1 Institute for Optical Sciences University of Toronto Distinguished Visiting Scientist Program Prof. Michel Piché Université Laval, Québec Lecture-3: Mode-locked lasers and ultrafast fiber-based laser systems
2 Mode-locked lasers and ultrafast fibre-based laser systems Michel Piché Département de physique, COPL Université Laval, Québec Presented at the Institute for Optical Sciences, University of Toronto, on March 7, 2006
3 Outline of presentation Principles of laser mode locking Pulse characterization (P 2 parameter) Mode locking by nonlinear Kerr interactions: Kinematic mode locking Interferential mode locking («additive pulse mode locking», or «coupled-cavity mode locking») Kerr lens mode locking Mode locking by nonlinear ellipse rotation Mode-locked fibre lasers Solitonic-pulse regime Stretched-pulse regime Self-similar («parabolic») pulse regime Ultrafast fibre-based amplifier systems
4 What is mode locking? When the phases of all laser modes are equal, the laser emission is a train of pulses of minimum duration. In general, mode locking is not a natural state of laser operation. A laser must be forced to operate in the mode-locked regime. Mode locking is generally forced by either: An active modulator A saturable absorber A conversion of a nonlinear phase modulation (Kerr effect) to a nonlinear amplitude modulation A combination of some these mechanisms
5 Active mode locking L gain AM Experimental setup. cos(ω mod t) RF 100% cos(ω mod t) I(t) t 0 T mod 2T mod Laser output in time domain. q 1 q q + 1 q + 2 ω / ω mod Mode coupling in frequency domain.
6 Passive mode locking with a nonlinear element gain nonlinear element Standing-wave cavity. gain nonlinear element non-reciprocal element Traveling-wave cavity. T(I) 1 nonzero initial slope I Nonlinear transmission.
7 Active vs passive mode locking Active mode locking requires accurate cavity length control Active mode locking produces relatively long pulses (t pulse ~ Δω gain -1/2 ) Passive mode locking was first achieved with saturable absorbers (resonant nonlinearity) Saturable absorbers may also lead to Q- switching Passive mode locking can be obtained from Kerr interactions (nonresonant nonlinearities)
8 Critical issues for passively mode-locked lasers For its optimal operation, a passively mode -locked laser requires: A nonlinear loss mechanism to enable the mode-locked regime A mechanism to initiate mode-locking Dispersion management to minimize pulse chirping, hence pulse duration A pulse limiting mechanism to prevent Q- switching instabilities
9 Spatial hole burning may prohibit selfstarting operation gain E (+) I(z) E ( ) z 0 L g Interference in standing-wave cavity. gain 0 L g z Spatial modulation of gain ("spatial hole burning") E 1 λ /2 E 2 Scattering by induced g rating produc es an effective filtering See A. E. Siegman, Lasers, University Science Books, Mill Valley (1986)
10 How to initiate passive mode locking? Use of a unidirectional ring cavity (no hole burning ) Insertion of a saturable absorber with a low saturation intensity (high transmission slope) Gentle transient perturbation of a standingwave cavity to remove hole burning N.B.: Semiconductor saturable absorbers can be designed with specific characteristics. Their recovery time is generally in the picosecond range.
11 Electronic Kerr nonlinearity Nonlinear contribution to the index of refraction n = n 0 + n 2 I Instantaneous nonlinear response (< 1 fsec) The nonlinear index n 2 leads to: - spectral broadening - frequency chirp - self-focusing - rotation of the polarization ellipse
12 Frequency chirp due to Kerr effect (n 2 < 0)
13 Kinematic mode locking First observed by P. W. Smith in the 60 s. A moving mirror produced reliable mode locking of a He-Ne laser. The technique was extended to many other lasers. More recently frequency shifters (acousto-optic Bragg deflectors) have been used, particularly with fibre lasers. Such a laser operation is said to be modeless (at least, in the unlocked regime). Principle of operation: the Doppler shift due to the moving mirror is compensated by nonlinear frequency reshaping due to the Kerr effect.
14 Interferential mode locking Stolen and Mollenauer, Soliton laser (1984). Ouellette and Piché, Mode locking with a nonlinear Michelson interrferometer (1986). Groups at Cornell, MIT and St.Andrews produce femtosecond pulses with a positive-dispersion fibre in a coupled-cavity configuration (1988). It has been mostly used with color centre lasers. High sensitivity to mechanical perturbations. Principle of operation: the Kerr phase shift tunes the interferometric setup as a function of time.
