Download STIMULATED RAMAN SCATTERING

Erik Jonsson School
PhoTEC
The University of Texas at Dallas
STIMULATED RAMAN SCATTERING (1)
• Origin: Inelastic scattering of light by optical phonons
EXCITED ELECTRONIC STATES
ωL
ωS
ωv
EXCITED
VIBRATIONAL
STATE
c C. D. Cantrell (11/1999)
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
STIMULATED RAMAN SCATTERING (2)
• Classical model of Raman scattering
Dipole moment induced in an atom or molecule by an external electric
field:
µ = αE
The polarizability α depends on the amplitude of vibration, q:
∂α q + ···
α = α0 +
∂q q=0
Approximate expression for macroscopic electric polarization:
∂α P = N µ = N αE = N α0 +
q + · · · E = PL + PN L
∂q q=0
◦ Linear polarization: PL = N α0E (same frequency as E)
∂α qE (different frequency)
◦ Nonlinear polarization: PN L = N
∂q q=0
c C. D. Cantrell (05/2000)
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
STIMULATED RAMAN SCATTERING (3)
• Work done per molecule by a slowly-turned-on external field in inducing a
dipole moment:
dW = E · dµ
= E · (αdE)
= d( 12 αE2)
W = 12 αE2
Force on a molecular vibrational coördinate q:
∂W
2
1 ∂α F =
E
=2
∂q
∂q q=0
c C. D. Cantrell (05/2000)
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
STIMULATED RAMAN SCATTERING (4)
• Equation of motion for vibrational coördinate:
2
dq
dq
m 2 + mΓ + mωv2q = F =
dt
dt
1
2
∂α 2
E
∂q q=0
Assume that E is the sum of a Stokes wave, ES , and a co-propagating
laser (pump) wave, EL:
E = EL + ES
i(βL z−ωL t)
EL(rT , z, t) = Re êLψL(rT )EL(z, t)e
i(βS z−ωS t)
ES (rT , z, t) = Re êS ψS (rT )ES (z, t)e
(EL + ES )2 = E2L + 2EL · ES + E2S
= 14 [2(êL · êS )ψL(rT )ψS (rT )∗
× EL(z, t)ES (z, t)∗ei[(βL−βS )z−(ωL−ωS )t] + · · · ]
c C. D. Cantrell (10/2001)
The University of Texas at Dallas
Erik Jonsson School
PhoTEC
STIMULATED RAMAN SCATTERING (5)
• Interference between EL and ES drives the vibrational motion:
2
dq
dq
(êL · êS ) ∂α ∗ i[(βL −βS )z−(ωL −ωS )t]
2
∗
+
ω
+
Γ
q
=
F
(t)
=
ψ
ψ
E
E
L
L
Se
v
S
2
dt
dt
4m ∂q q=0
Assume that q oscillates at ωL − ωS :
êL · êS i[(βL−βS )z−(ωL−ωS )t]
∗ −i[(βL −βS )z−(ωL −ωS )t] ∗
∗
Qe
q=
ψLψS + Q e
ψLψS
2
Resulting equation for Q:
2
2
Q
dQ
d
2
ωv − (ωL − ωS ) − i(ωL − ωS )Γ Q + Γ − 2i(ωL − ωS )
+ 2
dt
dt
1 ∂α ∗
=
E
(z,
t)E
L
S (z, t)
2m ∂q q=0
In the steady state, Q̈ = Q̇ = 0
c C. D. Cantrell (10/2001)
The University of Texas at Dallas
Erik Jonsson School
PhoTEC
STIMULATED RAMAN SCATTERING (6)
• The Green function for the vibrational motion satisfies the equation
d2g(t, t)
dg(t, t)
2
+
ω
+
2γ
g(t,
t
)
=
δ(t
−
t
) (where Γ = 2γ)
v
dt2
dt
and the causality condition: ∀ t > t : g(t, t) = 0
Particular integral:
1 ∞
q(t) =
g(t, t)F (t)dt
m −∞
Green function:
−γ(t−t)
1
θ(t − t)
g(t, t ) = sin ωv (t − t ) e
