We report for the first time an all-fiber laser system that generates tunable Watt-level femtosecond pulses at around 2 μm without an external pulse compressor. The system is based on amplification of a Raman shifted Er-doped fiber laser in a Tm-doped 25-μm-core fiber. We obtain 108-fs pulses at 1980 nm with an average power of 3.1 W and a pulse energy of 31 nJ. The peak power at the output of the amplifier is estimated as ~230 kW, which to the best of our knowledge is the highest peak power obtained from a femtosecond or a few-picosecond amplifier based on any doped fiber. The amplified output is frequency-doubled to produce 78-fs pulses at 990 nm with an average power of 1.5 W and a pulse energy of 15 nJ. We demonstrate broad wavelength tunability around 2 μm as well as around 1 μm.
©2005 Optical Society of America
High power tunable sources of femtosecond pulses in the wavelength range of 1.8 – 2.1 μm and frequency doubled to the 900 – 1050 nm range are useful for a variety of commercial and scientific applications, including remote sensing, micromachining, spectroscopy, pumping nonlinear frequency conversion processes, THz generation and two-photon microscopy. At wavelengths longer than 1.8 μm currently available sources of femtosecond pulses are bulk Tm and Cr:ZnSe lasers as well as synchronously-pumped optical parametric oscillators. In the range 900 – 1050 nm commercial bulk Ti:Sapphire lasers operating at the long-wavelength edge of the gain spectrum are available.
Fiber-based sources of femtosecond pulses have well-known benefits of compactness and environmental reliability compared to their bulk counterparts, as particularly advantageous for industrial applications. Tm-doped fibers have a broad amplification band of about 300 nm at around 1.9 μm supporting generation and amplification of femtosecond pulses and/or wide tunability. Femtosecond oscillators based on Tm-doped fiber had been demonstrated previously [1, 2], Nelson et al.  used additive-pulse mode-locking based on nonlinear polarization evolution to obtain tunable pulses in the range from 1.8 to 1.9 μm, whereas Sharp et al.  used soliton-pulse mode-locking to produce femtosecond pulses at a fixed wavelength of 1.9 μm. An alternative to a mode-locked Tm fiber oscillator is a Raman shifted Er fiber laser [3–5], that produces tunable femtosecond pulses over a very wide wavelength range, from 1.5 to 2.1 μm. Such Tm-doped and Raman shifted Er-doped mode-locked lasers are based on single-mode fibers and generally are limited to sub-nanojoule pulse energy and few-milliwatt average power.
The use of highly-doped cladding-pumped large mode area (LMA) fibers, in particular Yb- and Er/Yb-doped fibers, is an established approach for amplification of short pulses that allows to achieve high peak and high average powers [6–13]. Compared to Yb and Er/Yb fibers, the nonlinearity of Tm fiber is smaller mainly because of the explicit 1/λ scaling of the nonlinearity. The dispersion of Tm fibers at around 2 μm is dominated by the host silica material dispersion and is generally few times larger than that of Yb and Er/Yb fibers operating at shorter wavelengths. A larger dispersion can be advantageous for short-pulse amplification as we will discuss later.
Continuous-wave and Q-switched Tm-doped silica LMA fiber lasers operating at around 2 μm have been actively investigated recently, see, for example, Refs. [14–20], with output powers reaching 60 W from single-mode LMA fibers . However, amplification of femtosecond pulses in Tm-doped LMA fibers to beyond a nanojoule or a few-milliwatt level has not been demonstrated previously.
In this paper we report for the first time an all-fiber laser system that generates tunable Watt-level femtosecond pulses at around 2 μm without an external pulse compressor. The system is based on amplification of a Raman shifted Er fiber laser in a Tm-doped LMA fiber. We obtain 108-fs pulses at 1980 nm with the average power of 3.1 W and pulse energy of 31 nJ. The amplified output is frequency-doubled to produce 78-fs pulses at 990 nm with the average power of 1.5 W and pulse energy of 15 nJ. Broad wavelength tunability of both the amplifier output at around 2 μm and the frequency-doubled output at around 1 μm is demonstrated.
