Attosecond Polarisation Modulation of X-ray Radiation in a Free Electron Laser
AAttosecond Polarisation Modulation of X-ray Radiation in a Free Electron Laser
J. Morgan
1, 2, ∗ and B. W. J. M c Neil
1, 2, 3 University of Strathclyde (SUPA), Glasgow G4 0NG, United Kingdom Cockcroft Institute, Warrington, WA4 4AD, UK ASTeC, STFC Daresbury Laboratory, Warrington, WA4 4AD, UK
A new method to generate short wavelength Free Electron Laser output with modulated po-larisation at attosecond timescales is presented. Simulations demonstrate polarisation switchingtimescales that are four orders of magnitude faster than the current state of the art and, at X-Raywavelengths, approaching the atomic unit of time of approximately 24 attoseconds. Such polarisa-tion control has significant potential in the study of ultra-fast atomic and molecular processes. Theoutput alternates between either orthogonal linear or circularly polarised light without the need forany polarising optical elements. This facilitates operation at the high brightness X-ray wavelengthsassociated with FELs. As the method uses an afterburner configuration it would be relatively easyto install at exciting FEL facilities, greatly expanding their research capability.
The polarisation of light is a fundamental propertywhich affects its interactions with matter. These in-teractions are used experimentally to investigate vari-ous properties of matter. Current experiments can de-mand a greater control and flexibility of the polarisationthan the generation of purely circular, elliptical or lin-early polarised light. In particular, temporal switchingof light polarisation is desirable. If this can be done atthe fast timescales comparable to those of atomic pro-cesses, it can enable experimental investigation of theseprocesses. For example, control over the handedness ofcircular polarisation may be useful in the study of spinrelated processes[1, 2]. However, such fast switching ofthe polarisation properties of light is a non-trivial task asconventional polarising elements are quasi-static devicesat these timescales. While some conventional polarisingelements can be controlled by electric currents [3], theseare limited by their electronic components to gigahertzswitching speeds and also see large energy losses.Some recent methods have improved on this switch-ing rate via the use of plasmonic technologies to producelinear polarisation switching within 800fs [4], and circu-lar polarisation switching at pico-second timescales [2].However, these techniques are based on the active con-trol of polarising elements and operate primarily at visi-ble wavelengths or longer. As wavelengths shorten belowthat of the ultraviolet, polarising optics are more limitedand the radiation polarisation is primarily determined bythe method of generation.In electron accelerator based light sources, which cangenerate light into the hard X-ray, the motion of theradiating electrons propagating though magnetic undu-lators determines the polarisation of the photon beam.For example, circular polarisation modulation has beendemonstrated in a synchrotron by controlling electronbunch orbits through twin undulators [5]. Although thismodulates the X-ray polarisation, the modulation rate islimited to less than 500MHz. ∗ [email protected] In this Letter a method is described which could im-prove the polarisation switching rate of both linear andcircularly polarised high brighness X-rays towards theattosecond timescale regime. This is comparable to theperiod of for a ground state electron in the Bohr hydrogenatom, the atomic unit of time ≈ λ r = λ u (1 + a u ) / γ , where λ u is the undulator pe-riod, a u is the rms undulator parameter and γ is theelectron beam’s relativistic factor. The light is amplifiedvia a collective interaction which causes the electrons tomicro-bunch at the resonant wavelength and to emit co-herently [6]. The initial non-uniform phase distributionof electrons, or shot-noise, can provide the initial seedwhich is subsequently amplified in the process of Self Am-plified Spontaneous Emission, giving a temporally noisyoutput [7]. The relative propagation of a radiation wave-front through the electrons of one λ r every λ u , referredto as ‘slippage’, allows interaction between different re-gions of the electron bunch and radiation pulse. Thiscorrelates the phase of the radiation output at a lengthdetermined by the cooperation length l c = λ r / πρ - therelative slippage in an exponential gain length throughthe undulator l g = λ u / πρ . Here ρ , the FEL parameter,determines the strength of the FEL interaction [7].The FEL process generates high-power radiation with a r X i v : . [ phy s i c s . acc - ph ] A ug FIG. 1. Schematic layout of a section of afterburner used to generate a radiation