ωv
where ωv = ωv2 − γ 2 and θ is the unit step function
Vibrational amplitude when ωv ≈ ωv :
t
−γ(t−t)
1 ∂α sin
ω
(t
−
t
)
e
E
(t
)
·
E
(t
)
dt
q(t) =
L
R
v
mωv ∂q q=0 −∞
c C. D. Cantrell (05/2001)
The University of Texas at Dallas
Erik Jonsson School
PhoTEC
STIMULATED RAMAN SCATTERING (7)
• Steady-state solution for Raman vibrational amplitude:
1 ∂α EL(z, t)ES (z, t)∗
Q(z, t) =
2m ∂q q=0 ωv2 − (ωL − ωS )2 − i(ωL − ωS )Γ
When Γ ωv , the denominator is approximately Lorentzian:
ωv2 − (ωL − ωS )2 − i(ωL − ωS )Γ ≈ (ωv − ωL + ωS )(ωv + ωL − ωS ) − iΓωv
Γ
≈ 2ωv ωv − ωL + ωS − i
2
c C. D. Cantrell (10/2001)
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
STIMULATED RAMAN SCATTERING (8)
• Steady-state approximation to Q:
Q(z, t)
1 ∂α EL(z, t)ES (z, t)∗(ωv − ωL + ωS + iΓ/2)
≈
4mωv ∂q q=0
(ωv − ωL + ωS )2 + (Γ/2)2
• Vibrational envelope when ωv = ωL − ωS (on the Raman resonance):
∂α i
∗
E
(z,
t)E
Q(z, t) =
L
S (z, t)
2mΓωv ∂q
q=0
c C. D. Cantrell (10/2001)
The University of Texas at Dallas
Erik Jonsson School
PhoTEC
STIMULATED RAMAN SCATTERING (9)
• Slowly varying contribution, near the Stokes frequency, ωs, and in the direction of the Stokes electric field, êS , to the Raman electric polarization
PN L = N ∂α
qE:
∂q q=0
−i ∗ ∗ iωS t
−iωS t
êS + PS ψS e
êS + terms at other frequencies
PN L =
PS ψS e
2
êL · êS ∗ ∗
∗ −i(ωL −ωS )t
i(ωL −ωS )t
QψLψS e
qE =
+ Q ψLψS e
4 ∗ ∗ iωL t
−iωL t
× ELψLe
êL + ELψLe
êL + · · ·
êL · êS ∗
2
−iωS t
Q EL|ψL| ψS êLe
+ terms at other frequencies
=
4
Then
2
i ∂α ∗
2 ψS , |ψL | ψS PS (z, t) = N
Q (z, t)EL(z, t)(êL · êS )
2 ∂q q=0
ψS , ψS Note that PS is proportional to the product Q∗EL
c C. D. Cantrell (10/2001)
The University of Texas at Dallas
Erik Jonsson School
PhoTEC
STIMULATED RAMAN SCATTERING (10)
• Contribution at the Stokes
frequency ωs to the Raman electric polarization
PN L(rT , z, t) = N ∂α
∂q q=0 q(rT , z, t)E(rT , z, t) (including mode functions):
2
2 2
|
|ψ
|
d rT
|ψ
L
S
i ∂α ∗
2
(
ê
·
ê
)
E
(z,
t)Q
(z, t)
PS (z, t) = N
L
S
L
2 ∂q q=0
|ψS |2 d2rT
Fiber paraxial wave equation for Raman-Stokes scattering:
∂ES
α
2πωS
= − ES +
PS
∂z 2
n0 c
c C. D. Cantrell (10/2001)
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
STIMULATED RAMAN SCATTERING (11)
• Fiber paraxial wave equation for Raman-Stokes scattering:
∂ES
α
2
1
=
−
E
+
g
(∆ω)
|E
|
ES
S
R
L
2
∂z 2
Detuning from peak of Raman gain curve:
∆ω = ωv − ωL + ωS
Frequency-dependent Raman gain:
(Γ/2)2
2
gR (∆ω) = gR (0)
(
ê
·
ê
)
L
S
(∆ω)2 + (Γ/2)2
Maximum Raman gain:
πN ωS
gR (0) =
cn0mωv Γ
2
∂α ∂q q=0
W. Kaiser and M. Maier, “Stimulated Rayleigh, Raman and Brillouin Spectroscopy”, in F. T. Arecchi and E. O. Sculz-Dubois, editors,
Laser Handbook, Vol. 2, pp. 1077–1150, Eq. (30).