15 Kerr lens mode locking First reported by Spence, Kean and Sibbett (1990). Most successful technique of passive mode locking with solid-state lasers. Shorter pulses require compensation of various orders of dispersion. Prism pairs can compensate up to second order, leading to 10-fsec pulses in Ti:sapphire lasers. Dispersive mirrors can compensate for higher-order dispersion, leading to 5-fsec pulses in Ti:sapphire lasers. Principle of operation: the Kerr lens leads to minimum losses at an aperture and/or maximum gain extraction.
16 Kerr lensing and spectral broadening Kerr medium Aperture Input beam Low intensity High intensity I I λ λ
17 Femtosecond Ti:sapphire laser Periscope Argon laser INNOVA 310 M P M la L P 2 M sa M OC 95% A Ti:sapphire crystal of 4 mm length is used. An all-solid-state laser can be used as the pump. Femtosecond emission is triggered by translating a prism.
18 Experimental results (4-mm crystal) 50.4 THz 106. nm T p = 12.8 fs Spectral density (a.u.) 41.7 THz 88.8 nm 30.4 THz 65.1 nm 21.8 THz 47.4 nm Second harmonic intensity (a.u.) T p = 16.6 fs T p = 18.2 fs T p = 22.8 fs Wavelength (nm) Delay (fs)
19 Spectrum 10-fsec pulses (2-mm crystal) Power density (a.u.) 71.1THz 147. nm Autocorrelation signal Wavelength (nm) TPA signal (a.u.) Measurement From spectrum Delay (fs)
20 Definition of a Pulse Quality Factor P 2 We do not have access directly to the real pulse shape I(t), but to its intensity autocorrelation I ac (t): I ac ()= t I( t + t ) I ()d t t It can be shown that the second-order moments of I ac (t) and I(t) are related: 2 = 2 σ t 2 σ t,ac Hence we can define a Pulse Quality Factor P 2 according to: P 2 = 2 πσ t,min σ ν where σ ν 2 is the second-order moment of the pulse spectrum and σ τ,min is the minimum value of σ t The minimum value of σ t (hence P 2 ) is found with a dispersive line of variable length
21 Pulse Quality Factor (P 2 Parameter) The pulse quality Factor (P 2 Parameter) is the temporal counterpart of the Beam Quality Factor (M 2 Parameter). The P 2 Parameter predicts the evolution of the RMS duration of a pulse in a dispersive medium (fused silica glass). Pulse rms-duration (fs) P 2 = 1.02 P 2 = 1.11 P 2 = 1.35 P 2 = 1.43 P 2 = Position from the temporal waist (cm)
22 Experimental setup Mode-locked diode laser
23 Femtosecond fibre lasers Compact and practical sources of femtosecond pulses Very low noise Pulse durations as short as 50 femtoseconds Many possible regimes of operation High average power from amplified systems (>100 W) Pulse energies > 10 μj
24 Regimes of emission of femtosecond fibre lasers 1) Solitonic-pulse regime: - negative cavity dispersion - relatively long pulses, of low power - parasitic sidebands 2) Stretched-pulse regime: - near zero or slightly positive cavity dispersion - short pulses, of intermediate power 3) Self-similar pulse regime ( parabolic pulses, or similaritons ): - near zero or slightly positive cavity dispersion - short pulses, of high power - material with negative dispersion is linear (grating pairs)
25 Stretched-pulse fiber ring laser Segments of fibre with normal and anomalous dispersion (Tamura et al., Opt. Lett., 18, 1080 (1993)) Σβ 2i L i ~ 0.01ps 2
26 Typical all-fibre ring laser cavity Dispersion-managed cavity Anomalous round-trip GVD Output fibre may lead to temporal compression & spectral broadening
27 Passive mode locking by nonlinear rotation of the polarization ellipse Cross-phase modulation due to the Kerr effect rotates the polarization ellipse as a function of instantaneous power. This interferometric process can be designed to favor high-power signals.
28 Passive mode locking by nonlinear rotation of the polarization ellipse At high power, the oscillatory response leads to pulse breakup in multiple pulses.
