We present a serial pulse shaper design which allows us to shape the phase,
amplitude, and polarization of fs laser pulses independently and
simultaneously. The capabilities of this setup are demonstrated by
implementing a method for generating parametrically tailored laser pulses.
This method is applied on the ionization of NaK molecules by feedback loop
optimization, employing a temporal sub pulse encoding. Moreover, we introduce
and characterize a further development of this common path pulse shaper scheme
for full control of all light field parameters

Lindinger, Albrecht

Plewicki, Mattheusz

Weber, Stefan M.

Weise, Fabian

A. Lindinger

S. M. Weber

M. Plewicki

F. Weise

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Simultaneous phase, amplitude, and polarization control of femtosecond laser pulses

Institutional Repository of the Freie Universität Berlin

Simultaneous Phase, Amplitude, and Polarization Control ofFemtosecond Laser PulsesA. Lindinger, S. M. Weber, M. Plewicki and F. WeiseInstitut für Experimentalphysik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, GermanyE-mail: lindin@physik.fu-berlin.deAbstract. We present a serial pulse shaper design which allows us to shape the phase, amplitude, and polarization of fslaser pulses independently and simultaneously. The capabilities of this setup are demonstrated by implementing a method forgenerating parametrically tailored laser pulses. This method is applied on the ionization of NaK molecules by feedback loopoptimization, employing a temporal sub pulse encoding. Moreover, we introduce and characterize a further development ofthis common path pulse shaper scheme for full control of all light ﬁeld parameters.INTRODUCTIONThe manipulation of the polarization state of femtosecond laser pulses is an emerging topic in the expanding ﬁeld ofcoherent control [1]. Such pulses are optimally suited for the interaction with real-world, three-dimensional quantumobjects found on the molecular scale [2]. The possibility to control a light ﬁeld including polarization gives rise tointeresting fundamental research applied on different systems [3, 4, 5, 6] The underlying concept of pulse shaping isthe manipulation of the frequency components in the Fourier plane of a 4-f line by computer controlled spatial lightmodulators [7]. The ﬁrst attempts of shaping the polarization of femtosecond laser pulses were carried out using twoliquid crystal modulators without polarizer [8]. This allows for controlling the ellipticity of a polarization ellipse inwhich the orientation of the principal axis is ﬁxed at 0◦ or 90◦. The unequal reﬂectivity of the gratings for differentpolarization components requires compensation which was done with a stack of Brewster plates [9].Another approach to gain control over the light ﬁeld is to modulate the horizontal and vertical components separatelyin phase and amplitude before overlapping them in space and time. This enables unresticted modulation of the lightﬁeld and was ﬁrst implemented by incorporating a modulator in a Mach-Zehnder interferometer [10]. This idea wasimproved by using a Wollaston prism to achieve higher stability in a common optic setup [11]. However, theseinterferometric designs are still no common path arrangements and hence not entirely stable.The strategy usually employed to experimentally steer molecular reactions with pulse shapers is to utilize geneticsearch algorithms [12]. With a parameter-per-pixel encoding, the already vast search space grows even more whenappending the polarization. Reducing search space by more general encodings [13, 14], realized for phase and/oramplitude modulation, yields less complex solutions. Moreover, applying parametric shaping of physically relevantpulse features [15] is expected to aid comprehension of the underlying dynamical processes.In this paper, we ﬁrst present an analytical approach that produces tailored polarization sub pulse sequences,using a serial setup with a temporal parameter encoding. In the following, we show a polarization enabled coherentcontrol experiment where free and parametric feedback loop optimizations on the ionization of the NaK molecule arecompared. Finally, we demonstrate a novel setup in which we use four liquid crystal arrays which allows us to fullycontrol all parameters of the light ﬁeld, the phase, the amplitude, and the complete polarization state.PARAMETRIC PULSE FORMING APPROACHThe setup is a serial double-pass arrangement using the commercial CRi SLM-640 Spatial Light Modulator, that thediffracted laser beam passes twice at different locations, effectively employing four arrays at half the resolution (seeFig. 