Transcript OPTIČNI PARAMETRIČNI OSCILATOR

PHASE MATCHING
Janez Žabkar
Advisers: dr. Marko Zgonik
dr. Marko Marinček
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 conversion – second harmonic
generation
Nonlinear optics (1)
• The
EM field
waveofequation
a strong for
laser
a nonlinear
beam causes
medium is:
polarization of material:
• Putting in:
We get:
•• And
using:
Nonlinear optical
coefficient:
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:
Nonlinear optics (3)
• Hence the energy flow per unit area:
∆k=0
∆k≠0
=1 for ∆k=0
Birefringent phase matching (1)
type-I phase matching
for SHG:
Polar diagram showing the dependance of refractive
indices on propagation direction in a uniaxial, negative
birefringent crystal for type-I phase matching.
Birefringent phase matching (2)
type-II phase matching
for SHG:
Polar diagram showing the dependance of refractive
indices on propagation direction in a uniaxial, negative
birefringent crystal for type-II phase matching.
Poynting vector walk-off
Birefringent phase matching (3)
Dispersion in LiNbO3. The extraordinary refractive
index can have any value between the curves.
Quasi phase matching for SHG
Isotropic,
dispersive
Fundamental
fieldcrystal
(ω1)
lc = π/∆k, coherence length
∆k=k2-2k1
SH polarization of the
medium (ω2 = 2ω1)
SH field (ω2) radiated by
SH polarization
Periodically poled crystal
Nonlinear optical
coefficient:
d = ε0 χ / 2
A schematic representation of periodically poled nonlinear
crystal.
Performance of quasi phase matching
Recall:
growth of the SH field
Nonzero
elements
of tensor d:
For perfect birefringent PM (∆k=0)
and d(z)=d
eff:
d11 = - d12 = - d26
d14 = - d25
Where deff is an effective nonlinear coefficient obtained from
tensor d for a certain crystal, direction
of propagation
and
For ordinary
polarization:
polarization:
d = d cos(θ) cos(3φ)
eff
Nonzero
Example:elements
QUARTZof tensor d:
11
d11 = - d12 = - d26
For dextraordinary
polarization:
=
d
deff =14d11 cos252(θ) sin(3φ) +
d14 sin(θ) cos(θ)
Performance of quasi phase matching
growth of the SH field
lc
perfect periodically poled structure
We get:
Since:
Second harmonic field:
→
the difference to
birefringent PM
Performance of quasi phase matching
birefingent PM
∆k=0
QPM
∆k≠0
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
Fabrication of a periodically poled crystal
Conclusion
• Phase matching is necessary for efficient
nonlinear conversion
• Ideal birefringent PM: intensity has
quadratic dependence on interaction
length
• QPM: smaller efficiency than birefringent
PM (4/π2 factor in intensity)
• Advantages of QPM (larger nonlinear
coefficients,...)