DOCSLIB.ORG

Spectral Control of High Harmonics from Relativistic Plasmas Using

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Spectral Control of High Harmonics from Relativistic Plasmas Using Spectral control of high harmonics from relativistic plasmas using bicircular fields Zi-Yu Chen∗ National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621999, China (Dated: April 13, 2018) We introduce two-color counterrotating circularly polarized laser fields as a new way to spectrally control high harmonic generation (HHG) from relativistic plasma mirrors. Through particle-in- cell simulations, we show that only a selected group of harmonic orders can appear owing to the symmetry of the laser fields and the related conservation laws. By adjusting the intensity ratio of the two driving field components, we demonstrate the overall HHG efficiency, the relative intensity of allowed neighboring harmonic orders, and the polarization state of the harmonic source can be tuned. The HHG efficiency of this scheme can be as high as that driven by a linearly polarized laser field. I. INTRODUCTION as charge trajectories. It has already been shown both theoretically[23–26] and experimentally[27–29] that the High harmonic generation (HHG) from relativistically bicircular configuration with one fundamental frequency intense laser irradiating plasma surfaces is an extreme ω and its counterrotating second harmonic 2ω can be ef- nonlinear process, which converts the fundamental driv- fective in CP HHG from atomic gases, whereas the HHG ing laser frequency to its harmonics, which can span process is also greatly suppressed driven by a one-color thousands of harmonic orders[1–4]. One of the main CP pulse, due to an electron’s lateral spreading and re- mechanisms is the so called relativistically oscillating duced probability of re-collision with its parent ion. It mirror (ROM) model[5–9]. The physical picture can be is demonstrated that only specific sets of harmonic or- interpreted as relativistic Doppler up-shifting of the laser ders can be displayed and selectively enhanced in the field reflected by the plasma surface, which acts as a mir- harmonic spectrum driven by such bicircular fields[27– ror oscillating with speed close to that of light. The har- 32]. Although such a field configuration has been stud- monics are usually emitted in the form of a comb in the ied extensively in gas HHG, to our knowledge it has not frequency domain and attosecond pulses in the time do- been addressed for surface plasmas HHG before. It is not main due to the broad spectral range. This thus provides clear whether this scheme should work in the relativistic a powerful radiation source in the extreme ultraviolet and plasma HHG regime or not, since the two HHG mecha- x-ray spectral region with attosecond duration. While nisms are fundamentally different. Therefore, the results many an investigation has been carried out to control obtained before within the gas HHG regime cannot be the temporal structure of the harmonics, e.g., to obtain applied directly to relativistic plasma HHG without val- an isolated single attosecond pulse[10–13], methods to idation. control the HHG spectrum remain limited. Among the In this work, we use ab initio particle-in-cell (PIC) reported spectral control schemes, selected enhancement simulations to confirm the effectiveness of such a scheme of HHG has been achieved by modifying the plasma den- in the relativistic plasma HHG regime and find that the sity ramp[14] or plasma surface morpha[15–19]. similar selection rules discovered in gas HHG are also Here we consider controlling the harmonic spectrum by applicable to relativistic plasma HHG. Thus the bicircu- structuring the laser field with a two-color field. Recently, lar fields can be used to spectral control high harmonics a two-color field scheme, i.e., two paralleled linearly po- from relativistic plasmas. The harmonic spectral fea- larized (LP) fields, has been introduced to relativistic tures, such as the appeared harmonic orders and their plasma HHG[20], which shows great potential to enhance helicity, are found to be governed by the symmetry of the resulting high harmonic yield[21]. Our approach is the laser fields and the related conservation laws. As different, which is based on using circularly polarized a result, selective harmonic enhancement and CP har- arXiv:1802.00249v2 [physics.plasm-ph] 12 Apr 2018 (CP) two-color driving pulses rotating in opposite direc- monic generation can be achieved. It is also shown such tions. Interestingly, it is known that the ROM HHG pro- an HHG process can have a high efficiency although using cess is almost completely suppressed by using one single CP pulses and under