1. Introduction

Femtosecond and picosecond laser systems are passing more and more from the research laboratories to an ever growing community of laser users in fields as diverse as material processing, photonic device production, nonlinear spectroscopy, microscopy and biomedicine. Therefore it is highly desired to have these systems as compact, cost efficient and user friendly as possible. Cavity dumping is an efficient method to generate high pulse energies, sufficient for many applications such as ultrafast spectroscopy, micromachining, and nonlinear frequency conversion [1, 2, 3, 4, 5] directly from a laser oscillator and thus avoiding complex amplifier schemes. In the past the main focus of research was on cavity-dumped TEM₀₀-pumped Ti:sapphire laser systems [6, 7, 8, 9, 10]. However, since these lasers are pumped in the green spectral region, where no laser diodes are available, their application is quite limited due to the high cost of the green pump lasers. One way to reduce the complexity is the usage of directly diode-pumped laser media such as ytterbium-and neodymium-doped materials in combination with highly reliable mode-locking techniques using semiconductor saturable absorber mirrors (SESAMs) [11, 12]. Recently we presented a diode-pumped femtosecond oscillator with cavity dumping and later discussed the soliton dynamics of the system in more detail [13, 14].

In this publication we show for the first time electro-optical cavity dumping with dumping frequencies exceeding 1 MHz. Operation at high dumping frequencies improves the efficiency of the system and furthermore leads to a more stable operation as compared to lower dumping frequencies used in [13]. Two different laser systems, namely an Yb:glass and a Nd:YVO₄ mode-locked oscillator, were investigated. Whereas the first is mode-locked in the solitary regime, the latter is mode-locked in the normal dispersion region, where no soliton effects take place. The impact of the solitary mode shaping will be contrasted by the comparison of both systems.

2. Yb:glass femtosecond laser

2.1. Setup

The laser used for the experiments is based on a setup very similar to the one reported earlier [13]. It is based on an end-pumped Ytterbium-doped glass rod with a length of 3.5 mm. A laser diode at 976 nm delivered a pump power of 3.7W to the input facet of the laser rod; 1.4W of the incident pump power were transmitted under non-lasing conditions. The modal size in the active medium was estimated to have a diameter of 120µm, achieved by a combination of two curved mirrors with radii of 150mm and 200 mm, respectively. A schematic setup is shown in Fig. 1. The cavity was stretched by a combination of telescopes using four curved mirrors with 1000mm radius and two with 500mm radius, resulting in a total cavity length of 7.2m and a repetition rate of f _rep=21MHz. Cavity dumping was achieved by a combination of a 36mm long beta barium borate (BBO) Pockels cell (PC) and a thin film polarizer (TFP). The high voltage switch of the PC provided up to 1.8 kV at 600 kHz and up to 1.2 kV at 1.1 MHz in a pulse short enough to suppress a post-pulse with an extinction ratio of better than 1/2000. The laser is mode-locked by a semiconductor saturable absorber mirror (SESAM) in combination with 17 dispersive mirrors, each having a negative dispersion of approximately 240fs². The net dispersion was sufficient to achieve solitary operation. Focusing on the SESAM was accomplished by a curved mirror with 300mm radius, resulting in an estimated spot size of 340µm.

 

Fig. 1. Schematic setup of the cavity-dumped femtosecond Yb:glass laser system.

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2.2. Results

All experiments were done at maximum available pump power. In Fig. 2 the power spectra for increasing dumping frequencies f _dump from 475 kHz up to 1.1MHz are shown. The spectral side peaks result from the interference between the pulse and the phase matched continuum radiation, generated by the periodic perturbance of the soliton-like pulse and are known as Kelly sidebands [15, 16, 17]. At dumping frequencies lower than 475 kHz we observed regimes of subharmonic behavior of both the pulse duration and the pulse energy. The reason for this is discussed below.

It was experimentally observed that increasing the dumping frequency shifted the pulse towards shorter wavelength. This effect is caused by the quasi three-level nature of the laser. Increasing the dumping frequency is equivalent to an increased cavity loss and consequently the laser shifts its center wavelength towards higher emission cross sections although the reab-sorption losses are higher, as well. In order to fix the center wavelength at 1040 nm the dumping ratio had to be decreased from 65% to 55% while increasing the dumping frequency, such that the net loss remained constant.

 

Fig. 2. Power spectra for increasing dumping frequencies from 475 kHz to 1.1 MHz. On the right the autocorrelation signal in blue is depicted at 1.1MHz with a width of τ=420fs resulting in a pulse width of 250 fs, assuming a sech²-shaped pulse. The fit to the autocorrelation of a sech² pulse is shown as the dashed red curve.

