Spectral sidebands and multipulse formation in passively mode-locked lasers

Abstract

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. [1][2][3][4] studied the formation and of dispersive waves by solitons and their propagation in optical fibers with periodically spaced amplifiers. The same mechanism leads to the formation of sidebands in mode locked lasers, where inhomogeneities in the cavity act periodically on the pulse.When the power of a single pulse saturates the absorber, the steady state of a passively mode locked laser tends to bifurcate into configurations where two or more pulses run in the laser cavity simultaneously. Since the early experiments that demonstrated multipulse mode locking [5][6][7] it has been observed that the pulses display a very rich dynamics, often forming bunches, as a consequence of complex inter-pulse interactions. The interest in the dispersive waves in mode locked lasers, beyond their prominent effect on the pulse shape, arises because they have often been suggested as a means of inter-pulse interaction in multipulse mode locked lasers [8][9][10][11]. Here we focus on the role of the sidebands in multipulse mode locking.The absorber saturation leading to multipulse steady states is often modeled by adding a quintic term to the equations of motion. In former papers [12,13] we applied the statistical light-mode dynamics (SLD) theory to this system, and showed that multipulse mode locking is in effect a series of first order phase transitions. SLD uses the methods of statistical physics to analyze the dynamics of the interacting many body light mode system at an effective finite temperature generated by cavity noise [14][15][16]. Here we apply the SLD gain balance method [17] to derive the multipulse steady states with dispersive waves of mode locked lasers with cavity inhomogeneities.Our theoretical analysis is based on the master equation of mode-locked soliton lasers [18,19], with an additive noise term [20], where the inhomogeneities in the cyclic light propagation in the cavity are modeled by a periodic modulation of the gain and the saturable absorption. We first study the sidebands in a single-pulse steady state and show that, unlike free fiber sidebands, the mode locked laser sidebands reach a steady state with a well-defined bandwidth and a Lorentzian shape; in real time the dispersive waves form a wide pedestal with exponentially decaying tails. In particular we demonstrate how the overal...

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