normal incidence interactions. CP pulse at normal incidence[22], because the laser pon- deromotive force in this case contains only slowly varying components following the pulse envelop. The situation II. SIMULATION SETUP may change drastically when combining two CP pulses with different frequency and helicity, as the pulses super- The simulations were performed using the one- position can lead to very different field patterns as well dimensional (1D) PIC code VLPL (Virtual Laser Plasma Lab)[33]. The driving laser fields with fundamental fre- quency ω0 (corresponding to wavelength λ0 = 800 nm) ∗ [email protected] and its second harmonic 2ω0 are circularly polarized in 2 FIG. 2. Electric field waveform of the (a) 10th and (b) 11th harmonic shown in Fig. 1(b). In order to see the helicity clearly, only parts of the waveform are shown. The rotation direction is defined as seen by a wave receiver, and the har- monic waves propagate along the -x axis. III. RESULTS AND DISCUSSION Figure 1(b) shows the harmonic spectra obtained by fast Fourier transform of the reflected electric field. It is clearly seen that only the harmonic orders with n = 3m 1 (m = 1, 2, 3, ) have been generated, while ev- ery± third one with n···= 3m is missing. As the plasma is FIG. 1. (a) Electric field waveform of the incident laser isotropic and the interaction is at normal incidence, this pulses propagating along the x axis, composed of two-color unique harmonic feature can be explained by the sym- (fundamental frequency and its second harmonic) counterro- metry of the driving field as follows. We follow the argu- tating circularly polarized fields. (b) The corresponding high ments of Kfir et al[29] and Pisanty et al[34]. The laser harmonic spectrum from surface plasmas. field vector, rotated by 120◦ per cycle in the polarization plane, satisfies, L ˆ L the same plane but rotate in opposite directions: E (t + T0/3) = R(2π/3)E (t), (2) 1 ◦ iω0t 2iω0t ˆ E(t)= (E1e eˆ− + E2e eˆ+)+ c.c., (1) where R(2π/3) is the 120 rotation operator. Assuming 2i the emitted harmonic field conforms to the same dynam- ical symmetry and by taking Fourier transform, we can where eˆ± = (eˆ ieˆ )/√2 with eˆ and eˆ the unit vectors y z y z obtain the spectral field of the nth-order harmonic, EHω , along y- and z-axis,± respectively. The three-dimensional n (3D) electric field waveform is shown in Fig. 1(a), where satisfying the following eigenvalue equation − the intensity ratio of the two driving frequencies I2ω/Iω = 2πin/3EHω ˆ EHω 21 2 21 e n = R(2π/3) n . (3) 0.5 with Iω = 2.8 10 W/cm and I2ω = 1.4 10 2 × × W/cm . The Lissajous figure projected in the y z po- −2πin/3EHω − The solutions are (1) n =3m+1, so that e n = larization plane (in gray) displays a characteristic feature e−2πi/3EHω and (2) n =3m 1, so that e−2πin/3EHω = of threefold spatio-temporal symmetry. The electric field n − n e+2πi/3EHω . Apart from these two sets of harmonic or- experienced by the plasma electrons acts roughly as three n ◦ ders, the harmonic orders with n = 3m do not satisfy LP pulses rotated by 120 three times per optical cycle. Eq. (3) and are therefore forbidden by the threefold sym- This largely modified LP field pattern can give rise to metry. harmonic emission as will be shown later. The temporal The preceding selection rules are also consistent with intensity profile has a Gaussian envelope with a full-width the conservation laws for energy, parity and spin angular at half-maximum pulse duration of 30 fs. The laser pulse momentum[28, 34]. Considering the HHG process in a is normally incident onto a plasma target, of which the simple photon-exchange picture, conservation of energy peak density is n = 200n and the thickness is 200 nm. 0 c implies each harmonic frequency can be expressed in the Here n = m ω2/4πe2 is the plasma critical density with c e 0 form of respect to the fundamental laser frequency. An exponen- tial density ne(x) = n0 exp(x/Ls) exits in the front sur- H Ω(n ,n ) = n1 ω0 + n2 2ω0, (4) face of the plasma slab, where the preplasma scale length 1 2 · · Ls = 0.01λ0. The ions are taken to be immobile. The where n1 and n2 are integers. Applying parity operation simulation cell size is λ0/1000, and each cell is filled with on both the incoming and outgoing photons, we have 100 macroparticles. An absorption boundary condition is adopted for both fields and particles. P [h(ΩH )]= 1; (5) (n1,n2) − 3 FIG. 3. Polarization plane projections of the laser electric fields generated with intensity ratios (a) I2ω/Iω = 0.0, (b) 21 2 I2ω/Iω = 0.1, (c) I2ω/Iω = 0.5, and (d) I2ω/Iω = 2.0. The total intensity is kept constant (Iω + I2ω = 4.2 × 10 W/cm ). (e)-(h) The generated harmonic spectra corresponding to the lasers of panels (a)-(d).
