriate ray paths. As opposed to the classic Gaussian-beam method, FGA keeps the Gaussians frozen (at a fixed width) during the propagation pro...

We provide a correction factor to be added in ablation algorithms when a Gaussian beam is used in photorefractive laser surgery. This factor, which quantifies the effect of pulse overlapping, depends on beam radius and spot size. We also deduce the expected post-surgical corneal radius and asphericity when considering this factor. Data on 141 eyes operated on LASIK (laser in situ keratomileusis...

We study the complex Riccati tensor equation DċG+GCG−R = 0 on a geodesic c on a Riemannian 3-manifold. This non-linear equation appears in the study of Gaussian beams. Gaussian beams are asymptotic solutions to hyperbolic equations that at each time instant are concentrated around one point in space. When time moves forward, Gaussian beams move along geodesics, and the Riccati equation determin...

Gaussian Beam Decomposition of High Frequency Wave Fields

Light scattered by turbid tissue is known to degrade optical coherence tomography (OCT) image contrast progressively with depth. Bessel beams have been proposed as an alternative to Gaussian beams to image deeper into turbid tissue. However, studies of turbid tissue comparing the image quality for different beam types are lacking. We present such a study, using numerically simulated beams and e...

Optical coherence tomography (OCT) is an emerging, high-resolution near-infrared imaging and microscopy technique. The axial and transverse resolutions in OCT can each be analyzed independently, with the axial resolution inversely proportional to the spectral bandwidth of the optical source and the transverse resolution defined by standard Gaussian beam optics. While high numerical-aperture obj...