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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.

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simulation of a passively modelocked all fiber laser with nonlinear optical loop mirror

Simulation of a Passively Modelocked All-Fiber Laser with Nonlinear Optical Loop Mirror

Joseph Shoer ‘06

Strait Lab

solitons

Dispersion

(k)

Self-Phase Modulation

n(I)

  • Left: autocorrelation of sech2t
  • Propagates without changing shape
  • Could be used for long-distance data transmission
Solitons

Direction of propagation

Intensity

Distance

all fiber laser
All Fiber Laser

Light from

Nd:YAG

Pump Laser

Polarization

Controller

Faraday isolator

Nonlinear Optical Loop Mirror

51.3%

Er/Yb

48.7%

Polarization

Controller

90%

10%

Output

transmission model
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 model1
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
simulation goals
Simulation Goals

Gain

Fiber

NOLM

  • 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???
pulse shaping fibers

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

Distance of propagation

Time delay

pulse shaping fibers1
Pulse Shaping: Fibers

|E|2

Time delay

|E|2

Distance of propagation

Time delay

Time delay

pulse shaping nolm
Pulse Shaping: NOLM

10 round trips

Pulse

edge

Pulse

peak

50 round trips

pulse shaping laser gain
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?
the simulator
The Simulator

Calculate

PTC

Repeat n times

Standard Fiber

(NLSE)

NOLM

(apply PTC)

Er/Yb Fiber

(NLSE + gain)

Inject seed pulse

Adjust gain

Output pulse after i round trips

the simulator1
The Simulator

Calculate

PTC

Repeat n times

Standard Fiber

(NLSE)

NOLM

(apply PTC)

Er/Yb Fiber

(NLSE + gain)

Inject seed pulse

Adjust gain

Output pulse after i round trips

  • Power Transfer Curve is determined by polarization controller settings
  • Absorbs nonlinearity of NOLM fiber
  • Uses transmission model (Aubryn Murray ’05) fit from laboratory data
the simulator2
The Simulator

Calculate

PTC

Repeat n times

Standard Fiber

(NLSE)

NOLM

(apply PTC)

Er/Yb Fiber

(NLSE + gain)

Inject seed pulse

Adjust gain

Output pulse after i round trips

  • In the lab, pulses are initiated by an acoustic noise burst
  • The model uses E(0, t) = sech(t) – 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
the simulator3
The Simulator

Calculate

PTC

Repeat n times

Standard Fiber

(NLSE)

NOLM

(apply PTC)

Er/Yb Fiber

(NLSE + gain)

Inject seed pulse

Adjust gain

Output pulse after i round trips

  • 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
the simulator4
The Simulator

Calculate

PTC

Repeat n times

Standard Fiber

(NLSE)

NOLM

(apply PTC)

Er/Yb Fiber

(NLSE + gain)

Inject seed pulse

Adjust gain

Output pulse after i round trips

  • 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!
the simulator5
The Simulator

Calculate

PTC

Repeat n times

Standard Fiber

(NLSE)

NOLM

(apply PTC)

Er/Yb Fiber

(NLSE + gain)

Inject seed pulse

Adjust gain

Output pulse after i round trips

  • 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
the simulator6
The Simulator

Calculate

PTC

Repeat n times

Standard Fiber

(NLSE)

NOLM

(apply PTC)

Er/Yb Fiber

(NLSE + gain)

Inject seed pulse

Adjust gain

Output pulse after i round trips

  • 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
the simulator7
The Simulator

Calculate

PTC

Repeat n times

Standard Fiber

(NLSE)

NOLM

(apply PTC)

Er/Yb Fiber

(NLSE + gain)

Inject seed pulse

Adjust gain

Output pulse after i round trips

simulation results
Simulation Results

I (a.u.)

simulator output

sech(t)2

t(ps)

  • Simulation for 50 round trips – results averaged over last 40 round trips
  • Positive PTC slope at low power
  • No ASE
simulation results1
Simulation Results

I (a.u.)

t(ps)

  • Simulation for 50 round trips – results averaged over last 20 round trips
  • Negative PTC slope at low power
  • No ASE
simulation results2
Simulation Results

I (a.u.)

t(ps)

  • 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)
simulation results3
Simulation Results

I (a.u.)

t(ps)

  • 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)
simulation results4
Simulation Results

I (a.u.)

t(ps)

  • 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)
simulation results5
Simulation Results

I (a.u.)

t(ps)

  • 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)
future work
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
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
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