Structural and optoelectronic properties of amorphous GaN thin films

Amorphous gallium nitride (a-GaN) thin films were deposited on glass substrate by electron beam evaporation technique at room temperature and high vacuum using N ₂ as carrier gas. The structural properties of the films was studied by X-ray diffraction (XRD) and scanning electron microscope (SEM). It was clear from XRD spectra and SEM study that the GaN thin films were amorphous. The absorbance, transmittance and reflectance spectra of these films were measured in the wavelength range of 300–2200 nm. The absorption coefficient spectral analysis in the sharp absorption region revealed a direct band gap of E _g = 3:1 eV. The data analysis allowed the determination of the dispersive optical parameters by calculating the refractive index. The oscillator energy E ₀ and the dispersion energy E _d, which is a measure of the average strength of inter-band optical transition or the oscillator strength, were determined. Electrical conductivity of a-GaN was measured in a different range of temperatures. Then, activation energy of a-GaN thin films was calculated which equalled E _a = 0:434 eV.     

A diffractive optical element for shaping arbitrary beams

A design method is presented for an optical element that shapes an arbitrary collimated beam. The optical element consists of a pair of diffractive optical elements (DOEs). The outgoing beam is also collimated, and can have any desired intensity profile. The phase functions of the DOEs are computed by minimizing an appropriate cost function under an energy conservation constraint.     

LOM and HOM damping study in a superconducting deflecting cavity for ALS at LBNL

Superconducting deflecting cavities can be used in synchrotron light source to generate subpicosecond X-ray pulses while the impedance of the lower order modes (LOM) and higher order modes (HOM) in the cavity should be kept below an accepted level to avoid beam instability. These modes can be damped by adding waveguide on beam pipe. Detailed simulation of Q in CST Microwave Studio is introduced and experiment results on an aluminum model cavity with damping waveguide are reported to make a comparison.     

Design of the low energy beam transport line for the China spallation neutron source

The design of the China Spallation Neutron Source (CSNS) low-energy beam transport (LEBT) line, which locates between the ion source and the radio-frequency quadrupole (RFQ), has been completed with the TRACE3D code. The design aims at perfect matching, primary chopping, a small emittance growth and sufficient space for beam diagnostics. The line consists of three solenoids, three vacuum chambers, two steering magnets and a pre-chopper. The total length of LEBT is about 1.74 m. This LEBT is designed to transfer 20 mA of H-pulsed beam from the ion source to the RFQ. An induction cavity is adopted as the pre-chopper.The electrostatic octupole steerer is discussed as a candidate. A four-quadrant aperture for beam scraping and beam position monitoring is designed.     

Geometry of 2 × 2 hermitian matrices

LetD be a division ring which possesses an involution a → α . Assume that is a proper subfield ofD and is contained in the center ofD. It is pointed out that ifD is of characteristic not two, D is either a separable quadratic extension of F or a division ring of generalized quaternions over F and that if D is of characteristic two,D is a separable quadratic extension ofF. Thus the trace map Tr:D → F, a → a + a is always surjective, which is formerly posed as an assumption in the fundamental theorem of n×n hermitian matrices overD when n ≥ 3 and now can be deleted. WhenD is a field, the fundamental theorem of 2 × 2 hermitian matrices overD has already been proved. This paper proves the fundamental theorem of 2×2 hermitian matrices over any division ring of generalized quaternions of characteristic not two This research was completed during a visit to the Academy of Mathematics and System Sciences, Chinese Academy of Sciences.     

A Fast, Direct Algorithm for the Lippmann–Schwinger Integral Equation in Two Dimensions

The state-of-the-art, large-scale numerical simulations of the scattering problem for the Helmholtz equation in two dimensions rely on iterative solvers for the Lippmann–Schwinger integral equation, with an optimal CPU time O(m ³ log(m)) for an m-by-m wavelength problem. We present a method to solve the same problem directly, as opposed to iteratively, with the obvious advantage in efficiency for multiple right-hand sides corresponding to distinct incident waves. Analytically, this direct method is a hierarchical, recursive scheme consisting of the so-called splitting and merging processes. Algebraically, it amounts to a recursive matrix decomposition, for a cost of O(m ³), of the discretized Lippmann–Schwinger operator. With this matrix decomposition, each back substitution requires only O(m ² log(m)); therefore, a scattering problem with m incident waves can be solved, altogether, in O(m ³ log(m)) flops.     

Commutator inequalities associated with the polar decomposition

Let be a polar decomposition of an complex matrix . Then for every unitarily invariant norm , it is shown that

where denotes the operator norm. This is a quantitative version of the well-known result that is normal if and only if . Related inequalities involving self-commutators are also obtained.

     

Accurate computation of the smallest eigenvalue of a diagonally dominant -matrix

If each off-diagonal entry and the sum of each row of a diagonally dominant -matrix are known to certain relative accuracy, then its smallest eigenvalue and the entries of its inverse are known to the same order relative accuracy independent of any condition numbers. In this paper, we devise algorithms that compute these quantities with relative errors in the magnitude of the machine precision. Rounding error analysis and numerical examples are presented to demonstrate the numerical behaviour of the algorithms.