high ﬁdelity femtosecond pulses from an ultrafast ﬁber ... · k.ohno,t.tanabe,andf.kannari,...

High fidelity femtosecond pulses from anultrafast fiber laser system via adaptive

amplitude and phase pre-shaping

Jerry Prawiharjo, Nikita K. Daga, Rui Geng, Jonathan H.V. Price,David C. Hanna, David J. Richardson, and David P. Shepherd

Optoelectronics Research Centre, University of Southampton, Southampton SO17 1BJ, UK

[email protected]

Abstract: The generation of high-fidelity femtosecond pulses is experi-mentally demonstrated in a fiber based chirped-pulse amplification (CPA)system through an adaptive amplitude and phase pre-shaping technique. Apulse shaper, based on a dual-layer liquid crystal spatial light modulator(LC-SLM), was implemented in the fiber CPA system for amplitude andphase shaping prior to amplification. The LC-SLM was controlled usinga differential evolution algorithm, to maximize a two-photon absorptiondetector signal from the compressed fiber CPA output pulses. It is shownthat this approach compensates for both accumulated phase from materialdispersion and nonlinear phase modulation. A train of pulses was producedwith an average power of 12.6 W at a 50 MHz repetition rate from ourfiber CPA system, which were compressible to high fidelity pulses with aduration of 170 fs.

© 2008 Optical Society of America

OCIS codes: (060.2320) Fiber optics amplifiers and oscillators; (060.4370) Nonlinear optics,fibers; (320.5540) Pulse shaping; (320.7090) Ultrafast lasers.

References and links1. J. Limpert, F. Röser, T. Schreiber, and A. Tünnermann, “High-power ultrafast fiber laser systems,” IEEE J. of

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1. Introduction

Rare-earth doped fiber laser systems are a promising alternative to bulk ultrafast laser systems[1], whose power scaling is not straightforward due to their generally low single-pass gain,coupled with thermo-optical issues. Ytterbium-doped fibers are particularly interesting due totheir broad emission spectrum, allowing the generation and amplification of ultrashort opti-cal pulses, although the gain medium does not support the generation of pulses as short ascan be obtained with Ti:sapphire. The fiber geometry offers good thermo-optical properties, ahigh single-pass gain, excellent output beam quality, and coupled with continuous-wave diodepumping, has allowed the realization of compact ultrafast laser systems with more than 100 Waverage power at various repetition rates [2, 3]. Energy levels reaching the millijoule regimehave also recently been demonstrated, thanks to the utilization of novel fiber designs, such asphotonic crystal-fiber (PCF) [4].

The chirped-pulse amplification (CPA) technique is the preferred way to achieve high peak-power ultrashort pulses in ultrafast laser systems [5]. However, a multitude of factors can de-grade the pulse quality, such as uncompensated material dispersion, nonlinearity, and a non-uniform spectral gain profile with finite width. The pulse quality degradation is most notablymanifested in the presence of a pedestal, which limits the maximum peak intensity of the pulsesthat can be achieved [6]. Two factors leading to pulse degradation are uncompensated higher-order spectral phase between stretcher, compressor, and amplifier materials, and self-phase-modulation (SPM), which leads to a nonlinear spectral phase [7].

In ultrafast bulk solid-state laser systems, a great deal of effort has been spent to design ap-propriate stretcher and compressor pairs to minimize the uncompensated higher-order spectralphase [8]. However, this approach requires careful characterization and design of the system.Furthermore, it is non-adjustable and thus prevents easy reconfiguration of the system. Ulti-mately, programmable femtosecond pulse shaping [9] offers the possibility of almost arbitrarymodifications of the phase and amplitude of ultrashort optical pulses, and thus eliminate theneed for meticulous characterization and design of the entire system. In particular, in combina-tion with adaptive learning loop utilizing optimization algorithms, i.e. adaptive pulse shaping,it has allowed for the generation of high-fidelity pulses [10, 11, 12, 13, 14]. This approach alsoallows for the generation of arbitrary pulse shapes, using either phase-only modulation [15], orphase and amplitude modulation [16]. Nevertheless, femtosecond pulse shaping typically suf-fers from low throughput, associated with various losses in the setup, and usually a low damagethreshold from the programmable modulator, e.g. a pixelated liquid crystal array. In order tocircumvent this problem, the pulse shaper has to be incorporated into the system before anyhigh power amplification stages. In Ti:sapphire laser systems, a phase-only pulse shaping setuphas been successfully incorporated as part of the stretcher with [17, 18, 19], or without [20],global optimization algorithms to minimize the pulse duration at the output. The generation ofarbitrary shaped pulses has also been demonstrated using amplitude and phase shaping and aglobal optimization algorithm [21].

