Digital laser for on-demand intracavity selective excitation of second harmonic higher-order modes

In this article, we demonstrate selective excitation of second harmonic higher-order modes inside a diode end-pumped solid-state laser resonator that comprises of a nonlinear potassium titanyl phosphate (KTP) crystal and a digitally addressed holographic end-mirror in a form of a reflective phase-only spatial light modulator (SLM). The emitted second harmonic higher-order modes at 532 nm are generated by an intracavity nonlinear KTP crystal that is pumped by high-order fundamental modes operating at 1064 nm. The fundamental modes are digitally controlled by displaying a computer-generated hologram in the form of a grey-scale image to the SLM screen for on-demand high-order modes. The phase matching of the fundamental mode to the generated frequency-doubled mode is achieved by controlling the phase of the digital hologram to either achieve a high or quasi-degree of orbital angular momentum conservation. We show that we can intracavity generate frequency-doubled high-order Laguerre-Gaussian modes and Hermit-Gaussian modes that are either quasi or fully reproducible in the far-field. To the best of our knowledge, this is the first laser to generate frequency-doubled on-demand higher-order modes inside the cavity at the visible (green) wavelength of 532 nm.