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Fig. 3. Left: power spectrum of the 750 nJ pulse with a spectral width of 2.9 nm. The inset shows the autocorrelation signal (ACS) with a width of τ=780fs resulting in a pulse width of 470 fs, assuming a sech²-shaped pulse. The fit to the autocorrelation of a sech2 pulse is shown as the dashed red curve. Right: Intra-cavity energy transient.

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The pulse energy dropped from 550 nJ down to 300 nJ within the mentioned frequency interval, while the average power changed from 260mW to 330mW. As predicted in an earlier publication an increase of the dumping frequency leads to a shift of the Kelly sidebands off center because of the decrease of the accrued cavity phase [14]. The autocorrelation at 1.1MHz dumping frequency revealed a pulse width of 250 fs resulting in a time bandwidth product of 0.3 and transform limited pulses.

In Fig. 3 the power spectrum, the autocorrelation and the intra-cavity pulse energy transient are shown at a dumping frequency of f _dump=500 kHz. At this repetition frequency the Pockels cell could be operated with a higher voltage, resulting in an improved dumping ratio, a higher average output power of 375mW, and a pulse energy of 750 nJ. The RMS noise of the pulse energy was determined to be 0.3 %. With a pulse width of 470 fs the resulting peak power exceeded 1.5MW, whereas the measured spectral width is significantly smaller compared to the 1 MHz case from Fig. 2. The reason for that is the higher dumping ratio resulting in a lower average pulse energy in the cavity. Note, that the pulse became shifted to shorter wavelength, which is due to increased losses, since the dumping ratio was now more than 80%. Therefore the laser runs preferentially at a wavelength, where the emission cross section is larger, even though the reabsorption is higher.

2.2.1. Intracavity dispersion

Interestingly enough, our cavity-dumped system allows a simple method of measuring the net dispersion of the cavity. For this purpose the spectral positions Ω_±n of the Kelly sidebands need to be related to the oscillator’s phase. This relation is given by the well-known formula,

where N_R=f _rep/f _dump is the number of round-trips, and ϕ _cav(Ω) the acquired cavity phase per round-trip. ϕ _pulse is the phase shift of the pulse per dumping cycle and n is an integer number [17]. The data taken from the measured spectrum in Fig. 3 were fitted assuming a cubic phase dependence,

this led directly to the intracavity second order round-trip dispersion (GDD) of β ₂=-3100fs² and third order dispersion (TOD) of β ₃=-90000fs³ at a center wavelength of 1040 nm. The huge amount of TOD hereby limits the accessible spectral width. This method might be a useful tool for optimizing the pulse length in future setups.

2.3. Discussion

Two characteristic frequencies play a major role for the stability of the system, namely the relaxation oscillation frequency f _relax (here: ≈40 kHz) and the dumping frequency f _dump. According to these characteristic frequencies the operation of cavity-dumped lasers can be classified by three regimes [14]. In the “relaxed regime”, where f _dump ≪ f _relax, the pulse to pulse stability is very high. The “intermediate regime”, when f _dump and f _relax are of the same magnitude, period doubling instabilities of the pulse energy occur. Lastly the “transient regime” is established, when f _dump ≫ f _relax. With the cavity-dumped laser operated at frequencies in the MHz range we are clearly in the “transient regime”, as f _relax ≪ f _dump. Disregarding soliton effects the laser would be stable in this regime, but including the phase evolution of the solitary pulse the pulsing dynamics becomes rather complex. We define a third frequency f _phase=f _rep/n _phase with the number of cavity round-trips during one phase period of the fundamental soliton

Here, the full width at half maximum pulse duration is τ_FWHM and the GDD of one laser roundtrip is β ₂. In our case we estimate n _phase≈41 with τ_FWHM=250fs² and β ₂=-3100fs², leading to f _phase≈500kHz. With f _dump >f _phase the system is stable, and the experimentally observed destabilization for fdump <475kHz is in very good agreement with this simple estimate. Hence, in terms of pulsing stability the operation with dumping rates higher than both f _relax and f _phase is favorable. In this regime dumping ratios of more than 80% have been applied without destabilzation, which is much more than for lower dumping frequencies [13].

