The generation of cubicon pulses from an Yb fiber chirped pulse amplification system at pulse energies up to 200 µJ is demonstrated. After pulse compression 650 fs pulses with a pulse energy of 100 µJ are obtained, where pulse compression relies on the compensation of third-order dispersion mismatch between the stretcher and compressor via self-phase modulation of the cubicon pulses in the fiber amplifier. Values of self-phase modulation well in excess of π can be tolerated for cubicon pulses, allowing for the nonlinear compensation of very large levels of dispersion mismatch between pulse stretcher and compressor.
©2005 Optical Society of America
Ultrafast fiber lasers have many practical advantages over conventional Ti:sapphire lasers, particularly in industrial environments, due to their robustness and compactness . While the commercial reliability and stability of femtosecond fiber laser oscillators are well known, development of practical amplified ultrafast fiber lasers has been limited by the large dispersion manipulation required for chirped pulse amplification (CPA). The generation of >100 µJ femtosecond pulses from fiber lasers was demonstrated by Galvanauskus et al. , however the >1000:1 pulse stretching ratios were produced using stretchers and compressors based on bulk optical gratings with matched dispersion compensation. The size and alignment tolerances associated with bulk gratings, make them impractical for use in industrial laser systems. Thus, in order to realize the principal integration advantage of amplified ultrafast fiber lasers, fiber-based alternatives are required to replace bulk gratings.
While both fiber based stretchers and compressors can be implemented [3,4], the current state of technology limits the energy handling of fiber based compressors. Thus bulk grating compressors are used for the generation of the highest pulse energies. The combination of fiber stretcher and bulk grating compressor produces a significant third-order dispersion mismatch between stretcher and compressor for large stretching ratios. Here we demonstrate this third-order dispersion mismatch can be compensated by nonlinear self-phase modulation (SPM) in the amplifier fiber through the use of cubicons.
The name cubicon reflects that the pulse evolution in the nonlinear power amplifier is related to that of similaritons, however whereas similaritons (or parabolic pulses ) induce a quadratic nonlinear phase delay, cubicons also induce a significant component of cubical nonlinear phase delay. Unlike similaritons, cubicons are strongly chirped pulses with asymmetric temporal and spectral distribution for which SPM leads to a negative dispersion slope during amplification, thus cubicons allow for compensation of large values of third-order dispersion mismatch between pulse stretcher and compressor. Cubicons enable the operation of fiber CPAs at large levels of SPM, greatly expanding the power limits compared to similaritons, which have thus far been limited to pulse energies <1 µJ. The possibility of third-order dispersion compensation with SPM was first theoretically predicted by Galvanauskas , but has only recently been demonstrated experimentally [7,8]. Here we demonstrate for the first time the generation of cubicons at multi-W level average powers and pulse energies of 100 µJ in an Yb fiber based CPA system.
The evolution of pulses in an optical amplifier in the absence of gain saturation and a limited gain bandwidth can be described by the nonlinear Schrödinger equation with gain :
where, A(z,t) is the slowly varying pulse envelope in a co-moving frame, β2 is the group velocity dispersion (GVD) parameter, β3 represents the third-order dispersion, γ is the nonlinearity parameter γ=2πn2/λ (λ is the wavelength of operation and n 2 is the nonlinear refractive index=3.2×10-20 (mW)-1 for typical silica fibers) and g(ω,z) is the frequency dependent distributed gain coefficient, which is generally also length dependent in a fiber. By numerical modeling we found that the maximum tolerable amount of SPM in a fiber CPA system actually increases with stretched pulse width and can reach values exceeding 10π. However, in practice, other nonlinear effects (proportional to the peak amplifier power) in high energy fiber amplifiers, such as stimulated Raman scattering, nonlinear polarization evolution as well as four-wave mixing can lead to modulations of the pulse spectrum and the temporal intensity profile of the stretched pulse, which limit the achievable pulse energy at much smaller values of SPM and therefore a careful amplifier design is required to achieve high values of SPM.
Because of the large tolerable levels of SPM we can compensate for large values of dispersion mismatch between stretcher and compressor, where as shown by Galvanauskas  the amount of induced third-order dispersion can be related to the pulse spectrum. It can be shown that the third-order dispersion of bulk grating compressors with groove densities up to 1800 l/mm can be compensated with SPM.
3. Experimental setup and results
The experimental set up for the generation of high energy cubicons is shown in Fig. 1. A passively modelocked dispersion compensated all-polarization maintaining (PM) Yb oscillator  produces slightly chirped pulses with an average power of 20 mW at a repetition rate of 45 MHz and a wavelength of 1044 nm. The pulses are re-compressible to a pulse width of 150 fs. The pulses generated by the oscillator are stretched in a 900 m length of conventional step-index fiber with normal third-order dispersion to ~250 ps. The pulse repetition rate was set with an acousto-optic down-counter to 100 kHz, with two single-mode Yb pre-amplifiers to produce sufficient signal to seed the power amplifier.
