Glover stanford nov 14 2011

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  • Generally Epolarization opposes Emicro (or else run away)
  • Generally Epolarization opposes Emicro (or else run away)
  • Generally Epolarization opposes Emicro (or else run away)
  • One motivation for understanding what happens to valence charge ...
  • Glover stanford nov 14 2011

    1. 1. X-ray/Optical wave mixingMicroprobing how light manipulates matter Ernie Glover Advanced Light Source Division, LBNL
    2. 2. New Opportunities in Nonlinear X-ray Scattering (X-ray Lasers LCLS)
    3. 3. New Opportunities in Nonlinear X-ray Scattering (X-ray Lasers LCLS) Light scattering scattering generally decreases with ω scattering ~ polarization ~ displacement δx decreases with ω .. m x = eE cos(ωt) (force acts for shorter time)
    4. 4. New Opportunities in Nonlinear X-ray Scattering (X-ray Lasers LCLS) Nonlinear x-ray scattering to date Spontaneous processes (PDC & Raman) (large vacuum fields ~1019 W/cm2 at 1 Å)
    5. 5. New Opportunities in Nonlinear X-ray Scattering (X-ray Lasers LCLS) • Understand which xNLO processes are feasible • Understand similarities/differences in information obtainable
    6. 6. New Opportunities in Nonlinear X-ray Scattering (X-ray Lasers LCLS) New capabilities • Microprobe optical interactions (x/o sfg) (directly measure induced charge, microfields) (screening response) • Determine Valence charge density (x/xuv sfg) (backgnd free) (flow of valence charge during dynamics) • Pump and probe on microscopic level (x-ray four wave mixing)
    7. 7. X-ray Four Wave Mixing : Exciton Dynamics Tanaka & Mukamel PRL 89 043001 (2002) : polydiacetylene How is exciton transported along a molecular chain ? * delay kraman A B exciton dynamics FWM Spectroscopy (tunable source, multiple frequencies) creation detection • valence exciton is created at site A (k1, k2) migration • exciton migrates to site B • time delayed detection at site B (k3,kraman) k1 ~ 100 eV k2 k3 kraman A B
    8. 8. New Opportunities in Nonlinear X-ray Scattering (X-ray Lasers LCLS) New capabilities • Microprobe optical interactions (x/o sfg) (directly measure induced charge, microfields) (screening response) • Determine Valence charge density (x/xuv sfg) (backgnd free) (flow of valence charge during dynamics) • Pump and probe on microscopic level (x-ray four wave mixing) Today : x/o mixing & light-matter interactions
    9. 9. Light-matter interactions are important Vision Photosynthesis Photovoltaics
    10. 10. Light-matter interactions are important Photonics / Optoelectronics Quantum control over how matter evolves
    11. 11. How does light catalyze dynamics ? photochemistry Materials science (isomerization) (phonons) the Primary Light-Matter interaction is microscopic rearrangement of valence charge subsequent dynamics Problem We often lack a deep understanding of the microcopic details of how light manipulates matter ! • theoretically complex • tough to measure
    12. 12. How does light catalyze dynamics ? photochemistry Materials science (isomerization) (phonons) the Primary Light-Matter interaction is microscopic rearrangement of valence charge subsequent dynamics Problem We often lack a deep understanding of the microcopic details of how light manipulates matter ! • theoretically complex • tough to measure
    13. 13. Why is the optical response complex ? Coupling between induced dipoles Shine light on a material electron dipole field applied field (screening response) (over screening)
    14. 14. Screening response in a material Apply light to a material. Generally dont know magnitude (or even direction) of resulting force on charges in the system. Emicroscopic = Eapplied + Epolarization self-consistent internal field Local Field in the material (many body interactions) (to within self-field effects) Local Field Effects Apply light (Klight) to a crystal. Emicroscopic(Klight+G) Eapplied(Klight) Lattice vector Varies on scale of atoms Constant on atomic lengthscale
