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2	Acknowledgments
3	Introduction: Output of a Mode-Locked Laser
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6	Outline Compare/contrast fiber lasers to free-space lasers Fiber Dispersion and Nonlinearities Mode-locking in fiber lasers
7	Passively Mode-locked Lasers Elements of mode-locked lasers Pump source Gain element Saturable absorber for mode-locking Dispersion compensation for shortest pulses
8	Fiber Lasers: Advantages and Disadvantages Advantages Easy to align fiber laser cavity Less sensitive to misalignment Passive optical elements are inexpensive Uses less power than Ti:sapphire laser More compact Disadvantages More sensitive to environment (polarization) Optical fiber limits total laser power All fiber cavity limits ability to easily experiment with laser design Careful dispersion and nonlinearity management is needed for proper laser design
9	Gain Medium: Erbium-Doped Fiber (EDF) Use a fiber that is highly doped with Er as the gain element of the laser This fiber exhibits normal dispersion : D=-70 ps/nm-km
10	Saturable Absorber for Mode-Locking
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12	Fiber Dispersion and Nonlinearities
13	Fiber Dispersion and Nonlinearities Self Phase Modulation (SPM)
14	Characterizing Dispersion and Nonlinearity in an Optical Fiber
15	Characterizing Dispersion and Nonlinearity in an Optical Fiber
16	The Nonlinear Schrödinger Equation
17	Mode-locking in Fiber Lasers Active Mode-locking Typically use AOM or Mach Zehnder to achieve mode locking Sigma laser (Duling et al, Opt Lett Vol 21, 21 1996) Advantage: Can achieve high repetition rates (10 GHz) Passive Mode-locking Interferometric designs based on gain and saturable absorber sections Figure eight lasers (Sacnac switch) Stretched Pulse Lasers Advantage: sub-picosecond, high energy pulses
18	Figure Eight Laser
19	Nonlinear Loop Mirror: Linear Operation
20	Nonlinear Loop Mirror: Nonlinear Operation
21	Figure Eight Laser Performance
22	Stretched Pulse Laser
23	Nonlinear Polarization Rotation
24	Nonlinear Polarization Rotation
25	Nonlinear Polarization Rotation
26	Nonlinear Polarization Rotation
27	Nonlinear Polarization Rotation
28	Stretched-Pulse Operation
29	Stretched-Pulse Fiber Laser
30	Stretched-Pulse Laser Performance
31	Part Two: Optical Frequency Metrology
32	Electric Field from a Mode-locked Laser
33	Acoustic Frequency Metrology: Guitar Tuning
34	Optical Frequency Metrology
35	Stabilize frequency comb by Self-reference frequency locking Measure offset frequency f_o as shown and lock to zero Phase-lock f_r directly to an rf synthesizer
36	Supercontinuum Frequency Comb
37	A Fiber Laser-Based Frequency Comb Translate Ti:Sapphire results to Fiber-based system Most existing frequency combs limited to Ti:Sapphire laser-based systems No self-referenced frequency combs from a mode-locked fiber laser in use Locking of a fiber laser to other stabilized sources have been achieved* Until recently a full octave from fiber laser not available* A fiber-based frequency comb can provide Compact, inexpensive design Potential for stable “hands-free” operation Optical frequency metrology in the IR * References F. Tauser et al, Opt. Express 11, 594 (2003) F.-L. Hong et al, Opt. Lett. 28, 1 (2003) J. Rauschenberger et al., Opt. Express 10, 1404 (2002)
38	All-Fiber Supercontinuum Source
39	Highly Nonlinear Fiber (HNLF)
40	f-to-2f Interferometer
41	Phase-locked Frequency Comb
42	Fiber Laser-Based Frequency Comb
43	Frequency Stability
44	Phase Noise Measurements
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46	Standard Reference Materials
47	Spectroscopy of Acetylene
48	Metrology with Supercontinuum Comb
49	Conclusions Stabilized frequency combs have revolutionized optical clocks Previous systems limited to 400 nm to 1300 nm Fiber laser-based frequency comb demonstrated Potentially more robust than Ti:sapphire laser based frequency comb Extend phase-lock frequency combs into the IR Permit unprecedented accuracy in IR frequency metrology Can lock frequency comb to Cesium time standard or other atomic standard
50	Thank you for your time!
51	EXTRA SLIDES
52	Four-Wave Mixing and Self-Phase Modulation
53	Solitons
54	Stimulated Raman Scattering (SRS) SRS is from the non-instantaneous component of the c⁽³⁾ susceptibility SRS typically leads to a frequency downshift of the incident light The Raman gain curve (g_R) characterizes the frequency downshift (Dn) acquired by the incident light
55	The NLSE
56	Including SRS
57	Extended NLSE for Including SRS
58	Soliton Propagation Solitons are formed after a balance of GVD and SPM Higher order dispersion and nonlinearities cause soliton breakup
59	Pulse Propagation Regimes
60	How to Choose Fiber Lengths? Need enough EDF to provide sufficient gain in the laser cavity Need enough SMF to provide adequate nonlinear polarization Net cavity dispersion is anomalous: Soliton Regime Net cavity dispersion is slightly normal Stretched-pulse Regime Net cavity dispersion is strongly normal No mode-locking
61	Soliton vs. Nonsoliton Regime Sidebands (Kelly sidebands) indicative of soliton propagation Inhibiting soliton formation increases spectral bandwidth
62	Femtosecond-Laser-Based Optical Synthesizer Sounds great, but can you do it? Ti:Sapphire femtosecond laser + novel nonlinear fiber (‘00) D. J. Jones et al. Science 288, 635 (2000) Broadband Ti:Sapphire femtosecond laser (‘01/’02) Morgner et al., PRL, 86, 5462,’01, T. Ramond et al., Opt. Lett 27, 1842 Femtosecond Er Fiber laser + novel nonlinear fiber (‘03) Washburn et al., accepted to Opt. Lett, Oct. ‘03
63	Details on Locking Electronics
64	Frequency Stability verses Gate Time
65	Spectrum of Figure-Eight Laser
66	Spectrum of Stretched-Pulse Laser