Pre-chirp managed , core-pumped nonlinear PM fiber amplifier delivering sub-100-fs and high energy ( 10 nJ ) pulses with low noise

We demonstrate a pre-chirp managed amplification (PCMA) system that is based on two stages of core-pumped, polarization maintaining (PM) fiber amplifiers. It produces output pulses with <65 fs duration and >10 nJ pulse energy from single-mode fibers. Tailoring of the spectra in the amplification chain enables pulse compression to near-perfect transform limited pulses (Strehl-ratio >0.9) and low intensity noise levels (0.008%) despite Bintegrals >40 rad in the PCMA amplifier. Design strategies are presented. We expect this PCMA system to become an easy to implement add-on to a variety of existing sources while maintaining the advantages of the robustness of the PM standard fiber format. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement OCIS codes: (060.2320) Fiber optics amplifiers and oscillators; (060.4370) Nonlinear optics, fibers; (140.3280)


Introduction
Applications of ultra-short pulsed lasers, such as multi-photon or photo-electron spectroscopy, rely on the existence of very compact and robust laser sources that generate ultrashort pulses with durations shorter than 100 fs, and Watt-level powers at high-repetition rates as well as low noise and diffraction-limited beam quality.For nonlinear bio-optical imaging in which photo-induced damage is caused by pulse energy rather than average power, Watt-level outputs from the ultra-short pulse laser source will improve signal-to-noise ratio and reduce data acquisition time.Ytterbium-based Kerr-lens mode-locked lasers can provide sub-100 fs pulses at Watt-level average powers [1].However, it is Ytterbium-doped fiber-lasers that due to all optical wave-guiding exhibit superior robustness -making them suitable for the most demanding laser applications including space-applications that involve rocket launches [2].All-fiber, ultrashort pulse systems are typically setup in a masteroscillator power amplifier (MOPA) configuration: The fiber oscillator generates pulse energies around 1 nJ that are amplified to higher pulse energies.The MOPA configuration has the additional benefit that fiber-coupled optical modulators (having limited power handling capability) can be sandwiched in a fully fiber-integrated way between the oscillator and the power amplifier, and thus, greatly enhance the versatility and applicability of such fiber MOPA systems.
Besides inherent robustness, the light propagation in an optical waveguide also facilitates the occurrence of nonlinear effects.Specifically, self-phase modulation (SPM) is of relevance for ultra-short pulse amplification.SPM causes advantageous spectral broadening that allows the compression to even shorter pulse durations.However, without any special measures, the interplay of SPM, group-velocity dispersion and gain results in severe deterioration of the pulse quality at the output of the fiber amplifier.To mitigate nonlinear effects during amplification, the method of chirped-pulse amplification (CPA) is commonly employed in fiber systems [3].In this scheme, the peak intensity is significantly lowered during amplification by stretching the pulse prior amplification.Fiber-amplification systems based on CPA offer the highest output energies.Using standard single-mode fiber in an all-fiber configuration, pulses with durations of 120 fs and energies of 6 nJ have been obtained after free-space grating-based compression [4].Using rod-type fiber, pulses with mJ energies have been demonstrated from fiber-rod CPA-systems [5].At the output of fiber-CPA systems the pulse durations are typically longer than 100 fs due to a combination of effects: (a) Gain narrowing of the spectrum during amplification, (b) overall dispersion mismatching, and/ or (c) nonlinear phase shifts due to SPM [6].Particularly, the large stretching in fiber-CPA mitigates the nonlinear effect of SPM.Due to the waveguide-nature (i.e.confinement to small mode-areas and long propagation lengths), the effects of SPM start reappearing in CPA: At large nonlinear phase-shifts, pulse-splitting and energy transfer into satellite pulses imposes limitations on the quality of the output pulse [7,8].To reach sub-100-fs pulses from fiber-CPA systems, both the operation at B-integrals < 1 rad and the very careful optimization of overall third as well as fourth-order dispersion of the system are necessary.The latter is challenging due to the large stretching/ compression ratio required for fiber-CPA systems.Using large mode area photonic crystal fiber and dispersion-engineered fiber stretchers (typically non-PM), pulse durations as short as 75 fs have been reported at the output of a fiber-CPA system [9].However, for CPA-systems based on standard single-mode fibers, B-integrals > 1 rad are easily reached at low pulse-energies (~nJ) due to mode-areas as small as < 40 µm 2 [4].
