February 1, 2004 / Vol. 29, No. 3 / OPTICS LETTERS 271

Adaptive control of femtosecond solitonself-frequency shift in fibers

Anatoly Efimov and Antoinette J. Taylor

Materials Science and Technology Division, MST-10, MS K764 Los Alamos National Laboratory, Los Alamos, New Mexico 87545

Fiorenzo G. Omenetto

Physics Division, P-23, MS H803 Los Alamos National Laboratory, Los Alamos, New Mexico 87545

Evgeny Vanin

Acreo AB, Electrum 236 SE-164 40 Kista, Sweden

Received July 29, 2003

The Raman shift of a subpicosecond soliton in 100 m of fiber is controlled adaptively by pulse shaping beforelaunching into the fiber. We use a deformable-mirror-based shaper to control the spectral phase of the inputpulse. Wavelength tuning of the output pulse is also demonstrated. © 2004 Optical Society of America

OCIS codes: 060.4370, 060.5530, 060.7140, 190.2640, 190.5650, 190.7110.

Optical soliton formation in f ibers from arbitrarilyshaped femtosecond pulses has not been thoroughlyinvestigated in the past, either theoretically or experi-mentally. Mostly, the case of linearly chirped inputhas received attention1 for obvious practical reasons.Recently developed pulse-shaping techniques2 allowthe means not only of studying the femtosecondpulse propagation and soliton formation in f ibersfrom complex input pulses but also of controllingpulse in-fiber dynamics and output characteristics.Controlling pulse propagation in f ibers may finduse in telecommunication applications, f iber-basedmultiphoton f luorescence and multiharmonic micro-scopies, near-f ield scanning optical microscopy, andgeneral femtosecond pulse delivery for remote ex-periments. In addition, novel adaptive feedbackparadigms applied to output pulse optimization3 aswell as phase-sensitive diagnostics,4 such as frequency-resolved optical gating, comprise a powerful toolboxfor experimental investigation of ultrashort pulsedynamics in f ibers. It is well known that, in the fem-tosecond pulse duration regime, the main higher-ordernonlinear contribution to the standard nonlinearSchrödinger equation that describes the pulse evolu-tion comes from stimulated Raman scattering. TheRaman self-frequency shift that results from the en-ergy exchange between the propagating pulse and theoptical vibrational modes of the glass precludes thestable propagation of subpicosecond solitons alongthe fiber, leading to rapid displacement of the pulsespectrum to the red as it propagates. As a result,practical solitons in f ibers often have durations of 1 psor longer. Shorter pulses suffer self-frequency shiftsof Dv � L�t4, where t is the soliton width and L is thefiber length. In the case of the generalized nonlinearSchrödinger equation (Raman, self-steepening, andhigher-order dispersion terms included) that describesshort-pulse dynamics, t ø 1 ps, while key pulse pa-rameters undergo oscillations as a function of propa-

0146-9592/04/030271-03$15.00/0 ©

gation distance, higher-order nonlinear terms play adistance-dependent role and substantially change thepulse dynamics from that of the standard nonlinearSchrödinger case.

The potential practical use of subpicosecond solitonsin telecommunication or in general pulse delivery ap-plications requires control over soliton self-frequencyshift at the end of the f iber link. One technicalapproach to minimizing moderate self-frequencyshifts in long fiber links can be the use of spectralfilters5 or bandwidth-limited amplification.6,7 Otherapproaches include the use of phase-sensitive ampli-fiers8 or optical phase conjugation.9 Alternatively,novel photonic bandgap fibers that guide light mostlyin an air defect surrounded by a periodic lattice ofair and glass can be employed for high-energy pulsedelivery.10 However, soliton self-frequency shift isalso a standing problem in these f ibers, unless thefiber is f illed with an inert gas.

A natural question then arises of whether one cansteer soliton formation in the ultrashort pulse dura-tion regime by suitable preshaping before launchingthe pulse into the f iber. Shaping of the input pulsecan substantially modify the dynamics of the pulse’speak intensity and thus the strength of the nonlinearterms inside the fiber. The goal here would be to con-trol the Raman frequency shift of the output pulse, pre-serving its duration and intensity. The fact that thedispersion is anomalous and this problem is stronglynonlinear makes it difficult to predict a priori the op-timal pulse shape at the input.

Thus, to address this question we have performedan adaptive feedback experiment in a fiber usinga membrane-based deformable mirror pulse shaper.The experimental setup, shown in Fig. 1, includes atunable 100-fs laser source operating at 1550 nm, aref lective grating-mirror pulse shaper with the de-formable mirror serving as a phase mask placed in theFourier plane, and a feedback mechanism at the output

2004 Optical Society of America

272 OPTICS LETTERS / Vol. 29, No. 3 / February 1, 2004

Fig. 1. Experimental setup for the adaptive control of fem-tosecond soliton self-frequency shift in a f iber. Spectrallyresolved second-harmonic generation (SHG) is used as feed-back to the GA. OPO, optical parametric oscillator; l�2,half-wave plate; Pol, polarizer; PC, polarization controller;PD, photodiode.

