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 ‘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