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Abstract
In this paper, we report a high power and compact mid-IR ultrafast laser system consisting of an Er:ZBLAN fiber-based mode-locked oscillator and a nonlinear amplifier. The mode-locked pulses are amplified and simultaneously nonlinearly compressed to sub-100 fs, without using any external pulse compressor or dispersion-managing stretcher. The output pulses have ∼85 fs pulse durations at ∼2.85 µm, with an average power of up to 2.4 W, and pulse energies of >40 nJ. This constitutes the highest average power sub-100fs duration pulses generated from a mid-IR fiber laser system to date.
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1. Introduction
The development of ultrafast laser sources operating in mid-infrared (mid-IR) spectral range is motivated by high-impact applications such as molecular spectroscopy, remote sensing, high harmonic generation and laser surgery [1–5]. Among those sources, fluoride fiber lasers have the advantages of efficiency, compactness, robustness, and high mode quality, and therefore are drawing increasing attention in recent years. While silica fibers are used in the near-infrared region extending to up to ∼2 µm, the fluoride glass family, such as the ZrF4-BrF2-LaF3-AlF3-NaF (ZBLAN) composition with its transparency window extending up to 5 µm, enables a diversity of fluoride fiber lasers operating at mid-IR wavelength region with various rare-earth dopants such as erbium, holmium, and dysprosium [6].
The first reported fs mode-locked fiber oscillators in mid-IR were based on Er:ZBLAN fibers and operated at 2.8 µm using soliton mode-locking [7,8]. They produced ∼200–500 fs pulses with 0.8–3.6 nJ pulse energies, at ∼50MHz pulse repetition rates. More recently, demonstration of breathing-pulse mode-locking enabled to increase pulse energy to 9.3 nJ, for 215 fs pulses at 75 MHz repetition rate [9]. The shortest to date mid-IR mode-locked fiber oscillator pulses are 131 fs with 3 nJ energies, achieved by using short gain-fiber length [10]. Er:ZBLAN fiber oscillator mode-locking at 3.5 µm was also reported recently by applying a dual-wavelength pumping scheme, demonstrating 580 fs and 3.2 nJ pulses at 68 MHz [11].
Achieving shorter mid-IR pulses requires employing nonlinear spectral broadening after a mode-locked oscillator. The shortest pulses from a fluoride fiber laser system to date, have been reported from a laser system based on a HoPr:ZBLAN fiber mode-locked oscillator, followed by a highly nonlinear chalcogenide fiber. Spectrally broadened pulses at 2.86 µm were compressed with a grating pair compressor down to 70 fs [12]. However, the output pulse energy from this relatively complex system was only 0.44 nJ.
Since fluoride fibers possess a negative dispersion in mid-IR, rare-earth doped fluoride fibers can be used to simultaneously amplify and to nonlinearly compress ultrashort pulses. This technique, first proposed [13] and then demonstrated [14,15] at ∼1.55 µm with Er-doped silica fibers, is based on the adiabatic soliton compression which can occur under properly chosen conditions in a negative-dispersion fiber amplifier. Its principal advantage is the possibility of achieving high energy, and very short duration pulses (e.g., compressed to ∼50 fs from ∼120–140 fs in [14,15]) directly at the fiber amplifier output, without using any external pulse compressors. This technique was recently employed in an Er:ZBLAN fiber amplifier [16,17], exploiting its negative dispersion at ∼2.8 µm. The seed pulses from an Er:ZBLAN mode-locked oscillator were amplified from 4.7 nJ to ∼35 nJ. However, only a modest pulse compression from 440 fs to ∼200 fs was achieved, which does not constitute any pulse duration improvement compared to what is achievable directly from a mode-locked oscillator in mid-IR.
More recently, a more complicated approach using a dispersion managed (with a diffraction-grating stretcher) Er:ZBLAN nonlinear fiber amplifier followed by a high-order soliton compression in a passive ZBLAN fiber has been proposed as a pathway towards <100 fs pulse durations, demonstrating 16 fs pulses at 430 mW of average power at ∼2.8 µm [18]. The necessity of dispersion management in a nonlinear ZBLAN fiber amplifier for obtaining sub-100 fs pulses was reiterated in [19], reporting a complex amplification system where high pulse energies were enabled by down-counting seed pulse repetition rate from ∼40 MHz to 100 kHz, and dispersion-management of a nonlinear Er:ZBLAN fiber amplifier was achieved using Ge rods. It led to 49 fs pulses with energies of up to 100 nJ, but with a very low average power of ∼10 mW.