Load more

Recommended publications
  • Generation of Even and Odd High Harmonics in Resonant Metasurfaces Using Single and Multiple Ultra-Intense Laser Pulses
    Generation of even and odd high harmonics in resonant metasurfaces using single and multiple ultra-intense laser pulses Maxim Shcherbakov ( [email protected] ) Cornell University Haizhong Zhang Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research) Michael Tripepi Department of Physics, The Ohio State University https://orcid.org/0000-0002-4657-9826 Giovanni Sartorello Cornell University Noah Talisa Department of Physics, The Ohio State University Abdallah AlShafey Department of Physics, The Ohio State University Zhiyuan Fan Cornell University Justin Twardowski Department of Physics, The Ohio State University Leonid Krivitsky Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research) Arseniy Kuznetsov Institute of Materials Research and Engineering https://orcid.org/0000-0002-7622-8939 Enam Chowdhury Department of Physics, The Ohio State University Gennady Shvets Cornell University https://orcid.org/0000-0001-8542-6753 Article Keywords: High harmonic generation (HHG), resonant metasurfaces, ultra-intense laser pulses, Posted Date: October 26th, 2020 DOI: https://doi.org/10.21203/rs.3.rs-92835/v1 License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License Generation of even and odd high harmonics in resonant metasurfaces using single and multiple ultra-intense laser pulses Maxim R. Shcherbakov,1,* Haizhong Zhang,2 Michael Tripepi,3 Giovanni Sartorello,1 Noah Talisa,3 Abdallah AlShafey,3 Zhiyuan Fan,1 Justin Twardowski,4 Leonid A. Krivitsky,2 Arseniy I. Kuznetsov,2 Enam Chowdhury,3,4,5 Gennady Shvets1,* Affiliations: 1School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853, USA. 2Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research), 138634, Singapore.
    [Show full text]
  • High Harmonic Generation by Short Laser Pulses
    Louisiana State University LSU Digital Commons LSU Doctoral Dissertations Graduate School 2006 High harmonic generation by short laser pulses: time-frequency behavior and applications to attophysics Mitsuko Murakami Louisiana State University and Agricultural and Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_dissertations Part of the Physical Sciences and Mathematics Commons Recommended Citation Murakami, Mitsuko, "High harmonic generation by short laser pulses: time-frequency behavior and applications to attophysics" (2006). LSU Doctoral Dissertations. 769. https://digitalcommons.lsu.edu/gradschool_dissertations/769 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Doctoral Dissertations by an authorized graduate school editor of LSU Digital Commons. For more information, please [email protected]. HIGH HARMONIC GENERATION BY SHORT LASER PULSES: TIME-FREQUENCY BEHAVIOR AND APPLICATIONS TO ATTOPHYSICS A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Physics and Astronomy by Mitsuko Murakami B. Sc., McNeese State University, Lake Charles, LA, 1999 M. Sc., Louisiana State University, Baton Rouge, LA, 2001 May, 2006 To my grandmother ii Acknowledgements I am very grateful to my advisor, Dr. Mette Gaarde, who has been helpful and inspiring throughout my dissertation research. Her teaching is rigorous upon fundamental principles and yet extremely intuitive. I am also grateful to Dr. Ravi Rau, Dr. Dana Browne, Dr. Gabriela Gonzalez, and Dr. Xue-Bin Liang for serving as the members of my dissertation committee.
