Modification of Bertrand's theorem and extended Runge-Lenz vector

It is shown that for a particle with suitable angular moments in the screened Coulomb potential or isotropic harmonic potential, there still exist closed orbits rather than ellipse, characterized by the conserved aphelion and perihelion vectors, i.e. extended Runge-Lenz vector, which implies a higher dynamical symmetry than the geometrical symmetry O-3. The closeness of a planar orbit implies the radial and angular motional frequencies are commensurable.

The Complete Proof of the Virial Theorem in the Refined TFD Theory for all Electrons of an Atom in a Solid

The complete proof of the virial theorem in refined Thomas-Fermi-Dirac theory for all electrons of an atom in a solid is given.

Distortion of beam shape by a rotating double-prism wide-angle laser beam scanner

We describe the rigorous results of a wide-angle laser beam scanner, obtained with the help of the vector refraction theory. Using the rigorous results, the distortion of the beam shape is discussed. The distortion to the beam varies with the different relative angles of double prisms. The scanner expands the beam in some directions while it contracts the beam in other directions. According to the conservation of energy, the distribution of the laser intensity is changed as well. (c) 2006 Society of Photo-Optical Instrumentation Engineers.

Distortion of beam shape by a rotating double-prism wide-angle laser beam scanner

We describe the rigorous results of a wide-angle laser beam scanner, obtained with the help of the vector refraction theory. Using the rigorous results, the distortion of the beam shape is discussed. The distortion to the beam varies with the different relative angles of double prisms. The scanner expands the beam in some directions while it contracts the beam in other directions. According to the conservation of energy, the distribution of the laser intensity is changed as well. (c) 2006 Society of Photo-Optical Instrumentation Engineers.

Control of polarization signal distortion by frequency domain phase conjugation in optical fiber systems

Optical frequency domain phase conjugation (FDPC) is based on phase conjugation of spectrum of an input signal. It is equivalent to the phase conjugation and the time reversal of the temporal envelope of an input signal. The use of FDPC to control polarization signal distortion in birefringent optical fiber systems is proposed. Evolution of polarization signals in the system using midway FDPC is analyzed theoretically and simulated numerically. It is shown that the distortion of polarization signals can be controlled effectively by FDPC. The impairments due to dispersion and nonlinear effects can be suppressed simultaneously.

Depth dependence of the tetragonal distortion of a GaN layer on Si(111) studied by Rutherford backscattering/channeling

Rutherford backscattering and channeling have been used to characterize the structure of a GaN layer grown on a Si(111) substrate. The results show that a 1.26 mum GaN epitaxial layer with a rather abrupt interface and a good crystalline quality (chi(min)=3.4%) can be grown on a Si(111) substrate. Using the channeling angular scan around an off-normal <1 (2) over bar 13> axis in the {10 (1) over bar0} plane of the GaN layer, the tetragonal distortion e(T), which is caused by the elastic strain in the epilayer, can be determined. Moreover, the depth dependence of the e(T) can be obtained using this technique. A fully relaxed (e(T)=0) GaN layer for a thickness <2.8 mum is expected. (C) 2002 American Institute of Physics.

Distortion management of SBS slow light in a single-mode optical fiber by optimization of broadband SBS gain spectrum

SPIE

A 10-bit 50-MS/s sample-and-hold circuit with low distortion sampling switches

A fully-differential switched-capacitor sample-and-hold (S/H) circuit used in a 10-bit 50-MS/s pipeline analog-to-digital converter (ADC) was designed and fabricated using a 0.35-μm CMOS process. Capacitor fliparound architecture was used in the S/H circuit to lower the power consumption. In addition, a gain-boosted operational transconductance amplifier (OTA) was designed with a DC gain of 94 dB and a unit gain bandwidth of 460 MHz at a phase margin of 63 degree, which matches the S/H circuit. A novel double-side bootstrapped switch was used, improving the precision of the whole circuit. The measured results have shown that the S/H circuit reaches a spurious free dynamic range (SFDR) of 67 dB and a signal-to-noise ratio (SNR) of 62.1 dB for a 2.5 MHz input signal with 50 MS/s sampling rate. The 0.12 mm~2 S/H circuit operates from a 3.3 V supply and consumes 13.6 mW.