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

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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


Power transfer curves

Power Transfer Curves


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


Experimental autocorrelations

Background

Background

Experimental Autocorrelations


Experimental scope trace

Background

Experimental ‘Scope Trace


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)


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

No ASE


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

0.016 ASE


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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