For an erbium-doped fiber laser mode-locked by carbon nanotubes, we demonstrate experimentally and theoretically a new type of the vector rogue waves emerging as a result of the chaotic evolution of the trajectories between two orthogonal states of polarization on the Poincare sphere. In terms of fluctuation induced phenomena, by tuning polarization controller for the pump wave and in-cavity polarization controller, we are able to control the Kramers time, i.e. the residence time of the trajectory in vicinity of each orthogonal state of polarization, and so can cause the rare events satisfying rogue wave criteria and having the form of transitions from the state with the long residence time to the state with a short residence time.
Oleg Pronin, Jonathan Brons, Marcus Seidel, Elena Fedulova, Alexander Apolonskiy, Dominik Bauer, Dirk Sutter, Vladimir Kalashnikov, Vladimir Pervak, Ferenc Krausz
The goal of this contribution is to provide a guideline for Kerr-lens mode-locking (KLM) of thin-disk oscillators. This
includes cavity design, hard and soft-aperture optimization, handling of thermal effects in intra-cavity optics as well as
methods of average power and energy scaling. The main differences and similarities between mode-locking of
Ti:sapphire bulk and Yb:YAG thin-disk oscillators are presented.
We demonstrate mid-infrared (mid-IR) supercontinuum generation with bandwidth from 2 to 2.8 μm at 20 dB below the peak in nonlinear step-index chalcogenide fiber using femtosecond mid-IR pulses directly from the oscillator. We compare the results with a supercontinuum generated in a silica-based high germanium content fiber. Supercontinuum generation occurs at 90 mW of launched average pump power that is equal to the 0.9 nJ pulse energy. The distinctive feature of the obtained supercontinuum is its stability and coherence due to the deterministic supercontinuum generation by the femtosecond pump pulses
Oleg Pronin, Jonathan Brons, Marcus Seidel, Fabian Lücking, Christian Grasse, Gerhard Boehm, Marcus Amann, Vladimir Pervak, Alexander Apolonski, Vladimir Kalashnikov, Ferenc Krausz
A femtosecond thin-disk Yb:YAG oscillator in both the anomalous and the normal dispersion regime is demonstrated. Both regimes are realized with practically the same resonator configuration. The power scaling potential of the anomalous and normal dispersion regimes is analyzed both theoretically and experimentally. The recipe to obtain Kerr-lens mode-locking (KLM) in the thin-disk configuration is presented here and oscillator characteristics as well as start-up difficulties are described. The oscillator stability in terms of output power, beam pointing and sensitivity to back reflections is measured and corresponds to the level of commercial systems.
In this work, for the first time to our knowledge, stability and noise of a thin-disk mode-locked Yb:YAG oscillator operating in both negative- (NDR) and positive-dispersion (PDR) regimes have been analyzed systematically within a broad range of oscillator parameters. It is found, that the scaling of output pulse energy from 7 μJ up to 55 μJ in the NDR requires a dispersion scaling from -0.013 ps2 up to -0.31 ps2 to provide the pulse stability.
Simultaneously, the energy scaling from 6 μJ up to 90 μJ in the PDR requires a moderate dispersion scaling from 0.0023 ps2 up to 0.011 ps2. A chirped picosecond pulse in the PDR has a broader spectrum than that of a chirp-free soliton in the NDR. As a result, a chirped picosecond pulse can be compressed down to a few of hundreds of femtoseconds. A unique property of the PDR has been found to be an extremely reduced timing jitter. The numerical results agree with the analytical theory, when spectral properties of the PDR and the negative feedback induced by spectral filtering are taken into account.
A completely analytical theory of chirped-pulse oscillators is presented. The theory is based on an approximate integration of the generalized nonlinear complex Ginzburg-Landau equation. The obtained parametric space of a chirped-pulse oscillator allows easy tracing the characteristics of both solid-state and fiber oscillators operating in the positive dispersion regime.
A number of factors that influence spectral position of the femtosecond pulse in a Kerr-lens modelocked Cr:LiSGaF laser have been identified: high-order dispersion, gain saturation, reabsorption from the ground state, and stimulated Raman scattering. Using the one-dimensional numerical model for the simulation of the laser cavity, the relative contributions of different factors have been compared. The Raman effect provides the largest self- frequency shift from the gain peak (up to 60 nm), followed by the gain saturation (approximately 25 nm), while the high-order dispersion contribution is insignificant (approximately 5 nm). Comparison with the experimental data confirm that the stimulated Raman scattering is a main cause of the ultrashort pulse self-frequency shift observed in Cr:LiSGaF and Cr:LiSAF lasers.
The theoretical calculation for nonlinear refractive index n2 in Cr2+:ZnSe-active medium predicts the strong defocusing cascade second-order non-linearity within 2-3 micrometers spectral range. On the basis of this result the optimal cavity configuration for Kerr-lens mode locking is proposed that allows to achieve a sub-100 fs pulse duration. The numerical simulations testify about strong destabilizing processes in the laser resulting from a strong self-phase modulation. The stabilization of the ultra short pulse generation is possible due to spectral filtering that increases the pulse duration up to 300 fs.