Taking advantage of the high average power handling capabilities of air-clad photonic crystal fiber (PCF) , we used a 2 m long air-clad Yb PCF, with a core diameter of 40 µm and a fundamental mode area of ~1000 µm2, as the power amplifier. The front end of the fiber amplifier chain was PM. The PCF was non-PM, therefore additional waveplates were incorporated at its input and output end for polarization control. The power amplifier generated 10 W of output power given an incident pump power of 30 W at a wavelength of 976 nm. The uncompressed pulse energy of 100 µJ, corresponding to an estimated peak power of 400 kW, was close to the measured surface damage threshold fluence of 15 J/cm2 for ≈150 µJ pulses. The power amplifier produced a near diffraction limited output with an M2 ≤ 1.3.
A folded single diffraction grating compressor with a groove density of 1500 l/mm produced a second-order dispersion of -21 ps2 for pulse compression. Rather than having mutually compensating third-order dispersion, both the fiber stretcher and the bulk-grating compressor produce positive third-order dispersion. In fact, the ratio of third- to second-order dispersion in the bulk-grating compressor is ~4 times greater than in the fiber stretcher.
Autocorrelation traces of compressed pulses at pulse energies of 10 and 50 µJ, and the corresponding pulse spectra centered at 1040 nm are shown in Figs. 2 and 3. The compressed pulse energies are ~50% lower than the pulse energies in the amplifier fiber due to optical losses in the pulse compressor. According to the autocorrelations, the FWHM pulse width decreased from 800 to 500 fs (given a theoretically determined deconvolution factor of 1.5 for cubicon pulses), when increasing the pulse energy from 10 µJ to 50 µJ, due to SPM compensation of third-order dispersion mismatch. The pulse spectrum exhibits a shark fin shape, characteristic of cubicon pulses. The compressed pulses at 50 µJ have a time bandwidth product of ~0.80 compared to a time bandwidth product of ~1.3 at 10 µJ.
To obtain an improved measurement of the IR pulse form, we frequency doubled a portion of the beam and performed a cross-correlation between the IR pulse relative to the SH , shown in Fig. 4. As with the autocorrelations, the cross-correlations for pulse energies of 10 and 50 µJ show a reduction in the FWHM pulse width from 800 to 500 fs (Fig. 4 left, assuming a deconvolution factor of 1.2). Plotted on a logarithmic scale (Fig. 4 right) the cross-correlations prove that the contrast ratio is improved at higher pulse energy to a value of >1000:1. Furthermore, the cross-correlations show that the primary effect of SPM in the amplifier is to reduce the amount of energy in the pulse “tail” resultant from the positive third-order dispersion of the mismatched stretcher/compressor.
The experimental results were further modeled based on the application of Eq. (1). The theoretically obtained cross-correlation for 10 and 50 µJ pulses and the corresponding pulse spectrum for 50 µJ pulses are shown in Fig. 5. Here we assumed a nonlinear phase delay of 4π. The theoretically obtained pulse cleaning effect is more pronounced than observed experimentally. We attribute the difference to pulse imperfections at the amplifier input. The surface damage limit of the present PCF corresponds to pulse energies of around 75 uJ and from equation 1 we can derive that compressible pulses can be expected even at such larger values of SPM.
By increasing the stretcher length to 2.0 km we were able to increase the amplified pulse energy to 200 µJ before compression, with a compressed pulse width of 650 fs and pulse energy of 100 µJ. For these experiments, the repetition rate was reduced to 50 kHz, thus the average compressed power was 5 W. To minimize the size of the compressor in this case a bulk grating with 1740 l/mm was used, however this resulted in a longer compressed pulse duration and larger uncompensated third-order dispersion. Even more dramatic pulse cleaning effects compared to Fig. 2 were confirmed for compressed pulse energies in this configuration, i.e. the pulse width decreased from 2.2 ps to 650 fs with increased pulse energy from 10 to 100 µJ (Fig. 6). The pulse energy of 200 µJ before compression was limited again by surface damage of the PCF. Higher pulse energies should be reachable with the insertion of additional mode expanders.
We have demonstrated nonlinear pulse cleaning in µJ ultrafast fiber power amplifiers and its scalability to a compressed pulse energy of 100 µJ. By inducing the formation of cubicons in nonlinear fiber power amplifiers, large values of third-order dispersion mismatch between pulse stretchers and compressors can be compensated, enabling the construction of highly stable and compact high-energy femtosecond fiber amplifier systems. We believe that cubicons will enable the development of practical ultra-high average power ultrafast fiber laser sources operating at the mJ energy level. Based upon the proven performance of products such as IMRA America’s FCPA µJewel D-400, that already incorporate cubicon amplifiers, we believe that the development of higher energy/power femtosecond fiber lasers will facilitate industrial utilization of ultrashort laser technology in a wide variety of applications.
Note added in proof: After submission of this paper we learned that another group  also demonstrated high - quality pulse compression in fiber amplifiers with mismatched stretcher and compressor.
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