We note that we achieve average powers and pulse energies that are several times higher than those obtained previously by direct amplification of femtosecond pulses in Er/Yb LMA fiber amplifiers operating at a fixed wavelength [6, 11]. Moreover, we achieve pulses with the peak powers of ~230 kW directly from the amplifier, without the need for an external compressor. To the best of our knowledge this is the highest peak power obtained from a femtosecond or a few-picosecond amplifier based on any doped fiber, including more-established Yb- and Er/Yb-doped fibers.
2. Amplification of femtosecond pulses at 2 μm
In this work we use an amplifier fiber whose dispersion is high enough to result in a substantial dispersive stretching of an initially compressed seed pulse. To produce compressed amplified pulses we pre-stretch the seed pulses in a length of an undoped fiber. Such configuration actually allows to obtain higher peak power compressed amplified pulses than it would be possible to obtain from a low-dispersion amplifier.
The peak power at the output of a short-pulse fiber amplifier is generally limited by the onset of nonlinear effects that depends on fiber nonlinearity and the effective length of the amplifier. The effect can be quantified by calculating the B-integral,
where γ is the effective nonlinearity, P(z) is the propagation-dependent peak power, P 0 is the pulse peak power at the output of the amplifier, L eff is the effective length of the amplifier, and integration is carried over the length of the amplifier fiber. In the simple case of a constant gain per unit length, g, and a low-dispersion amplifier, i.e. when the pulse length does not change substantially, the effective length is where L is the physical length of the amplifier . For a large total gain, G = exp(gL), Eq. (2) reduces to L eff = 1/g .
In the case of a high-dispersion amplifier, i.e. when the pre-stretched seed pulse undergos a substantial dispersive compression in the amplifier, the effective length is shorter than it is for a low-dispersion amplifier because on the average the pulse peak power in the high-dispersion amplifier is lower, assuming the same peak powers at the output of the high- and low-dispersion amplifiers. The magnitude of the effect depends on the value of the amplifier characteristic gain length, L g = 1/g, relative to the dispersion length, LD = Δ/β2, where Δτ 0 is the compressed pulse length and β2 is the amplifier dispersion. When LD is on the order of Lg or slightly longer, i.e. when pulse length does not change substantially over the last Lg -long section of the amplifier, the effective length L eff ~ Lg the same as given by Eq. (2). When LD is much shorter than Lg , i.e. when substantial dispersive compression occurs over the last Lg -long section of the amplifier, L eff ~ LD , which can be a substantial reduction compared to a low-dispersion amplifier.
To better quantify the above intuitive considerations, we numerically calculated the B-integral as given by Eq. (1) by considering a Gaussian pulse that undergoes dispersive compression from pulse length of Δτ to Δτ 0, while being amplified in an amplifier with a constant gain per unit length. Figure 1 shows the calculated effective length (normalized on the effective length of a zero-dispersion amplifier, as given by Eq. (2)) as a function of the pulse compression ratio, Δτ/Δτ 0, for two values of the amplifier gain, G = 15 dB (Lg ≈ 0.29L) and G = 25 dB (Lg ≈ 0. 17L). As can be seen, for Δτ/Δτ 0 ~ 100, the amplifier effective length is reduced by a factor of 5–8, depending on the amplifier gain. Under the conditions of our experiment described below the effective length reduction by a factor of about 3 is estimated from Fig. 1.
The experimental setup is shown in Fig. 2. The femtosecond-pulse seed source was a mode-locked Er fiber laser implemented using polarization-maintaining (PM) components to ensure stable and robust operation . The laser operated at the repetition rate of 100 MHz and produced 400-fs pulses at 1557 nm with the average power of 20 mW. The output of the oscillator was amplified in a Er/Yb-doped fiber amplifier. The amplified pulses were then coupled to a Raman shifting PM fiber, that produced nearly-transform-limited 150-fs pulses at around 2 μm with about 60 mW average power in the Raman soliton. Such front end implementation of the system described here had an architecture similar to that described previously in Refs. [3–5].
