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Abstract
A theoretical method was proposed to compensate the burst envelope distortion in a solid-state master-oscillator power-amplifier (MOPA) system operating in burst mode at an intra-burst repetition rate of 40 MHz. Arbitrary envelope shapes were achieved at inter-burst repetition rate of 100 kHz with 40 pulses in the burst, showing excellent agreement with the calculated ones. This is the first demonstration of arbitrary burst envelope without an adaptive feedback loop in a solid-state laser system. The maximum pulse energy of 100 μJ was achieved at inter-burst repetition rate of 40 kHz, with 10 pulses in the burst.
© 2017 Optical Society of America
1. Introduction
Burst-mode lasers achieve high pulse energy in combination with high repetition rate operation by grouping a series of closely spaced pulses into short bursts, thus enabling high pulse peak power. MOPA architectures, combining different seed lasers and various gain media, have been used for producing bursts of femtosecond, picosecond, and nanosecond pulses, including Yb-doped fiber amplifiers [1, 2], Yb:YAG thin-disk multi-pass amplifiers [3], multi-pass amplifiers based on a cryogenically cooled Yb3+:CaF2 crystal [4], multi-stage Nd:YLF amplifiers [5], and Nd:YAG multi-stage amplifiers [6–8].
For ultrafast (pulse width < 10 ps) burst mode systems, they are applied in many fields, such as material processing [9, 10], combustion diagnostics [11], photoacoustic microscopy [12] and so on. For material processing, the low overall repetition rate is advantageous for thermal management while the useful cumulative effect (e.g., through plasma creation) benefits from the momentarily high repetition rate during the burst. Can Kerse et al. studied the possibility of ablation cooling material removal with excellent processing results using ultrafast bursts of pulses [9], whose envelope is pre-shaped into a square one [1]. For combustion diagnostics, bursts of high repetition rate, high-energy pulses are needed to increase the temporal and the spatial resolution [11]. In the field of photoacoustic microscopy, the signal-to noise ratio could be enhanced by virtue of pulse bursts [12]. Especially, for some highly interesting applications such as electron beam characterization [13] or free-electron laser seeding [14], the burst-mode laser systems are expected to be equipped with homogeneous level of pulse energies.
Burst mode ultrafast pulsed laser systems are popular in fiber systems due to its good robustness. In 2009, Makoto Murakami et. al. constructed a burst-mode Yb-doped fiber laser, operating at an inter-burst repetition rate of several hundred kilohertz and with 0.4 μJ per burst and used for pulsed laser deposition [10]. In 2011, Kalaycıoğlu et. al. demonstrated burst-mode operation of a polarization maintaining Yb-doped fiber amplifier, with an average pulse energy of ~20 μJ and total burst energy of 0.25 mJ [15]. However, the energy of each burst was inhomogeneous due to the gain saturation of the amplifiers. To enhance the burst energy and obtain uniform energy distribution, a feedback mechanism shaping the seed of the burst-mode amplifier was introduced by the same authors in 2012 [1]. The burst energy can be scaled up to 1 mJ, comprising 25 pulses with 40 μJ average individual energy. In the same year, Breitkopf et al. reported an Yb-doped laser system producing 58 mJ pulse bursts comprising 2000 ultrashort pulses at an intra-burst repetition rate of 10 MHz [16], with a very homogenous energy distribution during the burst. This is resulting from the continuous pump during the burst. In 2014, P. Elahi et. al. presented a Yb-doped fiber amplifier, utilizing doping management, that scales the average power up to 100 W. The laser system produces bursts at 1 MHz, with 10 μJ energy per pulse and reasonably uniform bursts [17]. In 2015, Jaka Petelin et. al. [18] experimentally obtained uniform energy distribution for 40 pulses by building a theoretical model in a multistage fiber amplifier chain and compensating the gain saturation effect, which eliminates the need for an adaptive feedback loop.
