Effect of normalized plasma frequency on electron phase-space orbits in a free-electron laser

Irregular phase-space orbits of the electrons are harmful to the electron-beam transport quality and hence deteriorate the performance of a free-electron laser （FEL）. In previous literature, it was demonstrated that the irregularity of the electron phase-space orbits could be caused in several ways, such as varying the wiggler amplitude and inducing sidebands. Based on a Hamiltonian model with a set of self-consistent differential equations, it is shown in this paper that the electron- beam normalized plasma frequency functions not only couple the electron motion with the FEL wave, which results in the evolution of the FEL wave field and a possible power saturation at a large beam current, but also cause the irregularity of the electron phase-space orbits when the normalized plasma frequency has a sufficiently large value, even if the initial energy of the electron is equal to the synchronous energy or the FEL wave does not reach power saturation.

Dispersion Properties in Total Internal Reflective Photonic Crystal Fiber

The dispersion properties in the short wavelength region of total internal reflective photonic crystal fiber have been studied by using the models of the equivalent twin waveguide soliton coupling,effective refractive index,effective normalized frequency and dispersion management solitons.It is shown that the dispersion in the cladding waveguide of the total internal reflective photonic crystal fiber is a positive dispersion,and the dispersion of its core waveguide is a negative dispersion.The method of the compensated probing laser diffraction by the phase hole induced by the stationary pumping laser in the cladding waveguide enables the average dispersion value of the total internal reflective photonic crystal fiber to be close to zero and the zero dispersion point to shift to the short wavelength region.

Mode-field half-widths of Gaussian approximation for the fundamental mode of two kinds of optical waveguides

This paper analyzes the characteristic of matching efficiency between the fundamental mode of two kinds of optical waveguides and its Gaussian approximate field.Then, it presents a new method where the mode-field half-width of Caussian approximation for the fundamental mode should be defined according to the maximal matching efficiency method. The relationship between the mode-field half-width of the Gaussian approximate field obtained from the maximal matching efficiency and normalized frequency is studied; furthermore, two formulas of mode-field half-widths as a function of normalized frequency are proposed.

Normalized estimation of fundamental frequency and measurement of harmonics/interharmonics

An adaptive notch filter is presented to estimate the fundamental frequency and measure both harmonics and interharmonics of an almost periodic signal with unknown time-variant fundamental frequency, which has the ro- bustness that the convergence speed is determined by neither amplitude nor frequency of fundamental component. The algorithm forms a one-dimensional slow adaptive integral manifold whose existence and stability are proved by averaging method and Lyapunov stability theorem. The local exponential stability and the ultimate boundedness of fundamental fre- quency estimation are proved. The local exponential stability makes sure that the fundamental frequency, the harmonic and interharmonic components can be all fast tracked. The principle for adjusting the parameters with their influences on tran- sient and steady-state performance is investigated and decreasing parameters can improve noise characteristic. The validity is verified by simulation results.

Compound solitons in fiber Bragg grating

Single soliton and compound solitons are described by coupled-mode equation. It is noted that three parameters, which are dimensionless group velocity, normalized frequency, and grating strength, influence formed solitons by emulation. The novel designs of parallel and serial multi-grating are advanced, and the compound solitons formed from parallel multi-grating are linear superposition; the compound solitons formed from serial multi-grating are nonlinear superposition, and finally two general formulae are obtained. Furthermore, it is theoretically shown that the compound grating solitons are prominent and flexible signals in optical communication.