    15. 15. Screening response in a material Apply light to a material. Generally dont know magnitude (or even direction) of resulting force on charges in the system. Emicroscopic = Eapplied + Epolarization self-consistent internal field Local Field in the material (many body interactions) (to within self-field effects) Local Field Effects Apply light (Klight) to a crystal. Eapplied(Klight) Polarization varies on scale of atoms Constant on atomic lengthscale
    16. 16. Screening response in a material Apply light to a material. Generally dont know magnitude (or even direction) of resulting force on charges in the system. Emicroscopic = Eapplied + Epolarization self-consistent internal field Local Field in the material (many body interactions) (to within self-field effects) Local Field Effects Apply light (Klight) to a crystal. Eapplied(Klight) Emicroscopic(Klight+G) Constant on atomic lengthscale Local field effects refer to distinction between the macroscopic field Eapplied(Klight) and the microscopic field Emicro(Klight+G)
    17. 17. Why is the optical response important ?  Practical reasons (develop devices)  Fundamental Materials Physics (material properties) (ground state charge distribution) Analogy with screening of ionic cores in a material Valence electron gas Ground state charge distribution Screening ions appear response
    18. 18. How does light catalyze dynamics ? photochemistry Materials science (isomerization) (phonons) the Primary Light-Matter interaction is microscopic rearrangement of valence charge subsequent dynamics Problem We often lack a deep understanding of the microcopic details of how light manipulates matter ! • theoretically complex • tough to measure
    19. 19. Microscopic details of Light-matter interactions ? No methods to directly measure ! Optical probes average over macroscopic (~µm) lengthscale Atomic lengthscale information is lost
    20. 20. “Seeing” matter on atomic lengthscales with X-rays 1935 Static Pictures Why not simply use diffraction to see changes to valence charge density ? X-rays in Theory & Experiment (Compton & Allison)
    21. 21. X-ray Diffraction Measures Qth Fourier component of the electronic charge density. Problem X-ray scattering dominated by scatter x-ray from core charge Q (Poor at probing valence charge !) Valence charge is important ! (determines chemistry, charge conduction, etc)
    22. 22. A Solution ? X-ray / Optical wave mixing Freund & Levine Phys. Rev. Lett. 25,1241 (1970) Eisenberger & McCall Phys. Rev. A 3,1145 (1971) X-rays : atomic lengthscales Optical : valence charge selectivity
    23. 23. X-ray / Optical wave mixing X/O Sum Frequency Generation x-ray + optical x-rays inelastically scatter from optically driven charge density oscillations optical hνx ± hνo h νo h νx x-ray hνx hνx+o |V> optical dipole |G> Directly microprobes optical interactions s p Freund & Levine Phys. Rev. Lett. 25,1241 (1970) Eisenberger & McCall Phys. Rev. A 3,1145 (1971) Selective x-ray diffraction ! (preferential oscillation of valence charge) ksum = kx + ko + GHKL momentum ωsum = ωx + ωo energy
    24. 24. X-ray / Optical Sum Frequency Generation What’s probed ? x-ray diffraction measures charge densities efficiency ~ ρ2Q x-ray in x-ray out momentum Q transfer laser Scattering regimes x-ray/optical SFG optically induced redistribution δρ = of valence charge Scattering Cross Section (Lorentz oscillator) frequency Rayleigh ~ 1/λ4 Resonant Thomson
    25. 25. X-ray / Optical Sum Frequency Generation What’s probed ? x-ray diffraction measures charge densities efficiency ~ ρ2Q x-ray in x-ray out momentum Q transfer laser Scattering regimes x-ray/optical SFG optically induced redistribution δρ = of valence charge Scattering Cross Section (Lorentz oscillator) frequency hv Rayleigh ~ 1/λ4 Resonant Thomson s p
    26. 26. X-ray / Optical Sum Frequency Generation What’s probed ? x-ray diffraction measures charge densities efficiency ~ ρ2Q x-ray in x-ray out momentum Q transfer laser Scattering regimes x-ray/xuv SFG δρ = full valence charge distribution Scattering Cross Section (Lorentz oscillator) frequency Rayleigh ~ 1/λ4 Resonant Thomson s p All valence charge scatters as a Thomson dipole.
