1. Introduction

The chirped-pulse amplification technique is now a routine approach to generate high-peak-power femtosecond pulses in Yb-doped fiber lasers. Since very high stretching/compression ratios of about 6000 with a help of diffraction gratings [1] and of about 1000 with a help of monolithic stretcher and a compact compressor [2] were demonstrated, the further peak power scaling is limited mainly by the characteristics of the Yb-doped fiber used in the final amplifier stage. The best results so far were achieved with the help of photonic crystal fibers (PCF), a peak power in the MW range directly from amplifier and more than a few GW of peak power after compression of the chirped pulses [1]. However, large mode area (LMA) Yb-doped PCFs are notorious for their extremely high bend sensitivity and their impossible integration into conventional fiber systems by fusion splicing, resulting in huge dimensions and non-monolithic designs. Moreover, the complicated technology behind the production of LMA Yb-doped PCFs results in its high cost. To overcome these drawbacks, much effort has been directed towards developing and testing novel LMA fiber designs. To date, many structures have been proposed: leakage channel fibers [3], fibers operating at high-order modes [4], step-index fibers with a microstructured cladding for suppressing high-order modes [5], helical-core fibers [6], chirally coupled core fibers [7], photonic bandgap fibers [8, 9] and other promising designs. However, no results comparable to those obtained with LMA Yb-doped PCFs have been reported. For example, in the case of monolithic chirped pulse amplifiers, the highest peak power does not exceed a few tens kW directly after the amplifier and 10MW after compression [2, 10, 11].

Recently, a novel promising design of LMA Yb-doped tapered fiber has been developed that allows the creation of compact and robust all-fiber systems with low bend sensitivity and simple power scaling [12–16]. This approach is quite simple: the core and cladding diameters monotonically increase along the fiber length to several times their original size. The fundamental mode LP₀₁, excited at the single-mode (thin) end, propagates towards the thick end of the tapered fiber adiabatically without exciting high-order modes (HOMs) [13]. In [14], the passive tapered fiber with an output D_core, of 110 µm was produced and adiabatic propagation of the LP₀₁ mode along the tapered fiber was demonstrated.

Recently, we demonstrated an active tapered fiber-based chirped pulse amplification (CPA) system that generated 100 kW of peak power in 7-ps pulses centered at 1040 nm, with possibility of compression down to 130 fs [15]. It is also worth to mentioning Ref [16], where amplification of non-chirped 25-ps pulses in a 4-m long tapered fiber with the output core diameter as large as 100 μm was studied. At a high repetition rate (4 MHz) the peak power up to 50-100 kW was demonstrated with a small power level in the 1st Raman Stokes (less than a few percents). A further increase of the peak power up to ~400 kW was accompanied by the appearance of a strong parasitic signal in the Raman Stokes (>60% relative to the net power). In the same paper achieving of 5-MW peak power was reported at 20-kHz repetition rate, but it was accompanied by a very high level (> 80%) of amplified spontaneous emission (ASE), which is inadmissible for most applications. In reality the reported peak power of 5 MW might be significantly overestimated as authors calculate the peak power based on direct detection of the pulse energy by means of an energy meter. This measuring technique can be misleading since the ASE signal is not a strictly continuous wave due to its time-dependent buildup [17, 18]. Special techniques like integrating photodetector [17] or time-domain characterization [18] must be used to evaluate the ASE content.

The present report is devoted to an optimized design of the tapered fiber and the study of a novel operation regime that achieves a high peak power. The chirped pulse amplification achieved power levels up to the sub-MW range directly from the tapered fiber amplifier (comparable to that of PCF-based systems) and further pulse compressions down to sub-ps durations were demonstrated. Special attention was paid to the characterization of the amplified and compressed pulses using various techniques (autocorrelation, FROG, integrating photodetector and independent estimation of the peak power by the self-focusing experiments), which confirmed a low ASE level and a high peak power.

2. Tapered fiber design and fabrication

Similar to [15], the fiber core was made of a photodarkening-free P₂O₅/Al₂O₃/SiO₂ (PAS) glass matrix with excess phosphorous, which allowed us to achieve a relatively low core numerical aperture (NA) of ~0.095 and a high Yb₂O₃ content of 2 wt% [19]. To achieve an extremely flat refractive index profile (RIP) the Modified Chemical Vapor Deposition (MCVD) technique was used to deposit all the dopants from the gas phase. SiCl₄, POCl₃, AlCl₃ and Yb(thd)₃ (thd = 2,2,6,6-tetramethyl-3,5-heptanedionate) were used as precursors. The AlCl₃ and Yb(thd)₃ precursors were solid at room temperature, were heated in excess of 100°C to obtain a sufficiently high vapor pressure, and were delivered into the reaction zone through separate heated lines. Such modification resulted in perfect control over the composition and refractive index of each deposited layer (up to ten layers were deposited to form the core). The flatness of the resultant active core was enough to achieve a perfect Gaussian beam shape of the fundamental mode, up to core diameter of 60-80 µm. The high purity of the PAS glass produced with this technique had essential features compared with those made by solution-doping or powder techniques — gray losses below 30 dB/km were achieved in the fabricated fibers.