In ultrafast fiber laser systems, material dispersion, nonlinearity, and a non-uniform spectral


gain profile with finite width, are critical considerations, because of the optical confinementand long interaction length in the fiber geometry. As temporal stretching is physically limitedby the finite size of the grating compressor, while the scaling of large-mode-area (LMA) fiberswill eventually undermine the advantages of fiber geometry, most of the work has concentratedat managing the SPM, by compensation of the nonlinear phase induced by SPM via the third-order material dispersion [22, 23, 24, 25], or utilization of the interplay between the SPM-induced spectral broadening and gain shaping [26, 27]. These approaches, however, cannotfully compensate the nonlinear phase-modulation due to the SPM, and require careful designof the laser system. Recently, another method was proposed to actively compensate for theSPM using phase modulation of the stretched pulses [28, 29], but the phase modulator can onlyimpose a limited amount of phase shift and is limited in terms of complexity of phase profilethat can be applied. Finally, the effects of the non-uniform spectral gain profile with finitewidth also becomes more prominent, further degrading the pulse quality. In fiber CPA systems,multiple amplifier stages are usually necessary to achieve the desired power level. Hence, fiberCPA systems present more technical challenges in producing high-fidelity pulses.

In view of the work in ultrafast bulk solid-state laser systems, adaptive pulse shaping priorto amplification has been adopted in fiber CPA laser systems with some success. Recently,amplitude-only shaping has been demonstrated to control the nonlinear-phase modulation in-duced by SPM at low energy [30], but it cannot compensate for higher-order spectral phase dueto the material dispersion. Our group recently demonstrated a phase-only shaping in a high-energy fiber laser system [31].

In this paper, we demonstrate, for the first time to our knowledge, the implementation ofadaptive amplitude and phase pre-shaping in a fiber-based CPA system to generate high-fidelitycompressed femtosecond pulses. A pulse shaper based on a dual-layer liquid crystal spatial lightmodulator (LC-SLM) was implemented in our fiber CPA system for amplitude and phase shap-ing prior to amplification. The LC-SLM is compatible with pulses at any repetition rate, makingit the preferred choice for our experiments, and contrasts with a recent post-amplification shap-ing work utilizing dazzler with limited repetition rate and output efficiency [32]. The LC-SLMwas controlled using a differential evolution (DE) algorithm, to maximize a two-photon absorp-tion detector signal produced from the compressed fiber CPA output pulses. We show that ourapproach compensates for both accumulated phase from higher-order material dispersion andnonlinear phase modulation. A train of pulses with an average power of 12.6 W at a 50 MHzrepetition rate was produced from the fiber CPA system, compressible to high fidelity pulseswith a 170 fs temporal full-width at half-maximum (FWHM).

This paper is organized as follows. The fiber CPA experimental setup and the implementationof the adaptive loop pulse shaping are described in Section 2. The experimental results arepresented and discussed in Section 3. Finally, we conclude the paper in Section 4.

2. Experimental Setup

2.1. Ultrafast fiber laser system

The experimental setup is schematically illustrated in Fig. 1. The seed source was a passivelymode-locked Yb-doped fiber oscillator [33], operated in the self-similar regime [34]. The laserproduced a train of chirped pulses with a duration of 2 ps at a 50 MHz repetition rate, and a16 nm spectral FWHM at a 1042 nm central wavelength. The spectrum of the pulse train hada sharp truncation at the edges, a signature of the self-similar regime, with a 20 dB spectralwidth of 23 nm. The oscillator produced an average power of 30 mW, corresponding to a pulseenergy of 0.6 nJ. Using a fiber coupler, part of the output power was routed for this experiment,such that 2 mW of average power was launched into a pre-amplifier, while the rest was usedfor another experiment. A 1.7 m long single-mode (SM) core-pumped Yb-doped fiber was used


Pump

FR

Pump

Yb-doped PCF

SM Yb-doped

PumpSM Yb-doped

Self-SimilarOscillator Coupler WDM

WDM

HWP

QWP

SLM

G1

Dichroic mirror

PBSOI Pulse shaper

DE

APP

CM

G2

Compressor

G2 TPA

SHG FROG

Wedge Flip mirror

T

Fig. 1. Schematic illustration of the ultrafast fiber laser system. HWP: Half-wave plate,QWP: Quarter-wave plate, OI: Optical isolator, WDM: Wavelength division multiplexer,SM: Single-mode, PBS: Polarizing beam splitter, FR: Faraday rotator, APP: Anamorphicprism pair, G: Gratings, CM: Cylindrical mirror, SLM: Spatial light modulator, PCF: Pho-tonic crystal fiber, T: Telescope arrangement, TPA: Two-photon absorption detector, SHGFROG: Second-harmonic generation frequency-resolved optical gating, DE: Differentialevolution algorithm on a computer.

