Noise-like pulse dynamics in passively mode-locked fiber lasers

1. Noise-like pulse dynamics in passively mode-locked fiber lasers O. Pottiez1, Y. Bracamontes-Rodriguez1, J. P. Lauterio-Cruz1, E. Garcia-Sanchez1, H. Santiago-Hernandez1, R. Paez-Aguirre1, J. C. Hernandez-Garcia2, M. A. Bello-Jimenez3, E. A. Kuzin4, B. Ibarra-Escamilla4 1Centro de Investigaciones en Óptica, León, Gto., Mexico 2Division de Ingenierias Campus Irapuato-Salamanca, Guanajuato Univ., Salamanca, Gto., Mexico 3Instituto de Investigación en Comunicación Óptica, Univ. SLP, SLP, Mexico 4Instituto Nacional de Astrofísica, Óptica y Electrónica, Puebla, Pue., Mexico

2. We discuss: • Presentation of noiselike pulses • Single- or multiple-pulsing regimes (including harmonic mode locking) • Challenge of characterizing precisely these pulses • Observation of original noiselike pulse dynamics • Applications

3. Most pulsed regimes of interest are stationary: solitons (conservative/dissipative) • High-power pump diodes and double-clad fiber technology (> W) • New theoretical developments (dissipative soliton) • High-rep-rate pulse trains (> GHz) • High-energy pulses ( J?) Application: telecom Bombeo Application: industry, medicine

4. Away from stationarity… • Stable solitons • Multiple pulsing: interpulse interactions  different states (molecules, cristal, glass, rain etc.) • Soliton explosions, pulsating, creeping solitons, period-doubling… • Noiselike pulses (global stability, internal variability) • Rogue (freak) waves • … Stationarity Chaos

5. Noiselike pulses are radically different objects Noiselike pulse = long, compact waveform with a very complex fine inner structure: large collection of sub-ps “pulses” suffering very fast, large variations in their amplitudes and durations. ~100 fs  Contains 103 – 107sub-pulses! Total duration : 10 ps – 1 s Global stability, strong and fast variability of inner details (changes completely after one round-tip)  Very complex objects (let alone phase and polarization aspects)

6. Noiselike pulses are currently attracting attention Applications: • Súperconinuumgeneration  spectroscopy, microscopy, sensingetc • Nonlinearfrequencyconversion • Micromachining • … Noise-like pulses are alsoattracting considerable interest in fundamental research (connectionwithopticalroguewaves) • You et al., CLEO (2015) JW2A.94  Özgörenet al., Opt. Express. 24 (2011), 17647

7. Figure-eight laser scheme  Polarizer Output 1 Isolator /2 90/10 HWR (/2)  NOLM (100 m SMF-28) PC EDF (4 m) 90/10 50/50 WDM /4 Twist (5 turns/m) QWR (λ/4) Output 2 • L = 120 m • Anomalous dispersion regime 980-nm pump (300 mW) • A polarization-imbalanced NOLM is inserted in the laser (operates through nonlinear polarization rotation) • Quarter-wave retarder (QWR) angle determines low-power NOLM transmission • Input polarization to the NOLM is set linear • Input polarization angle , controlled through half-wave retarder (HWR), determines switching power

8. Scheme used for numerical simulations  10% Output Polarization assumed linear 15 m SMF-28 90/10  Isolator NOLM EDF Filter 50/50 LA = 4m Low-power gain G0 = 2000 (uniform g0 = G0/LA = 500/m) Esat = 0.8 nJ QWR (λ/4) This scheme is very similar to the experimental scheme • A 50-nm FWHM bandpass filter takes into account the bandwidth limitation of EDF gain • Gain saturates on pulse energy • QWR angle adjusted for small nonzero low-power NOLM transmission (≈ 0.1)

9. Numerical model Propagation calculated using the coupled extended nonlinear Schrödinger equations: Fiber sections: Dispersion Kerr nonlinearity Gain (for EDF only) Integrated using Split-Step Fourier method Pulse energy • Small-amplitude gaussian white noise is used as initial signal • Integration is performed over several cycles until convergence is reached Filter: • In ordertokeepcomputational time withinreasonablelimits: • Laser length no longerthan a fewtens of m • Noiselike pulse duration~100 ps (1-2 orders of magnitudeshorterthan in experiment)

