Frequency Domain Spectroscopy in Rare-Earth-Doped Gain Media

Many spectroscopic techniques today rely on time-resolved measurements under short excitation pulses. Instead of using a chopped pump excitation, or ultrafast optical pulses, we expand on and apply the previously developed set of frequency domain methods to analyze the population level dynamics in rare-earth-doped media. By identifying the full frequency response of the gain medium, this method can accurately yield excited state lifetimes and can also be used to estimate transition cross-sections. The accuracy of the frequency domain methods are verified with ${\rm Er}^{3+}$ - and ${\rm Tm}^{3+}$ -doped fibers, and an ${\rm Al}_{2}{\rm O}_{3}{:}{\rm Tm}^{3+}{}$ waveguide, recovering similar results as reported by time-resolved techniques. The complete frequency domain model presented here can be used in characterization of novel optical gain media, and can provide insights into population dynamics in solid state amplifiers and lasers.