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ULTRAFAST PHENOMENA – LINEAR AND NONLINEAR

ULTRAFAST PHENOMENA – LINEAR AND NONLINEAR. OBJECTIVES. To present nonlinear optics as successive approximations of the semi-classical interaction between light and matter. To give the experimentalist view of the physics, with minimum of equations,

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ULTRAFAST PHENOMENA – LINEAR AND NONLINEAR

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  1. ULTRAFAST PHENOMENA – LINEAR AND NONLINEAR OBJECTIVES • To present nonlinear optics as successive approximations of the • semi-classical interaction between light and matter • To give the experimentalist view of the physics, • with minimum of equations, • maximum of analogies and hand waving. “Blessed the feeble minded, because the kingdom of heaven belongs to them”

  2. Ultrashort laser pulses WHY????

  3. 0~ 31 Å 1015 W/cm2, 800 nm F=ma 20 Electrons ejected by tunnel ionization can be re-captured by the next half optical cycle of opposite sign. The interaction of the returning electron with the atom/molecule leads to high harmonic generation and generation of single attosecond pulses.

  4. There will be some introductory lectures to this topic October 17, Optics Seminar by Jens Biegert October 18, Physics Colloquium by Jens Biegert (Very) High field physics Highest peak power, requires highest concentration of energy Create … shorter pulses (attosecond) Create x-rays (point source) Imaging Relativistic electrons in on optical cycle: 1018 W/cm2 Generate electron-position pairs from light: 1025 W/cm2 E L I Vacuum nonlinear optics  High fields  high nonlinearities

  5. Complex representation of the electric field A Bandwidth limited pulse No Fourier Transform involved Pulse description --- a propagating pulse Actually, we may need the Fourier transforms (review) Construct the Fourier transform of Pulse Energy, Parceval theorem Frequency and phase – CEP – is it “femtonitpicking”? Slowly Varying Envelope Approximation More femtonitpicking about the CEP

  6. A Bandwidth limited pulse Many frequencies in phase construct a pulse Electric field amplitude A review of advanced Optics 2 time 0

  7. A Bandwidth limited pulse E TIME FREQUENCY Time and frequency considerations: stating the obvious

  8. A Bandwidth limited pulse E TIME The spectral resolution of the cw wave is lost FREQUENCY

  9. A Bandwidth limited pulse Some (experimental) displays of electric field versus time Delay (fs) -20 -10 0 10 20 1 0 -1 -6 -4 -2 0 2 4 6

  10. A Bandwidth limited pulse Some (experimental) displays of electric field versus time Delay (fs) -20 -10 0 10 20

  11. Chirped pulse c t

  12. A propagating pulse t z z = ct z = vgt

  13. A Bandwidth limited pulse of 50 fs – what is its? bandwidth t

  14. 0 Klein and Furtak was the advanced optics textbook for decades in this Department Christopher Columbus discovered Americas in 1492 Shortly after 918th century) complex numbers were introduced But UNM physics still selected in the 21st century a book that know only trigonometric functions! Optics and Snobism If there is an easy way to explain things, there will always be a physicist preconizing a twisted, complex way! Fourier transforms (notations) Inverse Fourier transform(s) Decomposition in amplitude and phase The real physical function is:

  15. Real electric field: Eliminate Instantaneous frequency Description of an optical pulse How to get to complex notations the easy way Fourier transform: Positive and negative frequencies: redundant information Relation with the real physical measurable field:

  16. In frequency: FREQUENCY W TIME t TIME t Description of an optical pulse How to get to complex notations the easy way In time:

  17. Description of an optical pulse – the snob way Or how to make easy concepts complicated

  18. 1 And we are left with 1 0 (Field)7 Field (Field)7 Field 0 Instantaneous frequency -1 -1 -1 4 0 2 4 0 2 4 4 -2 -2 Time (in optical periods) Time (in optical periods) Frequency and phase – CEP – is it “femtonitpicking”? . In general one chooses: for bandwidth limited

  19. Slowly Varying Envelope Approximation Meaning in Fourier space??????

  20. Frequency and phase – CEP – is it “femtonitpicking”? W 0 -w w Does cw radiation propagate?

  21. Does cw radiation propagate? This guy says yes Robin K Bullough Mathematical Physicist Robin K. Bullough (21 November 1929-30 August 2008) was a British Mathematical Physicist famous for his role in the development of the theory of the optical soliton. J.C.Eilbeck J.D.Gibbon, P.J.Caudrey and R.~K.~Bullough, « Solitons in nonlinear optics I: A more accurate description of the 2 pi pulse in self-induced transparency », Journal of Physics A: Mathematical, Nuclear and General, 6: 1337--1345, (1973)

  22. CEP: a tricky definition Electric field Electric field Time Time Electric field Electric field Frequency Frequency C E P The areful xperimental hysicist The arrier to nvelope hase + c.c. Short pulse: what is the carrier? Long pulse: what is the envelope center? Witty and inexperienced Experienced and slower… ? ? Traditional CEP definition does not work for chirped pulses

  23. CEP: a tricky definition The CEP changes with propagation! We may not know what CEP is, but we (think to) know how to control it. Propagation through glass of thickness d, the group delay is: For D(CEP) = 2p, (group minus phase) delay = T = l0/c: The change in CEP is proportional to the thickness of glass:

  24. E In frequency: w0 W Blue:envelope 3) The CEP --- traditional definition and control Example for an ultrashort pulse In time: [w0 = 0.75p 1015s-1 (800 nm)] Red: real field E(t)

  25. In frequency: FREQUENCY W TIME t Electric field is just an oscillation in time CEP independent of C and E In time: TIME t Definition of CEP: difference between phase f1(t) and phase f2(t) at peak of real field at peak of amplitude,

  26. How to correctly propagate an ultrashort pulse without phase and group velocity We have to return to Maxwell's propagation equation: In frequency

  27. Blue:envelope Propagation maxwell Eq. Single pulse Definition of CEP: difference between phase f1(t) at peak of amplitude and phase f2(t) at peak of real field CEP = 0.319 CEP = 0.613 Red: real field E(t) CEP = 1.012 CEP = 1.321

  28. Traditional CEP measurement through high order nonlinear interaction High order effects depend on the CEP Two pulses of 2.5 optical cycle. The blue line is the electric field. The green dotted line is the seventh power. w = 2p/T

  29. The CEP – how to “measure” it? G.G. Paulus et al, Phys. Rev. Lett. 91, 253004 (2003)

  30. Electron energy (eV) counts / What the right (black) and left (red) MCP measure, for = CEP CEP High energy Total yield G.G. Paulus et al, Phys. Rev. Lett. 91, 253004 (2003)

  31. + = = 0 + Repeat every time interval Traditional CEP measurement rely on high order nonlinear interaction Ionization rate of sufficient high order to sense a difference between and . Measuring CEP changes optically, through interferometry? Intracavity Phase Interferometry Converting a phase shift D(CEP) into a frequency Dn “Beat note”

  32. Properties of Fourier transforms Linear superposition Shift Linear phase Real E(W) = E*(-W) Convolution Product Derivative Derivative Specific functions: Square pulse Gaussian Single sided exponential

  33. Construct the Fourier transform of w W 0 -w

  34. Construct the Fourier transform of Pulse Energy, Parceval theorem Poynting theorem Pulse energy Parceval theorem ? Intensity Spectral intensity

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