in the first pre-amplifier to boost the average power of the seed pulses to 80 mW. The pulseswere then sent into a pulse shaper [9], which will be explained in detail later, via a free-spaceoptical circulator. The pulse shaper had a throughput efficiency of 40%, resulting in an averagepower of 30 mW launched into the next pre-amplifier. The second pre-amplifier, comprised of a1.5 m long SM core-pumped Yb-doped fiber, further amplifying the pulses to an average powerof 150 mW. Both of the pre-amplifiers were pumped by SM fiber-coupled diodes at 976 nmin a co-propagating scheme, using wavelength division multiplexers to combine both the seedand pump into the amplifier fibers. The fiber ends were cleaved at an angle to avoid parasiticlasing, and optical isolators were placed at appropriate places to prevent any back-propagationthrough the system. The pulses were then routed by dichroic mirrors before being launched intothe final amplifier. A 1.7 m long double-clad LMA polarization-maintaining (PM) Yb-dopedphotonic-crystal fiber (Crystal-Fibre DC-200/40-PZ-Yb-01), with an active core diameter of40 μm (NA = 0.03) and an inner cladding diameter of 200 μm (NA = 0.55), was used for thisfinal amplifier. The Yb-doped PCF had 10 dB/m absorption at 976 nm for light launched intothe cladding, and was pumped by a multi-mode fiber-coupled diode generating up to 30 Wpower at 976 nm in a counter-propagating scheme. The input facet of the PCF was hermeticallysealed, while the output facet was spliced to a very short length of coreless fiber in order toreduce the intensity at the facet. Both ends were polished at 5◦ angle to avoid parasitic lasing.At the output of the power amplifier, the beam was passed through a telescope arrangement tocollimate the diverging beam and passed through an optical isolator. The train of pulses, at thispoint, had a maximum average power of 12.6 W, corresponding to a pulse energy of 252 nJ.Finally, a fraction of the output, taken from the Fresnel reflection of a wedge, was compressedusing a pair of gold-coated 900 lines/mm holographic gratings. A home-built second-harmonicgeneration (SHG) FROG, utilizing a 300 μm thick β -barium borate crystal and a spectrometer,


was employed to characterize the pulses. In addition, the pulse spectra at various points inthe fibre CPA system were measured using an optical spectrum analyzer with a resolution of0.1nm.

The pulse shaper consisted of a 4 f setup [9] arranged in a reflective configuration. The colli-mated output from the first pre-amplifier had a 0.9 mm 1/e 2 intensity half-width, which was ex-panded three-times by an anamorphic prism pair, before being sent into the pulse shaper setup.In the pulse shaper, the beam had its spectral components spatially dispersed by a 1200 gr/mmgold-coated plane-ruled grating, which were then focussed onto the Fourier plane by a 25.8 cmfocal length cylindrical mirror. The grating was operated at a quasi-Littrow condition with avertical tilt such that the beam was steered to another horizontal plane, where the cylindri-cal mirror lies [35]. A dual-layer LC-SLM (CRi SLM-128) was placed at the Fourier plane,allowing for the modulation of both the phase and amplitude of the spectral components ofthe pulses. However, since the two LC layers in the SLM have slightly different thicknesses,they do not yield the same phase retardance for the same voltage applied, making it difficultto impart phase-only or amplitude-only shaping. Both layers of the LC-SLM had N s = 128pixels, spanning 13.1 mm. The 23 nm 20 dB-spectral-width of the pulse occupied 97 pixels onthe SLM, and the spectrum at the Fourier plane varied linearly with wavelength at a rate of0.23 nm/pixel. The calculated time window for the pulse shaper optical setup (excluding theSLM) was 23.9 ps with a complexity of 346 [9]. No attempt was made to operate the pulseshaper at precisely zero-dispersion, because any small offset should be accounted for by theadaptive shaping method. An adaptive loop to control the phase and amplitude modulation ap-plied by the LC-SLM to the pulse train was implemented to maximize the signal from a GaAsPTPA detector, which is essentially ∝

∫I2(t)dt, where I(t) is the pulse intensity, using a global

optimization algorithm, which will be explained in more detail in the next section.

