Characterization of isolated homogeneous hypersurface singularities in C4

Let V be a hypersurface with an isolated singularity at the origin in Cn+1. It is a natural question to ask when V is defined by weighted homogeneous polynomial or homogeneous polynomial up to biholomorphic change of coordinates. In 1971, a beautiful theorem of Saito gives a necessary and sufficient condition for V to be defined by a weighted homogeneous polynomial.For a two-dimensional isolated hypersurface singularity V, Xu and Yau found a coordinate free characterization for V to be defined by a homogeneous polynomial. Recently Lin and Yau gave necessary and sufficient conditions for a 3-dimensional isolated hypersurface singularity with geometric genus bi.er than zero to be defined by a homogeneous polynomial. The purpose of this paper is to prove that Lin-Yau's theorem remains true for singularities with geometric genus equal to zero.     

Energy extraction of Porro resonator in Pockels cell Q-switch operation

Deviation of a practical Pockels cell Q-switch bias voltage from the ideal bias value significantly affects the extraction of useful output energy. The losses of two practical bias voltages are calculated and the properly rotated angle towards the right-hand side prism of the Porro resonator is determined to simulate the different losses. The losses are due to deviation of the Q-switch bias voltage from the ideal value. It not only degrades the useful output energy, but introduces a useless energy loss in the reverse output direction. For the different losses of these two practical Pockels cell bias voltages, the useful output energy difference is about 30%. The useful output energy and lost energy ratios of the two equivalent loss configurations are 0.54 and 0.89, respectively. These ratios agreed quite well with the theoretical results.     

Phase Conjugation with Picosecond Pulses in BaTi03

The self-pumped phase conjugate signal of picosecond laser pulses is observed. The width of the incident laser pulses is about 1.5 ps and their repetition rate is 82 MHz. The wavelength of the pulses can be tuned in the range from 710 nm to 850 nm. The pulse character of the conjugate signal is determined by an autocorrelator. The quality of the conjugate pulses is found to be good by the well-known phase distorter method.