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Modeling of transverse-mode competition in unstable resonators with large discharge current using the exact cavity equations of motion with dynamic gain

The transverse output profile and mode competition in CO2 lasers are significantly affected by the discharge current, as was reported by Witteman [IEEE J. Quantum Electron. QE-4, 786-8 (1968)]. He found that in a sealed laser, with a stable resonator, a spatial mode switching is observed upon increasing the current; due to a modification in the radial profile of the small signal gain. Through an atypical gain profile the lowest-loss bare cavity mode, usually dominant in laser dynamics, may have lower net cavity gain than a mode with higher diffraction losses. Through this work a dynamic differential equation for the homogeneously saturating gain is included in the original dynamic coupled modes method [Appl. Opt. 29, 3905-15 (1990)] and applied to a CO2 unstable resonator, with suitable high current small signal gain profiles. By expanding the gain loaded cavity field into the bare cavity oscillation eigenstates, this new model provides a realistic temporal evolution of mode competition, output power and gain saturation within the resonator. We have found that although unstable resonators have excellent transverse mode discrimination the spatial mode switching may also occur, resulting in a significant modification in the output intensity profile. Thus, under certain design parameters, the common assumption of the small signal gain to be constant through the lasing medium may incur in serious inaccuracies for determining the transverse intensity profile and output power. The application of the method is fully described, and the results and their connection to relevant physical properties of gas lasers are discussed.