Dynamics of a class- A nonlinear mirror mode-locked laser

Abstract

Using a delay differential equation model we study theoretically the dynamics of a unidirectional class-A ring laser with a nonlinear amplifying loop mirror. We perform linear stability analysis of the CW regimes in the large delay limit and demonstrate that these regimes can be destabilized via modulational and Turing-type instabilities, as well as by an instability leading to the appearance of square-waves. We investigate the formation of square-waves and mode-locked pulses in the system. We show that mode-locked pulses are asymmetric with exponential decay of the trailing edge in positive time and faster-than-exponential (super-exponential) decay of the leading edge in negative time. We discuss asymmetric interaction of these pulses leading to a formation of harmonic modelocked regimes.

Delay-differential-equation model for mode-locked lasers based on nonlinear optical and amplifying loop mirrors

“…It is seen from this expression that the threshold value of the pump parameter p = p 0 is minimal for K = 0 and K = 1, p 0 = − ln (κG), and tends to infinity for K → 0.5. This means that for symmetric beam splitter laser off solution is always stable [11]. Note that since linear gain in the nonlinear mirror loop cannot exceed the total losses in the cavity the product κG should be less than unity.…”

“…In this section we extend the NOLM-NALM modelocked laser model proposed by the last author of [11] to the case of finite carrier relaxation rate and arbitrary beam spliting ratio. A schematic presentation of the laser system under consideration is given in Fig.…”

“…[4][5][6][7][8][9][10] and references therein), where the dynamics of the gain is determined by the average intra-cavity laser power. An alternative approach to the modeling of NOLM-NALM lasers was proposed in [11] where a simple delay differential equation (DDE) model of a nonlinear mirror modelocked laser was developed using the approach of Refs. [12][13][14] and analyzed analytically and numerically.…”

“…However, since such important physical factor as spectral filtering of the laser radiation is missing in this model, similarly to the Poincare map model used in [21], it is hardly applicable to describe short pulse generation in mode-locking regimes. The aim of this paper is to generalize the model developed in [11] to the case of arbitrary population relaxation rates of the laser gain medium and beam splitting ratios. Note that similarly to the models discussed in [11,15] our model assumes that chromatic dispersion of the intracavity medium does not play an important role in the mechanism of the mode-locked pulse formation.…”

“…The aim of this paper is to generalize the model developed in [11] to the case of arbitrary population relaxation rates of the laser gain medium and beam splitting ratios. Note that similarly to the models discussed in [11,15] our model assumes that chromatic dispersion of the intracavity medium does not play an important role in the mechanism of the mode-locked pulse formation. Although the chromatic dispersion can be included into DDE models [22,23], this task is beyond the scope of the present work.…”