Hermite-Gaussian (HG) beams have many important applications in the optical frontier,and the limited output power of the high-purity HG beams is partly due to the small gain volume of the mode.The commonly used off-axis end-pumped scheme offers a narrow gain volume whose diameter is about a hundred microns.In this paper,a new method for generation of HG beams based on a slab resonator that has a large mode volume is proposed and experimentally demonstrated.According to the optical resonator theory,the intra-cavity modes in thickness and width direction of the slab resonator are restricted by inserting two size-adjustable apertures,respectively.The one-dimensional HG beam generation is mainly guaranteed by the size of the aperture along the thickness direction of the slab,which matches the diameter of the fundamental mode.The different order one-dimensional HG beams are obtained by refined intra-cavity mode modulation.Since the higher-order modes are less sensitive to the misalignment of the cavity mirror than the lower-order modes,the manipulation of the modes-loss at different orders is achieved by combining the tilt control of the coupled output mirror and the size control of intra-cavity apertures.Through the adjustment of the optical gain and loss in the resonator,the single mode wins out in the laser modes competition.Consequently,high-purity one-dimensional HG beams with orders 0 to 9(HG ₀₀to HG ₀₉) are generated.The pump module is comprised of a two-dimensional laser diode array which offers face-pumping to the large surface of the slab,therefore the width of the mode volume is extended to several millimeters.By further incorporating the 100mm-level length slab,the total gain volume is much larger than the off-axis pumping scheme.In this paper,the output power of the highest order HG ₀₉mode is up to 244 mW.Due to the large gain volume and uniform gain distribution brought by the face-pumped slab,the purity of high order HG modes is quite good.The correlation coefficient ρ between the measured intensity distribution and the theoretical value is larger than 0.95.The beam quality factor ρ is also in good agreement with the theory.Finally,a conversion from Hermite-Gaussian beams to the donut-shaped Laguerre-Gaussian beams is realized by using an astigmatic mode converter.Hopefully,power scaling of the HG beam output is also expected by employing cascaded slab amplifiers,and the approach in this paper provides a novel solution for generation of high power HG beams.