For energies in the range nJ…µJ, there exist also direct amplification schemes (i.e. that are not based on fiber-CPA) utilizing nonlinear effects.These methods include self-similar amplification (which is also known as parabolic amplification) [10,11].Pulses with durations of 48 fs and energies of 226 nJ and 18 W average power have been obtained [11].Note, the self-similar amplifier was constructed from a PM 25/250 double clad fiber that was bend to discriminate higher-order modes [12].Another nonlinear amplification technique uses passive pulse-shaping prior fiber-based amplification [13].In this way, pulses with 780 fs and 49 µJ after grating-based compression have been demonstrated from a rod-type nonlinear amplifier (with accumulated B-integral of 12 rad during amplification).
Lately, the method of pre-chirp managed amplification (PCMA) was reported [14][15][16].This technique and self-similar amplification offer the advantage of producing pulses with durations shorter than 100 fs.This is due to the spectral broadening originating from SPM during nonlinear amplification.
The main benefits of PCMA include the following: (a) nonlinear effects during pulse propagation in fibers are desired and not mitigated.The spectral broadening due to SPM allows for reduced pulse durations as compared to the input pulse duration from an oscillator.In fiber-CPA this is typically not the case.Also, fiber CPA suffers from a degradation of the pulse contrast due to pulse splitting at B-integrals > 1 rad [7,8].PCMA uses pulses that are not strongly chirped prior amplification, and thus, the formation and action of 'temporal phase-gratings' due to SPM of modulated strongly chirped pulses -which causes pulse contrast degradation in nonlinear fiber-CPA -does not impose limitations on operation at high B-integrals.Also, (b) besides the generation of shorter pulse durations at the PCMA output, it also leads to high pulse qualities.And, (c) only very compact compressors are needed for both pre-chirp and final pulse compression.This results in very compact setups.Moreover, (d) the lengths of the fiber amplifiers in PCMA can be made very short.So, it is applicable to many types of gain fibers.Specifically, the short fiber-lengths of PCMA correspond to high doping levels enabling higher small-signal-gain coefficients at smaller wavelengths.PCMA enables amplification also at lower wavelengths (< 1020 nm).Making the spectra compatible to the gain center of some of the most widely used high-energy solidstate amplifiers, e.g.Yb:YAG or Yb:YLF.Differently, self-similar amplification relies on nonlinear evolution of the pulse into a final parabolic shape over several meters.As a result of the lower inversion levels, amplification will be favored at longer wavelengths, e.g.see [11].PCMA can be operated with highly doped fiber as short as < 1 m.Thus, it can also be employed to >100 W fiber-rod amplifiers [15].
In this contribution, we develop design strategies for a PCMA configuration that is solely based on (standard) polarization maintaining (PM), core-pumped single-mode fiber.Average power scaling of PCMA was demonstrated by using free-space coupling into rod-type fiber [15].Here, the goal is design of a practical, robust PCMA front-end configuration that can be used to seed high-energy power amplifiers.The use of polarization maintaining (PM) singlemode fiber offers not only the potential of all-fiber configuration and robustness but also makes it compatible with the use of fiber-pigtailed optical modulators.We propose and demonstrate a two-stage amplification for PCMA with the goal of mitigating the impact of input fluctuations or system deteriorations enabling robust long-term operation.We present design strategies resulting in pulses exhibiting sub-100-fs durations and high pulse qualities as well as a low noise output.Emphasis is placed on tailoring the spectral evolution through the system.As shown in the following, this results in improved pulse qualities and very smooth output spectra even at accumulated nonlinear phase-shifts as high as B > 40 rad.

