Download Collinear and Non-Collinear Second Harmonic Generation

Collinear and Non-Collinear Second
Harmonic Generation in BBO
Crystal.
František Batysta
Petr Hříbek
Content
●
Introduction
●
Second harmonic generation
–
–
collinear
non-collinear
●
Goals of the project
●
Results
●
theoretical
●
experimental
●
Conclusion
●
Acknowledgement
Non-linear optics
●
Low intensities of
electric field
●
Very high intensity of
light
Several non-linear effects appears
Second harmonic generation
Third harmonic generation
High harmonic generation
Sum frequency generation
Optical parametric generation
…
(SHG)
(THG)
(HHG)
(SFG)
(OPG)
Goal of the project
●
To use nonlinear processes for frequency
conversion of the broadband fs pulses
●
Find the best configuration for broadband SHG
●
Determine spectral limits for common non-linear crystals
●
Both theoretical and experimental approach
Properties of ultra-short laser pulses
Electromagnetic wave
continuous wave
Spectra
   =2 k
  0 nm
150 fs pulse
 ≃10 nm
5 fs pulse
 ≃300 nm
Second harmonic generation
●
Conservation of
energy holds
automatically
●
Conservation of
momentum implies a
necessary condition:
k1 k1= k2
 11= 2
Phase velocities of fundamental beam and
second harmonic have to be synchronized
vf  1 =vf  2 
n 1 =n  2
Possible only in the birefringent crystals
Collinear second harmonic
generation (SHG)
●
The only one incoming fundamental beam
●
Simple geometry
●
The rest of fundamental beam has to be filtered
z
2ω
ω
ω
θ
c
x
y
Non-collinear second harmonic
generation
●
●
We can choose non-collinear angle α in order to
optimize SHG
The fundamental beam and the second harmonic are
automatically separated
z
ω
α
ω
2ω
θ
c
x
ω
y
Theoretical approach
3
2
[
]
2
32  
 2
2 sin  k l /2
2
I 2   l= 3 2
e 2   2  : e e l
I  0
 k l /2
c n  n 2 
∣
∣
n e c 
sin  pm =
o  b cos o  a cos  
{
2 1/2
2
o
 c −[o b  coso  a cos  ]
×
n 2o c −n 2e c 
[
 o b 
=asin
o a sin 
]
}
z
ω
α
ω
2ω
θ
c
H.J. Liu et al.
x
ω
y
Results – collinear mode
λ = 786 nm:
●
BBO
BBO
Δλ = 56 nm
Δt ≈ 40 fs
●
KDP
Δλ = 120 nm
Δt ≈ 20 fs
Δλ = 56 nm
Results – non-collinear mode
●
●
Both BBO and KDP are suitable for broadband
SHG in the near IR region
Wavelength ideal for broadband SHG slowly
varies with α.
α=10˚
∆λ≈300nm
α=1˚
KDP
λb≈1100nm
BBO
λb≈1500nm
LBO
λb≈1400nm
Experimental results
Collinear generation
λ = 786nm


2

Non-collinear generation

2

max =0.2
Non-collinear phase matching
Comparison of the theoretically
calculated phase matching
angle with the measured data
Power of the second harmonic
depending on the power of the
fundamental beam
BBO
α = 1˚
SHG of ultra-short visible pulses
●
●
BBO, LBO, KDP do not offer broadband SHG
with a visible light.
Possibilities:
●
try different nonlinear crystals
●
try different polarization of interacting beams
●
try different nonlinear process:
SHG of ultra-short visible pulses
●
●
BBO, LBO, KDP do not offer broadband SHG
with a visible light.
Possibilities:
●
try different nonlinear crystals
●
try different polarization of interacting beams
●
try different nonlinear process:
Other type of frequency conversion:
Parametric processes
Optical parametric generation
ki
idler
kp
pump
ks
BBO, λp = 393nm:
Phase matching for α = 3.5˚:
Δλ ≈ 300nm, Δt ≈ 4fs.
signal
α = 3.5˚
α = 5˚
kp= ki ks
 p =i  s
α = 1˚
Parametric scattering
The hottest news from the lab
Supercontinuum in glass
1500
a. u.
1000
500
0
400
450
500
550
600
650
700
750
650
700
750
wavelength [nm]
I/Io
OPA
1,2
1
0,8
0,6
0,4
0,2
0
400
450
500
550
600
wavelength [nm]
Conclusion
●
●
●
We have determined the maximum bandwidth
for the collinear and non-collinear SHG in the
most common nonlinear crystals (BBO, LBO,
KDP)
Calculated phase matching angles of crystals
are in a very good agreement with the
experiment
We are able to convert bandwidth of 150
nm via parametric amplification
Acknowledgements
Petr Hříbek
Thank you for your attention
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