The results of the study of ultra-short pulse generation in continuous-wave Kerr-lens mode-locked (KLM) solid-state lasers with semiconductor saturable absorbers are presented. The issues of extremely short pulse generation are addressed in the frames of the theory that accounts for the coherent nature of the absorber-pulse interaction. We developed an analytical model that bases on the coupled generalized Landau-Ginzburg laser equation and Bloch equations for coherent absorber. We showed, that in the absence of KLM semiconductor absorber produces 2(pi) -non-soliton pulses of self-induced transparency, while the KLM provides an extremely short soliton generation, 2(pi) - and (pi) -sech- shaped soliton solutions and variable-squared chirped solutions have been found. It was shown, that the presence of KLM loosens the stability requirements for ultra-short pulse generation removing the limitation on the minimum modulation depth in absorber necessary for the pulse stabilization. An automodulation stability and self-starting ability analysis is presented.
Using a modified ABCD-matrix approach accounting for nonlinear refraction in active medium, we determined the ranges of cavity parameters that provide a mode-locking of Yb:KYW-laser in usual z-fold cavity configuration. Taking the cavity parameters that provide a most efficient mode locking and based on fluctuation model, we performed a numerical simulation of laser operation. We used for our calculations the side-band pump power of 6 W at 982 nm with 1 cm X 50 micrometers beam cross section in active medium and the length of 1 cm for KYW crystal. Calculations showed that self-starting operation is possible with these parameters and dispersion compensation allows for bandwidth-limited ultrashort pulse generation. The shortest pulse duration was determined to be approximately 200 fs with self-starting build-up time of 130 microsecond(s) . Such a built-up time is comparable and even shorter than that one for the lasers with semiconductor saturable absorbers. The region of negative dispersion provided by prism pair where a stable ultrashort pulse generation takes place was determined to be (-17000 - -42000) fs2.
It is shown, that the linewidth enhancement in the semiconductor transforms essentially the ultra-short pulse parameters in cw solid-state laser with semiconductor modulator and can stabilize ultra-short pulse in the wide region of the group velocity dispersion.
It is shown that the fast saturable absorber effect due to the Stark shift of the excitonic resonance in the quantum- confined semiconductor can contribute to ultra-short pulse formation and stabilize the pulses with extremely short duration at the below band-gap excitation, i.e. in the presence of the Stokes mismatch between gain band center and excitonic line. This mechanisms is strong enough to provide self-starting over the full region of the cavity stability.
Formation and propagation of a new type of quasi-soliton in laser system was investigated. It was shown that the interplay between linear phase shift from the center of the luminescence band and nonlinear effect of the self-phase modulation enables to create the conditions for the self-ordering of the laser field. This technique is capable to generate stable ultra-short pulse trains. Analysis of the quasi-soliton stability allows to describe the cascade of oscillation effects in laser system accompanying the increase of the pump energy.
Based on rather simple mathematical calculatioIIB we propose an eftective procedure for optimal cavity design for a 'rariety of laser geometries. Besides the '\lell-kncv.n from the literatlL.re guidelines v..re succeed to perform a forth.er optimization of four -mirror cavity. T:ne possibilities of three- and tvv·on: llrror resonators for building compact Kerr-lens lasers ai.-e considered. Ke)~ords: solid-state lasers, ultra-shOJ.-t pulses, Kerr lens mode-locking, cavity design.
With the help of the self-consistent ABCD matrix method the fundamental normal mode of a four-mirror cavity with active rod and hard aperture is analyzed. Cavity parameters ranges with the small diffraction losses at hard aperture and the decreased diffraction losses for the increased mode intensities due to self-focusing in active medium are shown immediately for practical Kerr-lens mode-locked Ti:sapphire lasers. The fluctuation model of self-mode-locked lasers is used to demonstrate the generation of a stable ultra-short pulse train by the system under constant pumping for the obtained cavity parameters.
Efficient modelocking of cw solid-state lasers by SHG-based modulators has been considered. A new type of modulator that utilizes an interferometrical subtraction from the generation field of its replica attenuated by second-harmonic generation (SHG) is proposed for the first time to our knowledge. Tuning parameters that control the mode-locking efficiency are the initial transmission of the modulator and transmission derivative on intensity. Self-consistent analytical solutions of an operator equation describing the laser system were obtained which satisfactorily agree with numerical simulation results based on fluctuation theory.
With the help of the self-consistent ABCD matrix method the fundamental TEM00 mode of a four-mirror cavity with active rod and hard aperture is analyzed. Cavity parameters range with the small diffraction losses at hard aperture and the decreased diffraction losses for the increased mode intensities due to self-focusing in active medium are shown immediately for practical Kerr-lens mode-locked (KLM) Ti:sapphire lasers. To do this we have obtained the generalized solution of the wave propagation equation in self-focusing medium for the arbitrary curvature radius of phase front of incident Gaussian beam. The fluctuation model of self-mode-locked lasers is used to demonstrate the generation of a stable ultra-short pulse train by the system under constant pumping for the obtained cavity parameters.
Numerical simulation of self-modelocking of cw solid-state lasers with Kerr polarization modulator is developed. The limited ranges of laser and modulator parameters within which the laser generates stable train of ultra-short pulses are given.
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