    27. 27. X-ray / Optical Sum Frequency Generation What’s probed ? x-ray diffraction measures charge densities efficiency ~ ρ2Q x-ray in x-ray out momentum Q transfer laser Scattering regimes x-ray/xuv SFG δρ = full valence charge distribution Scattering Cross Section (Lorentz oscillator) frequency Rayleigh ~ 1/λ4 Resonant Thomson s p I. Freund Chem. Phys. Lett. 12, 583 (1972)
    28. 28. X-ray / Optical Wave Mixing Experiments tried in early 1970s failed presumably due to weak xray sources
    29. 29. Experiment optical wave mixing x-ray wave mixing
    30. 30. Experimental facility 4th Generation Light Source X-ray Free Electron Laser 2-3 miles injector to experiment
    31. 31. Experimental arrangement Detector Energy Filtering Si 220 Monochromator Si (111) Mixing Sample apertures x-ray o X-rays ~15 1 eV, 2 µrad Diamond 111δE ~ 20 eV δθ ~ 2 µrad optical hνx hνx + hνL Reflectivity Bragg angle
    32. 32. Experimental facility: X-ray Pump Probe Instrument Slits, Be lenses, Intensity Monitors 800 nm, <10mJ, 50fs, Diodes & 2MPixel array detectorHutch 2 8 keV, 50fs, 20x250µm2,120 Hz Hutch 3 Sample Mount (rotation & translation ) Courtesy David Fritz
    33. 33. Experimental facility: X-ray Pump Probe Instrument
    34. 34. Experimental apparatus
    35. 35. Experimental : Data Acquisition Monochromator Detector Si (111) X-rays x-ray 1 eV, 2 µrad δE ~ 20 eV δθ ~ 2 µrad Diamond 111 Diamond rocking curve
    36. 36. Experimental : Data Acquisition Energy Filtering Monochromator Si 220 Si (111) Detector X-rays x-ray 1 eV, 2 µrad δE ~ 20 eV δθ ~ 2 µrad Diamond 111 Diamond rocking curve Si 220 calibration
    37. 37. Experimental : Space-time overlap Translate to Bi (111) : laser perturbed diffraction for space-time overlap (D.M. Fritz et al. Science 315, 633 (2007)) Detector Energy Filtering Si 220 Monochromator Si (111) Bi (111) Sample apertures x-ray o X-rays ~15 1 eV, 2 µrad δE ~ 20 eV δθ ~ 2 µrad optical x/o delay
    38. 38. Experimental : SFG Data X-ray / optical cross-correlation SFG signal vs x-ray / optical delay
    39. 39. Experimental : SFG Data X-ray / optical cross-correlation
    40. 40. Experimental : SFG Data vary x-ray / optical time delay x-ray Diamond optical
    41. 41. Experimental : SFG Data Rotate sample angle No laser Yes laser Yes laser x/o SFG peak
    42. 42. Experimental : SFG Data rotate sample angle x-ray Diamond optical
    43. 43. Experimental : SFG Data rotate analyzer angle x-ray analyzer Diamond optical
    44. 44. Experimental : SFG Data rotate optical polarization x-ray Diamond optical
    45. 45. Experimental : SFG Data vary optical intensity x-ray Diamond optical