2.2. Adaptive loop

0 32 64 96 128500

1000

1500

2000

2500

3000

3500

4000

4500

SLM pixels

Vol

tage

dig

ital s

igna

l

M0

M1

Fig. 2. Illustration of the applied voltage on the two layers of the LC-SLM, M0 and M1,as interpolated from the pixels controlled by the adaptive algorithm, indicated by the opencircles.

Each pixel of the dual-layer LC-SLM was driven by up to 10 V electrical voltage with a212 level of digitization, but with a usable level between 600 and 4095, due to the nonlinearmapping between voltage and phase. Direct pixel-by-pixel optimization using global optimiza-tion algorithms would be too large a space to be efficiently searched. Many previous works,therefore, parameterized the search space using a truncated Taylor series [17, 18, 19, 31]. Inthis experiment, we instead optimized Nc pixels of the SLM, where Nc ≤ Ns, which were then


interpolated onto Ns pixels using the piecewise cubic interpolation method, as illustrated inFig. 2. During the optimization, the Nc controlled pixels can be gradually increased [14]. Sinceeach layer was controlled independently in the optimization procedure, there is no distinctionbetween the phase and amplitude shaping.

We argue that this approach has advantages over parametrization with a truncated Taylorseries. Firstly, in terms of optimization, changing the value of a parameter in a Taylor serieswould completely change the entire profile, while in the case of interpolation, the change wouldbe local. Secondly, in practice, the continuous profile inferred from the Taylor series does notnecessarily correspond to the one applied to the SLM, due to the SLM spatial pixellization anddriving voltage discretization. Finally, while it is easy to individually calculate the boundariesthat must be placed on each Taylor series coefficient due to the physical limitations impartedby the pixellization of the SLM, it is not easy to calculate such limits when many coefficientsneed to be applied simultaneously.

The problem was formulated as max{ f (X)|X}, where X is an integer vector of 1× 2N cparameters, bounded between 600 and 4096, i.e. each of its component X j ∈ [600,4096], wherej = 1, . . . ,2Nc, and f (X) is the evaluated TPA detector signal from the applied voltage. Notethat X is a concatenation of the Nc pixel voltages from the two layers of the LC-SLM. TheDE algorithm [36] was implemented as our global optimization algorithm in Matlab, whichwas also used to control the SLM, and to read the TPA detector signal. The DE algorithm waschosen, because it has been shown to consistently outperform simulated annealing or geneticalgorithms in most cases [36, 37], which we have confirmed both in many simulations andexperiments.

The DE algorithm that was applied to solve this maximization problem can be summarized asfollows. At each generation g, a population of N p candidate solutions are maintained, denotedas Xi,g, i = 1, . . . ,Np. The initial population consists of random integer vectors, which wouldthen undergo mutation, crossover, and selection to form the next generation. The mutationoperator that we implemented used a combination of dither and trigonometric operators [38].During mutation, three randomly selected individuals from the population, X r1 ,Xr2 ,Xr3 , wherer1,r2,r3 ∈ [1,Np], are used to generate the ith mutated individual Vi,g+1, with a condition r1 �=r2 �= r3 �= i, according to the following rule:

Vi,g+1 =

⎧⎪⎨

⎪⎩

Xr1,g +[F +(1−F)ug](Xr2,g −Xr3,g

)if u′g > 0.04,

(Xr1,g +Xr2,g +Xr3,g)/3+(p1− p2)(Xr1,g −Xr2,g)+ (p2− p3)

(Xr2,g −Xr3,g

)+(p3− p1)

(Xr3,g −Xr1,g

)otherwise,

(1)

where

p1 =∣∣ f (Xr1,g)

∣∣/p′, p2 =

∣∣ f (Xr2,g)

∣∣/p′, p3 =

∣∣ f

(Xr3,g

)∣∣/p′, (2)

andp′ =

∣∣ f (Xr1,g)

∣∣+

∣∣ f (Xr2,g)

∣∣+

∣∣ f

(Xr3,g

)∣∣ . (3)

In the above equations, ug,u′g ∈ [0,1] are uniformly distributed real random numbers, drawnevery generation, and F is called the scaling factor, which is a control parameter of the DEalgorithm.

