Femtosecond Fiber Lasers
Based on Dissipative Processes
F. W. Wise
Department of Applied Physics
Cornell University
Tuesday, August 2, 2011
Femtosecond fiber lasers…





Andy Chong
Will Renninger
Khanh Kieu
Simon Lefrancois
Hannah Liu



Brandon Bale
Edwin Ding
Nathan Kutz
Tuesday, August 2, 2011
Dissipative solitons…

Introduction to nonlinear pulse propagation,
short-pulse generation

Femtosecond lasers without anomalous dispersion

Dissipative solitons

Implications for useful devices
---------------------------------------------------------------------

Self-similar pulse evolution in a laser
Tuesday, August 2, 2011
Disclaimers

Lack of mathematical rigor

Meaning/use of “soliton”
Tuesday, August 2, 2011
Introduction to ultrafast science
Tuesday, August 2, 2011
Ultrashort light pulses
For λ = 1000 nm, 1 cycle = 3.3 fs
Tuesday, August 2, 2011
Why use ultrashort light pulses?

“Strobe light” to observe ultrafast processes
Tuesday, August 2, 2011
Why use ultrashort light pulses?

“Strobe light” to observe ultrafast processes

Produce high E field with modest energy/average power
nonlinear microscopies
Tuesday, August 2, 2011
Why use ultrashort light pulses?

“Strobe light” to observe ultrafast processes

Produce high E field with modest energy/average power
nonlinear microscopies

Precision control of (nonlinear) energy deposition
material processing (absorbing and transparent)
Tuesday, August 2, 2011
Applications of femtosecond lasers









Ultrafast phenomena
Precision material processing
Thin film characterization
Terahertz generation and detection
Nonlinear microscopy
High-field physics
Inertial confinement fusion
Attosecond science
Surgery
Tuesday, August 2, 2011
Applications of femtosecond lasers

Ultrafast phenomena
Tuesday, August 2, 2011
Applications of femtosecond lasers

Precision material processing
Tuesday, August 2, 2011
Femtosecond lasers
Ti:sapphire laser
+ power
+ stability
+ 700 nm < λ < 1000 nm
- $120k
- >100 W electrical input
- water cooling
- large size
Tuesday, August 2, 2011
Motivations
Tuesday, August 2, 2011
Motivations

Study a new class of nonlinear waves

Reach the performance of solid-state lasers, but with
practical benefits of fiber

Can we take femtosecond lasers out of labs and into
factories, clinics, …?
Tuesday, August 2, 2011
Introduction to short-pulse generation
Tuesday, August 2, 2011
Laser
gain
Tuesday, August 2, 2011
Laser oscillator
gain
Tuesday, August 2, 2011
Laser
gain
Tuesday, August 2, 2011
Laser
gain
Tuesday, August 2, 2011
Fiber laser
gain
Tuesday, August 2, 2011
Fiber laser
gain
Tuesday, August 2, 2011
Fiber laser
gain
Advantages

waveguide medium

not sensitive to alignment

perfect beam

high efficiency; reduced thermal effects

high power (1,000 W cw)

