Marco Polo Moreno de Souza - Marco Polo Moreno de Souza ......Marco Polo Moreno de Souza (UNIR) FWM...
Transcript of Marco Polo Moreno de Souza - Marco Polo Moreno de Souza ......Marco Polo Moreno de Souza (UNIR) FWM...
Parametric four-wave mixing in atomic vapor inducedby a frequency-comb and a cw laser
Jesus P. Lopez, Marcio H. G. de Miranda, Sandra S. ViannaDepartamento de Fısica, Universidade Federal de Pernambuco
Marco P. M. de SouzaDepart. de Fısica, Universidade Federal de Rondonia, Campus Ji-Parana
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 1 / 16
Introduction
The objective is to study the coherent blue light generated inrubidium vapor due to the combined action of an ultrashort pulsetrain and a cw diode laser.
Coherent blue beam
Rubidium vapor
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 2 / 16
Four-wave mixing
Four-wave mixing
Four-wave mixing is a nonlinear process that involves fourelectromagnetic waves.
In general, we have three incident beams and one generated beam.
In the weak interaction limit, it is a third-order process. We areinterested in the generated field that is the result from thepolarization that can be expressed as
P4 = ε0χ(3)E1E2E3
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 3 / 16
Four-wave mixing
Four-wave mixing
Four-wave mixing is a nonlinear process that involves fourelectromagnetic waves.
In general, we have three incident beams and one generated beam.
In the weak interaction limit, it is a third-order process. We areinterested in the generated field that is the result from thepolarization that can be expressed as
P4 = ε0χ(3)E1E2E3
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 3 / 16
Four-wave mixing
Four-wave mixing
Four-wave mixing is a nonlinear process that involves fourelectromagnetic waves.
In general, we have three incident beams and one generated beam.
In the weak interaction limit, it is a third-order process. We areinterested in the generated field that is the result from thepolarization that can be expressed as
P4 = ε0χ(3)E1E2E3
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 3 / 16
Correlated work
Correlated work
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 4 / 16
Correlated work
Correlated work
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 4 / 16
Setup
Setup
1/ 25S
3/ 25P
5/ 25D
6P
420 nm
5.2 mµ776 nm
780 nmDiode(generated)
(generated)
Ti:sapph
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 5 / 16
Experimental Results
Experimental Results
Icw = 1.9 W/cm2
Ifs = 1.0 mW/cm2
(each mode)
T = 85oC
Broad peaks:fluorescence induced byboth lasers
Flat Background:fluorescence induced byfemtosecond laser
-2 0 2 4 60.0
0.1
0.2
0.3
0.4
0.5
0.6
85Rb, Fg=2
85Rb, Fg=3
87Rb, Fg=2
Diode frequency (GHz)
Blu
e in
tens
ity (
arb.
uni
ts)
saturated absorption
87Rb, Fg=1
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 6 / 16
Experimental Results
Experimental Results
Icw = 1.9 W/cm2
Ifs = 1.0 mW/cm2
(each mode)
T = 85oC
Broad peaks:fluorescence induced byboth lasers
Flat Background:fluorescence induced byfemtosecond laser
-2 0 2 4 60.0
0.1
0.2
0.3
0.4
0.5
0.6
85Rb, Fg=2
85Rb, Fg=3
87Rb, Fg=2
Diode frequency (GHz)
Blu
e in
tens
ity (
arb.
uni
ts)
saturated absorption
87Rb, Fg=1
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 6 / 16
Experimental Results
Experimental Results
Icw = 1.9 W/cm2
Ifs = 1.0 mW/cm2
(each mode)
T = 85oC
Broad peaks:fluorescence induced byboth lasers
Flat Background:fluorescence induced byfemtosecond laser -2 0 2 4 6
0.0
0.1
0.2
0.3
0.4
0.5
0.6
85Rb, Fg=2
85Rb, Fg=3
87Rb, Fg=2
Diode frequency (GHz)
Blu
e in
tens
ity (
arb.