The mutated individual Vi,g+1 may not be a vector of integers, in which case its componentswill be converted to integers, before being subjected to a crossover operation with the currentpopulation member Xi,g to form candidates for the next generation population. The crossoveroperator works on a component by component basis, as follows:

Wj,i,g+1 =

{Vj,i,g+1 if u ≤Cr ∨ j = w,Xj,i,g otherwise,

(4)


where w ∈ [1,Np] is a random uniformly distributed integer, and Cr ∈ [0,1] is called thecrossover rate, another control parameter of the DE algorithm. If W j,i,g+1 goes beyond theboundary, then a random integer will be drawn between the X j,i,g and the boundary. Finally,the members of the next generation population are selected from the current generation andthe candidate individuals of the next generation in order to maximize f (X), according to thefollowing rule:

Xi,g+1 =

{Wi,g+1 if f (Wi,g+1) ≥ f (Xi,g),Xi,g otherwise.

(5)

In all of our experiments, we chose F = 0.75, Cr = 0.5, and Np = 30. In our experiments, theoptimization took an average of 0.145minutes per generation, which was mostly spent updatingthe SLM, integrating the detector signal, and on electronic communication with the instruments.Therefore, we did not implement a stopping condition based on convergence criteria, but, in-stead, we ran the DE algorithm for a specific number of generations. In each optimization, wemonitored the diversity among the individuals in the population to check for the convergence.

3. Results and discussions

1025 1030 1035 1040 1045 1050 1055Wavelength (nm)

Inte

nsity

(a.u

.)

Oscillator

Pre-amp 1

Pre-amp 2

Inte

nsity

(10

dB/d

iv)

Oscillator

Pre-amp 1

Pre-amp 2

1025 1030 1035 1040 1045 1050 1055Wavelength (nm)

(a) (b)

Fig. 3. Normalized measured spectra at the output of the oscillator, after the first pre-amplifier and the pulse shaper, and after the second pre-amplifier in logarithmic (a) andlinear (b) scale.

Figure 3 shows typical measured spectra at the output of the oscillator, after the first pre-amplifier and the pulse shaper, and after the second pre-amplifier. It is worth noting, at thispoint, that the fringes that appear on the oscillator spectrum, are possibly due to the etaloneffect. The fringes grow in subsequent amplifier stages, owing to the SPM [39]. These fringescould not be eliminated experimentally. The effect of the non-uniform spectral gain profile withfinite width is evident, as the spectral FWHM of the pulse was reduced from 16 nm at the outputof oscillator, to 12 nm after the first pre-amplifier, and to 11 nm after the second-preamplifier.Nevertheless, the 20 dB spectral width of 23 nm was maintained.

Firstly, the pulses from the compressor were characterized without intentional shaping bythe pulse shaper (by not applying any voltage to the SLM). The final amplifier was pumpedto produce a train of pulses with an average power of 2.3 W prior to the compressor, and thenthe separation of the grating pair in the compressor was adjusted to maximize the intensityof the TPA detector, and the second harmonic signal from the SHG FROG setup when thepulses from both arms were temporally overlapped. This resulted in a grating separation of10.2 cm. The output pulses were then characterized at two power levels using the SHG FROG;


Delay (ps)

Freq

uenc

y de

tuni

ng (T

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elay (ps)

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nsity

(a.u

.)In

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ity (a

.u.)

-9

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Inst. Freq. (THz)


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elay (ps)

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nsity

(a.u

.)In

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ity (a

.u.)

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Inst. Freq. (THz)

Delay (ps)

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uenc

y de

tuni

ng (T

Hz)

−3 0 3−8

0

8(a)

(c)

(e)

(b)

(d)

(f)

Fig. 4. (a,b) Contour plot of square-root of measured SHG FROG traces, after interpola-tion onto a 128× 128 Fourier grid, of the pulses after the compressor without intentionalshaping. The contour lines represent levels [0.02,0.06,0.1,0.2,. . . ,1]. (c,d) Retrieved spec-tral intensity (blue curves), spectral group delay (green curves), and measured spectra (redcurves). (e,f) Retrieved temporal intensity (blue curves) and instantaneous frequency (greencurves). The figures correspond to measured average powers of 2.3 W (a,c,e) and 12.6 W(b,d,f) prior to the compressor.


at 2.3 W and at 12.6 W average power, without changing the grating separation. We shall referto these as the low and high average power, respectively, throughout the remainder of this paper.Figure 4(a) and (b) show the square-root of the measured SHG FROG traces, after interpola-tion onto a 128× 128 Fourier grid, for both cases. Plotting the square root of the FROG tracewas aimed at emphasizing the detail at low intensity. The spectral and the temporal intensitywere then retrieved, as well as the group delay [dφ(ω)/dω] and the instantaneous frequency[−1/(2π)×dϕ(t)/dt], from these traces, as shown in Fig. 4(c) to (f). The root-mean-square(rms) retrieval errors of these traces were less than 8×10−3. The excellent agreement betweenthe retrieved and measured spectra, in Fig. 4(c) and (d), demonstrates the quality of the home-built SHG FROG.