pulse train with alternating x and y linear polarisation. In each undulator, those regions of the electron beam with modulated micro-bunching emit coherently.Chicanes delay the electron beam between undulator modules so that those sections of high micro-bunching overlap with theappropriately polarised pulse for the undulator in which they are propagating. its polarisation determined by the magnetic undulatorfield - either planar, elliptical or helical. A typical X-ray FEL facility uses planar undulators to microbunchthe electrons. Polarisation control can be enabled byadding additional undulators placed downstream of themain planar undulator amplification section once micro-bunching has been established [8]. Such additional down-stream undulators, or ‘afterburners’, are increasingly be-ing explored as a method to tailor FEL output in manyways not limited to polarisation control, e.g. short pulsegeneration [9, 10] and transverse phase manipulation [11].These afterburners can provide solutions to meet specificexperimental output requirements with minimal changesto an existing facility and therefore at relatively low cost.To generate FEL output with modulated polarisation,we propose an afterburner design consisting of a seriesof few period, alternate orthogonaly polarised undulatormodules as shown in Fig. 1. The undulators are sep-arated by electron delay chicanes which can introduceadditional slippage between the electron bunch and theradiation field. Both of the orthogonal, polarised radi-ation fields emitted in the afterburner are mode-lockedwhich creates trains of short pulses [9]. The orthogonallypolarised pulse trains are shifted temporally with respectto each other, so that the combined pulse train consistsof a series of alternate, orthogonally polarised pulses.Mode-locking in a FEL, first proposed in [9] and com-pacted into an mode-locked afterburner configurationin [10], creates trains of short radiation pulses via a pro-cess analogous with mode-locking in conventional cavitylasers [12]. In the mode-locked afterburner, normal FELamplification occurs first in an electron beam preparedwith an energy modulation, γ ( t ) = γ + γ m cos( ω m t ).This generates a periodic micro-bunching structure in theelectron beam at the energy modulation period by creat-ing higher FEL gain at the minima of the energy modu-lated beam. Chicane delays between the short undulatorsections in the afterburner then map the electron beammicro-bunching comb onto the radiation modal pulses.Here, a similar mapping of the micro-bunched comb tothe mode-locked radiation generated in the orthogonally polarised afterburner modules is used to generate alter-nately polarised pulse trains. Fig. 1 shows a schematicof how these pulse trains are generated in a planar un-dulator afterburner. Chicanes placed between undula-tor modules are chosen to delay the high micro-bunchedregions of the electron beam to the polarised radiationpulses corresponding to the similarly polarised undula-tor in which they interact. The orthogonally polarisedradiation pulses do not interact with the electrons in thisundulator module so that they simply experience freepropagation. The orthogonally polarised undulators theneffectively behave as additional alternate chicane delays.The combined slippage of the electrons with respectto a radiation wavefront between undulator modules ofthe same polarisation should therefore be the modulationperiod λ m . The temporal separation of the pulses ofradiation with the same polarisation is then T = λ m /c and the relative times of these pulses is: t = nT (1)The orthogonally polarised pulses will then have pulsepeaks at relative times: t = t + t + ∆ T (2)where ∆ T = s/c is the time for for the radiation to prop-agate the slippage length, s = λ m /
2, through the electronbunch between undulator modules of the same polarisa-tion and t is a constant which may shift the radiationpulse trains relative to each other. Here, we chose t = 0so that there is equal spacing between all pulses.The method is modeled using the FEL simulation codePUFFIN [13] using the parameters based on the LCLS-II project at SLAC [14] as listed in Table I. Dispersioneffects within the chicanes are included in the model al-though chicanes which reduce dispersion and dispersion-less chicanes are being developed [15, 16].The method is first demonstrated using an afterburnerwith alternating x and y planar undulators that will emitcorrespondingly linearly polarised light. The electronbeam is prepared with an energy modulation of period TABLE I. Simulation ParametersParameter Value
Amplifier Stage
Electron beam energy [GeV] 4Peak current, I [kA] 1rms energy spread σ γ /γ σ x [ µ m] 26Undulator period λ u [cm] 3.9Resonant wavelength λ r [nm] 1.25Modulation wavelength λ m [nm] 40.0Modulation amplitude γ m /γ a u ρ parameter 0.0012 Afterburner