uni
ts)
saturated absorption
87Rb, Fg=1
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 6 / 16
Experimental Results
Polarization and density dependence
-3 -2 -1 0 1 20.0
0.1
0.2
0.3
0.4
0.5 Blue fluorescence at 90o
-2 -1 0 10.15
0.20
0.25
0.30
Blu
e in
tens
ity (a
rb. u
nits
)
Diode frequency (GHz)
parallelpolarization
perpendicular polarization
P
Rubidium vapor
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 7 / 16
Experimental Results
Polarization and density dependence
-3 -2 -1 0 1 20.0
0.1
0.2
0.3
0.4
0.5 Blue fluorescence at 90o
-2 -1 0 10.15
0.20
0.25
0.30
Blu
e in
tens
ity (a
rb. u
nits
)
Diode frequency (GHz)
parallelpolarization
perpendicular polarization
P
Rubidium vapor
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 7 / 16
Experimental Results
Polarization and density dependence
-3 -2 -1 0 1 20.0
0.1
0.2
0.3
0.4
0.5 Blue fluorescence at 90o
-2 -1 0 10.15
0.20
0.25
0.30
Blu
e in
tens
ity (a
rb. u
nits
)
Diode frequency (GHz)
parallelpolarization
perpendicular polarization
P
Rubidium vapor
0.00
0.05
0.10
0.00
0.05
0.10
0.0
0.2
0.4
-2 -1 0 10.0
0.2
0.4
87 Rb, 2gF =
Blu
e in
tens
ity (
arb.
uni
ts)
o82 C
o87 C
o73 C
( )d
85 Rb, 3gF =
( )c
( )b
( )a o72 C
Diode frequency (GHz)
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 7 / 16
Experimental Results
Experimental Results
T = 85oC
Slow scanning
Average of 10measurements
Peak linewidths: ≈ 55 MHz
Frequency differencebetween two adjacentpeaks: 78± 4 MHz
-600 -300 0 300 6000.00
0.05
0.10
0.15
0.20
0.25
Blu
e in
tens
ity (
arb.
uni
ts)
Diode frequency (MHz)
85Rb, Fg = 3
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 8 / 16
Experimental Results
Experimental Results
T = 85oC
Slow scanning
Average of 10measurements
Peak linewidths: ≈ 55 MHz
Frequency differencebetween two adjacentpeaks: 78± 4 MHz
-600 -300 0 300 6000.00
0.05
0.10
0.15
0.20
0.25
Blu
e in
tens
ity (
arb.
uni
ts)
Diode frequency (MHz)
85Rb, Fg = 3
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 8 / 16
Experimental Results
Experimental Results
T = 85oC
Slow scanning
Average of 10measurements
Peak linewidths: ≈ 55 MHz
Frequency differencebetween two adjacentpeaks: 78± 4 MHz -600 -300 0 300 600
0.00
0.05
0.10
0.15
0.20
0.25
Blu
e in
tens
ity (
arb.
uni
ts)
Diode frequency (MHz)
85Rb, Fg = 3
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 8 / 16
Experimental Results
Density dependence
Femtosecond and diodelasers in resonance withyour transitions
Exponential growth
“Threshold” shift as afunction of the diodeintensity
0 10 20 30 400.0
0.1
0.2
0.3
0.4
0.5
Icw
= 9.4 W/cm2
Atomic density (1012 cm-3)PF
WM
sig
nal a
mpl
itude
(ar
b. u
nits
)
Icw
= 1.9 W/cm2
0
1
2
3
PF
WM
sig
nal a
mpl
itude
(ar
b. u
nits
)
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 9 / 16
Experimental Results
Density dependence
Femtosecond and diodelasers in resonance withyour transitions
Exponential growth
“Threshold” shift as afunction of the diodeintensity
0 10 20 30 400.0
0.1
0.2
0.3
0.4
0.5
Icw
= 9.4 W/cm2
Atomic density (1012 cm-3)PF
WM
sig
nal a
mpl
itude
(ar
b. u
nits
)
Icw
= 1.9 W/cm2
0
1
2
3
PF
WM
sig
nal a
mpl
itude
(ar
b. u
nits
)
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 9 / 16
Experimental Results
Density dependence
Femtosecond and diodelasers in resonance withyour transitions
Exponential growth
“Threshold” shift as afunction of the diodeintensity
0 10 20 30 400.0
0.1
0.2
0.3
0.4
0.5
Icw
= 9.4 W/cm2
Atomic density (1012 cm-3)PF
WM
sig
nal a
mpl
itude
(ar
b. u
nits
)
Icw
= 1.9 W/cm2
0
1
2
3
PF
WM
sig
nal a
mpl
itude
(ar
b. u
nits
)
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 9 / 16
Theory
Theory
Diamond-type four-level systeminteracting with four cw lasers.
