TY - JOUR
T1 - Bifurcation and stability in a low-dimensional model for multiple-frequency mode-locked lasers
AU - Farnum, Edward D.
AU - Bale, Brandon G.
AU - Kutz, J. Nathan
PY - 2010/3/31
Y1 - 2010/3/31
N2 - Recent theoretical investigations have demonstrated that the stability of mode-locked solutions of multiple frequency channels depends on the degree of inhomogeneity in gain saturation. In this article, these results are generalized to determine conditions on each of the system parameters necessary for both the stability and the existence of mode-locked pulse solutions for an arbitrary number of frequency channels. In particular, we find that the parameters governing saturable intensity discrimination and gain inhomogeneity in the laser cavity also determine the position of bifurcations of solution types. These bifurcations are completely characterized in terms of these parameters. In addition to influencing the stability of mode-locked solutions, we determine a balance between cubic gain and quintic loss, which is necessary for the existence of solutions as well. Furthermore, we determine the critical degree of inhomogeneous gain broadening required to support pulses in multiple-frequency channels.
AB - Recent theoretical investigations have demonstrated that the stability of mode-locked solutions of multiple frequency channels depends on the degree of inhomogeneity in gain saturation. In this article, these results are generalized to determine conditions on each of the system parameters necessary for both the stability and the existence of mode-locked pulse solutions for an arbitrary number of frequency channels. In particular, we find that the parameters governing saturable intensity discrimination and gain inhomogeneity in the laser cavity also determine the position of bifurcations of solution types. These bifurcations are completely characterized in terms of these parameters. In addition to influencing the stability of mode-locked solutions, we determine a balance between cubic gain and quintic loss, which is necessary for the existence of solutions as well. Furthermore, we determine the critical degree of inhomogeneous gain broadening required to support pulses in multiple-frequency channels.
UR - http://www.scopus.com/inward/record.url?scp=77950457274&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.81.033851
DO - 10.1103/PhysRevA.81.033851
M3 - Article
AN - SCOPUS:77950457274
SN - 1050-2947
VL - 81
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 3
M1 - 033851
ER -