In this letter, we report a simple and compact laser system consisting of an Er:ZBLAN fiber mode-locked oscillator and an Er:ZBLAN fiber amplifier, the later acting simultaneously as a nonlinear soliton-effect compressor and an energy/power amplifier, generating ∼85 fs pulses with up to 2.4 W of average power. To our knowledge, this constitutes the highest power sub-100 fs pulses generated from a mid-IR fiber laser system to date. More importantly, we demonstrate that this high-power sub-100 fs performance can be achieved without any complicated dispersion management for the nonlinear amplifier, nor any additional post-amplifier pulse compression, while maintaining the original high pulse repetition rate from a mode-locked oscillator. Such a simple and efficient approach is potentially suitable for monolithic laser system integration, and thus is very attractive for practical applications in mid-IR.
2. Nonlinear amplifier as soliton compressor
Adiabatic soliton compression occurs [13] when a soliton pulse propagates in a negative-dispersion fiber amplifier, under the condition of the adiabatic energy gain with the pulse duration readjusting with propagation so that the soliton order N is maintained along the fiber according to the equation [20]:
Here γ and β2 are the nonlinear and dispersion coefficients of the fiber (defined in the subsequent paragraph), P0 is the peak power of the pulse, and T0 is the soliton pulse width. The
N-th order soliton is a solution of the nonlinear Schrödinger equation (NLSE) with an initial amplitude of the form N·sech(t/T0) [20]. Since the pulse energy is increasing with propagation along a fiber amplifier, its duration is expected to decrease, according to Eq. (1). Because optical gain constitutes a perturbation to the NLSE, this pulse duration does not follow Eq. (1) precisely, but approaches its predicted value asymptotically, while exhibiting oscillations which gradually decrease with propagation distance. Adiabaticity means that the initial soliton order is maintained during the propagation. However, when the gain coefficient exceeds a certain critical value, the adiabaticity condition is no longer met, and the next-order soliton is also generated, resulting in a two-soliton bound state propagating along the fiber. The shortest achievable compressed pulse durations are mainly constrained by the fiber amplifier gain bandwidth [13]. At the highest energies, this adiabatic compression picture becomes more complex due to the onset of stimulated Raman scattering, which, on one hand, can lead to pulse wavelength shifting, as well as additional compression, but also can constraint the maximum energies once the pulse spectrum shifts outside the gain spectrum of the amplifier [21,22].
Although this adiabatic amplified-soliton compression technique was initially demonstrated and developed at ∼1.55 µm with Er:silica fibers [14,15], yielding sub-nJ pulses with durations as short as ∼50 fs, but as recent results [16,17] indicate, Er:doped ZBLAN fibers operating in the mid-IR wavelengths can produce orders of magnitude higher energies with this technique. Broad gain bandwidth of Er:ZBLAN fiber at ∼2.8 µm suggests that sub-100 fs pulses should be achievable, much shorter than the ∼200 fs that had been demonstrated so far. To determine conditions required to achieve these high energy sub-100 fs pulses in a nonlinear Er:ZBLAN fiber amplifier, we had developed a numerical model. The model is based on generalized nonlinear Schrödinger equation (GNLSE) [20], which describes the nonlinear evolution of the pulse electric-field envelope A(z, t) propagating along the fiber (left side), and contains the terms describing effects produced by fiber dispersion, net gain, and self-phase modulation (SPM) and stimulated Raman scattering effects (first, second, and third terms on the right side, respectively):
The GNLSE was solved numerically using a standard split-step Fourier method, where the nonlinear term is treated in the time domain, and the dispersion and net gain terms in the frequency domain [20]. In this equation, β2 is the anomalous-group-velocity dispersion (GVD) coefficient of the ZBLAN glass fiber equal to −8.1 × 10−26 s2 /m [23], g(z) is the wavelength-dependent fiber gain coefficient, which is calculated at each position through the fiber using population densities of the upper and lower laser levels, by solving the fiber amplifier rate equations, and the wavelength-dependent emission and absorption cross sections of Er:ZBLAN fiber reported in [24]. The coefficient γ is the ZBLAN fiber nonlinear coefficient at the carrier frequency ω0, corresponding to the central wavelength λ0 = 2.8 µm. It is expressed as $\gamma = ({{n_2}{\omega_0}{\; }} )/({c{A_{eff}}({{\omega_0}} )} )$, where n2 = 2.1 × 10−20 m2/W [25] is the nonlinear refractive index of the ZBLAN fiber, c is the speed of light in vacuum, and Aeff(ω0) is the effective mode field area of the fiber core [20]. The nonlinear response function $R(t )= ({1 - {f_R}} )\delta (t )+ {f_R}{h_R}(t )$, includes both the instantaneous and delayed Raman responses. The fraction of Raman contribution to the nonlinearity is taken to be 0.24, and the Raman response function hR(t) is expressed as an intermediate-broadening model [26].