telecom infrastructure
Tuesday, August 2, 2011
Fiber laser
gain
Challenge: nonlinear effects ~ intensity x length
energy x length/area
IL (waveguide)
≈ 10 3 − 10 7
IL (homogeneous)
Tuesday, August 2, 2011
Saturable absorber
T
SA
I
SA
•
molecules
•
semiconductors
•
nonlinear polarization evolution (NPE)
Tuesday, August 2, 2011
Saturable-absorber modelocking
gain
SA
•
Shorter pulse experiences less loss
•
Amplitude modulation directly shapes pulse
•
Good for picosecond pulses
animation by Carsten Krogh Nielsen
Tuesday, August 2, 2011
Saturable-absorber modelocking
gain
SA
•
Shorter pulse experiences less loss
•
Amplitude modulation directly shapes pulse
•
Good for picosecond pulses
animation by Carsten Krogh Nielsen
Tuesday, August 2, 2011
Terminology
“Modelocking”
frequency-domain view of short-pulse generation inside lasers
Tuesday, August 2, 2011
Shorter pulses: dispersion matters
n = n(ω)
v(ω) = c/n(ω)
animation by Carsten Krogh Nielsen
Tuesday, August 2, 2011
Shorter pulses: dispersion matters
n = n(ω)
v(ω) = c/n(ω)
animation by Carsten Krogh Nielsen
Tuesday, August 2, 2011
Shorter pulses: dispersion matters
Tuesday, August 2, 2011
•
LDS (1 ps, glass) ~ 10 m
•
LDS (100 fs, glass) ~ 10 cm
•
LDS (10 fs, glass) ~ 1 mm
Shorter pulses: dispersion matters
Tuesday, August 2, 2011
•
LDS (1 ps, glass) ~ 10 m
•
LDS (100 fs, glass) ~ 10 cm
•
LDS (10 fs, glass) ~ 1 mm
Dispersive phase accumulation
t
φ
t
normal group-velocity dispersion
Tuesday, August 2, 2011
Dispersive phase accumulation
t
t
φ
t
anomalous group-velocity dispersion
Tuesday, August 2, 2011
Dispersion control
Anomalous dispersion from
•
Fiber material or waveguide structure
•
Prism pairs
•
Grating pairs
•
Chirped mirrors
normal
dispersion
pulse duration
chirp
Tuesday, August 2, 2011
anomalous
position
Nonlinear phase accumulation
n
=
n0 + n2 I
Tuesday, August 2, 2011
Nonlinear phase accumulation
n
=
n0 + n2 I
Re χ(3)
€
Tuesday, August 2, 2011
P = χ(1) E + χ(2) EE + χ(3) EEE + ...
Nonlinear phase accumulation
I
n (t) = n0 + n2 I(t)
t
Tuesday, August 2, 2011
Nonlinear phase accumulation
I
n (t) = n0 + n2 I(t)
t
n
t
Tuesday, August 2, 2011
Nonlinear phase accumulation
I
n (t) = n0 + n2 I(t)
t
n
t
φ
φNL
φ(t) ~ n(t)
phase varies across pulse
t
ω
ω ~ - dφ/dt
Tuesday, August 2, 2011
t
Nonlinear Schrodinger Equation
E (z, t) = A(z, t) e i( kz −ωt )
∂A(z, t)
β (2) ∂2 A(z, t)
2
+i
=
in
|
A(z,
t)
|
A(z, t)
€
2
2
∂z
2
∂t
dispersion nonlinear refraction
•
Tuesday, August 2, 2011
Launched pulse generally decays
Soliton formation
∂A(z, t)
β (2) ∂2 A(z, t)
2
+i
=
in
|
A(z,
t)
|
A(z, t)
2
2
∂z
2
∂t
dispersion
Δφ
Δφ
nonlinearity
t
(anomalous) dispersion cancels nonlinearity for
A(t) = A0 sech(t / τ p )exp(iz / z sol )
Tuesday, August 2, 2011
t
Soliton laser
gain
saturable absorber
anomalous dispersion β2 < 0
self-focusing nonlinearity n2 > 0
Tuesday, August 2, 2011
Theoretical modeling of short-pulse lasers
Nonlinear Schrodinger Equation
GVD
Kerr Nonlinearity
E (z, t) = A(z, t) e i( kz −ωt )
€
Tuesday, August 2, 2011
Theoretical modeling of short-pulse lasers
Net Gain
Tuesday, August 2, 2011
Cubic SA Term
Spectral Filter
Theoretical modeling of modelocked lasers
Cubic Ginzburg-Landau Equation (CGLE)
•
Assumes homogeneous medium
•
Static solutions
•
Some coefficients depend on solutions
Tuesday, August 2, 2011
Numerical modeling