To pre-compensate for dispersion of Tm fiber (about -85 ps2/km) as well as for additional chirp due to self-phase-modulation in the amplifier, we added a 1.4-m length of ultra-high-NA dispersion control fiber that resulted in 3-ps stretched pulses with about 50 mW average power. The output of the dispersion control fiber was coupled to the Tm fiber amplifier using mode-matching optics.
The amplifier was based on 2.3 m of Tm-doped fiber with a core diameter of 25 μm and a core NA = 0.10. The cladding had a diameter of 250 μm and an NA = 0.46. The fiber had about 6.3 dB/m absorption at 790 nm. The amplifier was counter-pumped through the cladding with the output from a laser diode that produced up to 30 W power at 790 nm, from which up to 26 W power could be coupled to the amplifier fiber.
At the highest pumping level the amplifier produced 3.1 W average power (31 nJ pulse energy) at 1980 nm, as shown in Fig. 3. The slope efficiency with respect to the coupled pump power is 15%, as represented by the straight line in Fig. 3. The relatively low slope efficiency is mainly due to the quantum defect of 60% when Tm-doped fiber is pumped at 790 nm. In contrast, Yb- and Er/Yb-doped fiber amplifiers have much lower quantum defect and demonstrated slope efficiencies in LMA fibers are higher, about 40% for Er/Yb-doped amplifiers (see Ref.  and references therein) and about 80% for Yb-doped amplifiers (see, for example Refs. [7–10]). Nevertheless, utilizing cross relaxation and energy transfer processes in heavily-doped Tm fibers, it is possible to exceed the Stokes limit of 40% efficiency [17, 19] and achieve the slope efficiency as high as 74% from continuous-wave Tm-doped silica fiber lasers . Hence, Tm-doped silica short-pulse fiber amplifiers can potentially be very efficient, approaching the efficiency of Yb- and Er/Yb-doped fibers.
The autocorrelation trace of the 31-nJ amplified pulses at 1980 nm, as shown in Fig. 4(a), has a width of 167 fs. Assuming a sech2 pulse profile we estimate a pulse length of 108 fs (deconvolution factor of 1.54) and a 20% pedestal content apparent in Fig. 4(a). Subtracting the pedestal content from the total pulse energy, we estimate the pulse peak power at the output of the Tm amplifier as ~230 kW.
To put these results in perspective, we note that in an earlier work  direct amplification of 100-fs pulses in a 16-μm-core Er/Yb-doped fiber resulted in ~ 3.5-nJ amplified pulses and the peak power of 35 kW. Very recently, using a similar system architecture with a state-of-the-art 26-μm mode-field diameter Er/Yb-doped photonic crystal fiber, Shirakawa et al., Ref. , obtained 7.4-nJ, 100-fs pulses with the peak power of 54 kW. Also very recently, Limpert et al.  used a larger, 35-μm mode-field diameter, Yb-doped photonic crystal fiber amplifier and relied on strong spectral compression due to self-phase-modulation to produce 10-ps pulses with 200 kW peak power directly from the amplifier. To the best of our knowledge the peak power of 230 kW from the 25-μm-core Tm-doped amplifier that we report here is the highest value obtained from any femtosecond or few-picosecond amplifier based on any doped fiber including more-established Yb- or Er/Yb-doped fibers.
3. Frequency doubling
The output of the Tm amplifier was frequency-doubled in the periodically-poled lithium niobate (PPLN) crystal which had several grating segments with quasi-phase-matching (QPM) periods ranging from 26.4 to 28.7 μm. The crystal was anti-reflection coated and was held at elevated temperatures of > 120 °C to avoid photorefractive damage. The phase-matching conditions for optimum conversion were adjusted by temperature tuning and by transverse translation of PPLN to select different QPM grating segments. The group-velocity mismatch parameter for second-harmonic generation (SHG) in PPLN when pumped at 2 μm is calculated as 0.14 ps/mm using the Sellmeier equation of Ref. , hence the group velocity walk-off length for ~110 fs pulses as used here is about 0.78 mm. The expected theoretical small-signal conversion efficiency using a walk-off length long PPLN and confocal focusing is 160 %/nJ, Ref. . We used a shorter crystal, 0.31 mm long (100 nm acceptance bandwidth), and the beam was loosely focused.