    46. 46. Experimental : Measured Efficiency x-ray Diamond optical Ioptical ~ 1010 W/cm2 Absolute efficiency Relative efficiency efficiency relative SFG power / input x-ray power to ‘regular’ diffraction 2.4 x 10-7 1.7 x 10-6 estimated uncertainty ~ factor of 2
    47. 47. Wave Equation Model for x/o SFG Wave equation ∆ 2 1 d2 E 2β d E 4π d2 PNL E = c 2 dt 2 c dt c2 dt2 dPNL/dt = JNL (ωx + ωo) X-rays see free electrons . mv=F d v/dt = ∂v/∂t + ( v . ) v = (q/m) (E + vxB/c) ∆ JNL (ωx + ωo) = ρ(0)v(2) + ρ(1)v(1)
    48. 48. Wave Equation Model for x/o SFG Wave equation ∆ 2 1 d2 E 2β d E 4π d2 PNL E = c 2 dt 2 c dt c2 dt2 dPNL/dt = JNL (ωx + ωo) X-rays see free electrons . mv=F d v/dt = ∂v/∂t + ( v . ) v = (q/m) (E + vxB/c) ∆ JNL (ωx + ωo) = i(e/2m) Dωx ρo(1) Ex - Doppler (ρ(u)/2ωsum) (e2/2m2) Dωo Dωx (Eo. kx)E + Displacement (ρ(u)/2ωsum) (e2/m2) (Dωo/ωx) Eox(kx x Ex) Lorentz Dωj ≡ ωj /(ωb2- ωj2)
    49. 49. Wave Equation Model for x/o SFG Wave equation ∆ 2 1 d2 E 2β d E 4π d2 PNL E = c 2 dt 2 c dt c2 dt2 dPNL/dt = JNL (ωx + ωo) X-rays see free electrons . mv=F d v/dt = ∂v/∂t + ( v . ) v = (q/m) (E + vxB/c) ∆ JNL (ωx + ωo) = i(e/2m) Dωx ρo(1) Ex Eoe ωot -i Exe-iωxt x/o SFG : Optical Doppler term Dominates !
    50. 50. Wave Equation Model : SFG power vs angle & energy 1 um crystal δE ~ 720 meV δθ ~ 14 urads δ angle δ ω 10 um crystal δE ~ 210 meV δθ ~ 8 urads 500 um crystal δE ~ 130 meV δθ ~ 6 urads
    51. 51. Wave Equation Model : Predicted Efficiency Efficiency vs Crystal thicknesss Induced Charge/Microfields absorption induced charge is the single no absorption free parameter JNL = ρ(111) vx charge & microfield related by Gauss’ law 4π ρ ∆ . E = i G111 . E111 = 4π ρ111 Crystal thickness (m) ρ(111) ~ 7.3x10-5 e/Å3 Efficiency = SFG power / X-ray power in E111 / Emacro ~1/6input beam propertiesδΕx-ray ~ 1 eV δλoptical ~ 35 nm Reproduce measured efficiencyδθx-ray ~ 2 ur δθoptical ~ 4 mrδτx-ray ~ 80 fs δτoptical ~ 2 ps
    52. 52. Models for microscopic optical response • Bond Charge Model (semi-empirical) • Molecular Orbital Calculation (1974) • Pseudopotential Calculation (1972) • Density Functional Calculation (first principles)
    53. 53. Diamond unit cell and primitive cell Unit cell FCC with two atom basis Two types of bonding orientation Primitive cell 8 atoms (16 bonds) in Unit Cell 2 atoms (4 bonds) in Primitive Cell
    54. 54. Covalent Bond Formation isolated atoms Molecular Orbital View Diamond bond : sp3 orbitals covalently bonded atoms
    55. 55. Covalent Bond Formation isolated atoms Molecular Orbital View Diamond bond : sp3 orbitals o 109.5 covalently bonded atoms
    56. 56. Covalent Bond in Diamond Valence electron gas Pseudopotential Strategy Determine how a free (valence) electron gas responds to the sudden appearance of the ions. Replace ionic cores (nucleus & tightly bound electrons) with an effective (pseudo) potential.