Vector model accounts for both polarizations
2
∂ A x iβ 2 ∂ 2 A x
2
iγ * 2 − 2iΔβz
2

+
= iγ  A x + A y  A x + A x A y e
2
∂z
2 ∂t
3
3


2
∂
2
iβ 2 A y
2
iγ * 2 2iΔβz
2

+
= iγ  A y + A x  A y + A y A x e
2
∂z
2 ∂t
3
3


∂ Ay
Δβ = 2π
Tuesday, August 2, 2011
LB
Static pulse solutions
NLSE
CGLE
•
Stability?
Tuesday, August 2, 2011
Static pulse solutions
NLSE
CGLE
•
Stability?
Tuesday, August 2, 2011
Static pulse solutions
NLSE
CGLE
•
Stability?
Tuesday, August 2, 2011
Static pulse solutions
NLSE
CGLE
•
Stability?
Tuesday, August 2, 2011
Numerical modeling

Solve with appropriate terms in
each segment of oscillator

Periodic boundary condition

Launch noise, look for pulsed
solutions
Tuesday, August 2, 2011
Making a pulse
Starting dynamics
•
saturable absorber allows pulse to build up from noise
Steady state
•
pulse feels average (anomalous) cavity dispersion
•
phase modulations determine steady-state pulse
Examples
•
soliton fiber lasers
•
femtosecond Ti:sapphire lasers
Tuesday, August 2, 2011
Soliton lasers

Quantitative differences between solid-state and fiber
Tuesday, August 2, 2011
Femtosecond lasers
Soliton-like pulse-shaping
+
passive modelocking
-
limited energy
€
-
Eτ ∝ β2 n2
→
requires anomalous dispersion
materials have normal dispersion for λ < 1.3 µm
Tuesday, August 2, 2011
Femtosecond lasers
Solitons
-
limited energy => limited impact of fiber oscillators
Tuesday, August 2, 2011
Femtosecond lasers
Anomalous dispersion is required with
•
normal linear dispersion
•
self-focusing nonlinearity (n2 > 0)
“All femtosecond lasers include anomalous dispersion.”
Tuesday, August 2, 2011
Can we make a femtosecond laser
without soliton formation?
Tuesday, August 2, 2011
Can we make a femtosecond laser
without anomalous dispersion?
Tuesday, August 2, 2011
Pulse shaping at normal dispersion
t



Tuesday, August 2, 2011
I(t) ~ I(ω) in chirped pulse
Spectral filter acts as saturable absorber
Gain dispersion provides a filter
t
All-Normal-Dispersion Laser
Output
Spectral
filter
SMF
~3 m
Tuesday, August 2, 2011
Saturable
Absorber
Gain fiber
~20 cm
SMF
~1 m
ANDi
Laser
Output
Spectral
filter
SMF
~3 m
Tuesday, August 2, 2011
Saturable
Absorber
Gain fiber
~20 cm
SMF
~1 m
Simulation: temporal evolution


Tuesday, August 2, 2011
Highly-chirped pulse throughout cavity
Weak temporal breathing
Simulation: temporal evolution