An important modification to the design of the fiber was the utilization of the so-called W-shaped RIP. Similar to [20], a depressed layer was deposited just outside the core (see RIP in Fig. 1(a)), which reduced the cut-off wavelength for the core with a fixed diameter and NA. It allowed us to achieve a single-mode propagation regime (the cutoff wavelength was ~980 nm) at the thin end of the tapered fiber, where the core diameter was approximately 10 µm.

 

Fig. 1 (a) Measured refractive index profile of a fiber with an outer diameter of 125 µm. (b) Image of the fabricated fiber’s cross section. (c) Small-signal absorption from the cladding, measured in the fabricated tapered fiber. (d) Typical dependence of the outer diameter (black curve), first cladding diameter (blue curve) and core diameter (red curve) on the length in the fabricated tapered fiber. Red closed squares depict the value of output core diameter for 1.05-, 1.5- and 2-meter-long tapered fibers.

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The fiber had an outer cladding of fluorine-doped silica with a NA of 0.28. The diameters of the first (pure silica) and the secondary (F-doped) claddings were 71 µm and 85 µm, respectively, at the thin end. To ensure a perfect pump mixture the non-circular first cladding was fabricated prior to the F-doped overcoat. A cross section of the fiber is shown in Fig. 1(b). These factors enabled it to achieve a record high small-signal cladding absorption of 24 dB/m at 976 nm and 6.5 dB/m at 915 nm (see Fig. 1(c)). Another important advantage of the F-doped silica cladding was the simplicity of preparing the thick end, which could be glued into an adapter and angle-polished using standard equipment. Thus, a perfect angle-cleaved thick fiber end compatible with a high power end-pumping technique could be routinely obtained.

Boron-doped stress rods were introduced into the first cladding to create birefringence. The diameter of the rods were higher than those in [15], which allowed us to achieve a polarization extinction ratio of more than 20 dB (measured in the unpumped tapered fiber with a wideband source near 1080-1090 nm).

To produce the tapered fiber, we utilized a non-stationary fiber drawing process. This method was proposed and realized for the first time at FORC RAS in 1991 [21]. It was used to draw relatively long (10-1000 m) tapered fibers. Later, this method was modified to draw short (~1 m in length) tapered fibers [22]. After additional modifications, the non-stationary fiber drawing process allowed us to obtain a highly reproducible set of few tens tapered fibers with a variation in the parameters of less than 10%, with a tapered region length of less than 1 meter and a tapered ratio of more than 7. The diameter distributions of the core, first cladding and second cladding over the fiber length for a tapered fiber cut from such a drawing are presented in Fig. 1(d). The maximum core diameter was 62 µm, the fundamental mode field diameter (MFD) was estimated to be 36.3 µm at 1064 nm.

A smooth enough transition between the thin and the thick ends of the tapered fiber is required for the adiabatic transformation of the fundamental mode during its propagation to the thick end while avoiding the excitation of HOMs. For example, a local taper fabricated with the help of a Vytran splicing system does not allow obtaining M² better than 3.5 [23]. The situation is completely different in our case, when the tapered section was produced during drawing and was long enough. The latter was confirmed by measuring the beam quality factor M² at the output of the fabricated 2-meter-long tapered fiber. In the experiment, a continuous wave signal at 1064 nm was coupled into the thin end and amplified to 10 W in the tapered fiber, which was pumped through the thick end by a 976 nm multi-mode diode (in all the experiments, the fiber was counter-pumped through the thick end). The M² was measured with a Thorlabs M2MS-BC106VIS measurement system and found to be 1.08/1.05 (see Fig. 2).

 

Fig. 2 (c) Caustic measurement for a 2-meter tapered fiber operating at 1064 nm with an average power of 10 W at the far-field (taken way above Rayleigh length), at the near-field (taken between the beam waist and the Rayleigh length) and at the waist beam intensity distributions. Insets were cropped from original images.