c C. D. Cantrell (10/2001)
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
PROPAGATION OF RAMAN-STOKES POWER
• Fiber paraxial wave equation for Raman-Stokes scattering:
∂ES
α
2
1
=
−
E
+
g
(∆ω)
|E
|
ES
S
R
L
2
∂z
2
∗
Multiply ∂ES /∂z by ES , take the complex conjugate, and add:
∗
∂E
ES S
∂z
∂
∂ES ∗
2
E
+
=
|E
|
S
S
∂z ∂z Propagation equation for the intensity:
∂
2
2
2
2
|E
|
=
−α|E
|
+
g
(∆ω)
|E
|
|E
|
S
S
R
L
S
∂z Normalize: FL = (cn0,LAe/8π)1/2 EL ⇒ laser power is PL = |FL|2
∂
8πgR (∆ω)
PL PS
P
=
−αP
+
S
S
∂z
cn0,LAe
c C. D. Cantrell (05/2000)
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
STIMULATED RAMAN SCATTERING (12)
• Raman gain:
πN ωS
gR (0) =
cn0mωv Γ
2
∂α ∂q q=0
The peak Raman gain is proportional to the Stokes frequency, ωS
Propagation equation for Raman-Stokes power in practical units:
PS
dPS
= −αPS + (gR PL)
dz Ae
where
In SiO2 fiber:
1 × 10−22 cm · s 1 × 10−11
gR (0) ≈
=
cm/W,
λS (cm) erg
λS (µm)
gR (0)
8π
=
gR (0)
cn0
ωv ≈ 12−15×103 GHz
Crude fit to observed frequency dependence:

 (νL − νS ) (Hz) 13
g
(0),
if
ν
−
ν
<
1.5
×
10
Hz;
L
S
R
gR (∆ω) ≈
1.5 × 1013
0,
otherwise.
c C. D. Cantrell (05/2000)
The University of Texas at Dallas
Erik Jonsson School
PhoTEC
RAMAN GAIN SPECTRUM OF SILICA FIBER
• From G.E.Walrafen and P.N.Krishnan, “Model analysis of the Raman spectrum from fused silica optical fibers”, Applied Optics 21, 359-360 (1982)
c D. Hollenebck (7/2000)
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
UNITS FOR SRS GAIN
• Basic cgs mechanical units:
gm · cm2
−7
[work] =
unit:
1
erg
=
10
Joule
s2
• Basic Gaussian cgs electromagnetic units:
3 1/2
gm · cm
unit: stat-Coulomb (stC)
[charge] =
s2
gm 1/2 erg 1/2
=
unit: stat-Volt per cm (stV/cm)
[E] = [P] =
2
3
cm · s
cm ∂α 3
2
−3
[α] = cm ,
,
[N
]
=
cm
=
cm
∂q q=0
• Units of Raman gain:
s2
cm2
[gR ] =
=
,
gm
erg
[gR ]
cm · s
=
erg
c C. D. Cantrell (05/2000)
The University of Texas at Dallas
Erik Jonsson School
PhoTEC
LENGTH SCALING FOR SRS
• Normalized fiber paraxial wave equation for Raman-Stokes scattering,
assuming a co-propagating laser (pump) wave:
1 PL(z )
∂
P
P
(z
)
=
−αP
(z
)
+
(z
)
S
S
S
∂z
LR PL(0)
Characteristic length for e-fold growth of the Raman-Stokes wave:
Ae
cn0,LAe
=
≈ 3750 km if PL(0) = 1 mW
LR =
8πfR gR(∆ω)PL(0) fRgR (∆ω)PL(0)
• Normalized fiber paraxial wave equation for Raman-Stokes scattering,
assuming a counter-propagating laser (pump) wave:
∂
1 PL(z )
P
(z
)
=
−αP
(z
)
+
(z
)
P
S
S
S
∂z LR PL(L)
Characteristic length for e-fold growth of the Raman-Stokes wave:
cn0,LAe
LR =
≈ 3.75 km if PL(L) = 1 W
8πfRgR (∆ω)PL(L)
c C. D. Cantrell (05/2000)
The University of Texas at Dallas
Erik Jonsson School
PhoTEC
PROPAGATION OF SRS POWER
IN TERMS OF POLARIZATION
• Fiber paraxial wave equation for Raman-Stokes scattering:
∂ES
α
2πωS
= − ES +
PS
∂z 2
n0 c
∗
ES ,
Multiply ∂ES /∂z by
take the complex conjugate, and add to get
(∂/∂z )|ES |2
Propagation equation for the intensity:
∗ ∂
4πωS
2
2
|ES | = −α|ES | +
Re PS ES