The fiber used for the numerical calculations in this model is 3 m of Er:ZBLAN fiber (Fiberlabs), with an 18 µm diameter 6 mol. % doped core (NA=0.12), surrounded by a 250 µm diameter circular inner cladding (NA>0.5). This fiber, and the other parameters chosen for the simulations, such as input pulse energies and durations, amplifier gain, etc., are those used in the real experiment reported in the next section. The fiber has V < 2.405 (calculated assuming step-index core profile) for wavelengths longer 2.82 µm and is thus single-mode for these longer wavelengths. The calculated mode-field diameter is 19.7 µm, approximately twice larger compared to typical MFDs of single-mode Er:silica fibers at 1.55 µm. Consequently, although the n2 in ZBLAN fibers is very close to its value in silica fibers, fiber nonlinear coefficient γ is much smaller in Er:ZBLAN fibers at 2.8 µm compared to ∼1.55 µm of Er:silica fibers, due to much higher effective mode area and twice longer wavelengths. This combination of much smaller γ and similar dispersion compared to silica fibers enables much higher soliton pulse energies in Er:ZBLAN fibers in mid-IR.
In the simulation, the input sech2 pulses have 90 mW launched average power, 1.9 nJ pulse energy, 230 fs pulse width, and 48 MHz repetition rate, corresponding to a soliton N = 0.48 in the fiber amplifier. This seed signal, in the experiment, is the output from a mode-locked oscillator, containing part of its circulating fundamental soliton energy. While passing through an optical isolator, a dichroic mirror, a collimating lens, and then being coupled into the amplifier, it loses another 50% of its energy, therefore results in such input condition. The evolution of the pulse in time and spectral domain in the amplifier (left side), as well as the time profile and spectrum of the output pulse (right side) are shown in Fig. 1. The input pulses are broadened first, because initially the SPM effect induced by the input pulse energy cannot balance the dispersion. With the pulses keep gaining energy from the amplifier, a fundamental soliton is formed first, and a second soliton is then excited binding with the original one, once the soliton number reaches about 1.5, which can be seen from the soliton N evolution shown in Fig. 2.(a) inset. The pulses are then compressed rapidly, while maintaining the soliton N, with oscillations due to overshooting under sufficient gain [13]. In the later part of the gain fiber, the soliton self-frequency shift (SSFS) effect [21,22] starts to play a role, with an increasing strength inversely proportional to 4th power of the pulse width, which makes the fundamental soliton, containing most of the energy, to gradually red shifts its center wavelength, producing further spectral broadening and pulse compression. Above features can be verified from the pulse width evolution in Fig. 2.(a), and one can also tell that the pulse energy experiences a continuous increase as the pulse is amplified and starts to saturate at the end of the gain fiber. Eventually, the pulses are amplified to 2.2 W, and simultaneously compressed to 88 fs at the output, corresponding to ∼350 kW peak power.
Fig. 2. (a) Pulse duration, pulse energy and soliton number (inset) evolutions along the fiber simulating the experimental parameters. (b) Pulse duration evolutions with different input parameters.
In Fig. 2.(b), the pulse evolution of pulses with different input-pulse durations and average powers are shown as they propagate in the amplifier under the same pumping condition. With sufficient pump power, even though the pulses evolve with slightly different trends, they can be compressed to a similar pulse width level of about 80 fs. It means the pulse-compression capability of this soliton amplifier is dependent more on the pump level and the parameters of the gain medium, than the input pulse parameters.