10. Fundamental mode-locking was observed experimentally 1 1 Autocorre- lation 160 fs • For some adjustments, non-self-starting mode locking was observed at 1.6 MHz (fundamental mode locking) • Typical features of noise-like pulses : • - Double-scale (ns/fs) temporal structure • -Lowcoherence time • - Wide, smoothspectrum(10-100 nm) • Large pulse energy(nJ-J) Oscilloscope trace Amplitude (a.u.) Intensity (a.u.) > 200 ps 0 0 -50 0 50 -5 0 5 Time (s) Delay (ps) 1 0 ~ 40 nm Fast PD + sampling scope -10 Amplitude (a.u.) Normalized spectrum (dB) -20 Optical spectrum 200 ps -30 -40 0 1500 1600 0 0.5 1 Time (ns) Wavelength (nm)

11. Numerical results are consistent with experiment 700 0 1 Output waveforms for consecutive roundtrips Average output autocorrelation -2 600 -4 500 ~ 10 nm -6 1 ~ 120 ps 400 Relative spectrum (dB) Output power (W) -8 0.5 -10 300 0.5 -12 Optical spectrum 200 3 -3 -2 -1 0 1 2 -14 Delay (ps) Averaged 100 -16 Single pulse 0 -18 0 1540 1550 1560 1570 -200 -100 0 100 200 -50 0 50 100 -100 Time (ps) Delay (ps) Wavelength (nm) • Although there is no convergence to a constant pulse shape, a variable sub-nspacket of sub-ps pulses with stable caracteristics (peak power, duration) is maintained. Pulse energy = 1.4 nJ • Autocorrelation trace (averaged over many cycles) presents a sub-ps central peak riding a sub-ns pedestal (the ratio however is > 2, and may vary with simulation parameters) • After averaging over many cycles, a smooth and relatively wide (10-nm FWHM) output spectrum is obtained  Pottiez et al., Appl. Opt. 50 (2011), E24-E31

12. Multiple pulsing was observed in the normal dispersion regime 200-m DCF (-38 ps/nm/km)  Polarizer Output 1 EDF2 NOLM (100 m SMF-28) 90/10 50/50 WDM2 /2  Isolator EDF1 WDM1 PC 980-nm pump 90/10 /2 Twist /4 /4 Output 2 980-nm pump • L = 200 m • Normal Dispersion

13. 1 Amplitude (V) 0 -0.8 -0.4 0 0.4 0.8 Time (s) Fundamental mode locking was observed, followed by pulse breakup 1 Autocorre- lation 1 ps Scope traces • For some adjustments, mode locking (sometimes self-starting) is observed, with one pulse per 1.6 s period (fundamental mode locking) • Measurements confirm that pulses are noise-like pulses • Pulse properties (peak power, duration) adjustable through HWR rotation • Low-peak-power, long pulse eventually splits into multiple pulses Normalised aamplitude .5 5 ns 0 -80 -40 0 40 80 Delay (ps) .4 Amplitude (V) 22 ns .2 5 nm 15 nm 0 0 -0.8 -0.4 0 0.4 0.8 Time (s) .4 -10 .3 Optical spectrum Normalised aamplitude (dB) Amplitude (V) .2 .1 -20 0 -20 0 20 40 Time (ns) -30 1520 1540 1560 1580 1600 Wavelength (nm)

14. 1 1 ps .5 -1 0 1 Up to 12 pulses were observed 1 Autocorre- lation .3 2 ns Normalised aamplitude .5 Amplitude (V) .2 .1 • For some adjustments, the pulses synchronize, although their separation is not uniform • Some sub-groups with uniform separation of ~20 ns • Pulse autocorrelation and spectrum are unchanged • Same energy/round-trip as before, but distributed among the multiple pulses 0 0 -0.4 -0.2 0 0.2 0.4 0.6 -80 -40 0 40 80 Time (s) Delay (ps) 0 5 nm .2 -10 Amplitude (V) Normalised aamplitude (dB) .1 -20 0 -0.4 -0.2 0 0.2 0.4 0.6 Time (s)  Pottiez et al., Laser Phys. 24 (2014), 15103 -30 1520 1540 1560 1580 Wavelength (nm)

15. Noiselike pulse generation with a longfiber ring laser Output 1 980 nm pump PC 99/01 Beam combiner SMF (~1 km) EYDF (4 m) P-Isolator 99/01 PC 90/10 Output 2 Output 3 (10%) Fiber Bench  Pottiez et al., Laser Phys. 24 (2014), 115103

