Tunable structured laser over full spatial spectrum

Modern tunable lasers are indispensable instruments in fundamental science and optical frequency applications. With the growing interest in structured light, there's a need for tunable structured lasers with high transverse electromagnetic (TEM) modal purity across a broad spatial spectrum, but no commercial solutions exist. Here, we present the first tunable structured laser that can emit all possible single TEM modes with extremely high purity over a wide range. This is achieved by the collaborative use of intracavity pump geometry and astigmatic detuning to selectively gain a desired mode while blockading others. Our astigmatic oscillator can tunably generate any TEM mode within the spatial bandwidth, achieving over 40,000 orthogonal Hermite-Gauss modes in the experiment, and each can be further expanded into numerous Hermite-Laguerre-Gauss modes via unitary transformation. This approach does not require extra intracavity beam shaping components, offering a promising design for commercially available structured lasers with full spatial spectrum tunability.