The mainly parabolic profile of group delays shown in Fig. 4(c) and (d), and the side-lobes inthe temporal intensity profiles shown in Fig. 4(e) and (f), are a strong indication that the domi-nant effect on the output pulses of the CPA system was the accumulated third-order dispersion(TOD). These results are expected, since there was no compensation element for the TODplaced in our system. In addition, the departure of the group delay profiles from parabolic atboth low and high average power levels [Fig. 4(c,d)] suggests the presence of nonlinear phase-modulation, whose amount increases with power level, as signified by the spectral broadeningthat accompanied the increase in the average power. This increase in accumulated nonlinearphase modulation causes the side-lobes of the temporal profile in the high power case to notdecrease monotonically, as seen in Fig. 4(f).

The accumulated nonlinear-phase modulation evident in the above characterization is ex-pected, since there was no specific stretching of the pulses prior to amplification in our fiberCPA system. The estimated upper limit of the accumulated nonlinear phase was φ NL = π radat low power, and φNL = 1.6π rad at high power, of which the contribution prior to the pulseshaper was 0.7π rad. In this calculation, an exponential amplification with a constant gain perunit length with flat spectral gain profile in the fiber amplifiers was assumed. The accumulatednonlinear phase, coupled with non-uniform spectral gain profile, caused the large change inspectral intensity after the different amplifier stages. It is worth noting that we observed nonlin-ear polarization rotation (NPR) in both of our pre-amplifiers. Due to the NPR, environmentalchanges, particularly of temperature, induce small fluctuations in the output of our system, ex-plaining the discrepancy between the measured spectra after the pulse shaper and the secondpre-amplifier in Fig. 7 and 10. However, this fluctuation is a very slow process that happens ona day-to-day timescale, and thus did not affect our experiments.

Having characterized the pulses without intentional shaping, the optimization was then per-formed using the DE algorithm, as described in the previous section, initially at low averagepower. For this experiment, every 8th pixels of the SLM was controlled from pixel number 16to 112, corresponding to where the spectrum of the pulses was located on the SLM. In addition,pixels number 12 and 116 were also controlled to avoid overshoots at the edges of the pulsespectrum after interpolation. Thus, a total of Nc = 15 pixels were controlled on each layer ofthe SLM. The optimization algorithm was run for 350 generations, which took 51 minutes tocomplete.

Figure 5 shows the evolution of the TPA detector signal, normalized to the case without inten-tional shaping, evaluated from the applied SLM voltages of the best individual in the populationat each generation. Note that since the algorithm was run from a random initial condition, thebest individuals at the early stages of the optimization had lower TPA detector signal than thecase without intentional shaping. After 350 generations, there was not much diversity amongindividuals in the population, indicating that the algorithm had converged to a solution, and theTPA signal was improved by a factor of 4.2. The mask corresponding to the best individualin the population was then applied to the SLM, and the pulses were then characterized using


1 50 100 150 200 250 300 350 400 4500

1

2

3

4

Generations

Rela

tive

TPA

Inte

nsity

Nc=15

Nc=27

Nc=51

Nc=15

Fig. 5. Two-photon absorption detector signal, normalized to the case of without inten-tional shaping, and evaluated from the best individual in the population as a function ofgeneration, for average power of 2.3 W (blue dots) and 12.6 W (red dots). For the low av-erage power case, a constant number of controlled pixels, Nc = 15, was used throughoutthe optimization. For the high average power case, the number of controlled pixels Nc wereincreased from 15 to 51 during the optimization, at positions indicated by the arrows (seetext).

Delay (ps)

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.)

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elay (ps)

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Time (ps)

−10

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Inst. Freq. (THz)

Inte

nsity

(10d

B/di

v)

(a)

(b) (c)

Fig. 6. (a) Contour plot of square-root of measured SHG FROG trace, after interpolationonto a 128×128 Fourier grid, of the compressed low average power pulses, after the max-imization of the TPA signal by controlling every 8th pixels of the SLM (see text). The con-tour lines represent levels [0.02,0.06,0.1,0.2,. . . ,1]. (b) Retrieved spectral intensity (bluecurve), spectral group delay (green curve), and measured spectrum (red curve). (c) Re-trieved temporal intensity (blue curve) and instantaneous frequency (green curve), as wellas the calculated transform-limited intensity profile (red curve).


1025 1030 1035 1040 1045 1050 1055

Inte

nsity

(a.u

.)