    [Show full text]
  • Impact of the Electronic Band Structure in High-Harmonic Generation Spectra of Solids
    Impact of the Electronic Band Structure in High-Harmonic Generation Spectra of Solids The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Tancogne-Dejean, Nicolas et al. “Impact of the Electronic Band Structure in High-Harmonic Generation Spectra of Solids.” Physical Review Letters 118.8 (2017): n. pag. © 2017 American Physical Society As Published http://dx.doi.org/10.1103/PhysRevLett.118.087403 Publisher American Physical Society Version Final published version Citable link http://hdl.handle.net/1721.1/107908 Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. week ending PRL 118, 087403 (2017) PHYSICAL REVIEW LETTERS 24 FEBRUARY 2017 Impact of the Electronic Band Structure in High-Harmonic Generation Spectra of Solids † Nicolas Tancogne-Dejean,1,2,* Oliver D. Mücke,3,4 Franz X. Kärtner,3,4,5,6 and Angel Rubio1,2,3,5, 1Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany 2European Theoretical Spectroscopy Facility (ETSF), Luruper Chaussee 149, 22761 Hamburg, Germany 3Center for Free-Electron Laser Science CFEL, Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany 4The Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany 5Physics Department, University of Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany 6Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA (Received 29 September 2016; published 24 February 2017) An accurate analytic model describing the microscopic mechanism of high-harmonic generation (HHG) in solids is derived.
    [Show full text]
  • Enhanced High-Harmonic Generation from an All-Dielectric Metasurface
    LETTERS https://doi.org/10.1038/s41567-018-0233-6 Enhanced high-harmonic generation from an all-dielectric metasurface Hanzhe Liu 1,2*, Cheng Guo3,4, Giulio Vampa1, Jingyuan Linda Zhang3,4, Tomas Sarmiento 4,5, Meng Xiao 4, Philip H. Bucksbaum1,2,3,6, Jelena Vucković3,4,5 , Shanhui Fan3,4,5 and David A. Reis 1,3,6* The recent observation of high-harmonic generation from damage threshold of plasmonic-based metal structures is extremely solids creates a new possibility for engineering fundamen- sensitive to the fabrication quality and the high degree of confine- tal strong-field processes by patterning the solid target with ment in the vicinity of sharp features, such as edges or corners, sig- subwavelength nanostructures. All-dielectric metasurfaces nificantly limits the overall signal enhancement12,18,19. exhibit high damage thresholds and strong enhancement of A dielectric metasurface that hosts an optical resonance provides the driving field, making them attractive platforms to con- a promising solution to this issue. Electromagnetically induced trol high harmonics and other high-field processes at the transparency (EIT)20 can give rise to greatly enhanced nonlinear nanoscale. Here we report enhanced non-perturbative high- light–matter interactions in the spectral region of the resonance21. harmonic emission from a Fano-resonant Si metasurface Enhanced frequency conversion from EIT has been observed in that possesses a classical analogue of electromagnetically atomic systems21 and, very recently, enhanced perturbative third- induced transparency. The harmonic emission is enhanced by harmonic generation has been reported from photonic devices more than two orders of magnitude compared to unpatterned exhibiting a classical analogue of EIT14.
    [Show full text]
  • X-Ray Spectroscopy and Metrology with High-Harmonic Sources
    X-ray spectroscopy and metrology with high-harmonic sources Peter M. Kraus Advanced Research Center for Nanolithography (ARCNL), Amsterdam, The Netherlands. EUV Lithography Source Workshop, 06.11.2018 – HiLASE, Prague, Czech Republic. EUV lithography requires new XUV sources Resolve structures during lithography and Understand EUV (13.5 nm) interactions to after production with sub-nm precision improve masks, pellicles, mirrors, resists… L. Li et al., Chem. Soc. Rev., 2017, 46, 4855 Y. Zhang et al., J. Micro Nanolith. MEMS MOEMS 16, 023510 (2017) Broadband XUV and soft x-ray imaging Ulrafast XUV and soft x-ray spectroscopy We need an ultrafast, coherent, table-top XUV/soft x-ray source Solution: High-harmonic generation (HHG) High-harmonic generation argon atoms 1300 nm Space ~ 1 mJ ~1014 W/cm2 20 eV 50 eV 120 eV =^ 60 nm =^ 10 nm High-harmonic generation (HHG): Converting many IR-photons into one 3 XUV-photon Three-step model of HHG Typical parameters: E - 3 - Recombination 800 nm 3.17 Up - 2 - ~ 1 mJ Propagation ~ 1014 - 1015 W/cm2 XUV emission 0 r Active Figure from: electron P. M. Kraus, H. J. Woerner, Angew. Chem. 57, - IP 5228 (2018). - 1 - Three-step model of HHG: Core P. B. Corkum, PRL 71, 1994 (1993) Ionization J. L. Krause, K. J. Schafer, K. C. Kulander, PRL 68, 3535 (1992) Quantum theory of HHG: Electron M. Lewenstein et al., PRA 49, 2117 (1994) mean field Imaging needs in nanolithpgraphy Lensless imaging with x-rays from HHG Compared to a conventional microscope, the lenses are replaced with a computer algorithm Collaboration with Stefan Witte & Kjeld Eikema (ARCNL) Needs in lithography: Short wavelength, high average power Demonstrated HHG sources S.