As for the femtosecond system, we have demonstrated the generation of femtosecond pulses with 550 nJ pulse energy at 475 kHz and 300 nJ at 1.1 MHz. The condition to keep the pulses phase shift per dumping cycle much smaller than 2π limits the scalability in terms of peak power. There are two possibilities to meet this criterion while keeping the pulse length fixed. First, lowering the self-phase modulation of the system and second, increasing the dumping frequency. Both solutions have their limitations; as for the first a less tight focusing in the laser glass, currently playing the main role in generating SPM, leads to a less efficient lasing action. The second solution is also questionable since dumping frequencies are currently limited by the available high voltage switches.

Consequently, higher pulse energies are anticipated with picosecond lasers [18].

3. Nd:YVO₄ picosecond laser

The second cavity-dumped laser system of interest is the diode-pumped cavity-dumped picosecond Nd:YVO₄ laser. The general goal of this system is to produce high pulse energies in the picosecond pulse regime at repetition rates above 1 MHz. In the picosecond pulse regime the laser design is much simpler in comparison to the previously discussed system since no solitary pulse shaping and hence no dispersion management is required. Another advantage is the power scalability of the picosecond system. The actual power scaling limitation of both cavity-dumped systems is the self-phase modulation, because it takes more effect as the peak power increases. Consequently, the picosecond laser system is capable of achieving higher pulse energies.

 

Fig. 4. Schematic setup of the cavity-dumped picosecond Nd:YVO4 laser system

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3.1. Setup

The picosecond Nd:YVO₄ laser with cavity dumping was an end-pumped system, which was passively mode-locked with a SESAM. It did not contain any components for dispersion control. The schematic setup of the device is outlined in Fig. 4. The pump light was focused into the Nd:YVO₄ gain medium, which had a high reflection coating for the laser wavelength at 1064 nm on one side. Typically 14W of the pump power were absorbed inside the crystal. The other end of the 3.2mm long crystal was cut at Brewsters angle. The actual laser cavity of 27MHz repetition rate had to be folded multiple times to allow for a compact setup. The same dumping technique as for the solitary mode-locked femtosecond Yb:glass laser was employed using the combination of a PC and a TFP. The PC also had a double-BBO-crystal configuration, but for technical reasons the high voltage switches could only be driven up to 1.1 kV at dumping rates above 500 kHz. Due to a λ/4-voltage of 2.5 kV the dumping ratio was limited.

3.2. Results

The system was analyzed at dumping frequencies of 0.71, 0.83 and 1.02 MHz, and the pulse energy remained constant at 1.8µJ. The relaxation oscillation as the characteristic intrinsic frequency was measured to be 180 kHz and is far away from the targeted frequency range. Clearly, we are in the “transient regime” and it is no surprise that the system was stable in this frequency range. At the repetition rate of 1.02MHz the dumping efficiency was as high as 48 %, limited by the electronics as mentioned before. As for the laser system there is no physical reason why the dumping efficiency could not be increased further. The intracavity pulse energy was determined to be 3.8µJ corresponding to 102W of average power. This suggests potentially higher output pulses if voltages closer to the λ/4-voltage of the PC could have been applied.

 

Fig. 5. Left: Typical autocorrelation of the output pulses at a dumping rate of 1.02 MHz. Right: Normalized intra-cavity pulse energy in dependence on the number of round-trips (the residual ripples in the curve are due to aliasing).

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In Fig. 5 some experimental data, which were taken at the repetition rate of 1.02MHz are shown. The autocorrelation trace of the dumped pulses on the left was fitted with the autocorrelation of a sech², giving a typical pulse with of 7.1 ps. On the right the measured intra-cavity pulse energy transient is displayed in dependence on the number of round-trips.

The cavity dumping of the Nd:YVO₄ picosecond laser is much easier due to the fact that only two characteristic frequencies, the relaxation rate and the dumping frequency, determine the laser dynamics. At frequencies higher than 500 kHz destabilization was not observed in the Nd:YVO4 laser system, since only the stable ‘transient’ regime was targeted.

4. Conclusion

We have investigated the performance of diode-pumped mode-locked laser systems, cavity-dumped at high repetition frequencies exceeding 1 MHz. Two systems were discussed, a solitary mode-locked femtosecond Yb:glass and a picosecond Nd:YVO₄ laser. As anticipated by theory [14], it became apparent that it is favorable to operate the system at dumping frequencies higher than the relaxation oscillation frequency and also higher than the pulse’s phase repetition frequency in case of the soliton laser. This configuration gives the best stability and efficiency and led to pulse energies exceeding half a µJ. With picosecond pulses energies of 1.8 µJ at MHz repetition rates could be demonstrated.

Due to the high and variable repetition rate, and because of their compactness and improved mechanical stability, cavity-dumped lasers are well suited to replace complex amplifier systems for many applications in physics, bioscience, and material processing.