For nanosecond burst mode systems, long burst durations of 10-100 ms with high pulse energies up to a few Joules could be achieved in Nd:YAG multi-stage burst-mode systems [6–8]. Such lasers with narrow linewidth (< 1GHz) takes advantage in linear optical-diagnostic techniques, due to efficient coupling with molecular transitions. For such long burst duration, the amplification of intra-burst pulses does not rely on storage of energy before the bursts' arrival, resulting in a relatively flat-top burst envelope. However, for short burst durations of several hundreds of nanosecond, the envelope would be distorted due to the large gain of the first several intra-burst pulses, for both broadened ultrafast pules and nanosecond pulses. Few has proposed a theoretical way and demonstrated the compensation of envelope distortion.
Comparing the amplification of ultrafast and nanosecond pulses, it is found that they share some common characteristics, especially in burst mode. In chirped pulse amplification (CPA) systems, the mode-locked ultrafast pulses are firstly broadened to several hundreds of picosecond or even several nanoseconds, then amplified through amplifiers, and at last compressed into ultrafast pulses. The amplification of the broadened pulses is similar to those from a Q-switched pulses or modulated pulses with nanosecond pulse duration. The difference is the spectral bandwidth and coupled nonlinear effect. The detailed information will be given in the discussion.
In this paper, a theoretical method was proposed to compensate the burst envelope distortion and obtain homogenous pulses for a solid-state MOPA system operating in burst mode with nanosecond burst duration, at an intra-burst repetition rate of 40 MHz. Arbitrary burst envelope was achieved without an adaptive feedback loop, verifying the effectiveness of the theoretical method. The method could be applied in burst shaping for solid-state CPA systems, generating ultrafast pulses with desired envelope and pulse numbers.
2. Theoretical method for pre-compensation of burst envelope
Siegman firstly pointed out in his book the method to specify a desired output pulse shape Iout(t) in the presence of saturation [19]. To obtained a desired Iout(t), the required input pulse shape Iin(t) could be obtained using
where G(t) is the pulse shape transfer function and is the key factor for the process of pulse shaping.In amplifiers, G(t) is calculated by
where Gi is the initial gain for the pulse, Jout(t) is the cumulative output pulse energy fluence at time t after the arrival of the pulse and Jsat is the saturated energy fluence. Jout(t) is represented byFor Nd:YVO4 crystal, Jsat is represented by
where h is the Planck constant, ν is the laser frequency and σes is the stimulated emission cross section.Two practical means have been proposed to obtain pulse shape transfer function G(t). One is the experimental method, which is based on Eq. (1). By comparing the input and output pulse shapes, G(t) is obtained at a particular pump power for a given input pulse. However, variations among the pulse repetition frequency (RPF), pulse duration, input energy, pump power would lead to the change of saturation degree and thus the change of G(t).
The other is the theoretical method. Compared with the experimental method, the theoretical method to determine G(t) is convenient for different degrees of saturation. As seen in Eq. (2), Gi, σes and the effective beam radius in the gain medium reff are the three important parameters to theoretically determine G(t). For a fiber amplifier, reff and σes could be derived from the manufacturer of the fiber and G(t) could be obtained through a mature iterative method [20, 21]. However, the determination of G(t) is difficult and complicated for the solid-state Nd:YVO4 MOPA systems, due to the temperature-dependent stimulated emission cross section and fluorescent lifetime, as well as the varied beam radius in the thermally-affected gain medium.
For burst mode lasers, the envelope shape replaces the above-mentioned pulse shape. To pre-shape the envelope of the MOPA system and obtain a desired one, a theoretical method consists of three steps for pulsed amplification is demonstrated with a continuous-wave (CW) pump source.
First, the small-signal gain G0 could be calculated according to our previous model in [22] by replacing the key parameters with the ones for the amplifier. It would be regarded as the starting value for the following iteration method.