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3. Theoretical analysis

First, a theoretical analysis of the performance of the counter-pumped tapered fiber amplifier was conducted (where the pump power was coupled into the thick end and the signal power was coupled into the thin end). The aim of the analysis was to determine an optimal configuration in terms of a high threshold of nonlinear effects. The modeling was performed by solving the standard rate equations for a quasi two-level system, including forward and backward amplified spontaneous emission (ASE) and the first Raman component [24]. The change in the pump radiation NA during propagation along the tapered fiber and the corresponding pump power leakage was considered according to [25]. The feature of filtering of backward ASE (i.e. propagating from thick to thin end of the tapered fiber) [12] was also considered. Additionally, we accounted for the changes in the mode field diameter of the radiation propagating in the core along the fiber. The absorption cross-sections for the PAS fiber were estimated based on the measured absorption spectra and the ytterbium oxide concentration, as determined by X-ray microanalysis performed using a JEOL 5910LV electron microscope at the Analytical Center of FORC RAS. The emission cross-sections were estimated based on the measured luminescence spectrum and the lifetime of Yb³⁺ ions in the samples of the investigated tapered fibers using the Füchtbauer-Ladenburg equation.

The tapered fiber was considered as a set of short, uniform parts (~1000 pieces), with core and cladding diameters that changed according to the distribution shown in Fig. 1(d). For calculations, the length of tapered fiber was varied by “cutting” some length from the thick end, i.e., a tapered fiber with a length of L was identical to those in Fig. 1(d) that spanned from 0 cm to L. In the experiments, three tapered fibers with lengths of 1.05 meters, 1.5 meters and 2 meters were cut from different periods of the drawn fiber. The results of the calculations were verified experimentally using these three tapered fibers.

3.1 Saturation signal power in active tapered fibers

It is well known from conventional fibers that decreased input signal can noticeably increase the threshold of nonlinear effects. However, the input signal should be high enough to saturate the amplifier and obtain a high pump conversion efficiency. Most designs for LMA fibers with constant core and cladding diameters over the fiber length give significantly reduced intensities for the signal (due to increases in the mode field area) and the pump (as a typical first cladding diameter in most LMA fibers is increased to 200–400 µm) compared to conventional double clad single-mode Yb-doped fibers. Further shortening of the amplifier length to increase the threshold of non-linear effects results in a small net fiber gain and therefore a high input signal power is required to saturate the amplifier. Typically, saturating such an amplifier requires input signals in excess of hundreds of mW [1].

This behavior was completely different in the tapered fiber amplifiers. Our modeling showed a decrease in the seed signal power required to saturate the amplifier by orders of magnitude compared to conventional LMA fibers (see Figs. 3(a) and 3(b), top pictures). We modeled the operation of different fibers counter-pumped with 25 W at 976 nm. The tapered fibers had lengths of 1.05 meters for 1030 nm signal and 2 meters for 1064 nm signal. For comparison, we calculated the performance of regular fibers, fibers with the same length but constant core and cladding diameters equal to those at the thick end of the tapered fiber. The power required to saturate the amplifier (i.e., to obtain ~70-80% of the maximum output power) is two orders of magnitude higher in the regular fibers than in the tapered fibers.

 

Fig. 3 The calculated and experimentally obtained saturation curves for (a) the 1.05-meter-long tapered fiber and a comparable regular fiber and (b) the 2-meter-long tapered fiber and a comparable regular fiber. The pump wavelength was 976 nm and the power was 25 W. The tapered fiber had core/first-cladding diameters of 10/73 µm at the thin end and 46/338 µm at thick end for the 1.05-meter fiber and 62/450 µm for 2-meter fiber. The regular fibers in the simulations had core/first-cladding diameters of 46/338 µm for the 1.05-meter fiber and 62/450 µm for 2-meter fiber. Regular fibers in the experiments had core/first-cladding diameters of 30/220 µm for the 1.05-meter case and 56/410 for the 2-meter case.

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Our experiments on continuous-wave signal amplification supported the results of our calculations (see Figs. 3(a) and 3(b), bottom pictures). We compared a 1.05-meter-long tapered fiber with core/first-cladding diameters of 10/73 µm at the thin end and 46/338 µm at the thick end with a regular fiber of the same length and with core/first-cladding diameters of 46/338 µm. Additionally, we compared a 2-meter-long tapered fiber (10/73 µm to 62/450 µm) with a 2-meter-long regular fiber with core/first-cladding diameters of 62/450 µm. The regular fibers have the same core/cladding diameters ratio as the tapered fibers (note that the fact that the regular fibers tested were operating in a few mode regime did not influence the amplifier saturation signal power). The tapered fibers had very low saturation signals (below a few mW) without any sign of ASE or self-lasing, while the regular fibers of the same length required saturation signals of two orders of magnitude higher.