of a 100-m-long piece of polarization-maintainingfiber. The fiber (Thorlabs FS-PM-7811) was charac-terized as having a mode-field diameter of 6 mm anddispersion D � 11 ps�nm km. The experiment wascontrolled by a genetic algorithm11 (GA) that used thefeedback signal as an input to control the shape ofthe deformable mirror. The latter consisted of a thingold-coated membrane stretched on a frame and couldbe f lexed electrostatically by application of voltages to19 independent actuators positioned behind the mirrorsurface.12 Feedback was arranged so that we couldmonitor the time-integrated intensity of the spectrallyresolved second-harmonic (SH) signal generated bythe output pulse in a 0.2-mm-thick BBO crystal. Theamplitude of this signal was monotonically propor-tional to the pulse intensity as well as its spectralposition proximity to the specif ied wavelength of thespectral f ilter (a diffraction grating, lens, and slit).By tuning the spectral f ilter to different SH frequen-cies, vSH � 2v0, where v0 is the desired fundamentalfrequency, we could force the output pulse to havea specif ied amount of frequency shift, including theabsence of a shift.

The results for the latter case are shown in Figs. 2and 3. FROG traces of output pulses are shown inFigs. 2(a), 2(b), and 2(c) for the respective cases of atransform-limited (TL) pulse, a feedback-optimizedshaped input pulse, and a linearly chirped pulse,manually optimized for the highest feedback signal.It can be seen that in the TL input case the solitonspectrum shifts by as much as 50 nm. The adaptivealgorithm, on the other hand, successfully eliminatedthe shift of the output pulse [Fig. 2(b)], preserving theintensity and duration of the pulse. For comparison,chirping the input pulse linearly in the appropriateway also eliminates the frequency shift; however,a substantial temporal wing structure accompaniesthe main pulse. Adaptive feedback optimization alsoyields an �1.4 times higher feedback signal valuethan with just linear prechirping. The evolution of

the GA is shown in Fig. 3. Convergence can be clearlyobserved in that the average achievement (feedbacksignal magnitude) within each generation approachesa high saturation level and that the achievementspread within each generation, indicated by the ver-tical error bars, diminishes with time. Convergenceis achieved within 100 generations in the parameterspace defined by 19 independent genes correspondingto the control voltages applied to individual actuatorson the deformable mirror. The optimally shapedinput pulse is shown in the inset of Fig. 3 in thespectral domain. The input pulse’s spectral phase isindeed nonparabolic and does not correspond to simplelinear chirping.

Fig. 2. Output pulse FROG traces for (a) TL input pulseof 100-fs duration, (b) feedback optimized pulse, and(c) linearly chirped pulse. The gray scale is logarithmic.

Fig. 3. GA performance, with the f illed circles and errorbars signifying the average achievement and standard de-viation, respectively, in each generation and the solidcurves showing the best and worst achievements pergeneration. Inset, optimized input pulse spectral phaseand intensity distributions.

February 1, 2004 / Vol. 29, No. 3 / OPTICS LETTERS 273

Fig. 4. FROG traces of the output pulse with a specifiedamount of Raman self-frequency shift: (a) optimized at793 nm, (b) optimized at 815-nm central wavelength. TheSH generation wavelength of the pump laser is markedwith an arrow.

If the spectral filter in the experimental setup istuned to a wavelength longer than one half of thefundamental, then one can obtain specific soliton self-frequency shifts by running the adaptive feedbackexperiment again. Two examples of such spectraltuning of the output pulse are shown in Fig. 4. Inthese cases, the SH generation spectral f ilter wastuned to either 793 or 815 nm, whereas the SH ofthe fundamental wavelength is 775 nm. Apart fromthe minor satellite pulse, the main pulse’s spectralposition tracks the specif ied wavelength. The outputpulse duration is nearly the same as in previous cases.

First-order control over the soliton self-frequencyshift can be exercised with linear prechirping, whichstrongly inf luences the soliton dynamics in the fiber.13

In particular, the period of oscillations of the solitonpeak amplitude along the fiber length is increased ifthe input pulse is prechirped. At a certain value of(negative) chirp, the half-period of these oscillationsmay become equal to the f iber length. In this case thepulse disperses initially and propagates through mostof the f iber with low peak power so that the stimulatedRaman scattering, as well as other high-order non-linear effects, such as Cherenkov-type phase-matchedthird-harmonic generation, are negligible. The Kerrnonlinearity acts slowly to reassemble the pulse to a

temporal focus at the end of the f iber. More complexinput pulse shapes are expected to display yet morecomplicated propagation dynamics delivering higherfeedback values, thus outperforming linearly chirpedinput pulses, as was the case in our experiments.

In conclusion, we have demonstrated control ofsoliton self-frequency shift in 100 m of fiber, using acombination of input pulse preshaping and adaptivefeedback. Using a suitable feedback criterion, wecontrolled the amount of the frequency shift whileboth the pulse width and the intensity were preserved.This adaptive feedback approach appears to be a pow-erful tool for controlling ultrashort pulse propagationin optical fibers, as it allows the control of higher-ordernonlinearities that were heretofore believed to be lim-iting factors in fiber propagation of ultrashort pulses.Further extensions of this technique may allow us toharness and advantageously use such nonlinearities toincrease the functionality of future photonic networksand fiber delivery systems.

A. Efimov’s e-mail address is efimov@lanl.gov.

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