Second, the pulse shape (envelope shape) transfer function G(t) is obtained via an iteration method. A model is proposed to investigate the amplifier performance and the gain characteristics. The amplification is separated into many cycles with a period of 1/f. Each period consists of a pump period and a seed period as shown in Fig. 1. During the pump period, the pump beam is sent into the gain medium and population inversion is created. After the pump period the seed pulses propagates inside the gain medium and is amplified by the population inversion created during the previous pump period.
The output burst energy fluence Jout(t) (including the total energy of the pulse energy in the burst) is derived from F-N equation,
For the first envelope pulse entering into the amplifier, Gi is equal to the small signal gain G0. The gain at the end of the pulse Ge is found by using Jout(tp) in Eq. (2) where tp is the pulse duration,
To find the initial gain Gi for subsequent pulses, the gain with respect to the recovery time tr between pulses is given by Siegman [14]:
where τ is the fluorescence lifetime of the gain medium and tr is given bywhere f is the inter-burst pulse repetition rate of laser.Applying Eqs. (5), (2) and (7) iteratively and each time replacing the initial gain in Eq. (5) with new gain in Eq. (7), the initial gain Gi rapidly converges towards its steady state value. Therefore, it is possible to obtain the peak and average power gain of the amplifier for arbitrary envelope widths and inter-burst repetition rates even when the inter-burst repetition rate is larger than 1/τ. However, the model breaks down when the envelope width approaches the burst period because Eq. (5) assumes negligible pumping during the pulse. The flow diagram of the iterative process is shown in Fig. 2.
The temperature-dependent stimulated emission cross section σes could be obtained by measuring the temperature of the gain medium, while the effective beam radius in the gain medium reff could be obtained by measuring the thermal lens.
The last step is determining the required envelope shape by Eq. (1) based on the G(t) obtained, with the same input power and output power.
For a multi-stage amplifier chain, G(t) for each stage should be solved and the whole envelope shape transfer function is determined by their product.
3. MOPA setup
A schematic diagram of the master oscillator setup is depicted in Fig. 3. The seed laser was a DFB laser (Eagleyard), with peak power of 1000 mW and spectral line width (FWHM) of 2 MHz. The center wavelength was 1064 nm and could be fine-tuned by adjusting the temperature to best match the emission line of Nd:YVO4 crystal. The polarized continuous-wave from the DFB laser was coupled into two electro-optical modulators (EOM) with bandwidth of 10 GHz, which was controlled by an arbitrary waveform generator (AWG, Agilent 81150A). The first EOM generated intra-burst pulses at an intra-burst repetition rate of 40 MHz with pulse duration of 4.1 ns. The other EOM would gate several pulses at inter-burst repetition rate of 40 kHz ~1MHz and shape the burst envelope. The extinction rations of the two EOMs were 30 dB and 25 dB respectively. The bias current were controlled at the zero point by a bias controller (PlugTech). Two fiber amplifier stages made of Yb-doped single-mode polarization-maintaining fiber were introduced to boost the average power to tens of milliwatts. The length and the pump power were carefully designed to keep the good quality of the seed laser. All the fibers used in the experiment were polarized-maintaining single mode fibers and connected by FC/APC connectors. The modulated laser output from the fiber amplifiers was coupled into the Nd:YVO4 amplifiers by a coupling system, with polarization extinction ratio (PER) of 30 dB and beam radius of 215 μm.
Fig. 3 Schematic diagram of the master oscillator setup. AWG: arbitrary waveform generator, EOM: electro-optical modulator, OI: optical isolator, WDM: wavelength division multiplex, YDF: Ytterbium doped fiber, BPF: band pass filter (8 nm).
The setup of solid-stage amplifiers was almost the same with Ref [23] The differences were the pump beam diameters and laser beam diameters for the 2nd and 3rd amplifier. The pump beam diameters were all about 940 μm and laser beam diameters were all about 730 μm. What’s more, a 3° wedge on one of the facets of the Nd:YVO4 crystal for the 3rd amplifier prevented possible parasitic laser oscillation.
