Corresponding to optical Fresnel diffraction, we show that the exponential quadratic operator exp is actually a generalized single-mode Fresnel operator （GFO） in compact form, where [Q,P]=ih. We also demonstrate that exp{iα[（Q1＋Q2）2＋（p1-P2）2]＋iβ[（Q1-Q2）2＋（p1＋p2）2]＋iy（Q1P2＋Q2P1）} is a two-mode GFO. Their disentangling formula and normal ordering form are derived with the use of technique of integration within an ordered product （IWOP） of operators and the coherent state representation. The squeezed states generated by these two GFOs are obtained.
A new kind of four-mode continuous variable coherent-entangled state is proposed in the Fock space by using the technique of integration within an ordered product, which exhibits both the properties of a coherent state and an entangled state, and spans a complete and orthonormal representation. The conjugate state of the four-mode continuous variable coherent-entangled state is derived by using the Fourier transformation. Moreover, a simple experimental protocol of generating a four-mode continuous variable coherent-entangled state is proposed by using beam splitters. As applications of this four-mode continuous variable coherent-entangled state, a four-mode entangled state and a four-mode squeezing-Fresnel operator are constructed.
A pulsed master oscillator power amplifier system is constructed using a double-cladding polarized Yb- doped fiber and an all-fiber Q-switched narrow-linewidth pulsed laser used as seed laser. This system has a high repetition rate and provides a nanosecond pulsed laser with a narrow linewidth and linear polarization. Moreover, it generates amplified radiation with up to 14 W of average power, narrow linewidth （full-width at half-maximum is smaller than 0.12 am）, linear polarization at 1080-am wavelength, repetition rate of 51 kHz, and pulse duration of approximately 50 ns. Based on this pulsed amplified radiation, 3.5 W of green laser, with an optical-to-optical efficiency of 27.3%, is obtained via single-pass frequency doubling using a noncritical phase matching KTP crystal.
