phase matching janez Žabkar advisers: dr. marko zgonik dr. marko marinček
TRANSCRIPT
Introduction
• Motivation
• Basics of nonlinear optics
• Birefringent phase matching
• Quasi phase matching
• Conclusion
Motivation
• An eye-safe laser
• Problems with other laser sources (Er:glass – low repetition rates, diode lasers – small peak powers)
• Recent progress in growing large nonlinear crystals enables efficient conversion
• A basic condition for efficient nonlinear conversion is phase-matching
Nonlinear optics (1)
• EM field of a strong laser beam causes polarization of material:
• The wave equation for a nonlinear medium is:
• And using:• We get:
• Putting in:
Nonlinear opticalcoefficient:d = ε0 χ / 2
Nonlinear optics (2)
• The phase difference between the wave at ω3 and the waves at ω1, ω2 is:
• With the non-depleted pump approximation and condition for conservation of energy:
• We obtain:
Birefringent phase matching (1)
Polar diagram showing the dependance of refractive indices on propagation direction in a uniaxial, negative birefringent crystal for type-I phase matching.
type-I phase matching for SHG:
Birefringent phase matching (2)
Polar diagram showing the dependance of refractive indices on propagation direction in a uniaxial, negative birefringent crystal for type-II phase matching.
type-II phase matching for SHG:
Birefringent phase matching (3)
Dispersion in LiNbO3. The extraordinary refractive index can have any value between the curves.
Quasi phase matching for SHG
Fundamental field (ω1)
SH polarization of the medium (ω2 = 2ω1)
SH field (ω2) radiated by
SH polarization
Isotropic, dispersive crystal lc = π/∆k, coherence length ∆k=k2-
2k1
Periodically poled crystal
A schematic representation of periodically poled nonlinear crystal.
Nonlinear opticalcoefficient:d = ε0 χ / 2
Performance of quasi phase matching
Recall: growth of the SH field
For perfect birefringent PM (∆k=0) and d(z)=deff:
Where deff is an effective nonlinear coefficient obtained from tensor d for a certain crystal, direction of propagation and polarization:
Example: QUARTZNonzero elements of tensor d: d11 = - d12 = - d26
d14 = - d25
Nonzero elements of tensor d: d11 = - d12 = - d26
d14 = - d25
For ordinary polarization:deff = d11 cos(θ) cos(3φ)
For extraordinary polarization:deff = d11 cos2(θ) sin(3φ) + d14 sin(θ) cos(θ)
Performance of quasi phase matching
perfect periodically poled structurelc
growth of the SH field
We get:
Second harmonic field:
the difference to birefringent PM
Since: →
Some benefits of QPM• The possibility of using largest nonlinear
coefficients which couple waves of the same polarizations, e.g. in LiNbO3:
• Noncritical phase matching with no Poynting vector walk-off for any collinear interaction within the transparency range
• The ability of phase matching in isotropic materials, or in materials which possess too little / too much birefringence