    57. 57. Covalent Bond in Diamond Ionic cores appear Pseudopotential Strategy Determine how a free (valence) electron gas responds to the sudden appearance of the ions. Replace ionic cores (nucleus & tightly bound electrons) with an effective (pseudo) potential. Ions (pseudopotential) polarize the valence electrons leading to a self- consistent valence charge distribution (screening response)
    58. 58. Covalent Bond in Diamond Screening response to lowest order Pseudopotential Strategy overlap charge density Determine how a free (valence) electron gas responds to the sudden appearance of the ions. Replace ionic cores (nucleus & tightly bound electrons) with an effective (pseudo) potential. Ions (pseudopotential) polarize the valence electrons leading to a self- consistent valence charge distribution Co-ordinate and nonspherical (screening response) charge described beyond lowest order (nonlinear screening)
    59. 59. Covalent Bond in Diamond Nonlinear screening central to covalent bond formation Pseudopotential Strategy Determine how a free (valence) electron gas responds to the sudden appearance of the ions. Replace ionic cores (nucleus & tightly bound electrons) with an effective (pseudo) potential. Ions (pseudopotential) polarize the valence electrons leading to a self- consistent valence charge distribution (screening response)
    60. 60. Covalent Bond in Diamond Nonlinear screening central to covalent bond formation Pseudopotential Strategy Determine how a free (valence) electron gas responds to the sudden appearance of the ions. Replace ionic cores (nucleus & tightly bound electrons) with an effective (pseudo) potential. Ions (pseudopotential) polarize the valence electrons leading to a self- consistent valence charge distribution (screening response) The self consistent field / charge distribution develops
    61. 61. Covalent Bond in Diamond Nonlinear screening central to covalent bond formation Pseudopotential Strategy Determine how a free (valence) electron gas responds to the sudden appearance of the ions. Replace ionic cores (nucleus & tightly bound electrons) with an effective (pseudo) potential. Ions (pseudopotential) polarize the valence electrons leading to a self- consistent valence charge distribution (screening response) Covalent bonds stabalize lattice against shear distortion
    62. 62. Bond Charge Model Covalent bond charge is the polarizable J.C. Phillips PRL 1967 charge in the system Dielectric properties of covalent semiconductors dominated by bond charge B.F. Levine PRL 1969 The Optical polarizability confined to bond charge Optical pulse  Nonlinear optical susceptibilities χ(2), χ(3)  Raman scatteringSemi-empirical model(Freund & Levine, PRL 25, 1241 (1970) "Optically Modulated X-ray Diffraction") Basic idea Goal : compute optically induced charge density {magnitude of (average) optical response & microscopic spatial distribution} • Magnitude : from macroscopic optical measurements • Spatial distribution : make a guess Induced charge density identical to (measured) bond charge density. (rigid bond model)
    63. 63. Bond Charge Model Covalent bond charge is the polarizable J.C. Phillips PRL 1967 charge in the system Dielectric properties of covalent semiconductors dominated by bond charge B.F. Levine PRL 1969 The Optical polarizability confined to bond charge Optical pulse  Nonlinear optical susceptibilities χ(2), χ(3)  Raman scatteringSemi-empirical model(Freund & Levine, PRL 25, 1241 (1970) "Optically Modulated X-ray Diffraction") Equations Nonlocal response δρ(r) = - .P ∆ Polarization at ith bond P(r) = Ncell ∫cell αmicro(r,r’) Emicro(r’) d3r’ influenced by field from other polarized bonds P(q,G) = Ncell ∑G’αmicro(q,G,G’) Emicro(q,G’)
    64. 64. Bond Charge Model Covalent bond charge is the polarizable J.C. Phillips PRL 1967 charge in the system Dielectric properties of covalent semiconductors dominated by bond charge B.F. Levine PRL 1969 The Optical polarizability confined to bond charge Optical pulse  Nonlinear optical susceptibilities χ(2), χ(3)  Raman scatteringSemi-empirical model(Freund & Levine, PRL 25, 1241 (1970) "Optically Modulated X-ray Diffraction") Equations Local response approximation Local response approximation δρ(r) = - .P ∆ Polarization at ith bond P(r) = Ncell αmicro(r) Emacro(r) determined onlyith bond Polarization at by macroscoic field by determined only macroscoic field P(q,G) = Ncell αmicro(q,G) Emacro(q)
