Dark solitons in mode-locked lasers

Dark soliton formation in mode-locked lasers is investigated by means of a power-energy saturation model that incorporates gain and filtering saturated with energy, and loss saturated with power. It is found that general initial conditions evolve (mode-lock) into dark solitons under appropriate requirements also met in experimental observations. The resulting pulses are essentially dark solitons of the unperturbed nonlinear Schr?dinger equation. Notably, the same framework also describes bright pulses in anomalous and normally dispersive lasers.     

Dipole traps with mode-locked lasers

We investigate the properties of two separate dipole traps, realised using a cw mode-locked Ti:sapphire laser and a cw mode-locked Nd:YVO₄ laser, red-detuned by 25 nm and 284 nm, respectively. Approximately 10³ laser-cooled ⁸⁵Rb atoms were confined in the traps at ≈50 μK, with no observable heating after initial loading. The lifetimes of the traps were consistent with limitations imposed by wavelength-dependent photoassociation losses and collisions with background vapour. Determination of the ac Stark shift of the 780 nm cooling transition using a weak probe beam showed no observable difference between using narrow-bandwidth or mode-locked trapping light. Techniques for trapping and focusing of atoms based on the dipole force of blue and uv light become much more accessible through efficient doubling, tripling and quadrupling of mode-locked sources. This opens up the possibility of manipulating more technologically interesting species. Received: 30 September 1999 / Revised version: 21 December 1999 / Published online: 24 March 2000     

Carrier-envelope offset dynamics of mode-locked lasers

We investigate coupling mechanisms between the amplitude and the carrier-envelope offset phase in mode-locked lasers. We find that nonlinear beam steering in combination with the intracavity prism compressor is the predominant mechanism that causes amplitude-to-phase conversion in our laser. A second mechanism, induced by self-steepening, is also identified. These mechanisms are important for stabilizing the carrier-envelope offset phase and also explain the extremely low pulse-to-pulse energy fluctuations observed in some lasers with carrier-envelope lock. The coupling mechanisms described have important implications for applications of few-cycle optical pulses.     

Simulation of turbulence in mode-locked lasers

We establish the connection between a paper by Kartner et al. [F.X. Kartner, D.M. Zumbuhl, N. Matuschek, Phys. Rev. Lett. 82 (1999) 4428] entitled “Turbulence in mode-locked lasers”, and earlier work on the role of noise in mode-locked laser systems. We present numerical results that broadly support the analytical results of Kartner et al.     

Picosecond pulses from mode-locked dye lasers

Picosecond pulses have been generated in laser pumped (15 psec) and flashlamp pumped (6 psec) mode-locked dye lasers. Two-photon fluorescence and streak camera measurements are described.     

Multi-soliton complexes in mode-locked fiber lasers

We numerically investigate the formation of soliton pairs (bound states) in mode-locked fiber ring lasers in the normal dispersion domain. In the distributed mathematical model (complex cubic-quintic Ginzburg–Landau equation), we observe a discrete family of soliton pairs with equidistantly increasing peak separation. We show that stabilization of previously unstable bound states can be achieved when the finite relaxation time of the saturable absorber is taken into account. The domain of stability can be controlled by varying this relaxation time. Furthermore, we investigate the parameter domain where the region of stable bound states does not shrink to zero for vanishing absorber recovery time corresponding to a laser with an instantaneous saturable absorber. For a certain domain of the small-signal gain, we obtain a robust first level bound state with almost constant separation where the phase of the two pulses evolves independently. Moreover, their phase difference can evolve either periodically or chaotically depending on the small signal gain. Interestingly, higher level bound states exhibit a fundamentally different dynamics. They represent oscillating solutions with a phase difference alternating between zero and π.     

Femtosecond transform-limited Kerr-lens mode-locked dye lasers

Using SF6 glass plates as intracavity Kerr lenses and double-prism pairs for dispersion compensation, we achieve tunable femtosecond passive mode locking in rhodamine 590 (R6G) and 4-dicyanomethylene-2-methyl-16-p-dimethylaminostyryl-4H-pyran (DCM) dye lasers. The R6G laser produces transform limited 240–500 fs pulses between 577 and 606 nm, and the DCM laser produces 150 fs transform-limited pulses between 650 and 671 nm. We use dilute intracavity saturable-absorber jets to make the mode locking self-starting. Characteristics of the pulses and the stability regions of the lasers agree with general theories of passive mode locking.     

Fluctuations in synchronously mode-locked dye lasers

We present detailed experimental data on random fluctuations of the pulse properties of a cw rhodamine 6G dye laser synchronously pumped by an acousto-optically mode-locked argon ion laser. It is shown that quantitative information about the fluctuations of the energy, the pulse repetition time and the duration of the pulses can be obtained from the power spectrum of the laser intensity which is measured with the use of an electronic spectrum analyser. This method is capable of revealing small, subpicosecond temporal pulse jitter. We show that the dye laser pulses exhibit an absolute r.m.s. jitter of 20 ps which is induced by the pump laser. The relative jitter in a dual system can be less than 1 ps because well defined correlations of the output fluctuations exist when two lasers are pumped by a common source.     

Tunable all-normal-dispersion Yb-doped mode-locked fiber lasers

We experimentally investigate continuous wavelength tunability in an all-normal-dispersion Yb-doped mode-locked fiber laser with an Yb-doped fiber of a fixed length. The spectral tuning over 46.3 nm, from 1024.5 to 1070.8 nm, is achieved. Spectral dynamics with different pumping levels are demonstrated. The central wavelength of the dissipative solitons shifts 8 nm towards short wavelength with pump power increasing from 168 to 456 mW.     

