Exploring the frequency degenerate range of the three-dimensional structured lights in selectively end-pumped Nd:YVO₄...

Three-dimensional (3D) structured light is a complex form of structured light characterized by ray-wave duality. The principle for generating 3D structured laser transverse modes has been well-established through numerous experiments. However, little research has been focused on the frequency degeneracy range during the process of obtaining these modes. In this work, we utilize a Radio-Frequency (RF) spectrum analyzer to record frequency signal data at different accidental degeneracies. By analyzing the variation of the frequency signal as the resonator length changes, we determined the exact degeneracy range. Near the 1/5 degeneracy cavity, the exact range was found to be from 18.20 mm to 18.10 mm. Near the 1/6 degeneracy cavity, the degenerate cavity length range was determined to be from 12.55 mm to 12.45 mm. This work demonstrates that monitoring the RF signal changes with the analyzer enables precise identification of the resonator's fine cavity length and degeneracy range, based on ray-wave duality. It also introduces a novel method for evaluating the stability of 3D structured laser transverse modes in the frequency domain.