Simulation of a passively modelocked all fiber laser with nonlinear optical loop mirror
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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 Nonlinear Optical Loop Mirror

(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 Nonlinear Optical Loop Mirror

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


Power transfer curves
Power Transfer Curves Nonlinear Optical Loop Mirror


Transmission model
Transmission Model Nonlinear Optical Loop Mirror

  • 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 Nonlinear Optical Loop Mirror

  • 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 Nonlinear Optical Loop Mirror

Background

Experimental Autocorrelations


Experimental scope trace

Background Nonlinear Optical Loop Mirror

Experimental ‘Scope Trace


Simulation goals
Simulation Goals Nonlinear Optical Loop Mirror

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

Pulse Shaping: Fibers

Distance of propagation

Time delay


Pulse shaping fibers1
Pulse Shaping: Fibers nonlinear Schrödinger equation (NLSE):

|E|2

Time delay

|E|2

Distance of propagation

Time delay

Time delay


Pulse shaping nolm
Pulse Shaping: NOLM nonlinear Schrödinger equation (NLSE):

10 round trips

Pulse

edge

Pulse

peak

50 round trips


Pulse shaping laser gain
Pulse Shaping: Laser Gain nonlinear Schrödinger equation (NLSE):

  • 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 nonlinear Schrödinger equation (NLSE):

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 nonlinear Schrödinger equation (NLSE):

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 nonlinear Schrödinger equation (NLSE):

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 nonlinear Schrödinger equation (NLSE):

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 nonlinear Schrödinger equation (NLSE):

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 nonlinear Schrödinger equation (NLSE):

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 nonlinear Schrödinger equation (NLSE):

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 nonlinear Schrödinger equation (NLSE):

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 nonlinear Schrödinger equation (NLSE):

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 nonlinear Schrödinger equation (NLSE):

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 nonlinear Schrödinger equation (NLSE):

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 nonlinear Schrödinger equation (NLSE):

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 nonlinear Schrödinger equation (NLSE):

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 nonlinear Schrödinger equation (NLSE):

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)


No nonlinear Schrödinger equation (NLSE): ASE


0.016 ASE nonlinear Schrödinger equation (NLSE):


Future work
Future Work nonlinear Schrödinger equation (NLSE):

  • 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 nonlinear Schrödinger equation (NLSE):

  • 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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