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Simulation of a Passively Modelocked All-Fiber Laser with Nonlinear Optical Loop Mirror. Joseph Shoer ‘06 Strait Lab. Dispersion ( k ). Self-Phase Modulation n ( I ). Left : autocorrelation of sech 2 t Propagates without changing shape Could be used for long-distance data transmission. - PowerPoint PPT Presentation
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Simulation of a Passively Modelocked All-Fiber Laser with Nonlinear Optical Loop Mirror
Joseph Shoer ‘06Strait Lab
SolitonsDirection of propagation
Dispersion(k)
Self-Phase Modulationn(I)
-4 -3 -2 -1 0 1 2 3 4
Theoretical Autocorrelation
Sec
ond
Har
mon
ic G
ener
atio
n
Time Delay (ps)
• Left: autocorrelation of sech2 • Propagates without changing
shape• Could be used for long-distance
data transmission
Intensity
Distance
All Fiber Laser
Light from Nd:YAG
Pump Laser
Output
Nonlinear Optical Loop Mirror
Er/Yb51.3%
48.7%
90%
10%
PolarizationControllerFaraday isolator
PolarizationController
Power Transfer Curves
Transmission Model
• Different PTC at each point• Contours indicate light transmission
through NOLM (value of PTC at zero input) as a function of NOLM polarization controller settings
• Bright shading indicates positive PTC slope at low input
• Modelocking occurs at highest low-power slope
Transmission Model
• Different PTC at each point• Contours indicate light transmission
through NOLM (value of PTC at zero input) as a function of NOLM polarization controller settings
• Bright shading indicates positive PTC slope at low input
• Modelocking occurs at highest low-power slope
Experimental Autocorrelations
Background
Background
Experimental ‘Scope Trace
Background
Simulation Goals
• Model all pulse-shaping mechanisms over many round trips of the laser cavity– NOLM– Standard fiber– Er/Yb gain fiber
• Model polarization dependence of NOLM (duplicate earlier model)• Duplicate lab results???
Gain
Fiber NOLM
Pulse Shaping: Fibers
Time delay
Dis
tanc
e of
pro
paga
tion
• Solving Maxwell’s Equations in optical fibers yields the nonlinear Schrödinger equation (NLSE):
• The NLSE can be solved numerically
• Ordinary first-order solitons maintain their shape as they propagate along a fiber
• Other input pulses experience variations in shape
Pulse Shaping: Fibers
Time delay
Dis
tanc
e of
pro
paga
tion
Time delay
|E|2
Time delay
|E|2
Pulse Shaping: NOLM
Pulseedge
Pulsepeak
10 round trips
50 round trips
Pulse Shaping: Laser Gain• Pulses gain energy as they pass through the Er/Yb-
doped fiber• Gain must balance loss in steady state
• Gain saturation: intensity-dependent gain?– Not expected to have an effect
• Gain depletion: time-dependent gain?– Not expected to have an effect
• Amplified spontaneous emission (ASE): background lasing?
CalculatePTC
NOLM(apply PTC)
Standard Fiber(NLSE)
Er/Yb Fiber(NLSE + gain)
Inject seed pulse
Output pulse after i round trips
Repeat n times
The Simulator
Adjust gain
• Power Transfer Curve is determined by polarization controller settings• Absorbs nonlinearity of NOLM fiber• Uses transmission model (Aubryn Murray ’05) fit from laboratory data
CalculatePTC
NOLM(apply PTC)
Standard Fiber(NLSE)
Er/Yb Fiber(NLSE + gain)
Inject seed pulse
Output pulse after i round trips
Repeat n times
The Simulator
Adjust gain
• In the lab, pulses are initiated by an acoustic noise burst• The model uses E(0, ) = sech() – a soliton – as a standard input profile
– This is for convenience – with enough CPU power, we could take any input and it should evolve into the same steady state result
CalculatePTC
NOLM(apply PTC)
Standard Fiber(NLSE)
Er/Yb Fiber(NLSE + gain)
Inject seed pulse
Output pulse after i round trips
Repeat n times
The Simulator
Adjust gain
• 2 m of Er/Yb-doped fiber is simulated by solving the Nonlinear Schrödinger Equation with a gain term
• The program uses an adaptive algorithm to settle on a working gain parameter• Dispersion and self-phase modulation are also included here• ASE is added here as a constant offset or as random noise
CalculatePTC
NOLM(apply PTC)
Standard Fiber(NLSE)
Er/Yb Fiber(NLSE + gain)
Inject seed pulse
Output pulse after i round trips
Repeat n times
The Simulator
Adjust gain
• NOLM is simulated by applying the PTC, which tells us what fraction of light is transmitted for a given input intensity
• This method neglects dispersion in the NOLM fiber– Fortunately, we use dispersion-shifted fiber in the loop!
