Recently, harmonic imaging has been shown to increase image quality in medical imaging. This is believed to be caused by decreased sidelobes. It is also due to a decreased sensitivity to near-field aberrations owing to the lower transmission frequency, and the lower relative amplitude of the second harmonic in the near-field. One of the problems of limited diffraction beams has been the sidelob...

Title of Dissertation: Two Experiments with Cold Atoms: I. Application of Bessel Beams for Atom Optics, and II. Spectroscopic Measurements of Rydberg Blockade Effect Ilya Arakelyan, Doctor of Philosophy, 2010 Dissertation directed by: Prof. Wendell Hill, III Department of Physics In this dissertation we report the results of two experimental projects with lasercooled rubidium atoms: I. Applicat...

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...

Using Bessel-Muirhead system, we can express the K-bessel function defined on a Jordan algebra as linear combination of the J-solutions. We determine explicitly the coefficients when the rank of this Jordan algebra is three after a reduction to the rank two. The main tools are some algebraic identities developed for the occasion.

In a simple picture, a Bessel beam is viewed as a transverse standing wave formed in the interference region between incoming and outgoing conical waves. Based on this interpretation we propose an optical resonator that supports modes that are approximations to Bessel-Gauss beams. The Fox-Li algorithm in two transverse dimensions is applied to confirm the conlcusion.

Nondiffractive Bessel beams were generated experimentally and their propagation was characterized using the self-convergent width method. By the use of this criterion for the calculation of the truncated second-moment of the irradiance, the invariant propagation of the generated Bessel beams is confirmed.

We numerically investigate the possibility to generate freely accelerating or decelerating pulses. In particular it is shown that acceleration along the propagation direction z may be obtained by a purely spatial modulation of an input Gaussian pulse in the form of finite-energy Bessel pulses with a cone angle that varies along the radial coordinate.We discuss simple practical implementations o...

It is shown that the tail probability of a Bessel process is the distributio function of a random time which is related to first and last passage times of Bessel processes. AMS Classification 60 J 25, 60 J 60, 60 E 15, 60 G 44, 60 H 10.

We give a shorter proof of Kanter's (1976) sharp Bessel function bound for concentrations of sums of independent symmetric random vectors. We provide sharp upper bounds for the sum of modified Bessel functions I 0 (x) + I 1 (x), which might be of independent interest. Corollaries improve concentration or smoothness bounds for sums of independent random variables due toČekanavičius

We study the heat equation in n dimensional by Diamond Bessel operator. We find the solution by method of convolution and Fourier transform in distribution theory and also obtain an interesting kernel related to the spectrum and the kernel which is called Bessel heat kernel.