16. 1 1 Single-pulse energy up to 120 nJ wasobtained .02 Fundamental ML Rep. rate = 200 kHz Pulse energy = 120 nJ Single-pulse operation could not be maintained beyond some moderate value of pump power Amplitude (a.u.) Amplitude (a.u.) .5 .5 Oscilloscope trace 0 -4 0 4 Fast PD + sampling scope 0 0 -10 -8 -6 -2 0 2 4 6 8 10 -80 -60 -40 -20 0 20 40 60 80 -4 1 Time (s) Time (ns) Autocorre- lation 0 .5 1 Optical spectrum 0 5 -5 -10 Spectrum (dB) Normalized amplitude .5 -20 -30 0 1560 1570 -80 -60 -40 -20 0 20 40 60 80 Delay (ps) Wavelength (nm)

17. 1 1 1 1 Harmonicregimes of orders 2-48, 673 and 1270 wereobserved 1 1 1 .5 1 Amplitude (a.u.) Amplitude (a.u.) .5 .5 .5 .5 Amplitude (a.u.) Amplitude (a.u.) .5 .5 .5 0 -5 0 5 0 0 -.02 0 .02 0 0 10 -10 3 8 673 -.02 -.01 0 .01 .02 0 0 0 0 -60 -40 -20 0 20 40 60 -30 -20 -10 0 10 20 30 Time (ns) -4 -2 0 2 4 -2 -1 0 1 2 Time (ns) Time (s) Time (s) 1 20 48 1 1270 1 1 .5 .5 Rep. rate = 259 MHz!! Amplitude (a.u.) Amplitude (a.u.) 0 .5 0 .5 -.01 0 .01 -.01 -0.5 0 0.5 .01 0 0 -2 -1 0 1 2 -2 -1 0 1 2 Time (s) Time (s)

18. Figure-eight laser with 100-m near-zero-dispersion fiber 100-m DCF1 (-3 ps/nm/km) 55-m DCF2 (-38 ps/nm/km) Polarizer 980-nm pump WDM2 /2 Output 1 EDF2 NOLM (100 m SMF-28) 50/50  90/10 Isolator EDF1 WDM1 PC 90/10 /2 Twist /4 /4 Output 2 1 980-nm pump • A long piece of DCF with slightly normal dispersion is added (D -0.58 ps/nm) to boost NL effects • L = 300 m Amplitude (a.u.) .5 0 -8 -6 -4 -2 0 2 4 6 8 10 Time (s)

19. Raman scattering enhanced the spectrum up to 130 nm 1 0 .8 -10 .6 No clear correspon-dence between pulse temporal and spectral shapes Amplitude (a.u.) Spectrum (dB) -20 .4 -30 .2 0 -40 -5 -4 -3 -2 -1 0 1 2 3 4 5 1500 1600 1700 1 0 Output 1 .8 -10 130 nm .6 Spectrum (dB) Amplitude (a.u.) -20 .4 -30 .2 Other: Output 2 0 -40 -5 -4 -3 -2 -1 0 1 2 3 4 5 1500 1600 1700 Time (ns) Wavelength (nm)

20. Enigmatic “comb-like”noise-like pulses 1 1 Amplitude (a.u.) Amplitude (a.u.) .5 .5 0 0 1 1 Amplitude (a.u.) .5 Amplitude (a.u.) .5 0 0 -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 Time (ns) Time (ns)

21. The measurement problem Noiselike pulse measurement is very challenging: • ~100-fs details need for fs resolution (orders of magnitude below the resolution of the fastest optoelectronics) • ~ ns waveform with sub-ps details large number (105-106) of data points • Cycle-to-cycle variability  Average measurements give very poor information Single-shot measurements  Novel measurement techniques should be developed: • Single-shot optical spectrum • In our work, we rely on the ultrafast response of the optical Kerr effect in a NOLM (~fs) and focus on the statistics of the inner pulses • Sequence analysis using fast oscilloscope  Runge et al., Opt. Lett. 38 (2013) 4327

22. Pulse characterizationusing a NOLM Pulse envelopes using 25-GHz photodetector and sampling scope Input Output Input Output Valleys undergo higher transmission  Sub-pulses in the valleys are not smaller than at the peaks -2 Time (ns) 0 2 • Probably sub-ns sub-packets jittering around their mean positions • Intermediate level of organization of noiselike pulse: ~100 ps (between ~100 fs of inner pulses and ns of total waveform) Lower amplitude yields lower transmission Envelope maps amplitudes of sub-pulses -2 Time (ns) 0 2