The time characteristics of the laser was measured by a fast InGaAs PIN photodiode, with a rise time of 100 ps. Tek oscilloscope MDO3104 (1 GHz, 5GSa/s) was cooperated with the photodiode. The output power of 1064 nm was measured by the power meter (Ophir NOVA II) with the maximum detect power of 250 W. The spectrum characteristic was measured by an optical spectrum analyzer (Agilent 86142B) with spectral resolution of 0.06nm.
4. Results and Discussion
The pulses from the two EOMs were first tested. The first EOM was operating at 40 MHz. As shown in Fig. 4, the pulse shape was Gaussian-like with pulse duration of 4.1 ns, which was a little shorter than the AWG signal (4.3 ns, the limit of the AWG machine). Due to the modulation effect, the modulated pulse has a longer trailing edge than the AWG signal, which would decrease the pulse contrast. The spectrum of the intra-burst pulses after the two fiber amplifiers is shown in the inset, with line-width less than 0.06 nm (the resolution of the spectrometer, Agilent 86142B).
Fig. 4 Evolution of the pulse shape during the iteration process. (Inset: the spectrum of the intra-burst pulses after the two fiber amplifiers.)
To achieve the desired envelope shape, the pulse shape transfer functions were first obtained through the above-mentioned method. The input average power was 20 mW at inter-burst repetition rate of 100 kHz, with 40 pulses in the burst, corresponding to an envelope width of 1000 ns. The calculated initial gain for the three solid-state amplifiers were 334, 3.9 and 2.5, respectively [24].
The pre-compensated envelope shapes of the seed laser made up of 40 pulses were shown in Figs. 5(a), 5(c), 5(e) and 5(g), with same input average power of 20 mW. The output powers for each solid-state amplifier were 7.3 W, 21.2W and 44 W. The profile of each individual pulse did not distorted from the oscilloscope. The output envelope shapes were shown in Figs. 5(b), 5(d), 5(f) and 5(h). The computed average deviation between the measured and calculated pulse bursts were 2.26%, 1.83%, 2.42% and 1.05%, respectively. From Fig. 5(a), the pulse contrasts were a little different for the first 12 pulses and the next 16 pulses, due to the different response of the first EOM. The difference become larger after amplification. AWGs with higher precision and EOMs with quicker response would enhance the pulse contrast. What’s more, the introduction of a mode-locked laser or gain-switched DFB laser would generate intra-burst pulses with high pulse contrast.
Fig. 5 Input and output burst shapes consisting of 40 pulses at inter-burst repetition rate of 100 kHz for the solid-state MOPA system. (a), (c), (e), (g): input burst shapes for concave, figure of “M”, double rectangular and triangle shapes. (b), (d), (f), (h): output burst shapes for concave, figure of “M”, double rectangular and triangle shapes.
To enhance the pulse energy, seed laser with 20 pulses and 10 pulses at inter-burst repetition rate of 40 kHz were introduced into the MOPA system. The same input average power of 13.5 mW resulted in the same output average power of 39.4 W, corresponding to the total burst energy of about 1 mJ. For 20 pulses, the flat-top output burst envelope was shown in Fig. 6(b), corresponding to about 50 μJ for each pulse. The amplitude root-mean-square (RMS) was less than 3%. For 10 pulses, the corresponding pulse energy was 100 μJ with flat-top output burst envelope, which was much higher than that of fiber amplifiers.
Fig. 6 Input and output burst shapes consisting of 20 pulses at inter-burst repetition rate of 40 kHz for a flat-top output burst.
