Fundamental limits of sub-ps pulse generation by active mode locking of semiconductor lasers: the spectral gain width and the facet reflectivities

Short pulse generation using multisegment mode-locked semiconductor lasers

“…Over many round-trips, the secondary pulses are amplified to energy values that are significant compared to the main pulse. Simulations have shown that power reflection coefficients as small as lop5 can cause multiple pulse formation [6]. In order to suppress the formation of secondary pulses, the net gain for the secondary pulse should be much less than unity so that there is no amplification of the secondary pulse.…”

“…The magnitude and phase response versus frequency of the semiconductor medium is described by the optical transfer function in (6). The magnitude and phase response of the amplifier are modeled with a Lorentzian line shape.…”

Dynamic modal analysis of monolithic mode-locked semiconductor lasers

“…In multigigahertz lasers, we may expect these quantities to be small (7) since the characteristic time of the relaxation of is much longer than . In the resonant polarization , we can then separate several terms of different physical nature, namely (8) The first term is associated with the slow component of the carrier density and may be written as (9) where is the interband component of the dielectric constant, which includes the gain and the density-dependent refractive index . The polarization does not depend on the light intensity directly, only parametrically through the dynamics of .…”

“…Such effects include spectral hole burning, dynamic carrier heating, well-barrier nonequilibrium, and, for the case of quantum well-saturable absorbers, kinetics of exciton ionization. The final term in (8) is due to external resonant modulation of the dielectric constant at or near the round-trip frequency and/or its harmonics and is only present in active, hybrid, or synchronous ML. To achieve sufficient analytical progress in the model, we need to treat all three nonlinear and modulation-induced polarization terms as small corrections to the quasi-linear term.…”

“…Now, we substitute (8) and (9) into (3) and rewrite (3) with the aid of (4) in terms of amplitude vectors (5). The result is conveniently expressed in a matrix operator notation as in [26] and [27] (11) with the matrix operator defined as (12) Here, defines the local complex wavevector.…”