1 (a)). For the ﬁrst round trip, only the total spectral amplitude is modulated and the possibility to impose phases isdisregarded. In the second pass, the spectral phase and polarization are set. The optical axes of the crystals are alignedat 45◦ and -45◦ with respect to the incoming, linearly x polarized light (0◦). The 4f-setup features cylindrical lensesInternational Conference of Computational Methods in Sciences and Engineering 2009AIP Conf. Proc. 1504, 1275-1278 (2012); doi: 10.1063/1.4772162©   2012 American Institute of Physics 978-0-7354-1122-7/$30.001275with focal lengths of 250 mm and gratings with densities of 600 lines/mm with a reduced polarization dependentreﬂectivity g, corrected according to Ref. [16]. The laser pulses, produced by an oscillator (Mira, Coherent), have abandwidth of 22 nm and a central wavelengths of 782 nm. The pulses were detected by sum-frequency-generationcross-correlation (SFG-CC) with a reference pulse in a BBO crystal [10].GratingCylindricallensCylindricallensGratingModulatorPolarizer(a) (b) (c)FIGURE 1. (a) Serial shaper conﬁguration. The laser beam enters the ﬁrst grating, its spectral components are spatially separated,transmitted through the modulator located in the Fourier plane, and hit the second grating. Afterwards the beam is sent througha polarizer and redirected again on the second grating at a different incident angle. The spectral components are sent through adifferent part of the modulator, reenter the ﬁrst grating and leave the setup. (b) Double pulse with perpendicular linear polarizedsub pulses. (c) Double pulse with a linear and a circular sub pulse with second order chirp. The black (x) and gray (y) lines depictthe cross-correlations in horizontal and vertical direction, respectively, and the insets show the 3D representations of the parametricpulse shapes.An analytic method for producing tailored pulse shapes is presented in the following. The light ﬁelds are constructedby assembling several sub pulses having particular parameters including polarization. The sub pulse polarizationellipse parameters intensity I, major axes ratio r, and major axis direction are thereby transformed to the horizontal xand vertical y ﬁeld amplitudes and their phase shift ε , as shown in Ref. [17], yielding a complex vectorial ﬁeld afterthe pulse shaper. The introduced setup (excluding g) is capable of modulating a ﬁeld described by:˜Eout(ω) = ˜Ein(ω) ·R(ω)ei2 (φa(ω)+φb(ω))[cosφa(ω)−φb(ω)2isin φa(ω)−φb(ω)2](1)where ˜Ein is the linear input pulse, and φa and φb the phase retardances induced by the two second pass shaper arrays.Hence, this setup allows only polarization ellipses with horizontal and vertical principal axes for a given frequency.The procedure to generate tailored polarization pulse shapes needs solving the system of equations from Eq. 1 forthe retardances, which, assuming they are complex, yields ˜φ(ω)a,b = −i ln[( ˜Eout,x ± ˜Eout,y)/R(ω) ˜Ein] where + and− have to be selected for φa and φb, respectively, to obtain the desired ˜Eout . The complex solution for the ˜φ(ω) isexperimentally not feasible since a single liquid crystal element can not produce an imaginary phase, which wouldimply amplitude modulation. We instead proceed by using only the experimentally accomplishable real parts of theretardances. In the following we show that this method provides pulses that reasonably represent the desired forms.Fig. 1(b) shows the x and y component of the SFG-CC traces of two perpendicular linear polarized sub pulses. Theirpositions were set to 0 and 500 fs and the ﬂuences were chosen to be equal for the sub pulses. The routine yieldsthe intended sub pulse sequence accompanied by perpendicular linear polarized side pulses. Fig. 1 (c) shows the xand y component of the SFG-CC traces of a linear/circular double pulse. Their positions were set to 0 and 400 fs andthe ﬂuences were chosen to be equal. The circular pulse, furthermore, has a quadratic chirp of 106 fs3, yielding thecharacteristic sub pulse train. Simulations of the temporal intensities, calculated by substituting the real parts of theretardances φa and φb into Eq. 1, conﬁrms the positions and ellipticities of the main and side pulses in both cases.OPTIMIZATION OF THE IONIZATION PROCESS IN NAKThe NaK dimers were produced in a molecular beam by adiabatic co-expansion of the metal vapors with argon as acarrier gas (for details see [18]). The conditions were set to produce the molecules mostly in the vibrational groundstate. They