4.2: Built-up of Laser Oscillation and Continuous Wave Operation
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If \(P_{vac} \ll P \ll P_{sat} = E_{sat}/\tau_L\), than \(g = g_0\) and we obtain from Equation (4.1.10), neglecting \(P_{vac}\)
\[\dfrac{dP}{P} = 2(g_0 - l) \dfrac{dt}{T_R} \nonumber \]
or
\[P(t) = P(0) e^{2(g_0 - l) \tfrac{t}{T_R}}. \nonumber \]
The laser power builts up from vaccum fluctuations until it reaches the saturation power, when saturation of the gain sets in within the built-up time
\[T_B = \dfrac{T_R}{2(g_0 - l)} \ln \dfrac{P_{sat}}{P_{vac}} = \dfrac{T_R}{2(g_0 - l)} \ln \dfrac{A_{eff} T_R}{\sigma \tau_L}. \nonumber \]
Some time after the built-up phase the laser reaches steady state, with the saturated gain and steady state power resulting from Eqs.(4.1.9-4.1.10), neglecting in the following the spontaneous emission, and for \(\tfrac{d}{dt} = 0\):
\[g_s = \dfrac{g_0}{1 + \tfrac{P_s}{P_{sat}}} = l \nonumber \]
\[P_s = P_{sat} \left ( \dfrac{g_0}{l} - 1 \right ), \nonumber \]
Image removed due to copyright restrictions.
Please see:
Keller, U., Ultrafast Laser Physics, Institute of Quantum Electronics, Swiss Federal Institute of Technology, ETH Hönggerberg—HPT, CH-8093 Zurich, Switzerland.
Figure 4.3: Built-up of laser power from spontaneous emission noise.