    65. 65. Bond Charge Model Covalent bond charge is the polarizable J.C. Phillips PRL 1967 charge in the system Dielectric properties of covalent semiconductors dominated by bond charge B.F. Levine PRL 1969 The Optical polarizability confined to bond charge Optical pulse  Nonlinear optical susceptibilities χ(2), χ(3)  Raman scatteringSemi-empirical model(Freund & Levine, PRL 25, 1241 (1970) "Optically Modulated X-ray Diffraction") Equations Local response approximation Local response approximation P(q,G) = χG Emacro(q) FHKL χmacroscopic Polarization at ith bond structure factor determined onlyith bond Polarization at by macroscoic field by determined only (for bond charge) Emacro = {3/(2+ε)} Eoptical, vacuum macroscoic field ε = 1+ 4πχmacro
    66. 66. Bond Charge Model Covalent bond charge is the polarizable J.C. Phillips PRL 1967 charge in the system Dielectric properties of covalent semiconductors dominated by bond charge B.F. Levine PRL 1969 The Optical polarizability confined to bond charge Optical pulse  Nonlinear optical susceptibilities χ(2), χ(3)  Raman scatteringSemi-empirical model(Freund & Levine, PRL 25, 1241 (1970) "Optically Modulated X-ray Diffraction") Equations Local response approximation Local response approximation P(q,G) = χG {3/(2+ε)} Eoptical, vacuum Polarization at ith bond determined onlyith bond Polarization at by Overestimates measurement by ~ x2 macroscoic field by determined only macroscoic field ( 1 Fourier component )
    67. 67. Two models for induced valence charge Pseudopotential Molecular Orbital
    68. 68. Two 1970s calculations of microscopic fields How precisely does light exert its force ? Two predictions δρ laser via Molecular Orbital δρ laser via Pseudopotential Arya & Jha Phys. Rev. B 10,4485 (1974) Van Vechten & Martin Phys. Rev. Lett 28,446 (1972) agrees with semi-empirical δρ more delocalized (spreads beyond bond charge) bond charge model Mixing efficiency ~ x100 lower Presupposes a localized response Calculation decides degree of localization
    69. 69. Two 1970s calculations of microscopic fields How precisely does light exert its force ? Two predictions δρ laser via Molecular Orbital δρ laser via Pseudopotential Arya & Jha Phys. Rev. B 10,4485 (1974) Van Vechten & Martin Phys. Rev. Lett 28,446 (1972) agrees with semi-empirical δρ more delocalized (spreads beyond bond charge) bond charge model Mixing efficiency ~ x100 lower Presupposes a localized response Calculation decides degree of localization Overestimates measurement by ~ x2 Underestimates measurement by ~ x6
    70. 70. Density Functional Theory Calculation of induced charge in diamond covalent bondGround state valence charge density 0.25 0.20 0.15 Charge density 0.10 0.05 0.00 0.0 0.2 0.4 0.6 0.8 Position atoms
    71. 71. Density Functional Theory Calculation of induced charge in diamondInduced (valence) charge density Charge density
    72. 72. Density Functional TheoryOverlay Induced over ground state charge density ground induced x1000 Atoms Optical activity pretty well confined to the bond charge
    73. 73. Density Functional TheoryOverlay Induced over ground state charge density ground induced x1000 Atoms Optical activity pretty well confined to the bond charge
    74. 74. Density Functional TheoryOverlay Induced over ground state charge density ground induced x1000 Atoms Optical activity pretty well confined to the bond charge
    75. 75. Density Functional TheoryOverlay Induced over ground state charge density ground induced x1000 Atoms Optical activity pretty well confined to the bond charge
    76. 76. Compare model prediction to measurement Induced charge density (e/Å3) Absolute efficiency x/o SFG measurement 7.3 x 10-5 (x or / √2) 2.4 x 10-7 (x or / 2) DFT prediction 1.1 x 10-4 5.4 x 10-7 BC (MO) prediction 1.3 x 10-4 7.6 x 10-7 VVM pseudopotential ~ ρBC / 10 ~ 7.6 x 10-9 Density Functional Calculation & Bond Charge Model agree with data to within error bars optical How does light interact with Diamond ? To good approximation, optical activity confined to bond charge !
