  Vertical external-cavity surface-emitting lasers (VECSELs) augmented by
intra-cavity nonlinear optical frequency conversion have emerged as an
attractive light source of ultraviolet to visible light for demanding
scientific applications, relative to other laser technologies. They offer high
power, low phase noise, wide frequency tunability, and excellent beam quality
in a simple and inexpensive system architecture. Here, we characterize the
frequency stability of an intra-cavity frequency-doubled VECSEL with 690 mW of
output power at 475 nm using the delayed self-heterodyne technique and direct
comparison with a commercial external-cavity diode laser (ECDL). We measure the
fundamental's Lorentzian linewidth to be $2\pi\times5.3(2)$ kHz, and the total
linewidth to be $2\pi\times23(2)$ kHz. In addition, we perform Rydberg-state
spectroscopy via electromagnetically induced transparency (EIT), observing
narrow 3.5 MHz full-width half-maximum EIT. By doing so, we demonstrate that
intra-cavity frequency-doubled VECSELs can perform precision spectroscopy at
the MHz level, and are a promising tool for contemporary, and future, quantum
technologies.
