Ultrafast Laser Physics THz pulse generation and detection Goals: Explain why THz pulses are useful Explain conceptually some common methods to generate THz pulses Photoconductive switches Rectification Explain some common methods for phase-sensitive THz detection
More in-depth courses (in case you want more): 1) Modern Topics in THz Science (Fall semesters) 2) Ultrafast Methods in Solid State Physics (Spring semesters) Decent general reference: Y.-S. Lee, Principles of Terahertz Science and Technology
Electronics Waveguide Classical industry transport THz Gap Photonics Lens Quantum and industry mirror transition microwaves visible x-ray g -ray 10 0 dc 10 3 10 6 10 9 10 12 10 15 10 18 10 21 10 24 kilo mega giga tera peta exa zetta yotta Frequency (Hz) Hz Frequency: = 1 THz = 1000 GHz Angular frequency:! = 2º = 6.28 THz Period: ø =1/ =1ps Wavelength: = c/ = 0.3 mm = 300 µm Wavenumber: k = k/2º =1/ = 33.3 cm 1 Photon energy: h = h! = 4.14 mev Temperature: T = h /k B = 48 K ere is the speed of light in vacuum, is Pla
Other names. Millimeter wave (MMW): 1-10 mm, 30-300 GHz, 0.03-0.3 THz Submillimeter wave (SMMW): 0.1-1 mm, 0.3-0.3 THz Far infrared radiation (Far-IR): (25-40) to (200-350) µm, (0.86-1.5) to (7.5 to 12) THz Sub-THz radiation: 0.1-1 THz hese bands are also distinguished by their characteristic technologies. Mil-
THz interactions: atoms Low values of n: transitions frozen out for low fields n ~ 50: level spacing matches h for 1 THz Two main possibilities: 1) Tunnel ionization (high field limit) E E a 5 10 9 V/cm
THz interactions: atoms Low values of n: transitions frozen out for low fields n ~ 50: level spacing matches h for 1 THz Two main possibilities: 2) Rydberg state transitions big dipole moments long lifetimes (microseconds)
Crystals: vibrational excitations d a... m m - + k 2 k 1... u -,n u +,n ( n -1 ) a na ( n +1 ) a w( k) w = ck optical branch acoustic branch p - a p a k
Light-Induced Superconductivity in a Stripe-Ordered Cuprate D. Fausti et al. Science 331, 189 (2011); DOI: 10.1126/science.1197294
PRL 102, 247603 (2009) P H Y S I C A L R E V I E W L E T T E R S week ending 19 JUNE 2009 Collective Coherent Control: Synchronization of Polarization in Ferroelectric PbTiO 3 by Shaped THz Fields Tingting Qi, 1 Young-Han Shin, 1 Ka-Lo Yeh, 2 Keith A. Nelson, 2 and Andrew M. Rappe 1 1 The Makineni Theoretical Laboratories, Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104 6323, USA 2 Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA (Received 16 November 2008; published 19 June 2009)
Sn2P2S6: THz-induced switching [ S. Grübel et al., submitted] Simulated dynamics in simplified 2-well potential suggest nonlinearity, flip for multi-mv/cm, single cycle pulses
How to make THz? Photoconductive switches
Photoconductive switch
Photoconductive switch Metal electrodes simple dipolar antenna on surface (optional: silicon lens) Semiconductor substrate, usually low temperature grown (LT) GaAs
Photoconductive switch
Microscopic mechanism -Vb/2 E b +Vb/2 initially, (almost) no electron-hole pairs exist Bias field near surface
Microscopic mechanism -Vb/2 +Vb/2 Laser pulse arrives, makes e-h pairs
Microscopic mechanism -Vb/2 +Vb/2 Laser pulse arrives, makes e-h pairs
Microscopic mechanism -Vb/2 +Vb/2 Electrons and holes see oppositely directed forces from bias field
Microscopic mechanism -Vb/2 +Vb/2 Quickly brought to drift velocity, resulting in a current
Microscopic mechanism Assume acceleration to drift velocity is fast v d = µe b mobility is proportionality constant between E-field and drift velocity Also assume hole mobility is much smaller than electron mobility (often true) J(t) =N(t)ev d = N(t)eµE b density of electrons
Microscopic mechanism J(t) =N(t)ev d = N(t)eµE b In the far field (i.e. several wavelengths away from antenna): z E THz = 1 4 0 A c 2 z @J(t) @t sin A Illuminated gap area E THz = Ae 4 0 c 2 z @N(t) @t µe b sin
PC switch performance At low rep rates, can get ~ 1 microj Usually ~10 kv/cm peak field Broadband, single cycle, ~ 1 THz center freq. Usually limited by phonons in substrate (8 THz TO phonon in GaAs)
Optical rectification
Optical rectification P i (t) = X j (1) ij E j(t)+ X jk (2) ijk E j(t)e k (t)+... zero in inversion-symmetric materials Diamond structure: inversion symmetric Diamond, Si, Ge, Zinc blende: non-inversion symmetric GaAs, InSb,
Optical rectification P i (t) = X j (1) ij E j(t)+ X jk (2) ijk E j(t)e k (t)+... E(t) E 2 (t)
Optical rectification P i (t) = X j (1) ij E j(t)+ X jk (2) ijk E j(t)e k (t)+... THz = + Second harmonic
Optical rectification P i (t) = X j (1) ij E j(t)+ X jk (2) ijk E j(t)e k (t)+... Far field: E THz @2 P (t) @t 2
Phase matching Process is equivalent to DFG mixing for wavelengths within wavepacket For two frequencies, DFG! 1! 2 = THz phase matching conditions: k 1 k 2 = k THz! 1! 2 k 1 k 2 = THz k THz =) @! @k = THz k THz =) v g (pump) = v p (THz)
Phase matching Question: what happens if phase matching conditions satisfied but v g (pump) 6= v g (THz)?