23. Either the intensity OR the density of the sub-pulses vary  Santiago-Hernandez et al., Laser Phys. 25 (2015), 45106

24. Measurement of the statistics of a bunch of pulses using a NOLM Pout Power transfer characteristic QWR .12 Twist Pin .08 Output bunch Transmission T a .04 Input bunch 45 0 50/50 0 0.1 0.2 0.3 0.4 Input power Pout Pin Gaussian Pout Polarizer NOLM QWR Power transfer characteristic If the NOLM power transmission is known, output energy measurements allow reconstructing the statistics of a bunch of pulses Uniform Pin Output bunch Input bunch

25. The statistics of noiselike pulses was estimated x 10-3  Pottiez et al., Opt. Commun. 377 (2016), 41-51 1.6 Exp. data 1.4 Gaussian fit Fit 1.2 Transmission Number of sub-pulses 1 0.8 0.6 0.4 0 0.2 0.4 0.6 0.8 1 200 Pin [W] x 10-11 M = 8.46 14 Extreme events 100 Exp. data 12 Fit 10 Output energy 10 100 8 Number of sub-pulses 6 ai SWH = 13.61 4 1 0.4 0.6 0.8 1 0 0 5 10 15 20 25 30 35 Power (W) 0 10 20 30

26. Noise-like pulses:“noise” or deterministic?  Churkin et al, Nature Commun. 6 (2014), 7004

27. An original dynamics at sub-ns scale has been evidenced T • Starting from stable fundamental ML, small WR adjustments initiate the dynamics • Sub-ns sub-pulses are released from the main waveform and drift away from it, decay and vanish. Quasi-stationary regime. • Their excursion increases and finally, they no longer decay, drift over an entire round-trip and are recaptured by the main waveform • Sub-pulses are units traveling alone or in pairs • Analogy with the soliton rain/release of solitons dynamics  Santiago-Hernández et al., Opt. Express 23 (2015) 18840

28. Scope sequence measurement Sequenceswith 200-MHz scope (892 consecuticecycles) Ernesto García Sánchez et al., CIO 2016

29. 140 Trace number 120 100 Measuring sequences allows identifying peculiar dynamics 520 Trace number 500 Measuredwith 200-MHz scope (every 230 ms) Ernesto García Sánchez et al., CIO 2016 480 500 1000 0 Time (ns) 358 520 356 Trace number 500 480 354 0 0.1 0.2 0.3 -20 -10 10 0 Amplitude (V) Time (ns) 254 252 252 Trace number 250 250 248 248 -10 0 10 20 0 0.2 0.4 Time (ns) Amplitude (V)

30. 1000 0.9 900 Measuring sequences allows identifying peculiar dynamics 800 0.8 700 Trace number 600 500 Ernesto García Sánchez et al., CIO 2016 0.7 0 400 300 200 Time (ns) 0.6 100 0.5 500 0.4 0.3 1000 0.2 Amplitude (V) 0.1

31. Measuring sequences allows identifying peculiar dynamics Ernesto García Sánchez et al., CIO 2016 50 50 40 40 Sub-packet 1 Sub-packet 2 30 30 Sub-packet 3 Trace number Sub-packet 4 Trace number 20 20 10 10 0 200 400 600 800 1000 0 0.3 0.6 0.9 1.2 1.5 Time (ns) Amplitude (V)

32. Measuring sequences allows identifying peculiar dynamics Ernesto García Sánchez et al., CIO 2016

33. Measuring sequences allows identifying peculiar dynamics 1 60 Ernesto García Sánchez et al., CIO 2016 50 0.8 40 0.6 Amplitude (V) Trace number 30 0.4 20 10 0.2 500 1000 0 Time (ns)

34. Soliton-NLP fiber ring laser Yazmin Bracamontes Rodriguez et al., CIO 2016

35. Soliton-NLP fiber ring laser

36. Soliton-NLP fiber ring laser Yazmin Bracamontes Rodriguez, Hugo E. Ibarra Villalón et al., CIO 2016

37. Soliton-NLP fiber ring laser

38. Soliton-NLP fiber ring laser

39. Multiplepulsingbehaviorwasreproducednumerically Intrcavity evolution over 1 full cycle Evolution of output bunch over successive cycles NOLM D = 17 ps/nm/km DCF D = -3 ps/nm/km Amplifier + filter D = -70 ps/nm/km

40. Noise-like pulses were used for supercontinuum generation in standard fiber • Advantages of noise-like pulses for SCG: • High pulse energy • Wide optical spectrum • Hernandez-Garcia et al., Laser Phys. 22 (2012), 221-227 1 Pin = 20.4 mW Simulation 0.75 • The spectrum widens towards longer wavelength due to Raman self-frequency shift (SFS) • Random amplitudes of sub-pulses generate a relatively flat spectrum 0.5 Normalized Power Experiment 0.25 0 1400 1500 1600 1700 Wavelength (nm)