    [Show full text]
  • Spin Conservation in High-Order-Harmonic Generation Using Bicircular fields
    Spin conservation in high-order-harmonic generation using bicircular fields Emilio Pisanty1,∗ Suren Sukiasyan1, and Misha Ivanov1;2;3† 1Blackett Laboratory, Imperial College London, South Kensington Campus, SW7 2AZ London, United Kingdom 2Department of Physics, Humboldt University, Newtonstrasse 15, 12489 Berlin, Germany 3Max Born Institute, Max Born Strasse 2a, 12489 Berlin, Germany (Dated: October 3, 2018) We present an alternative theoretical model for a recent experiment [A. Fleischer et al., Nature Photon. 8, 543 (2014)] which used bichromatic, counter-rotating high intensity laser pulses to probe the conservation of spin angular momentum in high harmonic generation. We separate elliptical polarizations into independent circular fields with definite angular momentum, instead of using the expectation value of spin for each photon in the conservation equation, and we find good agreement with the experimental results. In our description the generation of each individual harmonic con- serves spin angular momentum, in contrast to the model proposed by Fleischer et al. Our model also correctly describes analogous processes in standard perturbative optics. §I. INTRODUCTION that in general the production of each individual harmonic is not a closed process. The process of high harmonic generation [1] is the flag- This model, which we call Model 1, suggests that spin ship experiment of extreme nonlinear optics. It consists of angular momentum is not conserved for certain harmonic irradiating atoms or small molecules with long-wavelength lines, so that some harmonics must be assumed to be emit- laser pulses whose electric field is comparable to the inter- ted in correlated pairs for the overall process to be paramet- nal electric fields of the atoms, which results in the emission ric.
    [Show full text]
  • High Harmonic Generation Physics 208A Presentation October 11, 2004
    High Harmonic Generation Physics 208A Presentation October 11, 2004 Tom Allison UC Berkeley Perturbative Nonlinear Optics P = ! (1)E + ! (2)E 2 + ! (3)E 3 + ... •Accurately treated by treating the polarization as a power series in E. •With sufficiently intense laser fields, the higher order terms give rise to Fourier components of the polarization at harmonics of the laser frequency, creating radiation at harmonics of the laser frequency. • First demonstration of second harmonic generation by P.A. Franken et al. (1961). • Laser intensity of ~1×107 W/cm2 • E ~105 V/cm = 10-3 V/Angstrom. • For reference, the atomic field is e Eat ! 2 ! 50 V/Angstrom a0 • With careful phase matching, generation of low order harmonics can be very efficient! XUV or X-rays? • ALS costs ~$100,000/day in operating costs. • Large facility shared by many users ⇒ beamtime is scarce. • X-ray pulse durations typically ~100 picoseconds - too slow to resolve ultrafast dynamics. • Can we use ~100th harmonic generation as a table-top, high brightness, ultrafast x-ray source? How can we extend this process to higher harmonics? • Most obvious first try would be to successively double: How can we extend this process to higher harmonics? • Most obvious first try would be to successively double: UV absorption in doubling crystals?! Phase matching in region of strong dispersion?! High Order Harmonics • In order to get harmonics of very high order, we need to go to extremely intense electric fields, and use gas density targets. Harmonic Spectrum Harmonic spectrum is flat! Sharp cutoff! Old odd harmonics appear! Not well described By expansion of the Polarization! Ferray et al.