This behavior can be explained by the fact that the pump radiation intensity was greatly increased near the thin end of the tapered fiber compared to the regular fiber. The pump NA used in the experiment was specified to be within 0.22, but direct measurements of the power distribution over the NA shows that more than 90% of the pump power was contained within NA = 0.13 (which we used in our calculations). The first cladding NA was approximately 0.28 and our estimations showed that the leakage loss did not exceed 4 dB up to the thin end of the 1.05-meter tapered fiber or 6 dB for the 2-meter-long tapered fiber. At the same time, the first cladding area decreased by 20-40 times (13-16 dB) near the thin end and the unabsorbed pump intensity increased proportionally. Due to the filtering effect of backward ASE, it sufficiently leaks from the active core at the transition region, preserving inversion level in thin part to depleting by signal. Moreover, the signal intensity was higher by an order of magnitude at the thin (signal input) end of the tapered fiber as compared to that of a regular fiber, as it propagated in a 10 µm core compared to the 40..60 µm core of the regular fiber. As a result, the unabsorbed pump was efficiently converted into signal without the generation of ASE, and the minimum signal required to saturate the amplifier was orders of magnitude less than that of the regular fiber.

3.2 Threshold of stimulated Raman scattering (SRS) in tapered fiber amplifier

In fiber-based chirped pulse amplification systems, there are two main factors that limit the maximum peak power at the output. The smallest threshold has a self-phase modulation (SPM) effect; however, this restricts the quality of further pulse compression, and not the maximum achievable peak power level at the amplifier output. The second nonlinear effect is stimulated Raman scattering (SRS), which leads to a power transfer from the amplified pulse to the first Stokes component shifted by approximately 440 cm⁻¹ [26]. For an amplifier operating at 1030 nm, the first Stokes component is centered at approximately 1080 nm, and in the case of a 1064 nm operating signal, the first Stokes component is centered at 1125 nm.

In this study, we calculated the SRS threshold by directly solving the rate equation, which included a seed due to thermal-induced photons [27] at the first Stokes wavelength and ASE generated in the amplifier at this wavelength. The SRS threshold was set at the amplification of the SRS signal at the first Stokes wavelength to more than 1% of the main signal.

We estimated the SRS thresholds for the tapered fiber amplifier operating at either 1030 or 1064 nm with 10 mW of input power and pumped with either a 915 or 976 nm multimode diode. The tapered fiber length was varied from 0.6 to 2 meters. In addition to the tapered fiber, we modeled a PCF fiber with core/cladding diameters of 40/200 µm (DC-200/40-PZ-Yb from NKT Photonics), which the absorption and emission cross-sections and the lifetime of ytterbium ions were taken from [28].

The results of the calculations, shown in Fig. 4(a), were very unusual. The SRS threshold for the PCF was inversely proportional to the fiber length, as expected. In contrast, the SRS threshold for the tapered fiber increased with the fiber length. The tendency was the most apparent in the case of a 1064 nm signal with a 976 nm pump, where the SRS threshold increased from 148 kW to 301 kW as the tapered fiber length is increased from 1.05 to 2 meters.

 

Fig. 4 (a) Calculated SRS threshold dependence on the length of the tapered fiber or the PCF (signal power = 10 mW, pump NA = 0.13). (b) Calculated signal distribution over the length of a 2-meter tapered fiber.

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This effect cannot be explained solely by the considerable increase in the MFD at the output of the tapered fiber as its length was increased. The cause for this phenomenon is apparent in Fig. 4(b), which shows that in the case of 976 nm pumping, the 1064 nm signal propagated along the first meter of the fiber without any gain or loss, whereas the 1030 nm signal showed some absorption, and in the last 0.8-1 meters of the fiber, where the MFD is high, the signal experienced a very high gain. As a result, the accumulated nonlinearity was very small. This behavior was caused by the fact that for the 2-meter fiber, the small-signal absorption at 976 nm exceeded 50 dB; thus, only a small part of the pump power reached the thin end of the fiber. Near the thick end of the tapered fiber, the growth of the signal was defined mainly by the pump absorption rate, which was very high because of the high Yb³⁺ content. The low signal saturation power in the tapered fiber amplifier (see previous paragraph) resulted in a low level of forward ASE in this regime. It is interesting to note that this propagation regime is a specific feature of the tapered fiber caused by the small MFD at the thin tapered fiber section. Our calculations show that in the case of a regular fiber with a similar clad absorption, the SRS threshold slowly decreases with fiber length.