Tuesday, August 2, 2011
Highly-chirped pulse throughout cavity
Weak temporal breathing
Filter dominates pulse-shaping
Output
SMF
~3 m
Saturable
Absorber
Gain fiber
~20 cm
Intensity
Wavelength
Tuesday, August 2, 2011
Wavelength
SMF
~1 m
Intensity
Wavelength
Spectral
filter
Intensity
Intensity
Simulation: spectral evolution
Wavelength
Analytic theory
Why should a partial differential equation work?
•
•
No dispersion map
Weak temporal breathing
CGLE fails
•
•
•
•
•
stability of solutions
multiple solutions with identical energy
spectral shapes
existence of maximum pulse energy
“area theorem” qualitatively wrong
Tuesday, August 2, 2011
Ginzburg-Landau Equations
(NLSE)
Tuesday, August 2, 2011
Ginzburg-Landau Equations
(NLSE)
(CGLE)
Tuesday, August 2, 2011
Ginzburg-Landau Equations
(NLSE)
(CGLE)
(CQGLE)
Tuesday, August 2, 2011
Ginzburg-Landau Equations
(NLSE)
(CGLE)
(CQGLE)
Quintic SA Term
Tuesday, August 2, 2011
Ginzburg-Landau Equations
(NLSE)
(CGLE)
(CQGLE)
Quintic SA Term
T
I
Tuesday, August 2, 2011
Known pulse solutions
NLSE
CGLE
CQGLE
Tuesday, August 2, 2011
Known pulse solution
CQGLE
Tuesday, August 2, 2011
Theoretical pulses
Tuesday, August 2, 2011
Theoretical pulses
δ>0 B=1 δ<0
Tuesday, August 2, 2011
Theoretical pulses
δ>0 B=1 δ<0
theoretically unstable
Tuesday, August 2, 2011
Dissipative solitons
CQGLE
Static solutions balance
 dispersion
 nonlinear phase
 gain, loss
 saturable absorption
 spectral filtering
Solutions not realized previously in a physical system
Tuesday, August 2, 2011
Dissipative solitons
CQGLE
Tuesday, August 2, 2011
Dissipative solitons
CQGLE
Tuesday, August 2, 2011
Dissipative solitons
CQGLE
Tuesday, August 2, 2011
Dissipative solitons
Tuesday, August 2, 2011
Dissipative solitons
Much theory, little experiment
Tuesday, August 2, 2011
Dissipative solitons
Much theory, little experiment



N. Akhmediev and A. Ankiewicz
Dissipative Solitons (Springer, Berlin Heidelberg, 2005)
Ultanir et al., Phys. Rev. Lett. 90, 253903 (2003)
Bakonyi et al., J. Opt. Soc. Am. B 19, 487 (2002)
Tuesday, August 2, 2011
Experiments
output
QWP
collimator
birefringent
plate
isolator
QWP
collimator
PBS
HWP
SMF
SMF
WDM
Yb-doped fiber
980nm pump
Fixed parameters
fiber nonlinearity (γ)
fiber dispersion (D)
Tuesday, August 2, 2011
Variable parameters
birefringent plate varies Ω
waveplates vary α, δ
pump power varies B
Experimental setup
ANDi laser
Tuesday, August 2, 2011
Comparison to analytic theory
Theory
Tuesday, August 2, 2011
Comparison to analytic theory
Theory
Tuesday, August 2, 2011
Comparison to analytic theory
Theory
Experiment
Renninger et al.,
Phys Rev A 2008
Tuesday, August 2, 2011
Comparison to analytic theory
Theory
Experiment
Renninger et al.,
Phys Rev A 2008
Tuesday, August 2, 2011
Comparison to numerical simulations
Experiment
Numerical simulation
Chong et al.,
JOSA B 2008
Tuesday, August 2, 2011
How do dissipative solitons form?
Tuesday, August 2, 2011
Amplitude balance