3. Experimental setup and results
The schematic of the experimental setup is shown in Fig. 3. The mode-locked oscillator has a ring cavity with a 3.8 m segment of Er:ZBLAN fiber (Le Verre Fluoré) providing the gain, which has a 15 µm diameter and 7 mol. % doped core (NA = 0.12), surrounded by a 260 µm diameter inner cladding (NA > 0.5), which is truncated by two parallel flats separated by 240 µm to maximize absorption of the 980 nm pump light. Self-starting mode-locking is achieved by nonlinear polarization rotation (NPR) with the combination of 2 quarter-wave plate, a half-wave plate, and an optical isolator (Faraday Photonics). The ZBLAN fiber has an anomalous dispersion at around 2.8 µm, therefore the mode-locking pulse has a soliton shape. The oscillator output is from the output port of the polarizing beam splitter (PBS), producing ∼180 mW, 48 MHz, and 230 fs pulses as the seed signal for the amplification stage. The signal light passes through another isolator to prevent the backward light of the amplifier from interfering with the mode-locking operation of the oscillator. After being combined by a dichroic mirror (Lattice Electro Optics), both the signal and pump beams are coupled into the gain fiber of the amplifier. Both gain fibers in the oscillator and amplifier are terminated with angle-polished AlF3 fiber endcaps to prevent fiber tip degradation and optical damage.
Fig. 3. Schematic of the laser system. DM: dichroic mirror, PBS: polarizing beam splitter, ISO: isolator
As the pump power for the amplifier is increased, the output pulses are not only amplified, but also compressed, as discussed in the previous section. The highest output average power achieved in this series of measurements is above 2 W, and the shortest pulse duration with recorded autocorrelation trace is 86 fs, measured by an interferometric autocorrelator, utilizing the two-photon absorption effect of a InGaAs photodiode (FGA21, Thorlabs) for nonlinear detection. The autocorrelation trace measurements with the corresponding output average powers are shown in Fig. 4, and the pulse width of 86 fs was measured with an output average power of 1.87 W. The output pulse duration is below 100 fs when the average output power is sufficiently high and exhibits pulse duration oscillations consistent with the model predictions. It is not clearly seen from Fig. 4, but it is validated theoretically and experimentally by the results in Fig. 5. Amplifier output was confirmed to be single-mode, as expected, since the amplified signal spectrum is above the fiber cut-off wavelength.
Fig. 5. Experimental measurement (blue) and simulation result (orange) for output pulse width with different output power and pulse energy. FWHM: full width half maximum.
The separately measured pulse width (blue line) versus the output average power is shown in Fig. 5. Simulation results (orange line) are also provided for comparison. When the output power is low, and the pulse is not yet compressed, the experimental and numerical results have some discrepancies, but for the most relevant region, where the pulse width is compressed to below 100 fs, the results agree with each other quite well. This measurement shows the shortest pulse duration of 83 fs with 2.11 W output average power, and 85 fs at the highest achieved average power of 2.4 W, exhibit slight pulse-duration oscillations consistent with the numerical model predictions for the output pulse characteristics.
The optical spectrum of the output pulse was measured by a setup consisting of a diffraction grating, followed by a microbolometer-based camera (WinCamD-IR-BB, DataRay). The calibrated spectra for 1.87 W and 2.11 W output powers are shown in Fig. 6, and the simulation results are also shown for comparison. The beating effect between the main pulse and the satellite pulse is expressed stronger in the simulation. For the output pulse with 1.87 W output power, the time-bandwidth product is calculated to be 0.372 for a Δt (FWHM pulse width) of 86 fs, and a Δν (FWHM of spectral width) of 116 nm. For the 2.11 W output pulse, Δt of 83 fs, and Δν of 106 nm give a time-bandwidth product of 0.327. This means the soliton order of the output pulse is somewhat larger than 1, thus slightly oscillating as the output power changes as expected from the theoretical analysis.
Fig. 6. Spectrums from simulation (blue) and experimentally measured (red) at 1.87 W and 2.11 W output power.
4. Conclusion
In conclusion, a compact laser system consisting of an Er:ZBLAN fiber mode-locked oscillator and a nonlinear Er:ZBLAN fiber amplifier/compressor using near-adiabatic soliton compression was demonstrated with ∼85 fs output pulses, up to 2.4 W average power, at 48 MHz repetition rate. This constitutes the highest average power sub-100 fs pulses in mid-IR (∼3 µm) obtained with a fiber laser system to date. Most importantly, we demonstrate that such short pulses, high powers and energies can be achieved with a simple and compact fiber laser system via proper choice of the amplifier gain to ensure near-adiabaticity of the soliton compression process, and without using any external dispersion management using pulse stretchers or compressors. Future improvement in pulse durations, energies and average power should be possible with further optimization. This approach is characterized by an overall simplicity and efficiency (resulting in high average power) of a system, making it suitable for monolithic laser system integration, all very important aspects for practical applications in the mid-IR.
Funding
Office of Naval Research (N00014-17-1-2705, N00014-20-1-2286).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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