It should be noted that the SRS threshold was calculated to be much smaller at 1030 nm than that of the 1064 nm signal. This feature was caused by ASE in the 1080 nm region that was generated by the tapered fiber amplifier, which acted as a seed for SRS. Moreover, there was additional gain in the first Stokes signal near 1080 nm due to the Yb³⁺ ions. The situation was completely different in the case of the 1064 nm signal, where both the ASE generated at the first Stokes wavelength (1125 nm) and the gain due to the Yb³⁺ ions were orders of magnitudes smaller.

Thus, our calculations predicted a new amplification regime, which allowed us to realize a very high threshold for nonlinear effects, particularly SRS. The use of a signal near 1064 nm (or any other wavelength whose 1st Stokes wavelength lies outside the amplification band of Y³⁺ ions) and a 976 nm pump were required to realize this regime. A relatively long Yb-doped tapered fiber length with a net small-signal clad absorption of approximately 50 dB at the pump wavelength were also necessary. For these conditions, a sub-MW SRS threshold was predicted in the fabricated Yb-doped tapered fiber.

4. Experiments

4.1 Experimental set-up

To verify the calculations, we realized the laser scheme depicted at Fig. 5. In the first set of experiments, our aim was to estimate the SRS threshold in the different amplifier configurations (tapered fiber length, signal wavelength). Picosecond narrow-bandwidth seed sources from Fianium were used (13 ps at 1030 nm and 5 ps at 1064 nm). Generated pulses were amplified in a low-power “Yb:1” amplifier, reduced in repetition rate by an acousto-optical modulator (AOM) down to 1 MHz, and amplified again in a low-power “Yb:2” amplifier up to an average power of 10 mW. The pulses duration at the tapered fiber input were 18 ps in the case of 1030 nm seed and 8 ps in the case of 1064 nm seed. These pulses were further amplified in the active tapered fiber, whose input end was spliced to the output of “Yb:2”. The output end of the tapered fiber was angle-polished to 8 degrees to avoid self-lasing. To properly align this end, we used a translation stage that provided five axes of adjustment (x, y, z, yaw and pitch). As light came out of the angle-polished end of the tapered fiber at an angle of approximately 12° relative to the fiber axis, the fiber was rotated to align incident light direction and the axis of the optical scheme. The tapered fiber was counter-pumped by a wavelength-stabilized (976 ± 0.5 nm) fiber-coupled diode laser that provided up to 50 W of output power within a NA of 0.13. The ASE at the output of the tapered fiber was measured using the so-called “integrating photodetector” [17] (see details in the Appendix).

 

Fig. 5 The experimental setup for the chirped pulse amplification. Yb:1 and Yb:2 are low power single-mode core-pumped amplifiers; AOM: acousto-optic modulator; L1, L2: aspheric lenses, f = 11 mm; DM1: dichroic mirror, HR@1064 nm, HT@976 nm; M1, M2: mirrors; Pump: multi-mode wavelength-stabilized pump diode 976@50 W; PD: integrating photodetector; OSA: optical spectrum analyzer; AC: optical autocorrelator; SHG FROG: second harmonic generation frequency-resolved optical gating set-up.

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4.2 Pump-to-signal conversion efficiency in the tapered fiber amplifier

First, we measured the pump-to-signal conversion efficiency in three different lengths of tapered fibers (1.05, 1.5 and 2 meters) and different signal wavelengths (1030 and 1064 nm). The signal power was set to 10 mW, and the repetition rate was 1 MHz. The results are shown in Table 1.

Table 1. The tapered fiber-based amplifier pump-to-signal conversion efficiency

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As can be seen in Table 1, the differential efficiency remained almost the same across the different fiber lengths. However, in the case of the 2-meter-long tapered fiber operating at 1030 nm, the ASE level near 1064 nm was so high that this fiber could not be used for amplification of a 1030 nm signal. In the case of the 1.05-meter-long fiber operating at 1064 nm, we also obtained a high ASE near 1030 nm, but its level was at acceptable level of a few percent. Note, that the pump-to-signal conversion efficiency shown in the Table 1 can be somewhat increased if a higher input signal power is coupled into the amplifier.