Design of the PCMA system
In the following, we present a design of a PCMA configuration that is solely based on (standard) polarization maintaining (PM), core-pumped single-mode fiber.The power and energy of this configuration is set by the PM, highly doped, core-pumped (standard) single mode fiber that is employed as the fiber amplifier.The modeling parameters are oriented towards the experimental configuration of section 3. Specifically, the available output power (or energy) is determined by the power of the multiplexed single mode pump diodes.
Ultrashort pulse amplification in fibers is governed by the interplay of fiber dispersion, nonlinear effects and gain.In general, this interplay does not lead to compressible pulses at the output of a direct amplification scheme.Conversely, PCMA corresponds to a beneficial operation region of the nonlinear pulse amplification.In PCMA a small chirp is imposed on the pulse prior amplification.In this way, the amplified pulse can be compressed to shorter pulse-durations and with very high pulse quality.In this paper, the pulse quality is measured in terms of the Strehl-ratio, which is the pulse peak-power after compression compared to the peak-power of the transform-limited pulse.Depending on the parameters of the nonlinear evolution, the pre-chirp required for PCMA may be positive or negative.Due to the nonlinear dynamics, the operation region of PCMA can -to the best of our knowledge -only be designed numerically by solving the generalized nonlinear Schrödinger equation.To obtain accurate results, the numerical model must include the spectral gain profile of the Ytterbiumdoped fiber and other parameters of the pulse amplification, such as inversion distribution and fractional mode power of pump and signal in core [14,17].
Due to the nonlinear nature of PCMA, the power levels define PCMA's operation point.Especially, for high gain (> 20..30 dB) fiber amplifiers this can be challenging as input power fluctuations can affect not only the noise performance of the amplifier but also the pulse parameters at the output.To mitigate such effects, we develop an amplification scheme that employs two amplifier stages.Each of these core-pumped amplifiers is saturated.The two Ytterbium fiber-amplifiers are made of polarization maintaining (PM) single mode fiber.For this experimental demonstration, goal is a 10 nJ output for repetition rates around 70 MHz.A "mini" CPA configuration is employed by stretching the pulse with approximately 6 m of PM980 fiber.The pulse-energy is low in this stage so that detrimental effects of SPM are avoided.After the first amplifier the pulses are compressed using a grating pair in a double pass configuration.The stretching that is followed by compression enables the use of either positive or negative pre-chirp for PCMA.The distance between the gratings is adjusted in such a way that it introduces the required pre-chirp for the second PCMA amplifier.The sign and amount of pre-chirp depends on the power level [15].Note, that this is a distinct feature of PCMA compared to self-similar amplification.In self-similar amplification the corresponding parabolic pulses always possess an up-chirp during amplification.In PCMA, the pre-chirp can be a down-chirp.In the case of initial down-chirp, the joint action of SPM and the down-chirp result in spectral compression in the initial stage of amplification of PCMA [18,19].The parameters of the PCMA configuration are displayed in Table 1.In the following, we calculated the required pre-chirp by characterizing the resulting output pulse.Figure 1 shows the result of the numerical simulation of the PCMA configuration with parameters of Table 1. Figure 1(a) and 1(b) show the pulse-quality in terms of the Strehl-ratio and the pulse peak-power, respectively.Here, the Strehl-ratio is defined as ratio of peakpower of the best-compressed pulse to peak-power of transform-limited pulse.The data of Fig. 1 is calculated as a function of both input power and amount of pre-chirp (shown in terms of the initial pre-chirp's GDDs, TOD is fixed at 0.0015 ps 3 ).At every data point in Fig. 1, the pulse is numerically compressed to highest peak-power.For this, we assume a grating compressor (with parameters of Table 1).As can be seen in Fig. 1(a), there are two optimal regions (that are highlighted via the blue and black dot) where the pulse-quality after compression is highest.However, the output pulse's peak-power in the region that is marked with the blue dot is higher than the region with black dot, as can be seen in Fig. 1(b).Around this region ("blue dot"), the regions of highest peak power and highest pulse quality overlaphowever, not completely.Also, it can be seen in Fig. 1 that the amount of pre-chirp has a strong impact on the peak-power of the compressed output pulse.The input pulse energy (or input power) also has an impact -however, it is not as pronounced.We analyze this power-dependence for a single pre-chirp value in more detail.Figure 2(a) shows a cross-section of Fig. 1.Essentially, this mimics the situation in a real experiment: the pre-chirp is set to a suitable value and then the input power into the PCMA is varied.The prechirping GDD is set to −0.144 ps 2 .As can be seen in Fig. 2(a), even for large variation of input energy, the output parameters of the pulse, namely Strehl-ratio and pulse-peak power stay close to constant (within approx.2%).As can be seen in Fig. 2(c), the output power levels also remain almost constant due to operation of the amplifier in saturation.At the same time, the B-integral (i.e. the amount of accumulated nonlinear phase-shifts) is larger than 40 rad and increases with input power by approximately 20%.Note, the B-integral shown in Fig. 2(c) is only that of the final PCMA amplifier and additional amplifiers may cause additional contributions to the B-integral.In comparison, conventional CPA-systems require operation with B-integrals below 1 rad to ensure good pulse quality at the output [6][7][8].Figure 2(b) shows that the duration of the compressed pulse remains the same (within approx.3%).Note, for each input power level the grating distance of the compressor is adjusted for best compression.For the case of a constant compressor at the ouput, Fig. 3 shows the output pulse's characteristic parameters for the different input powers (otherwise the situation is similar to Fig. 2).The grating distance of the final compressor is optimized for an input power of 26 mW.It can be seen that in this case there is a significant change of the output pulse's characteristics with input power.This clearly demonstrates the nonlinear dependency and sensitivity of the operation point of PCMA.
In the following, we exemplarily show the pulse shapes and spectra at the PCMA's output.For an input power of 22 mW and pre-chirp's GDD value of −0.144 ps 2 , Fig. 4 shows the input and output pulse, the input and output spectrum as well as the best compressed pulse and the corresponding transfer limit pulse from output of the PCMA amplifier.It can be seen from Fig. 4(a) that the interplay of dispersion, nonlinear effects and gain during pulse propagation in the PCMA results in a parabolic pulse shape before compression.This can be regarded as one of the main reasons for the good pulse quality at the output: the SPM results in a parabolic phase that can be removed by the final compressor.The asymmetry of the input pulse is due to TOD.Also it can be seen from Fig. 4(b), that there is significant spectral broadening.This enables reduced pulse durations at the PCMA's output.Figure 4(c) shows that the compressed pulse at the output is very close to the transform limit, i.e. resulting in a Strehl-ratio close to 1.