Number of undulator periods per module 8Chicane Delays [nm] 10Number of undulator modules 36 λ m = 40 nm = 32 λ r and the electron micro-bunchingcomb is first developed in a SASE FEL ‘pre-amplifier’using an x -polarised undulator similar to that found atmost current FEL facilities. The power growth in thispre-amplifier stage is inhibited by the electron beam en-ergy modulation. On subsequent injection into the after-burner, the power growth in the pulsed regions becomesexponential due to their overlap with the high qualityelectron beam regions being maintained. There is there-fore much greater radiation power generated in the af-terburner than in the pre-amplifier. The point at whichthe electron beam is extracted from the pre-amplifier ischosen such that the radiation is two orders of magnitudesmaller than the final saturated radiation power in thefollowing afterburner.Both the x and orthogonal y polarised undulator mod-ules in the afterburner are 8 periods long, each sepa-rated by a chicane that delays the electrons by a further8 resonant wavelengths. The total electron delay is then s = 16 λ r = λ m / λ m between undulators of the same polarisa-tion. This maintains overlap between the electron micro-bunching comb and the alternating orthogonaly polarisedradiation as shown in Fig. 1, leading to the amplifica-tion of radiation spikes. The orthogonal radiation spikesso generated should not interfere with each other dueto their orthogonal polarisation. However, as both fieldsare emitted by the same electron beam source, which seesonly small changes between undulator modules, fluctua-tions in the power of one pulse train envelope should besimilar to its orthogonal counterpart.Fig. 2 shows a section of the radiation power profilesand spectrum of the x and y polarised fields after 36 after-burner undulator modules (16 of each polarisation). Theadditional slippage between undulator modules leads toa frequency spectrum that is broader than typical FELoutput and discretied into frequency modes with modes spacing, ∆ ω s , as determined by the time taken for theradiation to travel the total slippage length between thesame polarised undulators. The radiation pulse peaksarise from the constructive interference between the fre-quency modes whose phase has been fixed by the modula-tion, ∆ ω m = ∆ ω s . This is the principle of mode-lockingas described in [9, 12]. FIG. 2. (Top) Power Vs relative time t for the x and y polarised fields and (bottom) the corresponsing spectra after36 undulator-chicane modules. As the undulator modules have equal lengths, boththe x and y polarised fields have approximately the samepulse FWHM duration of τ p ≈
19 as and with peakpowers of P pk ≈ s , is used to exam-ine the degree of linear polarisation in the pulses, where: s = ( E x | − | E y | ) / ( | E x | + | E y | ) is the intensity dif-ference between the x and y polarised fields normalisedto the total intensity of the field. Values of s = ± . x or y polarisation respectively.This is plotted as a function of time in Fig. 3 where itis seen that the polarisation is highly modulated, flip-ping between the two polarisation states. The high de-gree of polarisation contrast is seen at the peak powers is | s | > .
95 demonstrating a high degree of polarisationmodulation.Pulses with polarisation alternating between left andright-hand circular polarisation have also been modeled.For this case, the plane wave approximation was appliedin simulations. It is expected that full 3D simulationswill generate similar results as there was good agreementbetween the approximated linear polarisation case andthe 3D results presented above. Full 3D simulations ofalternating circular polarisation pulses will be subject offuture study. The amplifier section, which pre-bunches
FIG. 3. The on-axis normalised Stokes parameter s as afunction of relative time t after 36 undulator-chicane mod-ules. It is seen that s flips between positive and negativevalues with extremes at | s | > .
95, indicating high degree ofpolarisation modulation.FIG. 4. Power Spectrum for left and right hand polarisationvs relative time at the end an afterburner with alternatingpolarised helical undulator modules. the electrons using SASE, remains an ( x -polarised) pla-nar undulator similar to that above. The afterburner nowconsists of orthogonal left and right circularly polarisedhelical undulators.Fig. 4 shows the power profiles for the left-hand cir-cular, LCP, and right-hand circular, RCP, polarisation.The pulses now alternate between orthogonal circular po-larisation with the same FWHM pulse duration τ p andrate as the linearly polarised case above. At the pulsepeaks, there is a high degree of circular polarisation, | s | > .
