Set invariance in control

The properties of positively invariant sets are involved in many different problems in control theory, such as constrained control, robustness analysis, synthesis and optimization. In this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems.

Investigation of spectral bandwidth of optical parametric amplification

The spectral bandwidth of three-wave-mixing optical parametric amplification has been investigated. A general mathematical model for evaluating the spectral bandwidth of optical parametric amplification is developed with parametric bandwidth and gain bandwidth via three-wave noncollinear interactions. The spectral bandwidth is determined by expanding the wave-vector mismatch in a Taylor series and retaining terms through second order. The model takes into account the effects of crystal length, noncollinear angle, group velocity, group-velocity dispersion and gain coefficient. The relation between parametric bandwidth and gain bandwidth is clearly defined. The model is applied to a BBO OPA, a LBO OPA and a CLBO OPA.

Spectral relationship of photoinduced refractive index and absorption changes in fulgide films

Fulgides are one kind of organic photochromic compound, which are famous for their thermal irreversibility. In this report, from the difference spectra of the absorption A() of one kind of pyrrylfulgide, the spectral refractive index change n() was calculated by the Kramers-Kronig relation (KKR), and a good correlation of theoretically derived values and the experimental values of the n measured by a modified Michelson interferometer was found. Further, it is demonstrated that it was possible to calculate the spectral dependence of diffraction efficiency from the easily accessible absorption changes. This method will be a useful tool for the characterization and optimization of fulgide films. The results show that the diffraction efficiency is high at 488 and 750 nm, where the absorption is very small, so we can realize non-destructive reconstruction.