## 1 Introduction  
Hermite-Gaussian (\(\mathbf{HG_{mm}}\)) laser beams, with specific intensity and phase distribution, have potential applications in many cutting-edge scientific scenarios [1; 2; 3; 4; 5]. The typical methods for generating \(\mathbf{HG_{mm}}\) laser beams are off-axis diode-end-pumping gain modules [6; 7; 8] or inserting specific optical components such as a spiral phase plate [9] and spatial light modulator [10] in the laser cavity. Generally, the output power of most \(\mathbf{HG_{mm}}\) laser beams is only one watt level or less. For example, a 265 mW average power and 1.7 kW peak power \(\mathbf{HG_{mm}}\) laser beam was obtained using a passively Q-switched Nd:YVO\({}_{4}\) microchip laser based on off-axis pumping [11]. In another work, an average power of less than 1.3 W with nanosecond (ns) pulse width and \(\sim\)4 kW peak power has been achieved in a decentered Gaussian beam pumped Q-switched Nd:YAG microchip laser for different high-order transverse modes [12].  
A one-dimensional high-order \(\mathbf{HG_{0n}}\) laser beam is a typical \(\mathbf{HG_{mm}}\) laser beam, where \(m=0\). This means no dark bars are crossing the pattern in the x-direction, while the number of dark bars in the y-direction is \(n\), so the HG\({}_{0n}\) laser beams display as strip shape. Due to the fact that HG\({}_{0n}\) laser beams can be easily converted into vortex Laguerre-Gaussian (LG\({}_{pl}\)) beams carrying orbital angular momentum (OAM) by adopting the Astigmatic Mode Converter (AMC), the applications of HG\({}_{mn}\) laser beams have been further expanded [13; 14; 15], and the HG\({}_{0n}\) laser beams with both high average power and high peak power are expected to be obtained.  
As is well known, for the most commonly used off-axis pumping method, the radius of the pump beam with about a one-hundred-micrometer level is much smaller than the spot of the one-dimensional high-order HG\({}_{0n}\) mode beams, then the intensity of the HG\({}_{0n}\) mode beams inside and outside the pumping region is different. Consequently, the purity of the HG\({}_{0n}\) laser beams should be significantly reduced. On the other hand, in order to obtain HG\({}_{0n}\) laser beams with higher power, higher pump power is required, which will lead to significant thermal lens effects and thus affect the mode of the laser. Therefore, the development of a new method for obtaining high-average-power and high-peak-power, high-purity HG\({}_{0n}\) modes has become a hot research field.  
Slabs with large aspect ratios have been widely used in laser systems because of their large gain volume, great pump uniformity, and favorable thermal management [16; 17; 18]. Since the zig-zag optical path in the slab averages the thermal gradient, there is almost no first-order thermal lens effect, making it a promising method for extracting higher power while simultaneously maintaining good beam quality. In this letter, an alternative method for generating a high-purity, one-dimensional HG\({}_{0n}\) laser beam has been proposed and demonstrated. Different from traditional approaches, a Nd:YAG slab with a large aspect ratio of 7.5 is selected as the gain medium. By adjusting the pump intensity, the size of the aperture pair in thickness and width directions of the slab, and the tilt angle of the output coupler (OC), the intracavity mode is controlled, and high-purity, ns one-dimensional HG\({}_{0n}\) laser beams with orders 1 to 9 (HG\({}_{01}\) to HG\({}_{09}\)) are obtained from the slab oscillator in Q-switched operation. The beam quality factors \(M^{2}\) are in reasonable agreement with the theoretical values. Because the large aspect ratio slab provides an ideal amplifier for the strip-shaped HG\({}_{0n}\) laser beam, further power scaling is realized. The seed beam from the oscillator is directly injected into the other identical slab as the amplifier. For the highest order HG\({}_{09}\) mode beam, the average power is amplified from 289 mW to 4.73 W with a pulse width of 294 ns, corresponding to a peak power of 32 kW.