    [Show full text]
  • Time-Resolved High-Harmonic Spectroscopy of Ultrafast Photo
    Time-resolved high-harmonic spectroscopy of ultrafast photo-isomerization dynamics Keisuke Kaneshima,* Yuki Ninota, and Taro Sekikawa Division of Applied Physics, Hokkaido University, Sapporo, Hokkaido 060-8628, Japan *[email protected] Abstract We report the first study of time-resolved high-harmonic spectroscopy (TR-HHS) of a bond-making chemical reaction. We investigate the transient change of the high harmonic signal from 1,3-cyclohexadiene (CHD), which undergoes ring-opening and isomerizes to 1,3,5- hexatriene (HT) upon photoexcitation. By associating the change of the harmonic yield with the changes of the ionization energy and vibrational frequency of the molecule due to the isomerization, we find that the electronic excited state of CHD created via two-photon absorption of 3.1 eV photons relaxes almost completely within 80 fs to the electronic ground state of CHD with vibrational excitation. Subsequently, the molecule isomerizes abruptly to HT, i.e., ring-opening occurs, around 400 fs after the excitation. The present results demonstrate that TR-HHS, which can track both the electronic and the nuclear dynamics, is a powerful tool for unveiling ultrafast photo-chemical reactions. Body Measuring and understanding ultrafast dynamics in matter has always been a prime research goal. Recent developments of ultrashort-pulse light sources have allowed us to study electronic dynamics at the attosecond and angstrom scales, and progress has been made via high-harmonic generation (HHG), which provides attosecond pulses in the extreme ultraviolet (EUV) and enables the development of time-resolved techniques in the attosecond regime1–4. Not only as an ultrashort EUV light source, HHG process itself can also be used to investigate the state of the generating medium.
    [Show full text]
  • Basic Physics of High Harmonic Generation (HHG)
    Quantum Optics and Laser Science Group Blackett Laboratory, Imperial College London HHG Basic Physics: High Harmonic Generation & Matter in Strong Fields 1. Free Electrons in Strong Fields 2. Laser Ionisation 3. High harmonic generation 4. High harmonics from molecules Jon Marangos, Imperial College London [email protected] High intensity can be obtained at the focus of a lens mirror focal length f Spot waist size (radius) for a win Gaussian beam: w0 = f λ/ πwin CW 10W 530nm laser focused by 20 cm lens (1cm beam diameter) Intensity ~ 7 x 106 Wcm-2 Pulsed (10ns) 1J mode-locked SHG Nd:YAG laser focused by 20 cm lens Intensity ~ 7 x 1013 Wcm-2 Pulsed (20 fs) 10mJ mode-locked/CPA amplified Ti:S laser focused by 20cm lens Intensity ~ 5 x 1017Wcm-2 Amplified mode-locked lasers can very easily generate intensities > 1014Wcm-2 when moderately focused Electric Fields Peak electric field in Vm-1: 3 -2 1/2 E0 = 2.745 x 10 ( I (Wcm )) 15 -2 10 -1 e.g I = 10 Wcm E0 = 8.68 x 10 Vm (8.68 V per Ǻ) e =E 5 = . 1 ×11 10Vm− 1 - 4πε a2 Hydrogen atom E e 0 0 −11 + Bohr a0 = Radius= × 5m . 3 10 For the laser field to reach the magnitude of the atomic field need I ≈ 3.5x1016 Wcm-2 Basically same effects are seen in atoms or molecules when exposed to intense fields Motion of a free electron in a laser field e &&x = Ecos ω t m • ree electronF motion: e x& = Esin ω t Field: E(t)=E cos ωt m ω 0 e x= − Ecos ω t Charge: -e m ω 2 • Amplitude of oscillation x0 = eE/mω e.g.