were detected via a quadrupole mass ﬁlter. A Coherent RegA ampliﬁer, seeded by a Coherent Mira,produces pulses with a repetition rate of 100 kHz which is sufﬁcient to ensure that within the interaction region amolecule is not excited more than once. The pulse energies are about 400 nJ per pulse, hence the molecules are1276still governed by weak ﬁeld processes. The evolutionary algorithm employs evolution strategies with 10 parents, 30offspring, one survivor, and uniform cross-over and self-adapted mutation operators.We conducted optimizations of the 23Na39K+ ion yield at a center wavelength of 782 nm with free phase-onlymodulation, free phase, amplitude, and polarization modulation, and parametric phase, amplitude, and polarizationencoding, in order to compare the ionization efﬁciency and to uncover the effects of polarization modulation. Fig. 2(a)shows the cross-correlation trace of a phase-only optimized pulse with a yield of 1.79 compared to an unshaped pulse.It stands to reason to propose a stepwise excitation scheme for the resulting pulse train as most of the sub pulses canbe assigned to multiples of 1/2 · Tosc = 220 fs of the wave packet in the ﬁrst excited 1Σ+ state, similar as alreadyreported in Refs. [18, 19]. The result from a free phase, amplitude, and polarization optimization (Fig. 2 (b)) shows a19% increase to a factor of 2.13 compared to the phase-only case. The cross-correlations in x and y direction can beinterpreted as an alternating multi-step excitation, where every linear sub pulse in one direction is followed by anotherperpendicular one. The sub pulse distances ﬁt well to 1/2 · Tosc which suggests a repeated stepwise excitation scheme.(a) (b) (c)FIGURE 2. Cross-correlation traces of the optimized pulse shapes with free phase-only modulation (a), free phase, amplitude,and polarization modulation (b), and parametric phase, amplitude, and polarization encoding (c). The black (x) and gray (y) linesdepict the cross-correlations in horizontal and vertical direction, respectively. The distances are written in fs and the optimizationfactors are respective to the ion yield of the unshaped pulse.In an attempt to illustrate the simpliﬁcation capabilities of parametric shaping we apply the introduced parameteri-zation onto the feedback loop. For the optimizations we again used a double pulse scheme, restricted the major axesangles to 0◦ and 90◦, kept one pulse at time zero and encoded the position of the second major pulse position from-1000 fs to -100 fs. Other parameters were the relative ﬂuences [0.1 to 1], the zero order phases [−π;π], and the Δφ[−π;π] of the individual sub pulses. The optimization achieves a total factor of 2.08, see Fig. 2 (c), with a reducedcomplexity. The pulse shape with alternating perpendicular polarized sub pulses shows similarity with the results fromthe corresponding free optimization. These results can be understood by the consecutive Σ-Σ to Σ-Π transitions inNaK, having orthogonal transition dipole moments. Hence, the pulse polarization adapts to the transition dipole mo-ments on the optimized path, utilizing the vectorial properties displayed by μ ·E. This demonstrate the perspectives ofadding a new dimension by including also the polarization.FULL CONTROL OF THE LIGHT FIELDThe described pulse shaper is however limited regarding the polarization modulation since the direction of the principleaxes of the polarization ellipse cannot be altered. Full control of the polarization can be gained by passing throughfurther liquid crystal arrays, similar to the 8-f setup already reported [20] where yet amplitude modulation is lacking.Here we demonstrate a novel setup in which we use four liquid crystal arrays in the Fourier plane of a 4-f linewhich enables us to fully control the four independent degrees of freedom, phase, amplitude, polarization ellipticity,and polarization orientation. This can in principal be done with one modulator consisting of four arrays and onepolarizer in between. The ﬁrst pair of liquid crystal arrays should e. g. be aligned with their optical axis at ±45◦ to theincoming linearly polarized light followed by a polarizer. This would allow us to modulate the phase and amplitude.The combination of the next array aligned at +45◦ followed by one at 0◦ would permit to control the polarization state.Until now, there are no modulators commercially available with the conﬁguration described above. Therefore, weuse three modulators with a double array each (two SLM-640 and one SLM-256, CRi), having their optical axesat ±45◦. The ﬁrst one is used in