Wavelength (nm)

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Post compressor

Transmission

0

1

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−1

0

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2

3

Gro

up d

elay

(ps)

(a)

(b)

Fig. 7. (a) Calculated applied group delay (blue curve) for the low average power pulsesoverlayed with the negative of the retrieved group delay for the case without intentionalshaping [Fig. 4(c)]. The measured shaped spectrum after the shaper (shaded grey) is shownfor reference. (b) Calculated transmission (black curve) of the SLM after maximizing theTPA detector signal. Normalized measured spectra before (shaded) and after (curves) opti-mization after the pulse shaper, after the second pre-amplifier, and after the compressor areshown, as indicated by the labels.

the SHG FROG. Figure 6(a) shows square-root of the measured FROG trace, after interpola-tion onto a 128×128 Fourier grid. The retrieved spectral intensity and group delay are shownin Fig. 6(b), while the temporal intensity and instantaneous frequency are shown in Fig. 6(c).The rms retrieval error was less than 2× 10−3, and the temporal FWHM of the retrieved in-tensity is 195 fs. The calculated Fourier transform-limited profile is also shown in Fig. 6(c).The excellent agreement between the retrieved and calculated transform-limited profiles downto the -20 dB level, highlights the success of the optimization algorithm. The measured spectraat various points in our system are shown in Fig. 7, before and after optimization, as well asthe calculated transmission and group delay applied by the SLM. The optimization yielded aspectral broadening toward shorter wavelengths after the second pre-amplifier, as well as in thefinal spectrum.

The system was then operated at its highest power, generating 12.6 W average power prior tothe compressor, without changing the grating pair separation. The optimization algorithm wasrun with the same parameters as in the previous case for 350 generations, and the pulses werethen characterized. Figure 8 shows the measured SHG FROG trace and the retrieved tempo-


Delay (ps)

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Fig. 8. Same as Fig. 6, but for high average power, after the maximization of the TPA signalby controlling every 8th pixels of the SLM (see text). Note that the temporal intensity in (c)is shown in linear scale.

ral and spectral data. The rms retrieval error was less than 4× 10−3. The temporal FWHM ofthe retrieved profile is 200 fs. It can be easily seen from Fig. 8(c) that the pulses exhibit somepedestal on their trailing edge. Furthermore, the pulse has a lower intensity and a longer dura-tion compared to the calculated Fourier transform-limited profile. In an attempt to improve thetemporal intensity profile and to reach the Fourier transform-limit, the optimization algorithmwas extended to 450 generations and the control parameters of the optimization algorithm (Fand Cr) were varied, but this was not successful. Therefore, this inability to fully compress thepulse did not stem from shortcomings of the optimization algorithm.

Finer control over the pulse shaping was then attempted by increasing the number of con-trolled pixels, from every 8th pixel, to every 4th pixel at generation 51, and finally to every2nd pixel at generation 101, between pixels 16 to 112 of the SLM. In addition, pixels number12 and 116 were still controlled, resulting in a final total of Nc = 51 controlled pixels on eachlayer of the SLM. The DE algorithm was run with this condition for 450 generations, taking65 minutes to complete. The evolution of the TPA signal evaluated from the best individual inthe population, normalized to the case without intentional shaping, at each generation is shownin Fig. 5 (red dots).

After the optimization, there was little diversity among the members of the population, andthe TPA signal was improved by a factor of 4.3. As in previous experiments, the pulses re-sulting from the optimization were characterized by the SHG FROG as shown in Fig. 9. Therms retrieval error was less than 1.5× 10−2, which was mainly due to the large area the traceoccupies on the Fourier grid. The temporal FWHM of the retrieved profile is 170 fs. Althoughthe square-root of the measured SHG FROG trace exhibits wings that extend up to 2 ps de-lay, they have very low intensity, below 0.5%, and most of the trace mass is concentrated at


Inst. Freq. (THz)

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20


Inte

nsity

(a.u

.)

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0

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Group D

elay (ps)

(a)

(b) (c)

Fig. 9. Same as Fig. 6, but for high average power, after the maximization of the TPA signalwith increasing numbers controlled pixels of the SLM (see text).

the center, unlike the case of Fig. 8(a), for which case only every 8 th pixel was controlled bythe DE algorithm. Therefore, the temporal profile shows a high quality pulse with the mainpulse having an excellent agreement with the calculated Fourier transform-limited profile. Thepedestal of the retrieved temporal intensity is less than -20 dB everywhere, except for the smallsatellite pulse at t −1.5 ps. The measured spectra at various points in our system are shownin Fig. 10, before and after the optimization, as well as the calculated transmission and groupdelay applied by the SLM. As in the lower average power case, the optimization also yieldeda spectral broadening toward shorter wavelength after the second pre-amplifier and in the finalspectrum. In contrast to the low average power case, the use of more control points causes thethe pulse spectra to exhibit more oscillations after the nonlinear propagation through the secondpre-amplifier and the final amplifier.