Dispersion broadens pulse

Spectral filtering shortens the pulse
filter
Tuesday, August 2, 2011
Phase balance
dispersive phase
φ(z+Δz)
φ(z)
Δφ
t
t
•
Normal dispersion balances self-focusing nonlinearity
Tuesday, August 2, 2011
Overall balance
NLSE conservative soliton
anomalous
GVD
amplitude
(sech)
phase
Tuesday, August 2, 2011
Overall balance
spectral filter
dissipative
soliton
saturable absorber
nonlinear phase
amplitude
(chirped pulse)
NLSE conservative soliton
normal GVD
anomalous
GVD
(sech)
phase
Tuesday, August 2, 2011
Comparison to simulations
Tuesday, August 2, 2011
High-performance femtosecond lasers
Tuesday, August 2, 2011
High pulse energies
pulse evolution
maximum pulse energy in ordinary fiber
soliton
0.1 nJ
ΦNL ~ 0
dispersion-managed soliton
1 nJ
ΦNL < π/2
solid-state lasers (Ti:sapphire)
10 nJ
dissipative soliton
40 nJ so far
Tuesday, August 2, 2011
ΦNL ~ 20π
Dissipative soliton laser with double-clad fiber
output
filter
DC Yb-doped fiber
pump
Tuesday, August 2, 2011
Average power > 1 W
•
•
•
Tuesday, August 2, 2011
80 fs / 30 nJ / 2 W after dechirping
200 kW peak power
performance comparable to Ti:sapphire
Kieu et al.,
Opt Lett 2009
2-photon fluorescence imaging
(with C. Schaffer)
•
•
YFP labels pyramidal neurons
Texas Red labels vasculature
•
0-200 µm:
dendrites, surface vessels
•
400-600 µm:
cell bodies, capillaries
•
700-900 µm:
cell bodies, axons
Tuesday, August 2, 2011
Toward all-fiber instruments
Tuesday, August 2, 2011
All-fiber dissipative soliton lasers
•
130 fs / 3 nJ / 150 mW
Kieu et al., Opt Express 2008
Zhao et al. , unpublished
Tuesday, August 2, 2011
All-fiber laser
Tuesday, August 2, 2011
Self-similar evolution in gain fiber:
amplifier similaritons
Tuesday, August 2, 2011
Self-similar pulse propagation

Monotonic chirp avoids wave-breaking

(Anderson et al., JOSA B 1993)
Wave-breaking-free solutions of NLSE with normal dispersion
asymptotic solutions exist
a(t,z) = a0 (z) 1− (t / τ (z)) 2 exp(ib(z)t 2 )
parabolic intensity profile, linear chirp
€
Tuesday, August 2, 2011
Self-similar pulse evolution
passive fiber
Anderson et al. (1993)
(theory)
amplifier fiber
Fermann, Kruglov et al. (2000)
(expt, theory)
z
z
I(t,z)
I(t,z)

Tuesday, August 2, 2011
t
Pulse evolves self-similarly -- “similariton”
t
Amplifier similaritons



n2 > 0
normal dispersion
gain
asymptotic solution
Fermann, Kruglov et al, Phys. Rev. Lett. 2000
Tuesday, August 2, 2011
Amplifier similaritons



n2 > 0
normal dispersion
gain
nonlinear attractor
Fermann, Kruglov et al, Phys. Rev. Lett. 2000
Tuesday, August 2, 2011
Amplifier similariton laser
Can we stabilize an amplifier similariton in an oscillator?
amplifier
?
Tuesday, August 2, 2011
Amplifier similariton laser
Can we stabilize an amplifier similariton in an oscillator?
amplifier
?
Answer in 2002: No. Spectral breathing will be uncontrollable.
Tuesday, August 2, 2011
Amplifier similariton laser
Hypothesis: a spectral filter alone can stabilize an
amplifier similariton fiber laser.
amplifier
narrow spectral filter
Tuesday, August 2, 2011
Simulations
gain fiber
Tuesday, August 2, 2011
sat abs
filter
Simulations
evolution

narrow filter (2 nm) stabilizes an
amplifier similariton with feedback
Tuesday, August 2, 2011
output pulse
Simulations
filter

gain fiber
pulse evolves to parabolic self-similar solution in the amplifier
Tuesday, August 2, 2011
Experimental setup


all-normal-dispersion Yb fiber laser with NPE
grating filters provide narrow bandwidths (<4 nm)
Tuesday, August 2, 2011
Experimental results
theory