    [Show full text]
  • Enhancing Kev High Harmonic Signals Generated by Long-Wave Infrared Lasers
    Enhancing keV high harmonic signals generated by long-wave infrared lasers ZENGHU CHANG Institute for the Frontier of Attosecond Science and Technology, CREOL and Department of Physics, University of Central Florida, 4111 Libra Drive, PS430, Orlando, FL 32816, USA [email protected] Abstract: It is demonstrated by single-atom simulations that X-ray signals in the 3.4 to 4 keV region from an 8 micron laser driven high harmonic generation can be increased by more than two orders of magnitude when a single-cycle pulse centered at 800 nm is added. The ionization probability of a helium atom by the two-pulse field is set to 4.56× 10−5 , which is needed for balancing the index of refraction of free electrons with that of neutral helium atoms to achieve phase matching. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement 1. Introduction Since first demonstrated in 2001, table-top attosecond light sources have relied on high harmonic generation (HHG) in noble gases interacting with near-infrared (NIR) Ti:Sapphire lasers centered at 800 nm [1, 2]. The attosecond spectrum with sufficient flux for transient absorption and streaking experiments is limited to the extreme ultraviolet region (10 to 150 eV). It was demonstrated that the cutoff photon energy of high harmonics can be dramatically extended by driving the non-perturbative nonlinear process with long wavelength lasers [3]. In the last decade, mJ-level driving lasers centered in the 1.3 to 4 µm range have been developed for generating X-ray pulses in the water-window region (282 to 533 eV) and beyond [4-7].
    [Show full text]
  • High Harmonic Generation and Attosecond Physics
    Brief Introduction of Extreme Nonlinear Optics--- High Harmonic Generation and Attosecond Physics Abstract: High harmonic generation is to produce higher frequency harmonics radiation emission after the interaction between atoms and intense laser field. In this article, semi-classical simple man model has been introduced. The characteristic feature of the emission spectrum make the generation of attosecond pulses train and single attosecond pulse possible. Detailed generation principles are also covered here. Ⅰ. Introduction Since the first observation of high harmonic generation (HHG) in 1987 [1,2], intense research on high harmonic generation has been conducted over the past decades. As an effective source of coherent radiation in the XUV (extreme ultraviolet) spectral region, HHG provides a unique method of observing ultrafast phenomena in atoms and molecules on the attosecond time scale. Briefly speaking, HHG is a process in which noble gas atoms are driven by an intense laser field of frequency and produce radiation of higher frequencies q , where q is an odd integer. Ⅱ. Theory of HHG In 1993, P. B. Corkum proposed a semi-classical model of the physical processes of HHG [3]. According to this so called simple man’s theory, high-harmonics are generated in the following 3 steps shown in Fig. 1. 1. Due to the distortion effect of atomic binding potential by the intense laser electric field, an electron can tunnel through the potential barrier and get ionized. 2. The ionized electron is accelerated by the driving laser filed thereby accumulating kinetic energy. 3. The electron comes back to the nucleus and recombines into ground state. Meanwhile, photons radiation with the ionization potential and the accumulated kinetic energy of the electron are emitted.
    [Show full text]
  • Novel Method for the Generation of Stable Radiation from Free-Electron Lasers at High Repetition Rates
    PHYSICAL REVIEW ACCELERATORS AND BEAMS 23, 071302 (2020) Novel method for the generation of stable radiation from free-electron lasers at high repetition rates † Sven Ackermann ,* Bart Faatz, Vanessa Grattoni, Mehdi Mohammad Kazemi, Tino Lang, ‡ Christoph Lechner, Georgia Paraskaki, and Johann Zemella Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany Gianluca Geloni, Svitozar Serkez, and Takanori Tanikawa European XFEL, 22869 Schenefeld, Germany Wolfgang Hillert University of Hamburg, 22761 Hamburg, Germany (Received 17 April 2020; accepted 17 July 2020; published 29 July 2020) For more than a decade free-electron lasers (FELs) have been in operation, providing scientists from many disciplines with the benefits of ultrashort, nearly transversely coherent radiation pulses with wavelengths down to the Ångstrom range. If no further techniques are applied, the FEL will only amplify radiation from the stochastic distributed electron density in the electron bunch. Contemporary develop- ments aim at producing stable and single-mode radiation by preparing an electron bunch with favorable longitudinal electron density distributions using magnets and conventional laser pulses (seed), hence the name “seeding.” In recent years, short wavelength FELs at high electron beam energies and high repetition rates were proposed and built. At those repetition rates, an external seed with sufficient power to manipulate the electron beam cannot be provided by present state-of-the-art laser systems, thus no external seeding scheme could be applied yet. In this paper, we present ways to seed FELs to generate short wavelength radiation at high repetition rates, making use of tested electron beam manipulation schemes. For our parameter study, we used the parameters of FLASH, the free-electron laser in Hamburg.
    [Show full text]