1. Vladimir Kalosha Ultra-short pulse operation of all-optical fiber passively mode-locked Yb lasers Fiber Optics Group Dept. of Physics, U. of Ottawa to be published in Optics Express (May 2006)

2. Coauthors: • L. Chen • X. Bao • CIPI • NSERC • Research Chair Program Acknowledgment to:

3. Outline • Motivation • Advantages: Yb- vs Er-doped fiber lasers • Mode-locked Yb fiber lasers: SESAM vs. NPE • Round-trip Model • Results on dynamics modeling • Particular emphasis: How to generate ultimate shortest pulses directly from the cavity? • Discussion • Conclusion

4. Yb- vs Er-doped fiber lasers

5. Absorption & Emission cross-sections of Yb+3 in Ge:SiO2 glass

6. Passive mode-locking in Yb-doped fiber lasers • Tuennermann et al. OE 13, 9346 (2005): SESAM,self-similar pulsed regime • Wise et al. OE 11, 3550 (2003): NPE,stretched-pulsed regime, 36-fs, 2-nJ pulses by extra-cavity compression • Wise et al. OE 13, 3460 (2005): NPE, PCF, sub-100-fs pulses • Okhotnikov et al. OE 14, 4368 (2006): SESAM, both regimes • … • The aim: to create an environmentally robust all-fiber Yb fiber laser • generating high-power sub-ps pulses directly from the cavity, • with intra-cavity dispersion compensation by PCF, • with mode-locking by SESAM • Theory: to study generated pulse parameters in dependence on • Laser parameters for both regimes

7. Schematic of passive mode-locked Yb-doped fiber laser YDF: Yb-doped fiber SMF: single-mode fiber DCF: photonic crystal fiber as a dispersion-compensating fiber SBR: saturable Bragg reflector/SESAM OUT: output coupler PUMP: pump coupler/WDM Dispersion @ 1050 nm: YDF, SMFb2>0 DCFb2<0

8. Round-trip model of the laser generation:evolution equations in the intra-cavity fibers… YDF: GVD b2>0 Loss Kerr nonlinearity Saturated bandwidth-limited gain SMF & DCF: GVD b2>0 & b2<0

9. …and in the intra-cavity passive modulator Fast response to pulse intensity SESAM: parameters as for SESAM from BATOP Slow response to pulse energy Ref.: Kutz et al. JOSA B 14, 2681 (1997)

10. Intra-cavity fiber parameters used in the simulations of the laser dynamics

11. Characteristics of silica fibers used in the simulations of the laser dynamics YDF,SMF:Analytics for step-index fiber DCF:Vectorial FEM for photonic crystal fiber (inset) Normal GVD of YDF & SMF and anomalous GVD of DCF @ 1050 nm

12. Complete intra-cavity dispersion compensationin the case w/o fiber nonlinearity Steady-state spectrum, spectral peak location and duration vs. DCF length LYDF=LSMF=0.7m; LDCF=60…115cm LDCF=115cm dechirped pulse generated LDCF=60cm A complete compensation of intra-cavity GVD! Is it possible in the presence of Kerr nonlinearity in the fibers?

13. Importance of Kerr nonlinearity in intra-cavity DCF “Similariton”: tparabolic top tsteep edges tlinear chirp 3 3 1 1 2 2 1, no DCF 2, DCF with GVD w/o Kerr nonlinearity 3, DCF with GVD and Kerr nonlinearity N.B.: vertical scale for frequency and delay should be relative to 0th intensity levels

14. Pulse duration dependence on intra-cavity DCF with Kerr nonlinearity Long, phase-modulated, red-shifted pulses ‘similaritons’ LDCF=84cm t=2.70/0.13ps Normal net GVD =85cm =1.96/0.09ps Zero total dispersion =85.6cm Shorter, less phase-modulated, Stretched-pulse regime =1.30/0.06ps Anomalous net GVD =88cm =0.29/0.09ps Multi-pulsed regime Unstable regime LDCF

15. Pulse duration dependence on laser gain • Anomalous net GVD • Normal net GVD Generated pulse duration Dechirped Pulse duration • Stretched-pulse regime • Similar-pulse regime

16. Discussion Different mechanisms of ultra-short pulse generation at PML in fiber lasers: • Dispersion and nonlinearity compensation (soliton)1 • Interrelation of finite bandwidth gain and positive dispersion (similariton)2 • Stretched pulse mechanism (dispersion-managed solitons)3 For shortest-pulse generation these effects should be combined with pulse shortening by passive modulator and effect of finite gain bandwidth 1EL 27, 544 (1991) 2PRL 84, 6010 (2000) 3OL 18, 1080 (1993)

17. Pulse transformation along the cavity • Anomalous net GVD • LDCF=87cm, g0=0.6dB/m • Normal net GVD • LDCF=86cm, g0=0.5dB/m

18. Conclusion • Generation model for all-fiber Yb laser includes interrelation of PML/SESAM + saturable finite bandwidth gain + dispersion + Kerr nonlinearity • Dispersion compensation by intra-cavity photonic crystal fiber is shown • Laser parameters were found provided generation of sub-ps phase-modulated pulses • Development of an all-fiber passively mode-locked Yb laser system is under way