∂z n0 c
Normalize: FL = (cn0,LAe/8π)1/2 EL ⇒ laser power is PL = |FL|2
∗ ∂
ωS Ae
Re PS ES
PS = −αPS +
∂z
2
c C. D. Cantrell (05/2000)
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
STIMULATED RAMAN SCATTERING (13)
• Power amplification by stimulated Raman scattering:
From the gain equation:
PS (L) = egR(0)PLLe(L)/Aeff −αLPS (0)
◦ This assumes that the laser pump is not depleted
From the paraxial wave equation:
◦ Growth of Stokes power:
g (0) PL
dPS
PS
= −αPS + ωS R
dz
ωS
Aeff
◦ Depletion of laser pump power:
gR (0) PS
dPL
PL
= −αPL − ωL
dz
ωS
Aeff
c C. D. Cantrell (09/2000)
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
STIMULATED RAMAN SCATTERING (14)
• The Manley-Rowe relations for SRS:
Photon fluxes:
PS
,
NS =
ωS
At zero attenuation (α = 0),
PL
NL =
ωL
1 dPS dNS ωLgR (0)
=
=
NL NS
ωS dz
dz
Aeff
1 dPL dNL
ωLgR (0)
NL NS
=
=−
ωL dz
dz
Aeff
The Manley-Rowe relations:
dNL
dNS
=−
dz
dz
c C. D. Cantrell (11/1999)
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
SPONTANEOUS vs. STIMULATED RAMAN SCATTERING
• Propagation equation for Raman-Stokes photon number NS ∝ PS :
dNS
1
= −αS NS (z) + gR (0)IL(z) NS (z) +
dz
stimulated
spontaneous
Spontaneous scattering limit (NS 1):
L
NS (z) ≈
gR (0)IL(z) dz = gR (0)IL(0)Leff (L)
0
Stokes photon number flux grows linearly when z α−1
Stimulated scattering limit (NS 1):
NS (z) ≈ egR(0)IL(0)Leff (L)−αL
Stokes photon number flux grows exponentially when z α−1
c C. D. Cantrell (03/2001)
The University of Texas at Dallas
Erik Jonsson School
PhoTEC
STIMULATED RAMAN SCATTERING (15)
• Limits on number N of WDM channels imposed by SRS:
Reference: A. R. Chraplyvy, Electronics Letters 20, 58–59 (1984)
The highest-frequency channel (n = 0) is depleted by Raman-Stokes scattering into the N − 1 other channels, using a crude spectral fit:
N −1
P ωn n∆ν
1 dP0
= −α −
gR (0)
P0 dz
Aeff n=1 ω0
1.5 × 1013
P
∆ν
N (N − 1)
= −α − gR (0)
Aeff 1.5 × 1013
2
Nonlinear attenuation of channel 0 by SRS:
∆ν
N (N − 1)
P0(L)
P
αL + ln
= −gR (0)
Le(L)
13
P0(0)
Aeff 1.5 × 10
2
c C. D. Cantrell (11/1999)
The University of Texas at Dallas
Erik Jonsson School
PhoTEC
STIMULATED RAMAN SCATTERING (16)
• Spacetime approach to Raman scattering:
Coupled-wave theory breaks down for pulses shorter than ≈ 100 fs
Approach of Blow & Wood: Account for Raman scattering through a
time-delayed response function, replacing F(z , t)|F(z , t)|2 with
∞
∞
F(z , t)
r(t−t)|F(z , t)|2dt = F(z , t)
r(t)|F(z , t−t)|2dt
−∞
−∞
Electronic (instantaneous) + vibrational (delayed) response:
r(t) = (1 − fR )δ(t) + fR hR (t)
Delay-differential propagation equation:
2
3
∂
β2 ∂
β3 ∂
+
i
−
F(z
,t)
2
3
∂z
2 ∂t
6 ∂t
∞
α
2 ∂
2 = − F + iγ 1 + i
F(z
,
t
)
r(t
)|F(z
,
t
−
t
)| dt
2
ω0 ∂t
−∞
c C. D. Cantrell (03/2001)
The University of Texas at Dallas
Erik Jonsson School
PhoTEC
RAMAN RESPONSE FUNCTION
• Response function, hR (t), obtained from the experimental Raman gain spectrum by R. H. Stolen et al., “Raman response function of silica-core fibers”,
