A mechanism of QML lasing in solid-state laser with an acousto-optic travelling wave modulator

Abstract

Lasing which simultaneously combines Q-switch and mode locking (QML lasing) is of interest as it demonstrated high peak intensity of the pulse sequence. Recently a new method was offered and demonstrated experimentally for achieving QML lasing using only a single acousto-optic modulator (AOM) with travelling wave in combination with a spherical mirror of a cavity [1,2]. In this report we present for the first time theoretical description of QML lasing in solid-state lasers with travelling wave AOM. Traditionally travelling wave AOM is used to modulate the Q-factor and forced the laser to operate in Q-switch regime. The same AOM can be used for simultaneous mode-locking by returning twice diffracted beam into the cavity. In this case the frequency of the light beam, injected into the cavity is shifted in a frequency by a value equal to double frequency of the acoustic wave. If an intermode interval δvc = vj+1 — vj is equal to double frequency of the acoustic wave a part of the field of j mode will be injected into following (j + 1) mode. In our model the dynamics of lasing is described by a set of balance equations for complex amplitudes Ej and phases φj. The simulations were performed for a set of numerical parameters, which specifies Nd:YAG lasing at the significant excess of the gain over the threshold. The value of Id were varied in the range from 10^∼2 to 10^∼3. We assumes that the gain line is broadened uniformly in frequency and in a space. Field damping increment is consisted of two parts: γ = γph + γd. First one γph is associated with permanent losses of resonator and the second Yd varies with the AOM characteristics variations: γd = −2 ln(1 − κd)δvC. Here κd is diffractive coupling coefficient, which shows the rate of the injection defined as £ = Id δ5vc. The injection of the field into the following mode predetermines the regime of each mode. Only fundamental mode (j = 0) operates at saturated inversion, the rest operate in the regenerative amplification regime. The injection process forms the distribution of Ej in frequency. The distribution has a characteristic maximum. The position of the maximum is determined by Id value and does not depend on time. The main contribution into the average intensity Ī = Σj E²j gives a relatively small number of modes, located near the maximum of E²j(j) distribution. Under these conditions, the interference of coherent optical fields results in a complex structure of each pulse of mode locking. Changing γd leads to noticeable changes in Ī and the inversion. In this way a variation of the κd value forms the mechanism of Q factor changing. Periodic alteration of the Kd value provides periodic Q-switch regime of the laser.