The method originally proposed by Yu et al. [Opt. Lett. 23, 409 (1998)] for evaluating the zero-order Hankel transform is generalized to high-order Hankel transforms. Since the method preserves the discrete form of the Parseval theorem, it is particularly suitable for field propagation. A general algorithm for propagating an input field through axially symmetric systems using the generalized method is given. The advantages and the disadvantages of the method with respect to other typical methods are discussed.

Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields

A selective classified bibliography of symbolic computation in some areas of chemistry is provided together with some examples of computer algebra algorithms and techniques to facilitate future joint work of chemists and computer scientists. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Symbolic calculation in chemistry: Selected examples

A spectral, quasi-cylindrical and dispersion-free Particle-In-Cell algorithm

Laser-driven high-harmonic generation provides the only demonstrated route to generating stable, tabletop attosecond x-ray pulses but has low flux compared to other x-ray technologies. We show that high-harmonic generation can produce higher photon energies and flux by using higher laser intensities than are typical, strongly ionizing the medium and creating plasma that reshapes the driving laser field. We obtain high harmonics capable of supporting attosecond pulses up to photon energies of 600 eV and a photon flux inside the water window (284 to 540 eV) 10 times higher than previous attosecond sources. We demonstrate that operating in this regime is key for attosecond pulse generation in the x-ray range and will become increasingly important as harmonic generation moves to fields that drive even longer wavelengths.

https://advances.sciencemag.org/content/advances/4/5/eaar3761.full.pdf

High-flux soft x-ray harmonic generation from ionization-shaped few-cycle laser pulses.

The calculation of properties of Bose-Einstein condensates with dipolar interactions has proven a computationally intensive problem due to the long range nature of the interactions, limiting the scope of applications. In particular, the lowest lying Bogoliubov excitations in three-dimensional harmonic trap with cylindrical symmetry were so far computed in an indirect way, by Fourier analysis of time-dependent perturbations, or by approximate variational methods. We have developed a very fast and accurate numerical algorithm based on the Hankel transform for calculating properties of dipolar Bose-Einstein condensates in cylindrically symmetric traps. As an application, we are able to compute many excitation modes by directly solving the Bogoliubov-De Gennes equations. We explore the behavior of the excited modes in different trap geometries. We use these results to calculate the quantum depletion of the condensate by a combination of a computation of the exact modes and the use of a local density approximation.

http://grizzly.colorado.edu/~bohn/people/former-students/ronen_bogoliubov06_pra.pdf

Bogoliubov modes of a dipolar condensate in a cylindrical trap

A quasi-discrete Hankel transform (QDHT) is presented as a new and efficient framework for numerical evaluation of the zero-order Hankel transform A discrete form of Parseval's theorem is obtained for the first time to the authors' knowledge, and the transform matrix is discussed It is shown that the S factor, defined as the products of a truncated radius, is critical to building the QDHT

Wenzhong Chen

Papers

Quasi-discrete Hankel transform