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Vertical External Cavity Surface Emitting Lasers (VECSELs) have been used for mode-locked operation by using a Semiconductor Saturable-Absorber Mirror (SESAM), usually in the external cavity [1] but also integrated in the gain-chip [2]. Impressive progress has been achieved since the first demonstration of an SESAM mode-locked VECSEL in terms of pulse duration, average optical power, and peak power. While the shortest pulses have been achieved with optically pumped active layers, electrically pumped structures are promising for a number of applications. Α versatile and accurate, if fairly complex, delay-differential theoretical model for mode-locking in electrically pumping VECSELs based on the physical description of gain and SESAM chips has been presented [3], however only the linear cavity geometry has been studied. A somewhat different approach was taken in [4][5] where an experiment-informed model representing the laser somewhat artificially as a sequence of gain, absorber, and dispersion elements in a unidirectional ring cavity (reminiscent of the classic Haus theory) was developed, and successfully reproduced the measured laser parameters in both pico-and femtosecond regimes.
In the current work, we present a somewhat simplified model based on the physical laser design as in [3], which however can accommodate realistic geometry, both linear and folded-cavity. The model is applied to study different regimes of laser operation, including the possibility of colliding pulse mode locking at harmonics of the fundamental roundtrip frequency. As in [3], we base the derivation on the analysis of amplitudes of waves incident onto, and reflected from, elements of the laser cavity, using the amplitude of the field reflected from the “bulk” of the cavity as the dynamic variables for the description of light. Standard rate equations are used for carrier densities.
In the case of a linear cavity the model is thus somewhat similar to that used in [3] though somewhat simplified. No matrices of the type used in [3] are needed to recalculate the dynamic variables in our simplified model. The use of phenomenological gain-carrier density dependences and linewidth enhancement factors, while less rigorous than the simplified microscopic model of [3], enables relatively easy inclusion of polarization dependences, allowing double-polarisation frequency comb generation to be simulated.
In the case of a folded (Z-type) cavity either the gain chip or the SESAM chip can be positioned “inside” the cavity. The dynamic variables in the case of the gain chip in the middle are the fields reflected from the bulk of the gain chip in the directions of the output mirror and the absorber chip, and from the bulk of the SESAM back to the gain chip . In the case of the gain chip in the middle position, the difference in the dynamics of the saturation of the gain chip changes the pulse parameters and stability limits compared with the linear cavity, but there is no qualitative difference. In the case of the absorber section in the intracavity position, colliding pulse dynamics was simulated with a rational relation between the delay times. Further results will be presented at the conference.
References
[1] U. Keller, A. C. Tropper, Phys. Reports, 429, 67 (2006)
[2] D.J.H.C. Maas et al., Appl Phys B, 88, 493 (2007)
[3] J. Mulet and S. Balle, IEEE J. Quantum Electron., 41, 1148 (2005)
[4] M. Hoffmann et al., Opt. Express 18, 10143 (2010)
[5] O.Sieber et al., Appl.Phys.B., 113, 133-145 (2013)
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