Generation and Application of Terahertz Pulses

Transcription

1 Preparation of the concerne sectors for eucational an R&D activities relate to the Hungarian ELI project Generation an Application of Terahertz Pulses János Hebling Márta Unferorben TÁMOP-4...C-//KONV--5 projekt

2 7. lecture: Single-cycle terahertz pulse sources II. Optical rectification. The inverse process: Electro-optic sampling DFG can be use for generation of raiation Broa spectrum of ultrashort pump pulse contains spectral content with frequency ifference Optical rectification (OR) TÁMOP-4...C-//KONV--5 projekt

3 P P () () ( w) () () A Optical rectification ( w) E( w) E( w) E( w, t) Acos ( wt - kz) () cos( wt kz) A cos(wt kz) E( w, t) A cos ( wt - kt) Acos ( wt - k P () () () () () A A t A A A cos w OR SHG cos( w t k z) A cos( w t k z) cos( w ( w w t k A A w z) cos( w w cos ) t ( k ( w k t w ) z k ) z) ) t ( k k ) z SFG DFG, OR, generation TÁMOP-4...C-//KONV--5 projekt

4 Optical rectification Using ultrashort laser pulses for excitation: E( w, t) A( t)cos ( ωt - kt) P () () A ().... ( t)cos ( w A w ( t)cos ) t ( k ( w k w ) z ) t ( k k ) z EOS signal (r. u) 5-5 Amplitue FFT (r. e.) Frequency () Time (ps) Single-cycle pulse Spectral content is etermine by: pump pulse uration phase-matching banwith absorption Effect of ispersion in range TÁMOP-4...C-//KONV--5 projekt

5 For constructive generation k Optical rectification That part of the nonlinear polarization which responsible for pulse generation is: () () P A ( t)cos ( w w) t ( k k) z pulse: E ( w, t) A( t)cos ( ωt - kt) ω ω ω k k is neee Velocity matching (phase matching) is neee: n gr p n Without velocity matching generation only at the two surfaces of the nonlinear crystal Example: generation in.5 mm LiNbO 3 l. Xu et al.: Appl. Phys. Lett. 6, 784 (99) TÁMOP-4...C-//KONV--5 projekt

6 Optical rectification Velocity matching Isotropic crystals: only possibility (if any) for velocity matching is choosing appropriate pump an/or wavelength (frequency) Refractive inices of ZnTe n p n 3.l ( l) 4.7 l.4 ( n) n 9.6 n A. Nahata et al., Appl. Phys. Lett. 6, 3 (996) Lee Y.-S.: Principles of Sci. & Tech., Springer 9 TÁMOP-4...C-//KONV--5 projekt

7 Optical rectification Velocity matching Coherent length: l c k n n c gr p n ZnTe CTe GaP InP GaAs l p (mm) Velocity matche pump wavelengths for generation M. Nagaia et al., Appl. Phys. Lett. 85, 3974 (4) TÁMOP-4...C-//KONV--5 projekt

8 Optical rectification Velocity matching Anisotropic (birefrigent) crystal: velocity matching by angle tuning Example: GaSe (see lecture 3) Other phase/velocity matching methos: Cherenkov (small spot size neee limite energy) Waveguie (large ispersion, practically no single-cycle generation) Tilte-pulse-front pumping (LiNbO 3, see lecture 8) Quasi-phase matching (no velocity matching, no single-cycle generation, as many cycles as the number of perios in the crystal) TÁMOP-4...C-//KONV--5 projekt

9 In the case of velocity matching an no ispersion Using the il () ijk Optical rectification Efficiency w n n contracte matrix v eff L I exp 3 c L sinh L 4 L 4 where l = for jk = 33 3,3 3,3, P P P x y z Ex Ey Ez EyE EzE ExE z x y Eq. For given polarization irection set eff can be calculate from the [ il ] matrix TÁMOP-4...C-//KONV--5 projekt 9

10 Optical rectification -matrices of EO crystals use for generation w eff L I For L << 3 n n c TÁMOP-4...C-//KONV--5 projekt v w eff I For L >> 3 n n c v

11 Optical rectification FOMs of a few crystals supposing mm crystal length an Material n gr n (cm - ) at FOM (pm cm /V ) CTe GaAs GaP ZnTe GaSe LiTaO LiNbO DAST TÁMOP-4...C-//KONV--5 projekt

12 Optical rectification in ZnTe Describe the fiel of the exciting optical pulse by: where q is the polar angle, an f is the azimuthal angle. Then accoring to Eq. the nonlinear polarization is: TÁMOP-4...C-//KONV--5 projekt