29 Solitonic-pulse regime: parasitic sidebands
30 Bound states of pulses (stretchedpulse regime) 1 T FWHM = 84 fs P = 7 mw [a.u.] time [ps] 1 P = 14 mw 1520 wavelength [nm] 1600 [a.u.] 0-15 time [ps] 15 1 P = 22 mw [a.u.] [a.u.] Wavelength [nm] wavelength [nm] [a.u.] Wavelength [nm] 1565 [a.u.] [a.u.] [a.u.] 0-30 time [ps] wavelength [nm]
35 Temporally-resolved pulse collision Sampled autocorrelation traces of the collision of a solitary pulse with a pulse doublet
36 Solitonic-pulse laser: bound state with a strong interaction bisoliton or antisymmetric soliton
37 Solitonic-pulse laser: bound state with a weak interaction
38 Quantization of two-soliton bound states
39 Self-similar («parabolic») pulse regime When the medium providing negative dispersion is linear, then wave breaking is inhibited. Parabolic pulses are quasi-invariant under propagation in a nonlinear material with a positive dispersion. If negative dispersion is introduced by grating pairs, then a stretched-pulse fibre laser can generate parabolic pulses of high energy (up to 10 nj has been demonstrated)
40 Laser emitting self-similar pulses (from Ilday et al, Opt. Lett. (2002) QuickTime et un décompresseur TIFF (LZW) sont requis pour visionner cette image.
41 QuickTime et un décompresseur TIFF (LZW) sont requis pour visionner cette image.
42 QuickTime et un décompresseur TIFF (LZW) sont requis pour visionner cette image.
43 QuickTime et un décompresseur TIFF (LZW) sont requis pour visionner cette image.
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48 Infrared continuum: measurements with a Fourier transform spectrometer
49 Basic considerations for ultrafast fibrebased amplifier systems Chirped pulse amplification must be used Maximum power in fibre < 3 megawatts (self-focusing threshold) Fibre amplifiers have positive dispersion (β 2 > 0) at 1 μm Fibre amplifiers have negative dispersion at 1550 nm, except when they have a very small mode area (10 μm 2 ) Large mode area amplifiers can be made single mode through an appropriate mechanical configuration If the dispersion is negative, self-modulation of the pulse takes place beyond a power threshold This instability generates a stream of temporal solitons that are Raman shifted ( soliton self-frequency shift )
50 Bandwidth limiting by the gain profile of erbium (for an Er-Yb co-doped fibre) 6,00E-08 5,00E-08 spectre de fluorescence section-efficace d'ˇmission 6,00E-25 5,00E-25 4,00E-08 3,00E-08 2,00E-08 1,00E-08 4,00E-25 3,00E-25 2,00E-25 1,00E-25 Section efficace (m^2) 0,00E+00 0,00E Longueur d'onde (nm)
51 Femtosecond fibre amplifier system (λ = 1550 nm)
52 Spectral distortion due to soliton formation and Raman shift QuickTime et un décompresseur TIFF (LZW) sont requis pour visionner cette image.
53 Gain of fibre amplifiers as a function of input power
54 Output vs input power curves for fibre amplifiers
55 Interferometric autocorrelation trace of amplified pulses
56 Conclusion Kerr-based methods are state-of-the-art for short pulse generation. Dispersion compensation is the key issue for minimum pulse duration. Scaling of pulse energy from fibre oscillators appears feasible using the self-similar pulse approach. The development of microstructured active fibres with selective dispersion will offer new opportunities for amplified systems. Detailed pulse shape from fibre systems sensitive to beam delivery. New approaches are being investigated ( cubicons ).
57 Acknowledgements Thanks to A. April, F. Babin, L. Desbiens, D. Gay, M. Laprise, B. Morasse, M. Olivier, G. Rousseau, and V. Roy This work was supported by NSERC, FCAR, CIPI, and Femtotech Thanks to EXFO for the sustained support throughout the fibre laser program Thanks to the other partners: INO, CorActive, CRC, Bomem
58 List of references M. Piché, G. Rousseau, L. Desbiens, and N. McCarthy, "Femtosecond lasers: their operation and their characterization. Application to conical wave packets". International School of Quantum Electronics, 28th Course: Laser Beams and Optics Characterization, Erice, Italy, March H. Laabs, H. Weber, Editors, pp G. Rousseau, N. McCarthy, and M. Piché, "Description of pulse propagation in a dispersive medium using a pulse quality factor". Opt. Lett. 27, (2002). M. Olivier, V. Roy, M. Piché, and F. Babin, "Pulse collisions in the stretched-pulse fiber laser". Opt. Lett. 29, (2004). V. Roy, M. Olivier, F. Babin, and M. Piché, "Dynamics of periodic pulse collisions in a strongly dissipative-dispersive system". Phys. Rev. Lett. 94, , pp. 1-4 (2005). V. Roy, M. Olivier and M. Piché, "Pulse interactions in the stretched-pulse fiber laser". Optics Express 13, (2005). M. Olivier, V. Roy, and M. Piché, "Third-order dispersion and bound states of pulses in a fiber laser". Optics Letters (March 2006).
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