Experimental setup
Figure 5 shows the schematic of the experimental setup.It consists of an ultra-short pulsed oscillator and two amplification stages.The setup essentially implements the parameter configuration that was determined by the modeling in section 2.
The oscillator is based on an Ytterbium-doped fiber oscillator which is mode-locked by nonlinear-polarization rotation.The gain fiber is Coractive YB 401 with length of 0.4 m.The other fibers (of the pigtails and WDM) are Corning Hi 1060 with a total length of 1.8 m.Dispersion management is achieved by a pair of dielectric transmission gratings (1000 lpmm).Different mode-locking states -including soliton, stretched pulse and similaritonwere tested by adjusting the grating-separation in the intra-cavity grating compressor.The similariton type is chosen for the following demonstration.Note, the similariton type shows all positive chirp of the pulse during one round-trip of the pulse in the oscillator.In the experiment we find that the similariton state provided the highest pulse energy and best initiation of mode-locking.The perpendicular grating separation is set to approximately 7 mm.The characteristic parameters at the oscillator's output are 0.4-nJ energy, 40-nm spectral bandwidth (3dB) nm, and 100-fs compressed pulse duration.The repetition rate is set to exactly 70 MHz by using the variable section in the oscillator that is given by the combination of PBS, QWP and mirror.
The 1 st amplification stage ("mini" CPA configuration): The output of the oscillator passes through a band-pass filter with a bandwidth of 20 nm at full width at half maximum (FWHM).A HWP is set so that the polarization of the light is aligned to the slow axis of the PM fiber.The total length of passive fiber before the gain fiber is approximately 6 m.The gain fiber is Coractive PM-YB 501 with length of 0.6 m.The input and output powers at the fiber amplifier are 4 mW and 186 mW, respectively.The PM Ytterbium-doped fiber is corepumped.
The 2 nd amplification stage (PCMA amplifier): The pre-chirp of the pulse is adjusted by a grating compressor consisting of (1000 lpmm) dielectric transmission gratings.To control the input power of the PCMA, a HWP and a PBS is placed before grating compressor.The compressor's perpendicular grating separation and efficiency are 62 mm and 87%, respectively.The spectrum of the pulse is filtered by a second bandpass filter BPF2 with bandwidth of 10 nm before entering the second core-pumped polarization maintaining fiber.The bandpass filter clips uncompressible phase in the wings of the spectrum and facilitates evolution into a parabolic output spectrum.By slightly tuning the angle of BPF2, we can change the center wavelength of the input spectrum of the second amplifier to match it to the center of the gain spectrum [14].The input and output powers at the fiber amplifier are 26 mW and 820 mW, respectively.The PM Ytterbium-doped fiber is 3.2 m Nufern PM-YSF-LO, which is core-pumped.There is about 3-m passive of PM 980 before the gain fiber (pigtails of the WDM and the inline fiber isolator).The output pulse is compressed by a pair of dielectric transmission gratings with groove density of 1000 lpmm in a double pass configuration.Fig. 5. Schematic of the experimental setup.QWP: quarter wave-plate, HWP: half-wave plate, PBS: polarization beam splitter, ISO: optical isolator, WDM: wavelength division multiplexer, YDFA: Yttterbium doped fiber, SM: single mode non-polarization maintaining, PM: polarization maintaining, BPF: band-pass filter, SM pump: single-mode fiber pigtailed pump diode at 975 nm.