Due to the modulation effect, the spectral line-width would be 0.11 GHz (Fourier-transform limit), corresponding to Gaussian-like pulse shape with pulse duration of 4.1 ns, using Eq. (9) [25]. With the absence of amplified spontaneous emission (ASE) and parasitic oscillation, the spectral line-width was measured to be less than 0.060 nm (15.9 GHz) many times during the experiment, as shown in Fig. 7. Since the resolution of the spectrometer (Agilent 86142B) is 0.06 nm, it is believed that the true value was less than 0.06 nm. For such narrow spectral bandwidth, nonlinear effects in fiber amplifiers such as stimulated Brillouin scattering (SBS) could easily arise. Therefore the pump power was carefully controlled to avoid the phenomenon and protect the DFB laser.
The output beam quality after the third amplifier was good with M2 factor of 1.131 and 1.149 (90/10 knife) at horizontal and vertical directions, measured by a beam propagation analyzer (Spiricon M2-200-FW-SCOR).
To test the stability of the MOPA system, the input and output average power of the solid-state amplifiers were recorded for more than 10 minutes. The standard deviation were 2% and 1.14%, corresponding to the input and output powers as shown in Fig. 8.
Fig. 8 The stability of the input and output power for the MOPA system at inter-burst repetition rate of 100 kHz with 40 pulses in the burst. (Inset: the beam quality of the output laser beam).
In theory, the pre-compensating method is not expected to be precisely accurate for high duty cycle burst, since the analysis ignores pumping during the burst: there is no replenishment of the inversion population during the whole burst. The approximation is reasonable only for low duty cycle burst. However, we found that this approach was still efficient to produce burst envelope with homogenous pulse energy, even at 50% duty cycle, with a deviation from flat-top envelope of less than 10%.
As for ASE, it was not obviously observed in the experiment from the temporal and spectral characteristics, for both inter-burst repetition rate of 40 kHz and 100 kHz under continuous pumping. We attribute it to the high inter-burst repetition rate since Nd:YVO4 crystal behaves as if continuous-wave (CW) amplification takes place when inter-burst repetition rate is larger than 30 kHz. However, for high power and low inter-burst repetition rate systems, ASE should be taken into account [26, 27].
As for nonlinear effects, many of them could be neglected in solid-state amplifier, for example SBS and stimulated Raman scattering (SRS), due to large mode area and insufficient peak power density. For nanosecond burst mode systems using solid-state amplifier, taking our system as example, the gain narrowing effect is not obvious, resulting from its narrow bandwidth. For ultrafast burst mode systems, the spectral bandwidth of the seed laser is broad. Gain narrowing effect should be considered for the case of high peak power density. What’s more, it would certainly depend on and can be compensated by self-phase modulation (SPM). Although the spectrum of the broadened pulses might vary during the amplification and influences the compressed pulse width at last, the distortion of burst envelope during the amplification would still obey the same law as the nanosecond pulse. Xinglai Shen has proved that the Frantz–Nodvick model still works in fiber amplifiers with SPM, which is seeded by a super-radiation pulsed laser diode with spectral bandwidth of 10 nm [28]. For solid-state amplifiers, one could using the similar ways to calculated burst distortion and output spectrum for coherent pulses and incoherent pulses with any given temporal and spectral shapes with gain saturation.
5. Summary
In summary, a theoretical method was proposed to compensate the burst envelope distortion in a solid-state MOPA system operating in burst mode at an intra-burst repetition rate of 40 MHz. Burst envelope shapes such as concave shape, figure of “M”, double rectangular, triangle and square were achieved at inter-burst repetition rate of 100 kHz with 40 pulses in the burst, showing excellent agreement with the calculated ones. This is the first demonstration of arbitrary burst envelope without an adaptive feedback loop in a solid-state laser system, verifying the effectiveness of the theoretical method. The maximum pulse energy of 100 μJ was achieved at inter-burst repetition rate of 40 kHz, with 10 pulses in the burst. The pulse number and interval between the pulses could be conveniently tuned by adjusting the parameters of AWG. The method could be utilized to generate ultrafast burst lasers with high energy and desired envelope in solid-state laser system using CPA technology, showing great potential in industrial field such as precision manufacturing and so on.
Funding
National Natural Science Foundation of China (NSFC) (61475083).
References and links
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