Critical behavior of light in mode-locked lasers

Light is shown to exhibit critical and tricritical behavior in passively mode-locked lasers with externally injected pulses. It is a first and unique example of critical phenomena in a one-dimensional many-body light-mode system. The phase diagrams consist of regimes with continuous wave, driven parapulses, spontaneous pulses via mode condensation, and heterogeneous pulses, separated by phase transition lines that terminate with critical or tricritical points. Enhanced non-Gaussian fluctuations and collective dynamics are present at the critical and tricritical points, showing a mode system analog of the critical opalescence phenomenon. The critical exponents are calculated and shown to comply with the mean field theory, which is rigorous in the light system.     

Theory of passively mode-locked cw dye lasers

The circulation of an ultrashort light pulse in a continuously pumped modelocked dye laser with a linear cavity configuration containing the active dye, the saturable absorber and a bandwidth-limiting elements is treated. The steady-state condition that the pulse shape reproduces after each cavity round-trip leads to a nonlinear integro-differential equation for this pulse shape. An approximate method for the solution of this equation not limited to the case of low laser gain and small pulse energies is given. The stable single pulse region and characteristic pulse parameters, as energy, duration, intensity and asymmetry, are considered in dependence on the laser parameters.     

Ultrahigh-repetition-rate bound-soliton harmonic passive mode-locked fiber lasers

On the basis of numerical simulation results, we put forward a way to realize harmonic passive mode locking of fiber lasers with an ultrahigh-repetition-rate pulse train. The equidistant distribution of ultrashort pulses filling the total laser cavity is due to bound-soliton mechanisms. In the case of large bound energy, such long soliton trains are very stable and have the ideal periodic structure as a soliton crystal.     

Compact resonator designs for mode-locked solid-state lasers

Received: 16 February 1997/Revised version: 24 April 1997     

Delay differential equations for mode-locked semiconductor lasers

We propose a new model for passive mode locking that is a set of ordinary delay differential equations. We assume a ring-cavity geometry and Lorentzian spectral filtering of the pulses but do not use small gain and loss and weak saturation approximations. By means of a continuation method, we study mode-locking solutions and their stability. We find that stable mode locking can exist even when the nonlasing state between pulses becomes unstable.     

Picosecond pulses from passively mode-locked dye lasers

Successive stages of the development of ultrashort pulses in passively mode-locked dye lasers are studied. It is numerically shown that the initial fluctuations evolve into a picosecond pulse which retains its magnitude and particular shape and moves slower than the speed of light.     

Soliton strings and interactions in mode-locked lasers

Soliton strings in mode-locked lasers are obtained using a variant of the nonlinear Schrödinger equation, appropriately modified to model power (intensity) and energy saturation. This equation goes beyond the well-known master equation often used to model these systems. It admits mode-locking and soliton strings in both the constant dispersion and dispersion-managed systems in the (net) anomalous and normal regimes; the master equation is contained as a limiting case. Analysis of soliton interactions show that soliton strings can form when pulses are a certain distance apart relative to their width. Anti-symmetric bi-soliton states are also obtained. Initial states mode-lock to these states under evolution. In the anomalous regime individual soliton pulses are well approximated by the solutions of the unperturbed nonlinear Schrödinger equation, while in the normal regime the pulses are much wider and strongly chirped.     

Attosecond-resolution timing jitter characterization of free-running mode-locked lasers

Timing jitter characterization of optical pulse trains from free-running mode-locked lasers with attosecond resolution is demonstrated using balanced optical cross correlation in the timing detector and the timing delay configurations. In the timing detector configuration, the balanced cross correlation between two mode-locked lasers synchronized by a low-bandwidth phase-locked loop is used to measure the timing jitter spectral density outside the locking bandwidth. In addition, the timing delay configuration using a 325 m long timing-stabilized fiber link enables the characterization of timing jitter faster than the delay time. The limitation set by shot noise in this configuration is 2.2 x 10(-8) fs(2)/Hz corresponding to 470 as in 10 MHz bandwidth.     

Anticolliding design for monolithic passively mode-locked semiconductor lasers

The performance of two-section, passively mode-locked semiconductor lasers is theoretically analyzed for different cavity designs. Placing the saturable absorber section close to an antireflection-coated facet leads to a substantial increase in output power and a reduction in amplitude and timing jitter. Moreover, it broadens the bias current region of stable passive mode-locking operation.     

High-power diode-pumped passively mode-locked Yb:YAG lasers

We obtained 74-kW peak power and 3.5-W average output power in 1-ps pulses from a diode-pumped Yb:YAG laser at 1030 nm that was passively mode locked with a semiconductor saturable-absorber mirror. Another laser produced 57-kW peak power and as much as 8.1-W average output power in 2.2-ps pulses, split into two nearly diffraction-limited beams (M(2)<1.2) . To our knowledge, these are by far the highest reported peak and average output powers from a diode-pumped mode-locked laser in this pulse-duration regime.     

Diode-pumped passively mode-locked lasers with high average power

We discuss challenges arising from the quest for high average powers from passively mode-locked diode-pumped lasers. The recently obtained detailed understanding of Q-switching instabilities in passively mode-locked lasers turns out to be a crucial element on the way towards higher powers. We give an overview on results achieved with Nd:YAG (10.7 W, 16 ps and 27 W, 19 ps), Yb:YAG (8.1 W, 2.2 ps and 16 W, 0.7 ps) and Nd:glass (1.4 W, 275 fs).