    77. 77. Summary• Observation of x-ray/optical sum frequency generation• Measurement and ab initio simulations suggest simple bondcharge model accurate down to microscopic length scales• New opportunities in nonlinear x-ray scattering created by x-ray FELs X-ray/optical wave mixing particularly important sub-field of nonlinear x-ray scattering due to relatively high efficiency
    78. 78. X/O CollaborationJerry Hastings Steve Harris Jan FeldkampDavid Fritz Sharon Schwartz Diling ZhuMarco Cammarata David Reis Sinisa CohHenrik Lemke Ryan Coffee Tom Allison
    79. 79. X-ray Mixing Options : Relative StrengthsNonlinear Current at ω1 + ω2 JDoppler (ω1+ ω2) = i(e/2m) { ω1 /(ωB2- ω12)} ρ(E2)induced E1 JDisplacement (ω1+ ω2) = (-e2/4m2) (ρ(0)/ωsum) { ω1 /(ωb2- ω12)} { ω2 /(ωB2- ω22)} (E1 . k2)E2 JLorentz (ω1+ ω2) = (e2/2m2) (ρ(0)/ωsum) { ω1 /(ωB2- ω12)}(1/ω 2) E1x(k2 x E2)For free electrons (ωb=0) ρ(Ei)induced = ρ(0){G.Ei/e}αfree(ωi) ~ ρ(0) G.Ei / ωi2) Relative strength of JNL (ω1+ ω2) JDoppler (ω1+ ω2) ~ 1/ { ω1 ω22} x-ray = 8 keV xuv = 100 eV optical = 800 nm JDisplacement (ω1+ ω2) ~ 1/ { ω1 ωsum } JDoppler {x/x, x/xuv, x/o} ~ {1, 6400, 3x107} JDisplacement (ω1+ ω2) ~ 1/ { ω1 ωsum } JDisp/Lorentz {x/x, x/xuv, x/o} ~ {1, 160, 104} Must account for phasematching, different charge densities, absorption … Still efficiency x/o >> efficiency x/x or x/xuv !
    80. 80. X-ray / Optical wave mixing Now: Ultrafast x-ray diffraction Next: Non-linear Ultrafast diffraction follows motion of atom cores x-ray wave mixing selectively microprobes valence charge optical excitation (x-ray + ) optical excitation x-ray probe x-ray + VUV probe δt δt X-ray scattering dominated by atom cores View chemical bond dynamics on natural length (Å) & time (fs) scales ! (poor at probing valence charge density) (see breaking/formation of bonds)
    81. 81. X-ray Wave Mixing New scientific opportunity to microprobe valence charge A Bragg scattering experiment X-rays (atomic spatial resolution) hνx Upconverted X-rays hνx ± hνL (scattered solely from valence charge) Optical or VUV hνL (modulates VALENCE charge) How does light manipulate matter ? Probe full valence charge density (X-ray/optical wave mixing) (X-ray/VUV wave mixing) hvVUV > valence binding energy Micro-probes how visible light distorts the Micro-probes full valence charge density. All optically active valence charge (chemical bonds) valence electrons respond as Thomson dipoles
    82. 82. Wave Equation Model: Efficiency vs (δE,δθ) of input beams δΕ x-ray ~ 2.6 meV δλ laser ~ 140 nm δθ x-ray ~ 4 ur δθ laser ~ 90 mr
    83. 83. Wave Equation Model : SFG beam properties δΕx-ray ~ 130 meV δθx-ray ~ 6 ur δτx-ray ~ 0.9 ps input beam properties δΕx-ray ~ 1 eV δλoptical ~ 35 nm δθx-ray ~ 2 ur δθoptical ~ 4 mr δτx-ray ~ 80 fs δτoptical ~ 2 ps
    84. 84. Wave Equation Model : Predicted Efficiency absorption absorption no absorption no absorption Crystal thickness (m) Crystal thickness (m) Loss due to imperfect collimation & Efficiency = SFG power / X-ray power in monochromaticity of input beamsinput beam propertiesδΕx-ray ~ 1 eV δλoptical ~ 35 nmδθx-ray ~ 2 ur δθoptical ~ 4 mrδτx-ray ~ 80 fs δτoptical ~ 2 ps

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