4.3 SRS threshold in the tapered fiber amplifier

As mentioned above, the tapered fibers require very low signal powers to reach the saturation regime. Thus, to determine the minimal acceptable level of the input signal power, we measured the SRS threshold dependence on the input signal power. Additionally, we measured the amount of ASE in the output beam of the system. Measurements were performed with a 1.05-meter-long tapered fiber operating at 1030 nm (Fig. 6(a)) and for a 2-meter-long tapered fiber operating at 1064 nm (Fig. 6(b)). The SRS threshold was estimated by measuring the output spectrum of the amplified signal from the tapered fiber and evaluating the ratio of the power of the first Stokes component to the power of the whole spectrum. For the 1064 nm signal, this method is easy to use because the first Stokes component was far away from the ASE of the Yb³⁺ ions. However, for the 1030 nm signal, the first Stokes component was centered at 1080 nm, which overlaps with the ASE spectrum, making it difficult to obtain accurate measurements of the SRS component. The measured SRS threshold was varied within 30% from experiment to experiment due to variations in the coupled pump NA (due to inaccuracy in the rotational adjustments of the fiber). The pump NA defines the pump loss distribution and in this way affects the signal distribution along the tapered fiber length as well as SRS threshold.

 

Fig. 6 The dependence of the SRS threshold and the ASE on the input signal power for a 1.05-meter tapered fiber operating at 1030 nm (a) and for a 2-meter tapered fiber operating at 1064 nm (b).

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As shown in Fig. 6, the SRS threshold grew quickly as the input signal power decreased. The amount of ASE exhibited the same behavior. Thus, with an input signal power of a few mW, it was possible to achieve a high peak power with an acceptably low amount of ASE at the output of the system.

The SRS threshold was measured for all the available tapered fibers with a 10 mW input signal, and the results are shown in Table 2. The results agreed in general with our theoretical calculations. In the case of using a 1030 nm signal, a high level of ASE lead to decrease of the SRS threshold with increase of the tapered fiber length, and for the 2-meter tapered fiber it was even impossible to estimate the threshold because of an extremely high amount of ASE. In contrast, for the 1064 nm signal, the highest SRS threshold was observed with the 2-meter-long tapered fiber. When a 1064 nm signal was used with the 1.05-meter tapered fiber, the threshold was somewhat higher than that of the 1.5-meter fiber, but in this case a large amount of ASE appeared at 1030 nm. A threshold of 300 ± 50 kW was estimated for the case with 4% ASE.

Table 2. The measured SRS thresholds for different lengths of tapered fibers and different signal wavelengths

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In conclusion, a maximum SRS threshold of 380 kW was observed in the 2-meter-long tapered fiber with a 10 mW seed signal at 1064 nm, which agreed with our calculations. The amount of ASE in this case was below the accuracy of our measurements (2%). Moreover, the threshold could be further increased to 760 kW by reducing the seed signal power to 1 mW, but these conditions produced a large amount of ASE (7%) between the pulses.

4.4 Amplification of the chirped pulses

Finally, we conducted experiments on the amplification of chirped pulses centered at 1064 nm in the 2-meter-long tapered fiber. As a seed source, we used 100 fs master oscillator centered at 1056 with a full width at half maximum of 20 nm [29]. The pulses were stretched by propagation in 70 m of the commercially available passive polarization-maintaining fiber CS-98-3103 from 3M). To shift the pulse center wavelength to 1064 nm, we placed a bandpass filter with a 6 nm FWHM just before the “Yb:1” amplifier. Amplified pulses were compressed by a transmission grating compressor based on a pair of LSFSG-1000-3212-94 gratings from Lightsmyth. For pulse characterization, we used the well-known Second Harmonic Generation Frequency-Resolved Optical Gating (SHG-FROG) technique and, independently, the SHG Optical Autocorrelator (AC) Inrad 5-14B. The chirped pulse duration at the input to the tapered fiber amplifier was measured to be 28 ps. It should be noted that here and below, we consider only the final stage of the amplifier (i.e., that based on the tapered fiber); thus, by the input signal power, we mean the signal coupled into the tapered fiber.

During these experiments, we tried to find the optimal operational regime that gave high peak power directly from the amplifier and the possibility of further pulse compression. Thus, we needed to keep the SPM low to avoid severe deterioration the chirped pulse phase.

We conducted experiments at a relatively high repetition rate of 3.22 MHz. A 10 mW signal at 3.22 MHz was amplified up to an average power of 12.7 W, corresponding to a peak power of 141 kW. The spectra of the pulses at the tapered input and at the tapered output are depicted in Fig. 7(a). Then, these pulses were successfully compressed with 70% efficiency (an average power of 8.9 W after the compressor) down to 330 fs, which was confirmed by FROG measurements. The autocorrelation functions of the pulses before and after compression are shown in Fig. 8(b). The estimated peak power of the compressed pulses is 8.4 MW.

