Source: ResearchGate

Understanding Upper-State Lifetime in Laser Gain Media

Introduction to Laser Gain Media

Laser gain media are materials that amplify light through the process of stimulated emission. Within these media, amplification is associated with populations in excited states, from which stimulated emission can occur. The lifetime of the upper-state population, referred to as the upper-state lifetime, is a critical parameter in determining the performance and efficiency of lasers.

Decay Processes in Upper-State Populations

Even in the absence of stimulated emission, the upper-state population will decay over time due to spontaneous emission and other possible quenching effects. This decay is typically exponential, characterized by a specific decay time known as the upper-state lifetime, which is the time it takes for the population to reduce to approximately 37% of its initial value.

Spontaneous Emission and Fluorescence

Spontaneous emission results in fluorescence, and the fluorescence lifetime is identical to the upper-state lifetime. Ideally, decay should be due solely to spontaneous emission, with the inverse of this lifetime termed the radiative lifetime.

Factors Influencing Decay Rates

The decay rate can be accelerated by additional radiative or non-radiative transitions to lower energy levels. Quenching processes, such as deexcitation at impurities or energy transfers between laser ions, can lead to non-exponential decay patterns. For instance, some quenching processes may cause rapid decay when the upper-level population is high, but have less effect at lower populations.

Temperature Dependence and Effective Lifetime

In certain gain media, such as Cr:forsterite and Cr:YAG, the upper-state lifetime is highly temperature-dependent. Phonon-assisted non-radiative relaxation can become more pronounced at higher temperatures, impacting the lifetime.

Under lasing conditions, an effective upper-state lifetime can be defined, accounting for stimulated emission. In a four-level laser medium, this effective lifetime is reduced when the laser is pumped above the threshold power.

Typical Upper-State Lifetimes

The upper-state lifetimes of laser gain media vary widely. For dipole-allowed transitions, excited levels of atoms or ions have lifetimes around nanoseconds. In contrast, rare-earth-doped media, which operate on weakly allowed transitions, exhibit much longer lifetimes ranging from a few microseconds to several milliseconds.

Significance for Laser Performance

A long upper-state lifetime allows for maintaining a significant population inversion with lower pump power, enhancing gain efficiency. This is particularly advantageous for continuously pumped Q-switched lasers, enabling the storage of large energy amounts. The lifetime also influences laser dynamics, affecting relaxation oscillations and spiking tendencies.

Measuring Upper-State Lifetime

Upper-state lifetime can be measured by exciting the upper laser level with a short pulse and observing fluorescence decay. Alternatively, an optical chopper with a continuous-wave laser can be used, though this method is slower and suitable for longer lifetimes. In highly doped media, reabsorption of fluorescence can artificially extend measured lifetimes, a phenomenon that can be mitigated through specific experimental setups.

Source: arXiv
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