The multi-pulsing transition in mode-locked lasers: a low-dimensional approach using waveguide arrays (original) (raw)
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Transition dynamics for multi-pulsing in mode-locked lasers
Optics Express, 2009
We consider experimentally and theoretically a refined parameter space in a laser system near the transition to multi-pulse modelocking. Near the transition, the onset of instability is initiated by a Hopf (periodic) bifurcation. As the cavity energy is increased, the band of unstable, oscillatory modes generates a chaotic behavior between single-and multi-pulse operation. Both theory and experiment are in good qualitative agreement and they suggest that the phenomenon is of a universal nature in mode-locked lasers at the onset of multi-pulsing from N to N + 1 pulses per round trip. This is the first theoretical and experimental characterization of the transition behavior, made possible by a highly refined tuning of the gain pump level.
Characterizing and suppressing multi-pulsing instabilities in mode-locked lasers
Physics and Simulation of Optoelectronic Devices XIX, 2011
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.
Continuation of periodic solutions in the waveguide array mode-locked laser
Physica D: Nonlinear Phenomena, 2011
We apply the adjoint continuation method to construct highly-accurate, periodic solutions that are observed to play a critical role in the multi-pulsing transition of mode-locked laser cavities. The method allows for the construction of solution branches and the identification of their bifurcation structure. Supplementing the adjoint continuation method with a computation of the Floquet multipliers allows for explicit determination of the stability of each branch. This method reveals that, when gain is increased, the multi-pulsing transition starts with a Hopf bifurcation, followed by a period-doubling bifurcation, and a saddle-node bifurcation for limit cycles. Finally, the system exhibits chaotic dynamics and transitions to the double-pulse solutions. Although this method is applied specifically to the waveguide array mode-locking model, the multi-pulsing transition is conjectured to be ubiquitous and these results agree with experimental and computational results from other models.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2001
The complex Ginzburg-Landau equation (CGLE) is a standard model for pulse generation in mode-locked lasers with fast saturable absorbers. We have found complicated pulsating behavior of solitons of the CGLE and regions of their existence in the five-dimensional parameter space. We have found zero-velocity, moving and exploding pulsating localized structures, period doubling (PD) of pulsations and the sequence of PD bifurcations. We have also found chaotic pulsating solitons. We have plotted regions of parameters of the CGLE where pulsating solutions exist. We also demonstrate the coexistence (bi- and multistability) of different types of pulsating solutions in certain regions of the parameter space of the CGLE.
Principal Component Analysis for Low-dimensional Modeling of Mode-locked Lasers
The onset of multipulsing, 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 multipulsing instability. A proper orthogonal decomposition (POD) allows for the reduction of governing equations of a modelocked 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 sequence of bifurcations that are responsible for the multipulsing instability in the master mode-locking and the waveguide array mode-locking models. As a result, the POD reduction allows for a simple and efficient way to characterize and optimize the cavity parameters for achieving maximal energy output.
Pulse Dynamics in an Actively Mode-Locked Laser
Siam Journal on Applied Dynamical Systems, 2003
We consider pulse formation dynamics in an actively mode-locked laser. We show that an amplitudemodulated laser is subject to large transient growth and we demonstrate that at threshold the transient growth is precisely the Petermann excess noise factor for a laser governed by a nonnormal operator. We also demonstrate an exact reduction from the governing PDEs to a low-dimensional system of ODEs for the parameters of an evolving pulse. A linearized version of these equations allows us to find analytical expressions for the transient growth below threshold. We also show that the nonlinear system collapses onto an appropriate fixed point, and thus in the absence of noise the ground-mode laser pulse is stable. We demonstrate numerically that, in the presence of a continuous noise source, however, the laser destabilizes and pulses are repeatedly created and annihilated.
Effects of cavity topology on the nonlinear dynamics of additive-pulse mode-locked lasers
Journal of the Optical Society of America B, 1998
We study the effect of cavity topology on the nonlinear dynamics of additive-pulse mode-locked (APM) lasers configured in the Fabry-Perot and Michelson geometries. In experiments the Fabry-Perot laser often exhibits such behaviors as period doubling and quasiperiodicity as the nonlinearity is increased, whereas the Michelson APM (M-APM) exhibits none of these effects. Numerical studies confirm that the M-APM appears to be more resistant to such behavior and thus is more tolerant to excessive nonlinearity in the control cavity. Using the concepts of intensity-and phase-dependent two-beam and multiple-beam interference, we obtain a general empirical rule connecting cavity topology to pulse train instabilities for fast saturable absorber modelocked lasers employing coupled cavities.
Optics Communications, 1996
We present a method for simulating a passively mode locked laser. By selecting the simulation time step as the cavity round trip ti.me, we achieved a proper tracking of the temporal evolution of the individual cavity modes of the laser. Employing the split step Fourier algorithm using this natural modes base, an efficient simulation method was obtained, while retaining at each propagation step the direct physical relations between the calculated phase terms in the time and frequency domains to the actual optical field and individual cavity modes, respectively. Using this method, we tracked the formation of multiple pulses in a passively mode locked fiber laser cavity, and explored the effect of delayed optical feedback as a means for pulse ordering in fiber lasers.
Interaction of dual-frequency pulses in passively mode-locked lasers
We have found, numerically, that three stable pulses of diferent shapes can exist in systems described by the complex Ginzburg±Landau equation, such as passively mode-locked lasers with a fast saturable absorber. At the same cavity parameter values, however, only two of them can coexist, which two depending on the particular values of the parameters. The region of existence for each pulse is investigated numerically. The interaction between each pair of pulses is studied numerically. Using the interaction plane technique, we have found stable bound states of composite pulses.
Spectral sidebands and multipulse formation in passively mode-locked lasers
Physical Review A, 2011
Pulse formation in passively mode locked lasers is often accompanied with dispersive waves that form of spectral sidebands due to spatial inhomogoneities in the laser cavity. Here we present an explicit calculation of the amplitude, frequency, and precise shape of the sidebands accompanying a soliton-like pulse. We then extend the study to the global steady state of mode locked laser with a variable number of pulses, and present experimental results in a mode locked fiber laser that confirm the theory. The strong correlation between the temporal width of the sidebands and the measured spacing between the pulses in multipulse operation suggests that the sidebands have an important role in the inter-pulse interaction.