J. Opt. Soc. Am. B 6, 1159-1166 (1989)
c D. Hollenebck (3/2000)
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
STIMULATED RAMAN SCATTERING (17)
• Method of moments applied to Raman scattering:
Time-delayed response
∂
|F(z , t − t )| = |F(z , t )| − t |F(z , t)|2 + · · ·
∂t ∞
−∞
From
2
2
2
2
hR (t)dt
−∞ ∞
∂
2
− |F(z , t )|
thR (t)dt
∂t
−∞
hR (t )|F(z , t − t )| dt =|F(z , t )|
∞
−∞
∞
r(t) dt = 1, get
∞
−∞
Raman response time:
hR (t) dt = 1
TR =
∞
−∞
t hR (t) dt
c C. D. Cantrell (03/2001)
The University of Texas at Dallas
Erik Jonsson School
PhoTEC
STIMULATED RAMAN SCATTERING (18)
• Generalized nonlinear Schrödinger equation including Raman
scattering:
∂
β2 ∂ 2
β3 ∂ 3
+
i
−
F(z
,t)
∂z 2 ∂t2
6∂t3
α
2 ∂
∂
2
2
(1
−
2f
= − F + iγ 1 + i
)|F|
F
−
T
F
|F|
r
R
2
ω0 ∂t
∂t
Must be solved numerically
c C. D. Cantrell (11/1999)
The University of Texas at Dallas
Erik Jonsson School
PhoTEC
NUMERICAL METHODS (1)
• Numerical methods for the generalized nonlinear Schrödinger equation
2
3
∂
β2 ∂
β3 ∂
+
i
−
F(z
,t)
∂z 2 ∂t2
6
∂t3
α
2 ∂
∂
2
2
|F|
= − F + iγ 1 + i
F
+
f
T
F
|F|
R
R
2
ω0 ∂t
∂t
Strategy: Discretize the time derivatives, then solve the resulting ODE in
z
◦ Pseudospectral methods: Evaluate time derivatives in Fourier space,
where ∂/∂t → −iω
◦ Finite-difference methods: Approximate time derivatives with difference quotients
c C. D. Cantrell (11/1999)
The University of Texas at Dallas
Erik Jonsson School
PhoTEC
NUMERICAL METHODS (2)
• Generalized nonlinear Schrödinger equation:
∂F
= (D̂ + N̂ )F
∂z
Dispersion and attenuation operator:
2
3
β2 ∂
β3 ∂
α
−
D̂ = − − i
2
2 ∂t2
6 ∂t3
◦ “Diagonal” in Fourier space
Nonlinear operator:
∂
2 ∂
2
2
|F|
N̂ = iγ 1 + i
+
f
T
|F|
R
R
ω0 ∂t
∂t
◦ “Diagonal” neither in Fourier space nor in t-space
c C. D. Cantrell (11/1999)
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
NUMERICAL METHODS (3)
• Split-step Fourier method:
F(z + h, t)
= F −1 exp
h
D̂ F exp
2
z +h
z
N̂ (z ) dz F −1 exp
h
D̂ F F(z , t)
2
F = discrete Fourier transform operator with respect to t
This formulation is appropriate
finite-difference method is
if a single-step
z +h
used to approximate exp z N̂ (z ) dz How to apply the split-step method is ambiguous if one uses a multistep
method, due to the choice of whether the function for the previous step
is evaluated in signal space or transform space
◦ To eliminate this ambiguity, the function should be evaluated using a
previous step that has been propagated in both domains
c C. D. Cantrell (10/2000)
The University of Texas at Dallas
Erik Jonsson School
PhoTEC
MOTIVATION FOR USING RAMAN AMPLIFICATION
• Long-distance transmission systems require amplification, preferably optical,
to compensate for linear attenuation
Erbium-doped fiber amplifiers (EDFAs)
◦ The majority of installed fiber is in the 1310 nm region. In order to use
EDFAs, replacement of the installed fiber would be required due to the
small amplification region centered about 1550 nm.