Although the DE algorithm started with random initial candidate solutions, the optimizationresults had a high reproducibility. The resulting applied phase and transmission profiles showedlittle dependence on the initial condition, yielding similar compressed pulse profiles in eachcase, which implies that our results have to be in the vicinity of the global optimum. In fact,there is a consistency in the optimized spectra after the shaper in both low and high powercases, as shown in Fig. 7 and 10, i.e. suppression of the part of the pulse spectra between 1035and 1040 nm. In order to obtain the true global optimum, more generations would be required,but with diminishing returns that may not justify the effort. It is important to note that it is notnecessary to start from random initial candidate solutions. It is possible to feed a previouslyoptimized data as one of the initial candidate solutions in order to reduce the optimization time.

In interpreting the results of our experiments, it is worth remembering that the pulses wereamplified in three stages, using two different fibers having their own gain profile, nonlinearity,


1025 1030 1035 1040 1045 1050 1055Wavelength (nm)

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up d

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(a)

(b)

Fig. 10. Same as Fig. 7, but for the case of high average power, after the maximization ofthe TPA signal with increasing controlled pixels of the SLM [Fig. 9].

and dispersion. We believe that this is the main reason that the optimization did not yield groupdelays that strictly compensated for the group delay of the unshaped pulses in both low andhigh average power case (see Fig. 7 and 10), apart from the fact that the pulse shaper opticalsetup (without the SLM) may impart a non-zero dispersion. Furthermore, the algorithm foundthe necessity to shape the spectrum of the pulses prior to amplifications because of the interplaybetween gain shaping and spectral broadening due to nonlinear-phase modulation in the ampli-fiers. Therefore, phase-only modulation only, such as in our previous experiment [31], mightnot be sufficient to achieve the pulse fidelity that we have presented in this work.

Since the pulse propagation was nonlinear, it follows directly that the search landscape washighly nonlinear as well. However, it is evident that this did not pose a problem to our optimiza-tion algorithm. In fact, it highlights its superior performance. In addition, since the absolutephase does not matter, and thus one can apply similar phase profiles with a constant offset, onemay argue that the search landscape was highly multi-modal, i.e. having multiple optima. How-ever, this is not strictly true experimentally, since the pulse shaper exhibits a nonlinear mappingbetween voltage and phase, with a limited range, as well as having discrete phase values. Allof these factors reduce the modality of the problem. This has the benefit of reducing the timerequired to search for the global optimum.

In order to achieve high fidelity pulses, maximization of a TPA detector signal or, similarly,a SHG signal, is the simplest objective function to be implemented. Note that the maximiza-tion of TPA signal does not guarantee the generation of a specific spectral shape at the output.


The approach in Ref. [30] to produce a parabolic shaped spectrum after nonlinear amplificationvia an amplitude-only pre-shaping in order to obtain high fidelity pulses after compression canwork to a certain extent. However, as the authors themselves have pointed out, this methodrequires more effort to compensate for accumulated higher-order phase from the material dis-persion. Furthermore, when a more complex setup is involved, comprising multiple amplifierstages such as in our case, this approach is less likely to be successful.

4. Conclusion

In conclusion, we have successfully demonstrated an adaptive amplitude and phase pre-shapingtechnique for producing high-fidelity femtosecond pulses in a fiber CPA system. We havedemonstrated that this technique is very robust, effective, and efficient, in compensating forboth accumulated phase from higher-order material dispersion and nonlinear phase-modulation.We did not have to perform painstaking characterization and design to optimize our fiber CPAsystem to produce the high-fidelity femtosecond pulses presented here. We found that, withincreasing nonlinearity, a finer control over the pulse shaping was necessary to achieve highfidelity pulses upon compression. This technique should enable power-scaling to higher energyand/or average power at various repetition rates. In addition to producing high-fidelity com-pressed pulses, this technique has the potential to produce arbitrary shaped pulses necessary invarious applications, including coherent control [40].

Acknowledgment

This work was supported by EPSRC Instrument Grant EP/C009479/1. J.H.V. Price is supportedby a Royal Academy of Engineering/EPSRC research fellowship.


high ﬁdelity femtosecond pulses from an ultrafast ﬁber ... · k.ohno,t.tanabe,andf.kannari,...

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