Mode-locked oscillators in the positive and negative dispersion regimes: scenarios of destabilization

arXiv:0807.1029v1 [physics.optics] 7 Jul 2008 Mode-locked oscillators in the positive and negative dispersion regimes: scenarios of destabilization Vladimir L. Kalashnikov and Evgeni Sorokin Institut f¨ur Photonik, TU Wien, Gusshausstr. 27/387, A-1040 Vienna, Austria ABSTRACT We analyze the influence of spectrally modulated dispersion and loss on the stability of mode-locked oscillators. In the negative dispersion regime, a soliton oscillator can be stabilized in a close proximity to zero-dispersion wavelength, when spectral modulation of dispersion and loss are strong and weak, respectively. If the dispersion is close to zero but positive, we observe chaotic mode-locking or a stable coexistence of the pulse with the CW signal. The results are confirmed by experiments with a Cr:YAG oscillator. Keywords: Femtosecond laser pulses, Mode-locked oscillator, Solid-state laser 1. INTRODUCTION Oscillators providing stable sub-100 fs pulses in the near-infrared region around 1.5 µm are of interest for a number of applications including infrared continuum generation1, 2 and high-sensitivity gas spectroscopy.3 To date, the typical realization of such sources is based on a femtosecond Er:fiber oscillator with an external pulse amplification. A promising alternative to such combination is a solid-state Cr4+:YAG mode-locked oscillator.4, 5 Such an oscillator allows a direct diode pumping and possesses the gain band providing the few-optical cycle pulses. However, attempts to increase the pulse energy in a Cr:YAG oscillator is limited by its relatively small gain coefficient. Because of the low gain, the oscillator has to operate with low output couplers and, thereby, the intra-resonator pulse energy has to be high. As a result, the instabilities appear.4, 6 To suppress the instabilities in the negative dispersion regime (NDR) a fair amount of the group-delay-dispersion (GDD) is required. The resulting pulse is a relatively long soliton with reduced peak power. Such a pulse is nearly transform-limited and is not compressible. A remedy is to use the positive dispersion regime (PDR), when the pulse is stabilized due to substantial stretching (up to few picoseconds) caused by a large chirp.7 Such a pulse is dispersion-compressible down to few tens of femtoseconds. For both NDR and PDR, the oscillator will eventually become unstable at high power. The main scenarios of the pulse destabilization have been identified with the multipulsing in the NDR6 and the CW-amplification in the PDR.8 It has been found, that the higher-order dispersions (i.e., the frequency dependent GDD) and losses significantly modify the stability conditions.9, 10 Hence, the study of the stability conditions affected by both linear and nonlinear processes inherent in a mode-locked oscillator remains an important task. Here, we present a study of the destabilization mechanisms of a Cr:YAG mode-locked oscillator, operating in both NDR and PDR. We put a special emphasis on the influence of the spectral dependence of GDD and losses on the oscillator stability. 2. DESTABILIZATION OF A MODE-LOCKED OSCILLATOR IN THE PDR The Cr:YAG oscillator has been built on the basis of the scheme published in Refs.2, 11 The mode-locking and the dispersion control were provided by SESAM and chirped-mirrors (CMs), respectively. The GDD of intra- resonator elements as well as the net-GDD are shown in Fig. 1. As a result of the GDD variation of the 51-layer CMs and the uncertainty of the SESAM dispersion, the real net-GDD has some uncertainty, too (gray region in Fig. 1, a). Further author information: (Send correspondence to V.L.Kalashnikov) V.L.Kalashnikov: E-mail: kalashnikov@tuwien.ac.at, Telephone: +43 1 588 01 387 43 b) 1500 1550 1600 -400 -200 0 200 400 W avelength (nm)

GDD (fs 2 ) 1300 1400 1500 1600 1700 -200 -100 0 100 200 SESAM CM 1 CM 2

GDD (fs 2 ) W avelength (nm) CM 3 YAG 5 mm a) Figure 1. a) GDD of three sets of chirped mirrors CM (as designed), the YAG crystal, and the SESAM. b) The net dispersion of the resonator of Cr4+:YAG oscillator. Black line: as designed, grey area - uncertainty region due to the chirped mirrors. 1450 1500 1550 1E-3 0,01 0,1 1 OC 0.5% OC 0.2% Spectral intensity (rel. u.) W avelength (nm) 1450 1500 1550 120 mW = 830 pJ (130 nJ intracavity) 95 mW = 660 pJ (100 nJ intracavity) 75 mW = 520 pJ (80 nJ intracavity) Spectral intensity (rel. u.) W avelength (nm) b) a) Figure 2. a) Spectra of the Cr:YAG oscillator operating in the PDR at different values of intracavity pulse energy. b) Spectra of the Cr:YAG oscillator with different output couplers. Selection of the different CM combinations allows over- and under-compensation of the dispersion. Selecting a 2CM1+2CM1 allows stabilizing the oscillator at the 144.5 MHz pulse repetition rate and 150 mW average output power. The corresponding spectra shown in Fig. 2 have truncated profiles, that is typical for an oscillator operating in the PDR.8 To study the stability limits of

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