# Optical Vortex-Pumped KTiOAsO\({}_{4}\) Narrow-Linewidth Picosecond-Pulsed Parametric Oscillator
## 2 Experimental Setup  
The experimental setup of this work is depicted in Figure 1a. An all-solid-state Nd:YVO\({}_{4}\) laser served as the pump source for the OPO with an output wavelength of 1064 nm, a pulse width of 15 ps, a pulse repetition frequency of 120 MHz, a maximum average output power of 18 W, and a near-Gaussian spatial output profile (\(M^{2}\) < 1.3). A Faraday rotator (FR) was employed to eliminate the backward-reflected light and safeguard the Nd:YVO\({}_{4}\) laser from damage. The incident power of the OPO was regulated through the combined use of a half-wave plate (HWP) and a thin-film polarizer. The pump beam was transformed into a vortex beam using an SPP, which exhibits an annular spatial intensity profile as shown in Figure 1b. The topological charge characteristics of the generated vortex beam were determined with the tilted lens method, and the two lobes in the spatial intensity profile of the beam observed through the lens arrangement, as shown in Figure 1c, confirmed that the pump vortex beam has a topological charge of \(\ell\) = 1.  
The pump vortex beam was focused on the KTA crystal using a plano-convex lens with a focal length of 100 mm. The lens was installed on a high-precision translation stage that allowed the focal position of the pump vortex beam to be variable within the KTA crystal, thus altering the spatial overlap of the pump, signal, and idler fields. The KTA crystal, with a length of 30 mm and end faces sized 5 mm \(\times\) 5 mm, was precisely cut to achieve type II non-critical phase matching (NCPM). Both of the end faces were coated with an anti-reflection film (reflectivity \(<\) 0.5%) to enhance transmission at wavelengths of 1064 nm (pump field), 1535 nm (signal field), and 3468 nm (idler field). The OPO was singly resonant for the signal field and was formed using five mirrors in a \(Z\)-shaped standing wave cavity configuration. M\({}_{2}\) (R = 150 mm) and M\({}_{3}\) (R = 150 mm) were plane-concave mirrors placed on either side of the KTA crystal, and the distance between them was 167 mm. A flat mirror M\({}_{1}\) and two plane-concave mirrors M\({}_{4}\) (R = 500 mm) and M\({}_{5}\) (R = 1000 mm) also contributed to the formation of the OPO cavity. Specifically, M\({}_{1}\)-M\({}_{4}\) were high-reflection coated for the signal field (R \(>\) 99.9%) and anti-reflection coated for the pump and idler fields (R \(<\) 0.5%; R \(<\) 2%). M\({}_{5}\) was partially transmission coated for the signal field (R = 80%) to ensure resonance of the signal field. M\({}_{1}\) was firmly attached to a high-precision translation stage for precisely adjusting the cavity length of the OPO and attaining synchronization with the pump laser. The total round-trip optical path length of the OPO cavity amounted to 1250 mm. Additionally, a dichroic beam splitter was utilized to separate the co-propagating idler field from the remaining pump field. The output power and spatial intensity profiles of the signal field and idle field were measured with a power meter and a Spiricon pyroelectric camera III (Ophir-Spiricon, North Logan, UT, USA).