Energy rate equations for mode-locked lasers

Continuation of periodic solutions in the waveguide array mode-locked laser

“…Further increase of the cavity gain results in stable, two-pulse operation in both cases. This transition behavior is generic for N to N +1 pulses in the laser cavity, thus confirming mode-locking experiments [1,7,20,21] and theory [8,9,20,21]. The demonstrated transition repeats itself for the 2-to 3-pulse transition, the 3-to 4-pulse transition and so on as demonstrated in [4].…”

“…Clearly the most important connection to make is with direct experimental observations of mode-locked laser cavities. Although early observations demonstrated the multi-pulsing transition (see, for instance, Namiki et al [7]), more careful experiments near the multi-pulsing transition point were not performed for another decade [20,21]. The recent experimental observations in 2009 by the Wise group at Cornell University [20] and in 2004 by the Grelu group at the University of Bourgogne [21] both carefully considered the multi-pulsing transition points and found all the key features of the bifurcation diagram constructed here.…”

“…This suggests that our study in this paper will be relevant to the study of the multipulsing transition sequence in mode-locked laser systems. Given that the only transitions observed experimentally [1,7,20,21] and theoretically [8,9,20,21] are from N to N + 1 pulses, the method developed characterizes this fundamental behavior.…”

“…One of the most recently envisioned methods for generating stable mode-locking incorporates the intensity discrimination induced by the nonlinear mode-coupling properties in a waveguide array [2][3][4][5][6]. The waveguide array mode-locking produces robust mode-locking and displays the ubiquitous multi-pulsing transition instability [7,8] whereby an increase in the laser cavity energy above a given threshold causes a single pulse per round trip to bifurcate to two pulses per round trip. This multi-pulsing transition dynamics is the primary focus of this manuscript.…”

Mode-locked laser pulse sources for wavelength division multiplexing

“…To obtain analytic insight into the dynamics of this model, a variational method can be used to describe the complete evolution problem with ordinary differential equations that govern the evolution of a finite set of pulse parameters. The literature regarding variational reductions in nonlinear Schrödinger systems is vast, 20 and has been used to describe various aspects of mode-locking behavior [21][22][23][24][25][26][27] as well as general Ginzburg-Landau systems. 28 The variational method is traditionally rooted in the Hamiltonian nature of the system, i.e.…”