9, where s = ( | E R | − | E L | ) / ( | E R | + | E L | ).This is very promising as most ultra-fast polarisationswitching techniques cannot achieve full-handedness re-versal.This Letter demonstrates a novel method to generateattosecond polarisation modulation in a short wavelength FEL without the need for any optical components. Thisrepresents a considerable improvement in wavelength andtimescales over any other methods currently available,and could be expected to drive forward new experimen-tal opportunities in fundamental science. The simulationparameters used considered soft X-ray pulses similar tothe LCLS-II, however, this is by no means the limit ofthe wavelengths available with this set up. Extrapolatingfrom the simulations of a hard X-ray mode-locked after-burner as presented in [10], the same parameters adaptedto generate alternating polarised pulses here would gen-erate pulse separation times of 5 as, approximately onefifth of the atomic unit of time. Discussion of scaling themode-locked afterburner to yet higher photon energiesprovided in [10] should also apply to the methods de-scribed here. Given the broad scaling of FEL wavelengthoperation, the method described will also be applicableto longer wavelengths, again opening up new experimen-tal opportunities.As well as operating across a broad range of wave-lengths, the method could be adapted to meet other spe-cific experimental requirements. The temporal shift be-tween pulse trains of orthogonal polarisations may becontrolled to bring alternating pulses close together fol-lowed by a longer time interval. The time duration of thedifferent pulse types may also be altered by the length ofthe different types of undulators to generate pulse trainswith a pulse of one polarisation followed by a shorterpulse with the orthogonal polarisation. However, it isnoted that this will also result in different pulse powersand bandwidths which would need further consideration.This method also provides a promising broader avenueto tailor FEL output and provide bespoke radiation forexperiments. Further development of the method to beinvestigated will be to include alternating other pulseproperties such as the wavelength, e.g. using the workof [17], or orbital angular momentum of the pulses [18].While experimental implementation of mode-locking hasnot yet been trialed, it may be advantageous to consideralternating pulse structure capabilities when upgradingFELs to include mode-locking.We are grateful to funding from the Scienceand Technology Facilities Council (Agreement Number4163192 Release [1] J. S´anchez-Barriga, E. Golias, A. Varykhalov, J. Braun,L. V. Yashina, R. Schumann, J. Min´ar, H. Ebert, O. Ko-rnilov, and O. Rader, Phys. Rev. B , 155426 (2016).[2] L. H. Nicholls, F. J. Rodr´ıguez-Fortu˜no, M. E. Nasir,R. M. C´ordova-Castro, N. Olivier, G. A. Wurtz, andA. V. Zayats, Nature Photonics , 628 (2017). [3] J. D. Bull, N. A. Jaeger, H. Kato, M. Fairburn, A. Reid,and P. Ghanipour, in Photonics North 2004: OpticalComponents and Devices , Vol. 5577, edited by J. C.Armitage, S. Fafard, R. A. Lessard, and G. A. Lam-propoulos, International Society for Optics and Photon-ics (SPIE, 2004) pp. 133 – 143. [4] Y. Yang, K. Kelley, E. Sachet, S. Campione, T. S. Luk,J.-P. Maria, M. B. Sinclair, and I. Brener, Nature Pho-tonics , 390 (2017).[5] K. Holldack, C. Sch¨ussler-Langeheine, P. Goslawski,N. Pontius, T. Kachel, F. Armborst, M. Ries,A. Sch¨alicke, M. Scheer, W. Frentrup, et al. , Commu-nications Physics , 1 (2020).[6] B. W. McNeil and N. R. Thompson, Nature Photonics , 814 (2010).[7] R. Bonifacio, L. De Salvo, P. Pierini, N. Piovella, andC. Pellegrini, Phys. Rev. Lett. , 70 (1994).[8] A. A. Lutman, J. P. MacArthur, M. Ilchen, A. O.Lindahl, J. Buck, R. N. Coffee, G. L. Dakovski,L. Dammann, Y. Ding, H. A. D¨urr, et al. , Nature pho-tonics , 468 (2016).[9] N. R. Thompson and B. W. J. McNeil, Phys. Rev. Lett. , 203901 (2008). [10] D. J. Dunning, B. W. J. McNeil, and N. R. Thompson,Phys. Rev. Lett. , 104801 (2013).[11] E. Hemsing, Phys. Rev. Accel. Beams , 020703 (2020).[12] A. E. Siegman, Mill Valley, CA , 169 (1986).[13] L. Campbell and B. McNeil, Physics of Plasmas ,093119 (2012).[14] R. W. Schoenlein, New Science Opportunities Enabled byLCLS-II X-ray Lasers , Tech. Rep. SLAC-R-1053 (SLACNational Accelerator Laboratory, 2015).[15] J. Clarke, J. Jones, and N. Thompson, Conf. Proc. C , 1759 (2012).[16] N. Thompson, in
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