Experimental results
The goal of the experiment is to prove the predictions of the simulations and to verify the general design guidelines of section 2. To obtain a clean compressed pulse at the output of the PCMA, we follow the guideline of simulation and set the grating compressor in such a way that the pre-chirp corresponds to a GDD of −0.144 ps 2 .By turning the input power to the level of 26 mW, PCMA works on saturated state and deliver a total output power of 820 mW.This corresponds to a pulse energy of 12 nJ.The compressor's perpendicular grating separation and efficiency are ~7 mm and 89% respectively.Behind the compressor, the average power is 734 mW.Thus, the energy of the compressed pulses is above 10 nJ.The autocorrelation trace of compressed pulse and the transfer limit pulse from PCMA output are shown in Fig. 6, which corresponds to a high quality pulse with duration of 63 fs.This is in good agreement with the simulation (note the same input and output power as well as GDD; however, 10 nm super Gaussian input spectrum, which is close to the experimentally observed spectral shape).Control of the spectral evolution through the amplifier is key to accomplish best system performance.Specifically, it enables the generation of smooth output spectrum of common shape.Figure 7 shows the spectral evolution through the amplifier chain (corresponding to the output pulse that is shown in Fig. 6).The oscillator is mode-locked at close-zero-dispersion region, which facilitates the generation of a broad output spectrum, as shown in Fig. 7(a).Also, in this case, the oscillator should exhibit low timing jitter noise [20].However, such broadband spectrum will undergo strong gain narrowing during amplification and the spectrum edge will accumulate nonlinear phase that is not compressible.To enhance the compression, a band-pass filter with bandwidth of 20 nm is inserted between the oscillator and the first amplifier.The first amplifier following the oscillator is a "mini" CPA system.The input and output spectrum of the 1 st amplifier show similar shapes, as shown in Fig. 7(b) and (c).The gain of the Yb-doped fiber shows a limited bandwidth and a certain gain-peak location (depending on the actual inversion level).Thus, some narrowing of the spectrum is visible.Another band-pass filter is inserted between the first amp and the second amplifier to further reduce the spectrum's bandwidth to 10 nm.This removes the un-compressible phase due to SPM and/or the limited gain of the first amplifier.Furthermore, it produces a clean spectrum with close to parabolic shape at the input of PCMA system.By tuning the angle of the second band-pass filter, we can match input spectrum's center to the gain center of the second amplifier.Note, simulations have shown that the bandwidth of the spectrum at the input of the PCMA does not have a strong impact on the generation of output pulses with sub-100 fs durations.In principle, filters with narrower pass-band could be used.However, in this case, further adjustments may be needed to obtain the best operation point of the PCMA.As shown in Fig. 4, the experimental spectrum is in excellent agreement with the prediction,.Note, the spectrum is smoother as compared to other PCMA systems [16].
We have also characterized the intensity noise level in the frequency range 10 Hz to 20 MHz of the output power after the oscillator, the 1 st amp and the 2 nd amplifier (using photodetector Thorlabs DET36A).The noise spectrum and the accumulated noise are displayed in Fig. 8.It can be seen that the integrated noise level reduces in every stage.This is in good agreement with the fact that the amplifiers are saturated.The lifetime of Ytterbium is about 1 ms, suppressing noise frequencies > 1 kHz.The low intensity noise from the output of the first amplifier ensures good performance of the overall system.

