SFG and SHG with ultrafast pulses 1
Second order nonlinear phenomena • No centrosymmetry: Non-zero • Long l (limited by coherence length, ) Angle tuning for phase matching ( D k = 0) • • High intensity of incident beam (limited by damage threshold) • Polarization of second harmonic: Perpendicular to that of fundamental
Birefringence and Phase matching Ordinary ( o ) ray (Incident angle-independent refractive index) Extraordinary ( e ) ray Optic axis, Z (Incident angle-dependent refractive index) Negative crystals Positive crystals n o and n e for 2 w Z Z n o (2 w ) = n e ( w ): n o n o n o ≥ n e n o ≤ n e Phase matching direction n e n e Second harmonic generation Polarization of SH is perpendicular to that of the fundamental Birefringent crystals can have one or more optic axes
Types of Phase matching for SFG l p ≤ l s ≤ l i Pump Signal Idler Scheme Material Phase- } e o o Type I Negative Uniaxial matching e o e Type II ( or IIA) type e e o Type III (or IIB) KD*P II e e e Type IV KTP II o o o Type V (or Type 0) LBO I o o e Type VI (or IIB or IIIA) } BBO I o e o Type VII (or IIA or IIIB) Positive Uniaxial LiNbO 3 I o e e Type VIII (or I) (5%MgO)
SHG for ultrafast pulses Ultrashort pulses: High Intensity Spectral bandwidth Phase matching: Entire band D k . l ≤ 2.78: Sufficient R. C. Miller, Phys. Lett. 26A (1968) 177: 1 cm KDP crystal: Dn = 20 cm -1 1 cm LiNbO 3 crystal: Dn = 0.5 cm -1 for 1064 nm
Group delay Plane waves: Phase velocity Pulsed light: Wavepacket Expanding
Group delay Wavepacket traveling Fundamental and SH: Different group velocities with group velocity of Amplitude of wavepacket
Group delay Wavepacket traveling Fundamental and SH: Different group velocities with group velocity of Difference in times of passage of fundamental and SH through NLO crystal: For
Group delay D t ( ps cm -1 ) Wavepacket traveling Crystal with group velocity of LiNbO 3 6 LiIO 3 0.7 KDP 0.08 Difference in times of passage of fundamental and SH through NLO crystal: For
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