CalculatePTC
NOLM(apply PTC)
Standard Fiber(NLSE)
Er/Yb Fiber(NLSE + gain)
Inject seed pulse
Output pulse after i round trips
Repeat n times
The Simulator
Adjust gain
• 13 m of standard communications fiber is simulated by solving the Nonlinear Schrödinger Equation
• Soliton shaping mechanisms, dispersion and SPM, come into play here• Steady-state pulse width is the result of NOLM pulse narrowing competing with
soliton shaping in fibers• All standard fiber in the cavity is lumped together in the simulator
CalculatePTC
NOLM(apply PTC)
Standard Fiber(NLSE)
Er/Yb Fiber(NLSE + gain)
Inject seed pulse
Output pulse after i round trips
Repeat n times
The Simulator
Adjust gain
• Output pulses from each round trip are stored in an array• We can simulate autocorrelations of these pulses individually, or averaged
over many round trips to mimic laboratory measurements• Unlike in the experimental system, we get to look at both pulse intensity
profiles and autocorrelation traces
CalculatePTC
NOLM(apply PTC)
Standard Fiber(NLSE)
Er/Yb Fiber(NLSE + gain)
Inject seed pulse
Output pulse after i round trips
Repeat n times
The Simulator
Adjust gain
CalculatePTC
NOLM(apply PTC)
Standard Fiber(NLSE)
Er/Yb Fiber(NLSE + gain)
Inject seed pulse
Output pulse after i round trips
Repeat n times
The Simulator
Adjust gain
Simulation Results
• Simulation for 50 round trips – results averaged over last 40 round trips• Positive PTC slope at low power• No ASE
I (a.u.)
(ps)
simulator output
sech()2
Simulation Results
• Simulation for 50 round trips – results averaged over last 20 round trips• Negative PTC slope at low power• No ASE
I (a.u.)
(ps)
Simulation Results
• Simulation for 50 round trips – results averaged over last 40 round trips• Positive PTC slope at low power• ASE: Random intensity noise added each round trip (max 0.016)
I (a.u.)
(ps)
Simulation Results
• Simulation for 50 round trips – results averaged over last 40 round trips• Positive PTC slope at low power• ASE: Random intensity noise added each round trip (max 0.016)
I (a.u.)
(ps)
Simulation Results
• Simulation for 50 round trips – results averaged over last 40 round trips• Positive PTC slope at low power• ASE: Constant intensity background added each round trip (0.016)
I (a.u.)
(ps)
Simulation Results
• Simulation for 50 round trips – results averaged over last 40 round trips• Positive PTC slope at low power• ASE: Random intensity noise added each round trip (max 0.009)
I (a.u.)
(ps)
No ASE
0.016 ASE
Future Work
• Obtain a new transmission map so the simulator can make more accurate predictions
• Produce quantitative correlations between simulated and experimental pulses– Peak intensity, background intensity, wing size
• Determine the quantitative significance of simulation parameters– Are adaptive gain and amount of ASE
reasonable?
Conclusions• Investigation of each mechanism in the simulator
helped us better understand the laser• The simulator can produce qualitative matches for
each type of pulse the laser emits – near-soliton pulses
• The overall behavior of the simulator matches the experimental system and our theoretical expectations
• The simulator has allowed us to explain autocorrelation backgrounds, wings, and dips as results of amplified spontaneous emission
• The simulator can now be refined and become a standard tool for investigations of our fiber laser