Tuesday, August 2, 2011
output 2
output 1
output 2: approximates pulse at end of gain
output 1: beam splitter output
Features of amplifier similariton

narrowband filter allows pulse to reach self-similar solution

contrast with dissipative solitons
large (10-20x) spectral breathing
smooth, broad spectra

local nonlinear attractor in cavity
suppress fluctuations?
Ilday et al., Nat Photon 2010
Renninger et al., Phys Rev A 2010
Harvey et al., Opt Express 2010
Tuesday, August 2, 2011
amplifier
High energy and short pulses

40 fs / 10 nJ output  250 kW peak power

Much broader bandwidths can be generated
Nie, Dantus, Wise
Opt Express 2011
Tuesday, August 2, 2011
Summary and outlook
(Temporal) dissipative solitons
 new nonlinear waves
 chirping and filtering
Tuesday, August 2, 2011
Regimes of propagation
soliton
anomalous GVD
phase modulations
Tuesday, August 2, 2011
ANDi
normal GVD
dissipative processes
Summary and outlook
(Temporal) dissipative solitons
 new nonlinear waves
 chirping and filtering
Major performance advantages
 10-100x energy of prior fs fiber lasers
 Competitive with solid-state lasers
Tuesday, August 2, 2011
Summary and outlook
(Temporal) dissipative solitons
 new nonlinear waves
 chirping and filtering
Major performance advantages
 10-100x energy of prior fs fiber lasers
 Competitive with solid-state lasers
What is the maximum pulse energy?
 What is the minimum pulse duration?

Tuesday, August 2, 2011
Summary and outlook
(Temporal) dissipative solitons
 new nonlinear waves
 chirping and filtering
Major performance advantages
 10-100x energy of prior fs fiber lasers
 Competitive with solid-state lasers
What is the maximum pulse energy?
 What is the minimum pulse duration?

Self-similar evolution in gain segment
 Strong spectral breathing
 Benefits of local attractor?
Tuesday, August 2, 2011
Summary and outlook
(Temporal) dissipative solitons
 new nonlinear waves
 chirping and filtering
Major performance advantages
 10-100x energy of prior fs fiber lasers
 Competitive with solid-state lasers
What is the maximum pulse energy?
 What is the minimum pulse duration?

Self-similar evolution in gain segment
 Strong spectral breathing
 Benefits of local attractor?
Simple, inexpensive construction
Tuesday, August 2, 2011
Acknowledgements
Tuesday, August 2, 2011
Tuesday, August 2, 2011
Laser
gain
Tuesday, August 2, 2011
Laser
gain
Tuesday, August 2, 2011
Modes of a cavity
Tuesday, August 2, 2011
Modes of a cavity
Tuesday, August 2, 2011
Modes of a cavity
Tuesday, August 2, 2011
Modes with random phases
Intensity
Time
Tuesday, August 2, 2011
Modes with phases locked to same value
Intensity
Time
Tuesday, August 2, 2011
Modelocked
Intensity
Time
Tuesday, August 2, 2011
Analytic approach to pulse evolution



Variational principle yields coupled
equations for parameters of solution in
homogeneous segments
Fixed-point analysis yields stable node
Filter creates strong evolution about
fixed point
Bale, Kutz et al., Opt Lett 2008
Tuesday, August 2, 2011
Scaling to large mode area
PCF with 40-micron core
Theory: stable to 300 nJ
Experiment: limited by pump
• 100 nJ / 115 fs
• 1 MW peak power
• 8 W average power
Lefrancois et al., Opt Lett 2010
(also Lecaplain et al., Baumgartl et al.)
Tuesday, August 2, 2011
What about stability?
δ>0 B=1 δ<0
theoretically unstable
Tuesday, August 2, 2011
What about stability?
δ>0 B=1 δ<0
experimentally stable
Tuesday, August 2, 2011
What about stability?
δ>0 B=1 δ<0
stabilized by gain saturation?
Tuesday, August 2, 2011
Reduced pulse structure
•
Output after filter
chirped 1.4 ps
Tuesday, August 2, 2011
dechirped 75 fs