Ω1: diode laserΩ2: one mode of the femtosecond laserΩ3: seed fieldΩ4: blue beam generated
Hint = −µ · E
(Dipole electric approximation)
1
2
3
4
1Ω
2Ω3Ω
4Ω
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 10 / 16
Theory
Theory
Diamond-type four-level systeminteracting with four cw lasers.
Ω1: diode laserΩ2: one mode of the femtosecond laserΩ3: seed fieldΩ4: blue beam generated
Hint = −µ · E
(Dipole electric approximation) 1
2
3
4
1Ω
2Ω3Ω
4Ω
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 10 / 16
Theory
Maxwell-Bloch equations
∂ρ
∂t= − i
[H, ρ
](Liouville-Neumann)
∂2E
∂z2− 1
c2∂2E
∂t2= µ0
∂2P
∂t2(Wave equation)
P = N 〈µ〉 (Polarization)
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 11 / 16
Theory
Maxwell-Bloch equations
∂ρjk(z, t)
∂t= −(iωjk + γjk)ρjk(z, t)− i
〈j| [Hint, ρ] |k〉
∂Ωj(z, t)
∂z= −iαjkγjkσjk(z, t)
where
Ωj =µjkE
0j
(Rabi frequency)
αjk =µ2jkωj
2cε0γjkN
σjk = ρjke−iωjt
1
2
3
4
1Ω
2Ω3Ω
4Ω
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 12 / 16
Theory
Theoretical result
Numerical solution of the equations
All fields at resonance
Initial conditions:Ω1 = 0.7γ22, Ω2 = 2.4γ33, Ω3 = 2.4× 10−7γ33 and Ω4 = 0ρ11 = 1, ρij = 0 for (i, j) 6= (1, 1)
0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
1.0 Diode Blue
α12
z
Ω1 (
norm
aliz
ed)
0
500
1000
1500
2000
2500
Ω4
(rad
/s)
0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
1.0
α12
z
ρ11
ρ22
ρ33
ρ44
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 13 / 16
Theory
Theoretical result
Numerical solution of the equations
All fields at resonance
Initial conditions:Ω1 = 0.7γ22, Ω2 = 2.4γ33, Ω3 = 2.4× 10−7γ33 and Ω4 = 0ρ11 = 1, ρij = 0 for (i, j) 6= (1, 1)
0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
1.0 Diode Blue
α12
z
Ω1 (
norm
aliz
ed)
0
500
1000
1500
2000
2500
Ω4
(rad
/s)
0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
1.0
α12
z
ρ11
ρ22
ρ33
ρ44
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 13 / 16
Theory
Theoretical result
0 2 4 6 8 10
0
20
40
60
80
α12
z
Ω4 (
rad/
s)
0
500
1000
1500
2000
2500
Ω1 = 1.4γ
22
Ω1 = 0.7γ
22
Ω4 (
rad/
s)
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 14 / 16
Conclusions
Conclusions
We have investigated the coherent blue light generated in atomicvapor using a parametric four-wave mixing process due to thecombined action of a cw laser and a train of ultrashort pulses.
Many modes can be responsible for inducing the nonlinear process.
Blue signal characterization: exponential growth with saturation.
The density dependence was theoretically modeled.
Next step: frequency diode dependence modeling with CUDAparallel programming (See poster P116 this afternoon).
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 15 / 16
Acknowledgments
Thank you very much!
Marco Polo Moreno de Souza (UNIR) FWM in Rb vapor Seminario de grupo 16 / 16