◦ EDFAs must be placed periodically along the fiber to achieve proper
amplification
Stimulated Raman scattering (SRS) amplification
◦ Since the Raman gain spectrum can include the 1310 nm region, it is
possible to use currently installed fiber
◦ Useful SRS amplification can be achieved with only the addition of a
counter-propagating pump beam originating at the receiver
◦ However, Raman amplification may lead to spatial hole burning
c D. Hollenebck (07/2000)
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
RAMAN AMPLIFICATION
• “A photon for a photon”
Manley-Rowe relation and Raman rate equation (for zero attenuation):
dNL
dNS
1 NL(z )
=
−
=
−
(z
)
N
S
dz
dz
LR NL(0)
◦ NS =
PS
ωS
is the Stokes photon flux; NL =
• Co-propagating laser and Stokes pulses
PL
ωL
is the laser photon flux
1st Stokes gain goes to zero when pump is depleted; then 1st Stokes pumps
2nd Stokes, etc.
1st Stokes intensity goes to zero when pump is depleted (InSb)
• Counter-propagating laser wave and Stokes pulse
Gain stays constant while Stokes grows exponentially
Stokes wave may be many times more intense than the pump
Stokes pulse acquires characteristic “shark fin” shape and shifts towards
earlier times
c C. D. Cantrell (10/2000)
Depletion of a co-propagating Raman pump beam
Pump
pulse
Externally
generated
Stokes
input pulse
t=0
t=
c
2L
Depleted pump
pulse
Amplified Stokes
pulse out
t=
c
L
© C. D. Cantrell and Dawn Hollenbeck 10/2001
The University of Texas at Dallas
Erik Jonsson School
PhoTEC
ANALYTICAL MODEL OF
CO-PROPAGATING RAMAN CONVERSION
c C. D. Cantrell (10/2000)
Co-propagating Raman pump depletion (Los Alamos, 1974)
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
EFFECTIVE LENGTH AND RAMAN LENGTH
• Effective length
1
1 − e−αz
≈
Lef f (z) =
α
α
αz 1
if
Pump and Raman gain vs. z
1e+03
1e-01
1e-03
1e-05
1e-03
1e-07
Raman pump
Raman gain
1e+00
1e-06
1e-09
1e-09
1e-11
0
125
250
375
500
z (km)
• Raman length
LR =
cn0,LAe
≈ 4.2 km if PL(L) = 1 W.
8πfR gR (∆ω)PL(L)
c C. D. Cantrell (10/2000)
Depletion of a counter-propagating Raman pump beam
Externally
generated
Stokes
input pulse
Length τp
pump pulse
t=0
t=
Interaction
zone
length
τp
2
τp
4
Amplified Stokes
pulse out
Depleted pump
pulse
t=
τp
2
After J. R. Murray et al., JQE 15, 342 (1979)
C. D. Cantrell and Dawn Hollenbeck 10/2001
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
“SHADOW” CAST BY A DEPLETING PULSE
T
T
T
−L/2
L/2
Z
c C. D. Cantrell (08/2000)
The University of Texas at Dallas
Erik Jonsson School
PhoTEC
“SHARK FIN” SHAPE OF AMPLIFIED STOKES PULSE
c C. D. Cantrell (10/2000)
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
STOKES POWER
100 W PUMP
5.0x10+08
Power (mW)
4.0x10+08
3.0x10+08
2.0x10+08
1.0x10
0.2
+08
0.1
0.0x10
+00
-18
-9
z (km)
0.0
0
9
18
Time (ps)
c D. Hollenbeck (07/2000)
Erik Jonsson School
PhoTEC
The University of Texas at Dallas
STOKES POWER
2 W PUMP
Power (mW)
5x10+08
4x10+08
3x10+08
2x10+08
1x10+08
0x10+00
-18
-14
-9
-5
0
Time (ps)
5
9
14
40.00
39.00
38.00
z (km)
37.00
36.00
18
c D. Hollenbeck and C. D. Cantrell (10/2001)