Mode-locked Regions Research Articles

Theoretical analysis of picosecond pulse development of passively mode-locked Nd-glass lasers

A realistic numerical theory of the temporal and spectral development of picosecond light pulses in a passively mode-locked Nd-glass laser is presented. The effects of the inhomogeneous gain profile of the active medium are considered. The calculations include the pulse development in the prelaser, the linear laser and the mode-locking region. In the mode-locking region twophoton absorption and self-phase modulation in the active medium as well as the bleaching dynamics of the mode-locking dye are included. The influence of self-phase modulation on the temporal pulse shape in active media of finite spectral gain width is analysed. The theoretical results are compared with the experimental findings.

Destruction of Invariant Tori as an Eigenvalue Problem

It is shown that the criterion for smoothness of invariant tori in certain dissipative dynamical systems approaching chaos can be formulated in terms of an eigenvalue problem---a discrete Schr\"odinger equation in a potential generated by the map. By this method it is shown that there exists a continuous line through parameter space---the "critical line"---on which the invariant circles lose smoothness. It is explained why this line should approach smoothness for the very-high-order mode-locking regions and this corroborates earlier numerical results relating global scaling properties of dynamical systems to those of circle maps. Further, this method yields effective approximation schemes for obtaining the critical line.

Route to mode locking in a three-mode He-Ne 3.39-μm laser including chaos in the secondary beat frequency

A helium-neon laser at 3.39 ..mu..m has been operated under cavity and discharge conditions permitting three modes to simultaneously oscillate for some regions of cavity tuning. Both mode-locked and -unlocked regions have been found. For unlocked three-mode operation, the laser output may include a secondary beat frequency. As the cavity length is tuned to the mode-locked region, this secondary beat frequency approaches zero and displays critical fluctuations at the transition to mode-locked operation. As the discharge current is increased, for fixed cavity length, the peaks in the power spectrum representing the secondary beat and its harmonics undergo a 100-fold broadening enroute to a broad chaotic spectrum before the laser reaches a mode-locked, low-noise configuration. This appears to be the onset of a deterministically chaotic behavior of the coupled modes that is distinct from the critical fluctuations. Details of cavity tuning and current variation on the laser output, including hysterisis effects, are reported here.

Influence of argon laser parameters on mode-locking conditions

An experimental study was made of active mode-locking in an argon laser and the mode-locking range was calculated. The time dependences and the spectral characteristics of the radiation emitted by a multimode laser were investigated as a function of the detuning of the modulation frequency from the intermode beat frequency and also as a function of the rate of pumping of the active medium. The influence of the active medium gain on the width of the mode-locking region and on the shift of the optimal mode-locking frequency was studied. Multipulse operation was investigated.

Investigation of the Red Laser Transition in Neon by Mode-Crossing and Zero-Field Level-Crossing

An intracavity neon absorber has been subjected to an axial magnetic field in order to achieve coupling between the laser modes and the absorber atoms. Mode-crossing and zero-field level-crossing methods were used to obtain the line width and the pressure broadening coefficient for the 2p4-3s2 transition, the result being 32 MHz + 0.048 MHz/Pa. Investigations of the amplitude-pressure dependence on the mode-crossing and zero-field level-crossing signals have been performed. Magnetic field induced mode-locking on every one, every second one and every third one of the longitudinal modes is presented. The widths of the mode-locking regions are determined and compared with the width of the crossing signals.

Laser mode locking by three-level resonances

Zeeman tuning of an intracavity Ne absorber has been used for studying three-level resonances and mode-locking behaviour in a He-Ne laser. Resonances of the (3s 2)→(2p 4) transition were measured both in free-running and mode-locked operation. For specific ranges of the magnetic field and absorber discharge current mode-locking occurred on every one, second one and every third one of the laser cavity modes. The mode-locking regions are presented and a brief discussion of the results is given.

Mode Locking of a Standing-Wave Laser with a Homogeneous Spectral Line

A theoretical investigation has been made in the time domain on the mode locking phenomena of a standing-wave laser with a homogeneous spectral line. 1) The dependence of the self-mode locked solutions is obtained by numerical calculation on the pumping parameter, the cavity-length, and the position of the laser medium in the cavity. 2) The fundamental mode locking by internal loss modulation is derived to exactly correspond to the mode-locked bidirectional oscillation of the corresponding ring laser. The standing-wave laser is unlocked with the modulation frequencies of the unidirectional mode-locked region of the ring laser. 3) The second harmonic mode locking by internal loss modulation is also investigated. Depending upon the modulation frequency and the position of the laser medium, “O-type”, “π-type”, “second O-type”, or “second π-type” locking occurs. Their peak power is comparable to that of the fundamental mode locking.

Laser mode locking using saturable absorbers

A theoretical model for mode locking induced by saturable absorbers is presented, employing an unidirectional ring laser cavity. Both the gain and loss media are assumed to be homogeneously broadened two-level systems, on-resonance with the radiation field. The loss of the cavity is treated as discrete and is supposed to occur at an equivalent mirror. Laser coupled equations are then derived, employing the density matrix formalism together with Maxwell's equations, using the rotating wave and slowly varying envelope approximations. Time-invariant solutions of the coupled equations are deduced exactly and mode-locking regions are predicted by a perturbation method. It is found that a suitable absorber can produce mode locking if the laser parameters are appropriately chosen. Generation of the steady-state pulses (SSP) by the finite-difference method shows that relatively short intense pulses can be obtained from a mode-locked laser. In addition, the theoretical model is extended to account for the possibility that the absorbing medium may be less easily saturated than the gain medium and/or the phase coherence times of the two media are very different. It is pointed out that our model can be a good approximation to a real laser system under certain circumstances. It can also be used as a guide in the search for a suitable absorber for particular laser systems.