The onset of multi-pulsing, a ubiquitous phenomenon in laser cavities, imposes a fundamental limit on the maximum
energy delivered per pulse. Managing the nonlinear penalties in the cavity becomes crucial for increasing
the energy and suppressing the multi-pulsing instability. A Proper Orthogonal Decomposition (POD) allows for
the reduction of governing equations of a mode-locked laser onto a low-dimensional space. The resulting reduced
system is able to capture correctly the experimentally observed pulse transitions. Analysis of these models is
used to explain the the sequence of bifurcations that are responsible for the multi-pulsing instability in the master
mode-locking and the waveguide array mode-locking models. As a result, the POD reduction allows for simple
and efficient way to characterize and optimize the cavity parameters for achieving maximal energy output.
The manipulation and routing of light-bullets in a VCSEL-like planar waveguide array is studied numerically. By
partitioning the gold contact layer used for current injection into discrete and individually addressable segments,
an electronically controllable and non-uniform gain profile is created. Light-bullets typically follow the gradient
of the gain and are therefore completely controllable by manipulating the gain profile. In addition, by exploiting
gain-mediated interactions between nearby light-bullets, the NAND and NOR gates are also constructed. Therefore,
planar waveguide arrays with addressable gain profiles appear to be an ideal technology for optical routing
applications as well as for photonic logic devices.
A theoretical proposal is presented for the generation of mode-locked light-bullets in planar waveguide arrays,
extending the concept of time-domain mode-locking in waveguide arrays to spatial (transverse) mode-locking
in slab waveguides. The model presented yields three-dimensional localized states that act as global attractors
to the waveguide array system. Single pulse stationary and time-periodic solutions as well as the transition to
multi-pulse solutions as a function of gain are observed to be stabilized in such a system.
The intensity dynamics of a five-emitter laser array subject to a linearly decreasing injection current are examined numerically.
We have matched the results of the numerical model to an experimental AlGaAs quantum-dot array laser and
have achieved the same robust oscillatory power output with a nearly π phase shift between emitters that was observed in
experiments. Due to the linearly decreasing injection current, the output power of the waveguide decreases as a function of
waveguide number. For injection currents ranging from 380 to 500 mA, the oscillatory behavior persists with only a slight
change in phase difference. However, the fundamental frequency of oscillation increases with injection current, and higher
harmonics as well as some fine structures are produced.
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