13 Optical rectification in ZnTe Has maximum if pump electric fiel in the {} plane Lee Y.-S.: Principles of Sci. & Tech., Springer 9 TÁMOP-4...C-//KONV--5 projekt

14 Optical rectification in ZnTe The [] irection is the irection of the bon between the Zn an Te in ZnTe Lee Y.-S.: Principles of Sci. & Tech., Springer 9 TÁMOP-4...C-//KONV--5 projekt

15 Optical rectification absorption of EO crystals Phonon-polariton ( )= + = ( + ) : h h : h : : h = Im ( ) amplitue absorption Multi-phonon absorption Free-carrier (see lecture ) TÁMOP-4...C-//KONV--5 projekt

16 Optical rectification absorption of EO crystals Phonon-polariton an two-phonon absorption in TnTe Dashe: polariton absorption Solie: total absorption G. Gallot et al., Appl. Phys. Lett. 74, 345 (999) TÁMOP-4...C-//KONV--5 projekt

17 Optical rectification Lowest TO-phonon frequencies of a few EO crystals ZnTe CTe GaP InP GaAs GaSe LiNbO 3 LiTaO 3 n TO () TO phonons have a role in the linear an nonlinear susceptibility, too! TÁMOP-4...C-//KONV--5 projekt

18 Electro-optic effect Electro-optic effect Pockels effect Pockels effect: static electric fiel inuce change of refractive inex (birefrigence) Pockels effect is use for example for Q-switching of lasers P () i ( w) where () ijk ( w, w,) j ( w) Ek () j, k () () ij ijk ( w, w,) E k ( w) k E ( w) E ( w) j () ij j Eq. EO Use Pockels effect for the quasi-static fiel of pulse: w Optical rectification: P () i ( w ) j, k () ijk ( w, w, w w ) E j ( w) E k ( w w ) TÁMOP-4...C-//KONV--5 projekt

19 Electro-optic sampling Using EO effect for measuring pulse shape The quasi-static fiel of pulse can inuce birefrigence through the Pockels effect Lee Y.-S.: Principles of Sci. & Tech., Springer 9 TÁMOP-4...C-//KONV--5 projekt

20 Electro-optic sampling in ZnTe-type material The fiel inuce birefringence is maximize when both an optical probe is polarize in the [] irection in a {} oriente crystal In this case the nonlinear polarization is given by: TÁMOP-4...C-//KONV--5 projekt

21 Electro-optic sampling in ZnTe-type materials In the case of velocity matching the phase retaration ifference between the two orthogonal component of the probe is: where n o is the refractive inex of the optical probe, an r 4, =4,4 /n o4 is the EO coefficient. The intensities at the two photoetector are: The signal of the balance photoetector is: TÁMOP-4...C-//KONV--5 projekt

22 Finite probe uration Dispersion of nonlinear susceptibility Velocity mismatch Group velocity ispersion of probe Phase velocity ispersion of Absorption of probe Absorption of Temporal step of the probe elay Electro-optic sampling Limits of resolution The response function of the sampling taking into account the most important limiting effects are: The spectrum of the measure EO (sampling) signal is: Eq. R The temporal shape of the EO signal is obtaine by Fourier transformation: TÁMOP-4...C-//KONV--5 projekt

23 Electro-optic sampling Limits of resolution The three terms in Eq. R are the autocorrelation of the optical probe fiel, the secon orer susceptibility, an the frequency filtering arising from the velocity mismatch, respectively. The later is given by: where the wave vector mismatch is given by: TÁMOP-4...C-//KONV--5 projekt

24 Electro-optic sampling Limits of resolution Normalize amplitue of the response function for ZnTe with ifferent thicknesses an fs probe uration Lee Y.-S.: Principles of Sci. & Tech., Springer 9 TÁMOP-4...C-//KONV--5 projekt

25 Control questions. What is optical rectification?. What are the main factors which etermine the spectral content of the pulses generate by optical rectification? 3. What types of velocity matching or phase matching can be use for optical rectification? 4. Which nonlinear optical tensor components are responsible for optical rectification for ZnTe, GaAs, GaSe an LiNbO 3? 5. What type of crystal cut an pump polarization result in maximal generation efficiency for zincblene-type crystals? 6. What are the main effects responsible for absorption in crystals? 7. How is an electro-optic sampling pulse shape measuring set-up built up an how oes it work? 8. What are the main limiting factors of the temporal resolution of EOS system? 9. What etermine the spectral range an the spectral resolution of an EOS system? TÁMOP-4...C-//KONV--5 projekt 5