This paper reports a robust and systematic approach to generate high-order scalar Laguerre-Gaussian (LG_p,l) beams in end-pumped solid-state lasers by introducing loss control. Based on the spatial distributions of Laguerre-Gaussian modes and the theory of transverse mode selection, the "loss control" is implemented by an amplitude mask in the resonator. This proposed mechanism can be divided into three categories: radial loss, azimuthal loss, and the combination of radial and azimuthal loss, which correspond to excite radial high-order modes (LG_p,0), azimuthal high-order modes (LG_0,l), and regular high-order modes (LG_p,l), respectively. By controlling the locations and thicknesses of opaque rings and lines on the mask, all kinds of LG_p,l modes can be obtained. With the application of mode purity, all the generated modes possess high mode purities greater than 93% in simulation.

A method for selective excitation of InceGaussian modes is presented. The method is based on the spatial distributions of Ince-Gaussian modes as well as the transverse mode selection theory. Significant diffraction loss is introduced in a resonator by using opaque lines at zerointensity positions, and this loss allows to excite a specific mode; we call this method ''loss control.'' We study the method by means of numerical simulation of a half-symmetric laser resonator. The simulated field is represented by angular spectrum of the plane waves representation, and its changes are calculated by the two-dimensional fast Fourier transform algorithm when it passes through the optical elements and propagates back and forth in the resonator. The output lasing modes of our method have an overlap of over 90 % with the target Ince-Gaussian modes. The method will be beneficial to the further study of properties and potential applications of Ince-Gaussian modes.

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