41. Numerical simulations predictfurther widening to the right Experiment 1 ~70% of the total pulse energy moved towards other wavelengths Simulation Intensity (a.u.) 0.5 • Hernandez-Garcia et al., Opt. Comm. 285 (2012) 1915-1919 Initial spectrum 0 1400 1600 1800 2000 2200 2400 Wavelength (nm)

42. Recent results Pablo Lauterio et al., CIO 2016

43. NLP-SC laser Spectrum at laser output After 100-m HNLF No pulse breaking, NLP energies up to 300 nJ, wide and flat opticalspectrum • Lauterio-Cruz et al., Opt. Express 285 (2016) 13778-13787

44. Adjustability is observed numerically 0 600 16.5 nm FWHM = 16.5 nm 11 nm Spectrum (dB) 400 -20 10 nm Power (W) 11 nm FWHM = 8 nm 200 10 nm 1530 1540 1550 1560 1570 8 nm Wavelength (nm) 1 1 0 0.8 0 50 100 150 200 250 -50 0.6 Time (ps) 0.4 FWHM = 8 nm -500 0 500 Delay (fs) 0.5 Intensity (a.u.) 10 nm 11 nm  Pottiez et al., Appl. Opt. 50 (2011), E24-E31 16.5 nm 0 -50 0 50 100 -100 Delay (ps)

45. Figure-eight laserwith dispersion compensation EDF2  Polarizer 980-nm pump WDM2 55-m DCF (-38 ps/nm/km) Output 1 NOLM (100 m SMF-28) 50/50 /2  1 90/10 Isolator EDF1 WDM1 PC Amplitude (a.u.) 90/10 /2 Twist /4 /4 Output 2 0 -5 -4 -3 -2 -1 0 1 2 3 4 5 980-nm pump Time (s) • L = 200 m • Dispersion close to 0

46. Pulses with adjustable duration(60 ps – 6 ns) and spectrum (3 – 60 nm) 0 1 1 -10 .8 Short-pulse regime Spectrum (dB) .6 Amplitude (a.u.) .5 Normalized amplitude -20 .4 .2 -30 0 0 -1 0 1 1500 1550 1600 1650 1700 -80 -40 0 40 80 0 1 Long-pulse regime -10 1 Spectrum (dB) Amplitude (a.u.) .5 Normalized amplitude -20 -30 0 0 -4 -2 0 2 4 1500 1550 1600 1650 1700 -80 -40 0 40 80 Time (ns) Wavelength (nm) Delay (ps) Tworegimes of noiselikepulsing  Pottiez et al., Laser Phys. 24 (2014), 105104

47. Controlling pulse duration is essential for applications Case of micromachining (Ti):  Özgörenet al., Opt. Express. 24 (2011), 17647 Range of pulse duration between those of conventional mode-locked lasers (solitons, ~ ps) and Q-switched lasers (~ s)

48. Summary • We studied noiselike pulse formation in different fiber laser architectures. • Pulse energies as high as 0.3 J have been obtained experimentally. • Wide and smooth spectral bandwidths beyond 100 nm have been reached at the laser output, readily extendable by further propagation through different kinds of fiber. Flat supercontinuum spectra up to 400 nm have been obtained, which illustrates the potential of these sources for many applications. • By simple WR tuning, it is possible to adjust the noiselike pulse duration by a factor of 100 (60 ps – 6 ns) and its spectral bandwidth 20-fold (3 nm – 60 nm). Such adjustment possibility is crucial for applications like materials processing. • Although single noiselike pulsing is most common, pulse splitting occurs in some conditions and multiple pulsing is observed, in particular in the form of harmonic mode locking. Harmonic orders beyond 1200 have been evidenced. • Information on the inner structure of the noiselike pulses has been extracted using the ultrafast response of a NOLM transmission. In particular, the existence of an intermediate degree of organization at the sub-ns scale has been evidenced for a specific variety of pulses. Besides, the statistics of the sub-pulses has been measured, indicating the existence of optical rogue waves in the inner structure of the bunch. • The study of noiselike pulse dynamics is also progressing thanks to sequence analysis in the time domain. In particular, an original dynamics, in which sub-ns sub-pulses are released from the main waveform and drift away from it, has been evidenced, which bears some analogy with the soliton rain/release of solitons.