 

Fig. 7 (a) Spectra before and after the tapered fiber. (b) Autocorrelation functions for the pulse after the tapered fiber (dashed curve) and after the compressor (solid curve). The small peak to the right side of the ACF peak for the compressed pulses was due to a ghosting beam.

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Fig. 8 (a) The observed self-focusing and supercontinuum generation effects at the peak power of 8.4 MW. (b) Self-focusing and supercontinuum generation effects at their threshold (4.8 MW).

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To confirm the obtained peak power, we observed the self-focusing (SF) effect in a BK7 glass rod. According to [30], the critical power for the SF effect in BK7 glass at 1064 nm is in the range of 3-4 MW. To observe the SF threshold, we placed, after the compressor, a half-wavelength plate, a polarizer (which was set for full transmittance of the beam), a lens with a focal length of 200 mm and a BK7 glass rod with lens focal point inside it. The half-wavelength plate was rotated to achieve the maximum transmission of the system, and we observed the SF effect at an average power of 8.9 W (i.e., ~8.4 MW of peak power, or much higher than the effect’s threshold) (Fig. 8(a)). Then, we attenuated the beam by rotating the half-wavelength plate to see the threshold of the effect. The threshold was at 5.1 W of average power, corresponding to 4.8 MW of peak power (Fig. 8 (b)), which agrees with literature and independently confirms the estimated peak power of 8.4 MW.

Finally, we varied both the signal power and the repetition rate to find an optimal regime for pulse compression, whose quality is limited by the onset of self-phase modulation, which occurs much earlier than the onset of SRS. For all cases, the average power after the tapered fiber was 10 W, and the average power after the compressor was 8.3 W. We decreased the pulse repetition rate, thus increasing the pulse energy, and monitored the compressed pulse quality using FROG and the autocorrelator. The compressor length was slightly adjusted to compensate for the nonlinear phase shift. The estimated peak powers of the stretched 28 ps pulses after the tapered fiber were 0.11 MW for 3.22 MHz, 0.23 MW for 1.56 MHz, 0.35 MW for 1.03 MHz and 0.65 MW for 0.55 MHz. The measured autocorrelation functions (labeled with repetition rate/input average power), the FROG-retrieved compressed pulses, and the FROG-traces are shown in Figs. 9(a) and 9(b). The autocorrelation function for the compressed pulses at the tapered fiber output at a repetition rate of 3.22 MHz exhibited almost the same form as did those from the compressed seed pulses (at the input of the tapered fiber amplifier) (Fig. 9(a), green curve). The autocorrelation functions generated from the retrieved pulses agreed well with the measured ones. The pulses were successfully compressed at repetition rates as low as 1.03 MHz. The pulse duration of the FROG-retrieved pulses remained almost the same (in range of 315 ± 10 fs), whereas the pulse quality decreased slightly as a result of the increasing pedestal due to SPM. At 0.55 MHz, the nonlinear phase becomes too large, resulting in a significant uncompressed pulse pedestal and long wings in the autocorrelation function. The estimated peak powers of the FROG-retrieved pulses (with their real shapes considered) were 22 MW at 1.03 MHz, 15 MW at 1.56 MHz and 7 MW at 3.22 MHz. Thus, compression of the chirped pulses to a maximum peak power was limited by SPM in the tapered fiber amplifier at a peak power of 350 kW just after amplifier, which was only three times less than the record peak power achieved just after a PCF-based amplifier (before compression) in [1].

 

Fig. 9 (a) Autocorrelation functions for compressed pulses at different repetition rates and input powers, labeled as repetition rate/input average power. (b) The FROG-retrieved pulse duration and FROG-trace for the same repetition rates and input powers, labeled with repetition rate/pulse duration.

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The obtained peak power in the compressed pulses was also indirectly confirmed by observing the self-focusing effect in the BK7 glass rod. Identical to the first experiment the SF was observed at the maximum power and then its threshold was measured by attenuating the beam using rotation of the half-wavelength plate. The SF thresholds were estimated to be 4.36 MW at 3.22 MHz, 5.1 MW at 1.56 MHz, 6.1 MW at 1.03 MHz and 4.7 MW at 0.55 MHz, which agree with literature and previously obtained threshold.

