Properties of normal-dispersion femtosecond fiber lasers

1. Properties of normal-dispersion femtosecondfiber lasers Speaker: TzungDa Jiang Adviser : Dr. Ja-Hon Lin

2. Outline • EXPERIMENTAL • DISCUSSION • USEFUL FEATURES OF ANDi FIBER LASERS • CONCLUSION

3. EXPERIMENTAL SETUP • In the experiments, the NPE port takes the role of a saturable absorber. • A birefringent plate betweenpolarization-dependent components constitutes a spectral filter. • The birefringent plate was inserted roughly at Brewster’s angle to minimize loss. Schematic of the experimental setup PBS: polarizationbeam splitter HWP: half-wave plate QWP: quarter-wave plate WDM: wavelength division multiplexer DDL: dispersion delayline.

4. Parameter Perturbation of ANDi laser • Independent control of the parameters of a laser is generally challenging, and two of the three key parameters are difficult to control individually in the ANDi laser. • The spectral filter BW can be changed by inserting a birefringent plate with a different thickness. • However, insertion of a new component within a cavity may introduce perturbations in the laser efficiency and therefore fluctuations in L. • Variation of the GVD by cutting or splicing a desired length of a SMF may cause the same problem. • Changing the length of the cavity influences not only the GVD, but also the NPE characteristics, which will eventually perturb the value of L. • With the given experimental setup, the only parameter that can be altered continuously without seriously affecting other parameters is L, which can be adjusted by controlling the pump power.

5. Simulated and experimental spectrum and autocorrelation at different nonlinear phase shift • The spectra recorded for increasing L are presented in Fig . along with the measured autocorrelationsof the dechirpedpulses. • The secondary lobes in the time domain contain from 4% [Fig. 12(g)] to 7% [Fig. 12(e)] of the pulse energy. Experimental results. Top: simulated output spectrum with NL: (a) ~1, (b)~3, (c)~4, (d) ~8; middle: experimental output spectrum with approximated NL: (e) ~1, (f) ~3, (g) ~4, (h)~8; bottom: corresponding experimental dechirpedinterferometric ACs.

6. Approximate of nonlinear phase shift • To investigate the scaling of the important pulse parameters with NL, we recorded the laser performance at different pulse energies, and then estimated the corresponding values of NL. • We assume for simplicity that thetemporal profile is constant in the three fiber segments, and approximate the nonlinear phase as • The peak power in the gain fiber and SMF following the gain fiber was assumed to be equal to that before the NPE port, and then pulse at each step used in the split-step Fourier method. r: nonlinear coefficient L:fiber length

7. Experimental and numerically simulated laser performance • The important point is that the measured trends in all four parameters agree with those of the numerical simulations. • As a result, we conclude that we have a satisfactory understanding of pulse shaping in ANDi lasers. Experimental and numerically simulated laser performance versus approximated NL; dots: experiment; curves: numerical simulation; (a) pulse energy before the NPE port, (b)breathing ratio, (c) dechirped pulse duration, (d) chirp.

8. Difference between simulation and experiment • The numerical simulations that model the NPE as a monotonic saturable absorber and the filter as a Gaussian transmission account for all of the modes of operation of the ANDi lasers presented here. • We do find in experiments that the laser can produce a limited number of modes with spectral shapes that are not matched well by these simulations. • NPE constitutes an pproximatelysinusoidal intensity transfer function, while the saturable absorber in the simulation was assumed to be an ideal monotonically increasing transfer function. • As a result, the output coupling depends on the NPE parameters, while it was assumed to be constant in the simulation.

9. Discussion of other soliton and fiber laser • These regimes are based on some balance of anomalous GVD and positive nonlinearity. • DM solitons can even exist at small net normal GVD. In solitonlike pulse shaping, selfamplitude modulations mostly play a secondary role, namely starting and stabilizing the mode locking. • The mode-locking regimes at large normal GVD rely ondissipative processes such as spectral filtering to fundamentally shape the pulse, not just to start and stabilize it. Laser operating regimes according to the net cavity dispersion and the existence of a dispersion map.

10. Discussion of CPO and ANDi laser • As mentioned above, ANDi laser and CPO exploit pulse-shaping processes that are conceptually and qualitatively the same as those described by the master equation [2] and first observed by Proctor et al. in a Ti:sapphire laser [3]. • However, there are clear differences in operation and implementation. • All work to date on CPOs has considered only static solutions, while the temporal breathing ratio varies from 1 to 4 in ANDi lasers, as shown in Figure. A :CPO B :ANDi laser [2]H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Structures for additive pulse mode locking,” J. Opt. Soc. Am. B 8,2068–2076 (1991). [3]B. Proctor, E. Westwig, and F. Wise, “Characterization of aKerr-lens mode-locked Ti:sapphire laser with positivegroup-velocity dispersion,” Opt. Lett. 18, 1654–1656 (1993).

11. Discussion of CPO and ANDi laser • Spectral filtering plays a role in pulse shaping inCPOs and in gain-guidedsoliton formation [11]. • The relativelyweak and constant spectral filtering action of thegain limits the range of mode-lockedoperations. • The ANDi lasers are the first to include a controllable filter and to optimize the performance with respect to the filter parameters. • Finally, CPOs to date have been constructed experimentally with elements that provide anomalous GVD, such as prism pairs and chirped mirrors. [11]. L. M. Zhao, D. Y. Tang, and J. Wu, “Gain-guided soliton in apositive group-dispersion fiber laser,” Opt. Lett. 31,1788–1790 (2006).

12. USEFUL FEATURES OF ANDiFIBERLASERS • ANDi fiber lasers have some practically useful features,in addition to the immediate advantage of removal of the anomalous-dispersion segment. • One remarkable feature of the ANDi fiber laser is its continuous tunabilitywithoutlosing mode locking. • It is quite possible to go continuouslyamong the spectra without losing mode locking, by rotating the wave plates in a laser. • Thechirping can be tuned to generate transform-limitedpulses after dechirping in a fixed dispersive delay. • Finally, the center wavelength can be tuned easily by adjusting the spectral filter center wavelengthwithout perturbing the pulse shape.

13. Improvement ofpulse quality by coupling out at different cavity locations • Figure demonstrates that a cleaner pulse can be obtained after the NPE port. • The pulse from the NPE output (output 1) has a sharply peaked spectrum with significant major sidelobesafter dechirping [Figs(a) and (b)]. • The spectrum and the dechirpedinterferometric AC [Figs(c) and (d)] demonstrate the dramatic improvement. Experimental result of the laser with two output ports. Output 1: (a) spectrum, (b) dechirpedinterferometric AC; output 2: (c) spectrum, (d) dechirpedinterferometric AC.

14. CONCLUSION • A key contribution to pulse shaping in these lasers arises from the spectral filter, which converts frequency chirp to self-amplitude modulation. • The ANDi fiber laser can support a wide variety of pulse shapes and evolutions, which include the CPO and the self-similar laser as limiting cases. • The ANDi fiber laser is a robust pulse source capable of highenergyultrashort pulses, with significant tunabilityof the pulse duration and chirp. • It should be reasonably straightforward to extend the ANDi lasers to higher pulse energies by technical approaches such as the use of largemode-area fibers; with larger mode area, higher energy is reached at fixed nonlinear phase shift.

15. Schematic of the experimental setup