Conclusion
In conclusion, we have presented design strategies for a PCMA configuration that is solely based on core-pumped PM single-mode fibers.Based on these findings, we have designed and demonstrated a PCMA system that produces <100 fs output pulses even for B-integrals above 45 rad.Furthermore, in this proof-of-concept demonstration, we accomplished integrated RIN noise as low as 0.008%.We reveal that the pulses in the PCMA amplifier show a parabolic shape before final compression which can be regarded as the main reason for good compression even for large B-integrals.The compressed output pulses exhibit nearperfect transform-limited quality (with Strehl-ratios >0.9).Robustness of the PCMA configuration is ensured by a 2-stage configuration in which each PM-fiber amplifier is operated in saturation and for which the pre-chirp element in form of a grating compressor is sandwiched between the two fiber amplifiers.Placing a stretching fiber before the first amplifier enables fine-tuning of the pre-chirp from negative to positive for the final PCMA amplifier.Note, we have shown simulation and experimental demonstration for 3 m of gain fiber.However, in other experiments, not shown, we found that the scheme also works with only 0.6 m of highly doped PM gain fiber.
We reveal that the output pulse characteristics of the PCMA remain constant (after adjusting the final compressor) even for +/− 30% variations of the power at the PCMA's input while the corresponding B-integrals change by approximately 20%.This makes it particular appealing for applications where long-term operation is required: a degradation of pump diodes (or other system components) can be easily accommodated by adjusting the final compressor.The proposed configuration may be also of interest for ultra-short pulse applications that depend on the output pulse's duration: a fast variation of the first amplifier's pump current causes a direct variation of the output pulse duration.
There is a distinct feature of the demonstrated PCMA configuration: By tailoring the evolution of the spectra in the amplifier chain using band-pass filters, we can reduce the effect of the oscillator and the first amplifier on the output spectrum.Thus, it can be easily used with many types of seed fiber oscillators showing different output spectra.Despite (or perhaps because of) the underlying nonlinear principle, the resulting output spectra should remain the same and smooth.We think that these advantageous features will render the PCMA configuration as a simple and robust add-on to a variety of existing fiber oscillators while maintaining the advantages of the robustness of the PM fiber format.The PCMA's s output parameters make it very suitable for a variety of ultrashort pulse applications.For instance, the broad (~30 nm) output spectra can seed a variety of solid-state Ytterbium-doped booster materials such as Yb:YLF, Yb:YAG or Yb:KYW.The MOPA configuration is also ideally suited for the insertion of low-damage threshold components -such as fiber-coupled optical modulators -after the master oscillator.This permits production of versatile laser sources.Future efforts will be concerned with replacing the band-pass filters and grating compressors by chirped fiber Bragg gratings enabling a fully fiber-integrated and compact solution using PM fibers.

Fig. 1 .
Fig. 1.Simulation: (a) Output pulse quality and (b) pulse peak-power as a function of the prechirp's GDD and the input power of the PCMA configuration.

Fig. 2 .
Fig. 2. Simulation of (a) output peak-power and Strehl-ratio (b) output pulse duration and compressor grating separation, and (c) output power and B-integral as a function of input power at fixed pre-chirp and adapted compression at output.

Fig. 3 .
Fig. 3. Simulation of (a) output peak-power and Strehl-ratio, and (b) output pulse duration and compressor grating separation as a function of the input power at fixed pre-chirp as well as constant compression at output (optimized for input power of 26 mW)

Fig. 4 .
Fig. 4. (a) Simulation of input and output pulse (uncompressed), (b) simulation of input and output spectrum, (c) simulation of the best compressed pulse at the output and the corresponding transfer limited pulse for the PCMA configuration of pre-chirp's GDD of −1.44 × 10 5 fs 2 and input power of 22 mW

Fig. 7 .
Fig. 7. Spectra of the pulse: (a) at the output of the oscillator, (b) after passage through BPF1, (c) after the first fiber-amplifier, (d) after passage through BPF2, (e) after the second fiberamplifier.

Fig. 8 .
Fig. 8. Noise spectra (y-axis on left) and integrated RIN (y-axis on right) after the oscillator (blue), after the first amplifier (red), after the second amplifier (yellow).