Because the Tm-doped fiber used here was non-PM, we used waveplates after the amplifier to prepare a linear polarization state for optimal frequency-doubling utilizing the d33 nonlinear coefficient of PPLN. Figure 5(a) shows the second-harmonic power at 990 nm versus the amplified power at 1880 nm. The highest second harmonic average power is 1.5 W that corresponds to pulse energy of 15 nJ. The SHG efficiency, shown in Fig. 5(b), starts to saturate after about 15%, deviating from the linear small-signal behavior indicated with a straight line in Fig. 5(b). At the maximum fundamental power we achieve a very respectable 50% efficiency, which also indirectly indicates a very good amplified beam and pulse quality. The autocorrelation trace of the 15-nJ frequency-doubled pulses is shown in Fig. 4(b). From the autocorrelation width of 117 fs, we estimate a pulse length of 78 fs and a pedestal content of 9% assuming a sech2 pulse profile. The peak power of the second harmonic pulses is thus estimated as 175 kW.
4. Wavelength tunability
Wavelength tunability was achieved by changing the pulse energy output from the Er/Yb amplifier to tune the Raman soliton wavelength [3–5] within the Tm fiber amplification band. Figure 6(a) shows the amplifier output power for different wavelengths at around 2 μm when the amplifier was pumped with 26 W coupled power. As can be seen, over the range of about 140 nm, from 1900 nm to 2040 nm, the average power exceeds 1.5 W. The measured pulse lengths, shown in Fig. 6(b), are the shortest at around 1980 nm, the wavelength at which the length of the dispersion control fiber was optimized. When wavelength is tuned away from ~1980 nm, pulse lengths increase because the dispersion balance changes. For example, for shorter wavelengths, dispersion of the Tm fiber becomes less negative (in ps2 units) while dispersion of the dispersion control fiber becomes more positive leading to the net positive dispersion. In principle, one can use an engineered nonlinearly-chirped fiber Bragg grating in place or in addition to the dispersion control fiber to maintain the dispersion balance in the system over the whole tuning range .
To obtain maximum frequency-doubled power when the Tm amplifier output was wavelength tuned we adjusted the phase-matching condition of the PPLN crystal by temperature tuning and by translating the PPLN crystal to access different QPM periods. The SHG efficiency depends not only on the fundamental pulse energy but also on the fundamental pulse length. Since the latter increases when the fundamental wavelength is detuned from 1980 nm, the frequency-doubled power decreases relatively fast when the second harmonic wavelength is detuned from 990 nm, as evident in Fig. 6(a). The second harmonic pulse length, Fig. 6(b), is generally slightly shorter than that of the fundamental but follows the same general trend. We note that temperature tuning of the PPLN crystal is relatively slow, but one can use a fan-out structure  for continuous tuning at rates much faster than it is possible with temperature.
In conclusion, we demonstrated for the first time amplification of femtosecond pulses in Tm-doped 25-μm-core silica fiber at around 2 μm. The all-fiber laser system produced Watt-level tunable output over the range of 140 nm. At 1980 nm, the peak of the Tm amplifier gain, we obtained 108-fs pulses with the average power of 3.1 W and pulse energy of 31 nJ. Relying the low nonlinearity of the amplifier and shortening of its effective length due to high dispersion of the Tm-doped fiber we achieved an estimated peak power of 230 kW at the output of the amplifier. To the best of our knowledge this is the highest peak power obtained from a femtosecond or a few-picosecond amplifier based on any doped fiber, including more-established Yb- and Er/Yb-doped fibers. The amplified pulses were frequency-doubled to produce tunable output at around 1 μm. At 990 nm we obtained 78-fs pulses with the average power of 1.5 W and pulse energy of 15 nJ. The demonstrated laser system is useful for a wide variety of applications.
The authors would like to thank S. D. Jackson for useful discussions.
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