Formation of high-quality vortex laser beams with different orbital angular momenta in the laser resonator.

A scheme for forming high-quality vortex laser beams by employing spiral phase elements inside a laser resonator is presented theoretically. The calculated results show that the purity of the generated mode will decrease slightly as the mode order increases. However, the purity can achieve higher than 0.97 even for the high-order mode. More important, the value of the orbital angular momentum is controllable. Then, the influence of production and alignment errors, including the number of phase levels of the spiral phase elements, the surface roughness of the reflective mirrors, and the decenter of the reflective mirrors, is discussed in detail. The results show that the diffraction loss of the proposed system is more sensitive to production errors, and the purity of the generated mode is more sensitive to alignment errors. Thus, we estimate that the height of one step of the spiral structure should be less than one-fifteenth of the wavelength, the maximum surface fluctuation should be less than one-twentieth of the wavelength, and the vertical distance between the centers of the two reflective mirrors should be less than 20 μm if one wants to obtain high-quality vortex laser beams with high efficiency. The requirements for precision are acceptable for existing microfabrication and operation technologies.