Optical Rectification: Phase matching =) v g (pump) = v p (THz) Accidentally true in some materials: ZnTe and GaP at 800 nm pump DAST, OH1, DSTMS at ~ 1.5 microns pump Possible using birefringence in GaSe at 800 nm (800 nm is convenient since this is where Ti: Sapphire femtosecond lasers like to lase)
Optical Rectification: General requirements Material must be transparent at both pump and THz wavelengths Material cannot possess a center of inversion symmetry Second-order susceptibility should be high Phase matching over all THz frequencies in pulse (need low dispersion of permittivity) ZnTe: GaP:! TO 5 THz! TO 11 THz
How to cheat at phase matching Tilted pulse front LiNbO3 Good: robust, transparent, reasonable nonlinear coefficient Bad: v ph (THz) v g (800nm) (mismatch by about a factor of 2)
How to cheat at phase matching Tilted pulse front
How to cheat at phase matching Tilted pulse front V g (800nm) cos c = v ph (THz)
How to cheat at phase matching Tilted pulse front Grating
How to cheat at phase matching Tilted pulse front
How to cheat at phase matching Tilted pulse front Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO 3 H. Hirori, A. Doi, F. Blanchard, and K. Tanaka Citation: Applied Physics Letters 98, 091106 (2011); doi: 10.1063/1.3560062 View online: http://dx.doi.org/10.1063/1.3560062 > 1 MV/cm using 10 Hz Ti:Sapphire drive laser Can be improved by LN cooling THz electric field (MV/cm) Intensity (arb. units) 1.5 1.0 0.5 0.0-0.5 0 1 0 0 2 1 4 2 (a) 6 Delay time (ps) (b) Frequency (THz) 3 Vertical position (mm) 1.0 0.0-1.0 (c) -1.0 0.0 1.0 Horizontal position (mm) 1 (d) Intensity (arb. units) 0 Horizontal Vertical -1.0 0.0 1.0 Position (mm)
Phase sensitive detectors Measure electric field vs. time As name suggests, gives phase information that is lost in thermal detection Most examples of phase sensitive detectors look like pulse generators operated in reverse : Photoswitches EO sampling ABCD detection All rely on some type of nonlinearity involving THz and optical/nir light
Photoswitch Side view ammeter + current amplifier A THz pulse optical probe THz pulse optical probe Fig. 3.24. Schematic representation of THz pulse detection with a PC antenna Measure E-field via current across antenna Similar bandwidth limitations as generator (up to about 1.5 THz)
Photoswitch A Measurement procedure: pump-probe Vary relative delay between THz and NIR pulses
EO Sampling Electro-optic effect: ij = ij + (2) ijk E k (in materials without inversion symmetry) Applied E-field changes dielectric tensor New tensor may have different symmetry Can measure changes to dielectric tensor induced by THz field using higher frequency light
EO Sampling THz pulse Optical pulse EO crystal l/4 plate Wollaston prism Balanced photo-detector Probe polarization without THz field I y = I x = 1 I 2 1 I 2 0 0 with THz field I y I x = I0 ( 1 + D ) 2 f = I0 ( 1 - D ) 2 f
ABCD (Air Break-down Coherent Detection) Filter λ/2 wave plate Lens Si filter THz pulses Parabolic mirror Plasma Lens Filter Detector Delay BBO Lens Laser pulse 120 fs, 800 µj 800 nm, 1 khz Beam splitter FWM-like effect where E-field bias on gas is used Uses third order susceptibility to generate SHG Very broad bandwidth E signal 2! / 3 E! E! E THz
ABCD low probe intensity: I SHG / (E signal 2! ) 2 2 / E 2 THz Normal i zed SH Signal I 2ω (a.u.) x 4.5 x 1.5 x 1 1.8 x 10 14 W/cm 2 4.6 x 10 14 W/cm 2 9.2 x 10 14 W/cm 2 0 2 4 6 8 10 12 14 Delay (ps) high probe intensity: Simultaneous emission from plasma/self phase modulation I SHG / (E signal 2! + E LO 2! ) 2 heterodyne detection / ( (3) I 2! ) 2 I THz +(E LO 2! ) 2 +2 (3) I! E LO 2! E THz cos
ABCD (Air Break-down Coherent Detection, or Air-Biased Coherent Detection (if biased)) Also variants where DC bias is explicitly applied, gives better sensitivity Advantage: huge bandwidth, overlaps with conventional FTIR