In seismic exploration, regularized migration inversion of seismic data usually requires solving a weighted least-squares problem with constrains. It is well known that directly solving this problem using some decomposition techniques is very time-consuming, which makes it less possible for practical use. For iterative methods, previous research is mainly on solving the inverse model in a full ...

The initial objective was to implement a 3D Gaussian beam model on multi-core, high-performance computing hardware in order to support mid and high frequency applications like reverberation modeling and acoustic channel simulation. As graphic processing unit or GPU hardware rapidly emerged as a compelling platform for such work, my objective became to adapt selected acoustic wave propagation mo...

Electromagnetic beams in a uniaxial crystal are treated with emphasis on the extraordinary mode. A virtual source that generates a basic elliptical Gaussian wave propagating obliquely to the optic axis is identified. An exact expression is obtained for this basic elliptical Gaussian wave that simplifies to the corresponding basic elliptical Gaussian beam in the appropriate limit. In the directi...

The beam quality parameter Mx for self-phase modulated Gaussian and super-Gaussian beams has been calculated analytically. These results can be used for experimental measurements of nonlinearities in optical materials. A super-Gaussian beam with a size comparable to a Gaussian one demonstrates much more stable behavior with propagation through Kerr media. The deteriorated beam quality parameter...

Gaussian beams play such an important role in optical lasers as well as in longer wavelength systems that they have been extensively analyzed, starting with some of the classic treatments mentioned in Chapter 1. Almost every text on optical systems discusses Gaussian beam propagation in some detail, and several comprehensive review articles are available. However, for millimeter and submillimet...

The diffraction characteristics of a volume grating (VG) illuminated by a three-dimensional (3-D) converging-diverging Gaussian beam at conical incidence are investigated by applying 3-D finite-beam (FB) rigorous coupled-wave analysis (RCWA) based on the conventional 3-D RCWA in conjunction with two-dimensional plane-wave decomposition. The Gaussian beam is assumed to have an arbitrary incidenc...

The solution to the Schrödinger equation is highly oscillatory when the rescaled Planck constant ε is small in the semiclassical regime. A direct numerical simulation requires the mesh size to be O(ε). The Gaussian beam method is an efficient way to solve the high frequency wave equations asymptotically, outperforming the geometric optics method in that the Gaussian beam method is accurate even...

The propagation of the light that is emitted from both the tunable Ti:Sapphire laser (single mode) and the Coherent FAPs (multimode) is found to be modeled very well using gaussian optics. This is useful when trying to obtain a beam of a certain size at some prescribed distance from a converging lens. This technote will describe (1) gaussian optics, (2) how to calculate the beam radius after pa...