5. Discussion

In this paper, we presented an improved Yb-doped PM tapered fiber for high peak power amplification systems. During preliminary simulations, we revealed that the stimulated Raman scattering threshold increased with the length of the tapered fiber (up to 2 meters) and achieved its maxima for signal wavelength at approximately 1064 nm and pump wavelength at 976 nm. This unusual behavior was explained by a new amplification regime, when a signal propagated without amplification through most of the tapered fiber and experienced high gain only near the tapered fiber’s output, where the fundamental mode has a maximum MFD.

During experiments, we confirmed our predictions and realized amplification pulses centered at 1064 nm with a peak power of up to 760 kW, which was limited by the SRS appearance (1% of power was in the 1st Stokes), and up to 350 kW when limited by SPM for chirped pulses. In the last case, pulses with duration of 28 ps were efficiently compressed down to 315 ± 10 fs with 70% efficiency. The demonstrated peak power at the amplifier output is about an order of magnitude higher than that demonstrated in the previous papers for monolithic (all-fiber) chirped pulse amplifiers [2, 10, 11]. Moreover, it is only three times less than the best value demonstrated with a PCF rod-type fiber [1]. Even this result can be further improved by increasing the tapered ratio. With the output core diameter of about 100 µm [14, 16] and a perfectly flat step-index core, the MFD at the thick end can be increased up to 70 µm (by factor of 2 relative to the results of this paper). In this case, one could expect the MW-peak power level for the chirped pulse amplification (which is comparable to the best value demonstrated with PCF [1]) and a few MW-peak power in the regime with a low ASE and a low 1st Stockes power.

Note that we demonstrated peak power of 22 MW in the compressed pulses, which is few times higher than the best values reported previously for monolithic amplifiers [2, 10, 11]. This value was limited by stretching/compressed ratio (~100) of our set-up and can be improved by an order of magnitude using a monolithic stretcher and a compact chirped volume Bragg grating compressor, similar to [2]. Thus, the maximum peak power after compression can be increased up to sub-GW level using the proposed concept of tapered fiber amplifier (by simple modification of the stretcher/compressor and by using a tapered fiber with improved parameters). This value is very close to the best results achieved with PCF [1], but in contract to PCF, the tapered fiber amplifier retains all the advantages of the all-fiber design, such as reliability, compactness and low production cost.

It is worth mentioning that achieving a high average signal power was not the primary goal of this paper and the average power of about 13 W obtained herein is far below the maximum value achievable with this type of amplifiers. Recently an average power of 120 W was demonstrated using an Yb-doped tapered fiber nearly identical (except for 1.5 times smaller output core and clad diameters) to the one presented in the current work [31].

6 Appendix: measurements of ASE level using integrating photodetector

The principle scheme of the “integrating photodetector” device is shown in Fig. 10(a). The investigated pulses were seeded into a 1 GHz photodetector, which charged the capacitor. The voltage at the capacitor was measured by an oscilloscope with 500 MHz bandwidth (in contrast to [17] we omit operational amplifier to reduce time response of the system). After each set of 8 pulses, the capacitor was shorted to ground. The measured voltage reflected the total optical power integrated over time. Shown in Fig. 10(b) is the case where CW radiation at 1064 nm with an average power of 1.5 mW was combined with pulsed radiation (8 ps, 1.03 MHz) with an average power of 3 mW in one fiber. The top graph depicts the dependence of power on time: the blue curve shows the case where only the pulsed source was turned on, and the red curve shows the case where both the CW and the pulsed sources were on. The bottom graph shows the obtained oscillograms. When only the pulsed signal was used, the capacitor charged only when the pulse reached the photodiode, resulting in a step-like oscillogram (blue curve). When CW (acting as the ASE) was also used, the capacitor was charged between pulses by CW signal, resulting in some charge accumulation between the steps (red curve). The CW part of the signal could be evaluated by measuring the h₁ and h₂ values and using a simple equation: (h₁/(h₁+ h₂))*100%. We obtained a value of 34%, which was close to the real value of 33%. This technique allowed us to measure the amount of ASE in the output beam to within a few percent.

 

Fig. 10 The schematic and operating principle of the integrating photodetector. The data is obtained for 8 ps pulses at 1064 nm with a 1.03 MHz repetition rate and an average power of 3 mW combined with a CW signal at 1064 nm with an average power of 1.5 mW. PD is the photodetector, C is the capacitor.

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Funding

Russian Science Foundation (RSF) (17-13-01343); Program of the Presidium of the Russian Academy of Sciences (Extreme Laser Irradiation: Physics and Fundamental Applications, project 5.6).

Acknowledgments

The authors are grateful to E.M. Dianov for his continued interest in and support of this work and to L.D. Iskhakova for measurement of fiber preform composition with X-ray microanalysis.

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