1. Simulation of a Passively Modelocked All-Fiber Laser with Nonlinear Optical Loop Mirror Joseph Shoer ‘06 Strait Lab

2. Solitons Direction of propagation Dispersion  (k) Self-Phase Modulation n(I) Left: autocorrelation of sech 2  Propagates without changing shape Could be used for long-distance data transmission Intensity Distance

3. All Fiber Laser Light from Nd:YAG Pump Laser Output Nonlinear Optical Loop Mirror Er/Yb 51.3% 48.7% 90% 10% Polarization Controller Faraday isolator Polarization Controller

4. Power Transfer Curves

5. 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

6. 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

7. Experimental Autocorrelations Background

8. Experimental ‘Scope Trace Background

9. 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

10. Pulse Shaping: Fibers Time delay Distance of propagation 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

11. Pulse Shaping: Fibers Time delay Distance of propagation Time delay |E| 2 Time delay |E| 2

12. Pulse Shaping: NOLM Pulse edge Pulse peak 10 round trips 50 round trips

13. 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?

14. Calculate PTC 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

15. Power Transfer Curve is determined by polarization controller settings Absorbs nonlinearity of NOLM fiber Uses transmission model (Aubryn Murray ’05) fit from laboratory data Calculate PTC 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

16. 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 Calculate PTC 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

17. 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 Calculate PTC 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

18. 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! Calculate PTC 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

19. 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 Calculate PTC 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

20. 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 Calculate PTC 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

21. Calculate PTC 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

22. 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

23. 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)

24. 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)

25. 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)

26. 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)

27. 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)

28. No ASE

29. 0.016 ASE

34. 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?

35. 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