A novel Smith-Purcell (S-P) free electron laser composed of an electron gun, a semi-elliptical resonator, a metallic reflecting grating and a collector, is presented for the first time. This paper studies the characteristics of this device by theoretical analysis and particle-in-cell simulation method. Results indicate that tunable coherent S-P radiation with a high output peak power at millimeter wavelengths can be generated by adjusting the length of the grating period, or adjusting the voltage of the electron beam. The present scheme has the following advantages: the semi-elliptical resonator can reflect all radiation with the emission angle θ and random azimuthal angles, back onto the electron beam with same-phase and causes the electrons to be modulated, so the output power and efficiency are improved.

The rate equations of fiber lasers with three-energy-level dopants are anglicized. An expression of the unit step response of the fiber laser with three-energy-level dopants has been obtained from rate equations in a constant pump power. With these expressions, output characteristic of the fiber laser with three-energy-level dopants has been studied. The output characteristic of the fiber laser with three-energy-level dopants depends on its damping ratio, and the different damped oscillation curves and over-damped monotonic decay curves can be obtained for various damping ratio of the fiber laser with three-energy-level dopants. If 0 < ξ < 1, the photon density curves of stimulated radiation of the fiber laser will be a damping oscillation curves. If ξ = 1 or ξ > 1, the photon density curves of stimulated radiation of the fiber laser will be non-oscillating monotonic decay curves.

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