phase and amplitude conﬁguration with a polarizer behind. The second modulator1277provides just one array at -45◦, while the second array is set to a constant retardance. In order to obtain an orientationof the optical axis at 0◦ in the last array, the modulator is placed between two zero order half wave plates at -22.5◦ each.Again, only one array of this modulator is used. The second wave plate is no constraint but helpful for an intuitiveunderstanding of the formulas and the analytical grating correction.In order to demonstrate the potential of this setup, we carried out measurements using the Mira oscillator witha spectral width of 28.2 nm at a central wavelength of 781 nm. The whole sequence of the three modulators, thepolarizer and the ﬁrst wave plate is 51 mm thick which, according to test measurements, does not lead to a reductionof the effective shaping resolution.-90˚ -60˚ -30˚ 0˚ 30˚ 60˚ 90˚0.00.51.01.52.02.5Power behind polarizer / a.u.Orientation ( γ  )   r = 0.0 r = 0.4 r = 0.6 r = 0.8 r = 1.0Polarizer @ 0˚Half Wave Plate @ -22.5˚Half Wave Plate @ -22.5˚+45˚FA-45˚FB+45˚FC-45˚FD-45˚FE+45˚FFl/2-22.5˚l/2-22.5˚POL@ 0˚Sequence of optical components+45˚FA-45˚FB+45˚FC0˚FEPOL@ 0˚Identical Sequence(a) (b)FIGURE 3. (a) Shaper setup consisting of a 4-f line with three double liquid crystal modulators separated by a polarizer and twowave plates at -22.5◦ in the Fourier plane. (b) Rotation of the ellipse for different r measured behind a vertically aligned polarizer.To gain intuitive control of the electric ﬁeld, the parameters φa,b,c,e are transformed to the ellipse parametersintensity I, orientation γ , and principal axes ratio r by comparing the equations of the ellipse and the electricalﬁeld [10], yielding φa − φb = 2arccos[√I],φc = 2arctan[g(−1 + 2(1 + r2)/(1 + r2 − (r2 − 1)2cos(2γ)))1/2], andφe = −π2 + arccos[(2(r2 − 1)2sin(2γ)2)/(1+ 6r2 + r4 − (r2 − 1)2cos(4γ)))1/2]. In order to analyze the capabilitiesof the setup, we scanned the polarization ellipse orientation from -90◦ to +90◦ at different principal axis ratioswhile measuring the power transmitted through a polarizer (Fig. 3(b)). These curves exhibit a cosine modulationwith decreasing amplitude for increasing r up to circular polarization where a constant signal is observed.The presented novel pulse shaping setup is the ﬁrst non-interferometric setup which is capable of modulating thephase, the amplitude, and the full polarization ellipse simultaneously and independently. Accurate control of the ellipseparameters has been demonstrated which will provide the opportunity for unrestricted polarization shaping.REFERENCES1. D. Goswami, Physics Reports 374, 385 (2002).2. Y. Silberberg, Nature 430, 624–625 (2004).3. T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt, and et al., Phys. Rev. Lett. 92, 208301 (2004).4. T. Suzuki, S. Minemoto, T. Kanai, and H. Sakai, Phys. Rev. Lett. 92, 13 (2004).5. N. Dudovich, D. Oron, and Y. Silberberg, Phys. Rev. Lett. 92, 103003 (2004).6. M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. de Abajo, W. Pfeiffer, and et. al., Nature 446, 301 (2007).7. A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, Opt. Lett. 15, 326 (1990).8. M. M. Wefers, and K. A. Nelson, Opt. Lett 20, 1047 (1995).9. T. Brixner, and G. Gerber, Opt. Lett. 26, 557 (2001).10. M. Plewicki, F. Weise, S. M. Weber, and A. Lindinger, Appl. Opt. 45, 8356 (2006).11. M. Ninck, A. Galler, T. Feurer, and T. Brixner, Opt. Lett. 32, 3379 (2007).12. R. S. Judson, and H. Rabitz, Phys. Rev. Lett 68, 1500–1503 (1992).13. T. Hornung, R. Meier, and M. Motzkus, Chem. Phys. Lett. 326, 445–453 (2000).14. A. Bartelt, C. Lupulescu, Š. Vajda, and L. Wöste, ed. A. Douhal and J. Santamaria, 2002, World Sci. Publishing edn., p. 481.15. S. M. Weber, A. Lindinger, F. Vetter, M. Plewicki, A. Merli, and L. Wöste, Eur. Phys. J. D 33, 39 (2005).16. M. Plewicki, S. M. Weber, F. Weise, and A. Lindinger, Appl. Phys. B 86, 259 (2007).17. S. M. Weber, F. Weise, M. Plewicki, and A. Lindinger, Appl. Opt. 46, 5987 (2007).18. A. Bartelt, A. Lindinger, S. Vajda, C. Lupulescu, and L. Wöste, Phys. Chem. Chem. Phys. 6, 1679 (2004).19. B. Schäfer-Bung, R. Mitric, V. Bonacic-Koutecki, A. Bartelt, and et al., J. Phys. Chem. A 108, 4175 (2004).20. L. Polachek, D. Oron, and Y. Silberberg, Opt. Lett. 31, 631 (2006).1278

Simultaneous phase, amplitude, and polarization control of femtosecond laser
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Simultaneous phase, amplitude, and polarization control of femtosecond laser pulses

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