Ultrafast Laser Physics

Ultrafast Laser Physics Ursula Keller / Lukas Gallmann ETH Zurich, Physics Department, Switzerland www.ulp.ethz.ch Chapter 8: Passive modelocking Ultrafast Laser Physics ETH Zurich

Pulse-shaping in passive modelocking U. Keller, Ultrafast solid-state lasers, Landolt-Börnstein, Group VIII/1B1, edited by G. Herziger, H. Weber, R. Proprawe, pp. 33-167, 007, ISBN 978-3-540-6033-

Slow saturable absorber and dynamic gain saturation loss gain pulse time Conditions for stable modelocking: 1) at the beginning loss is larger than gain: l 0 > g 0 ) absorber saturates faster than the gain: 3) absorber recovers faster than the gain: E sat,a < E sat,l A A σ A τ A < τ L < A L σ L

Colliding pulse modelocking (CPM) Amplifier jet: Rhodamine 6G (R6G) Saturable absorber jet: DODCI (3,3-Diethylocadicarbocyanin) Rhodamine 6G (R6G) σ L = 1.36 10 16 cm τ L = 4 ns DODCI σ A = 0.5 10 16 cm τ A =. ns Photo-isomer σ A = 1.08 10 16 cm τ A 1 ns

Colliding pulse modelocking (CPM) CPM Rhodamine 6G-laser FWHM pulse duration τp Emission wavelength λl Average power Pav Resonator length L Repetition rate frep Pulse peak power in resonator Ppeak Output coupling transmission Tout Pump power Amplifier jet thickness (at focus) and pressure Absorber jet thickness (at focus) and pressure Prisms for GDD-compensation Typical Best [86Val] 100 fs 7 fs 60 nm 60 nm 5 mw 0 mw 3.3 m 3.3 m 100 MHz 100 MHz 100 kw 190 kw.5 % 3.5 % 5 W at 514 nm 4 W at 514 nm 80 m 300 m nozzle, 40 psi 30 50 m 10 m nozzle, 15 psi Quartz glass

Loss modulation for a slow and fast saturable absorber dq( t) dt = q( t) q 0 τ A q t ( ) P ( t) E sat,a slow saturable absorber: τ p << τ A fast saturable absorber: τ p >> τ A neglect recovery within pulse duration follows immediately incoming power dq( t) dt q t ( ) P ( t) E sat,a 0 = q( t) q 0 τ A q t ( ) P ( t) E sat,a T R P ( t) = E p f ( t), where f t 0 ( )dt = 1 ( ) ( ) P sat,a = E sat,a, P t = I t A τ A P sat,a I sat,a ( ) = q 0 exp E p q t t f ( t )d t E sat,a 0 q( t) = q 0 1+ I A t ( ) I sat,a

Slow saturable absorber and dynamic gain saturation q( t) = σ A N A d A e E p( t) E sat,a P ( t) = E p f ( t) E p ( t) = A L A t t ( ) d t loss gain pulse time g( t) = σ L N L d L e E p( t) E sat,l Assume slow saturable absorber and slow gain saturation net gain window: g T ( t) = g t ( ) q( t) = g 0 e E p t ( ) E sat,l q A e E p( t) E sat,a l R resonator loss: s-parameter: l 0 = q A + l R s E sat,l E sat,a q A = σ A N A d A

Slow saturable absorber and dynamic gain saturation g T ( t) = g( t) q( t) = g 0 e E p( t) E sat,l q A e E p( t) E sat,a l R e x 1+ x + x g T (E) (g 0 q A l R ) + (q A g 0 s ) E + 1 g 0 s q A For stable pulse generation we need to have g T < 0 at both beginning and end of the pulse. (see later that this does not always need to be the case - see soliton modelocking) E loss gain g T ( 0) 0 g T Shorter pulses for larger max ( E p ) 0 g T pulse time g T max = g T ( E max ), with g T E E=Emax = 0

Slow saturable absorber and dynamic gain saturation g T (E) (g 0 q A l R ) + (q A g 0 s ) E + 1 g 0 s q A E For stable pulse generation we assume to have g T < 0 at both beginning and end of the pulse. g T max loss gain pulse time g T ( 0) 0 g T max E Shorter pulses for larger ( p ) 0 g T g T max = g T g T max = l 0 ( E max ), with ( 1 1 s) 1 1 s ( ) g T E E=Emax = 0 optimize s-parameter: goal in CPM s 3 < s = σ AA L σ L A A < 1

Colliding pulse modelocking (CPM) jet thickness 30-50 µm jet thickness 80 µm Amplifier jet: Rhodamine 6G (R6G) Saturable absorber jet: DODCI (3,3-Diethylocadicarbocyanin) 3 < s = σ AA L σ L A A < 1 Optimization of s-parameter: mode size: factor of 4 colliding pulse in absorber (bi-directional pulse propagation in ring laser): factor of - 3 need thin absorber < spatial extend of pulses (100 fs pulses) d s 1 A < c n τ p 0 µm

Slow saturable absorber and dynamic gain saturation Master equation: A( T,t) T R T = g t ( ) q( t) + g 0 Ω g d dt + t D d dt A T,t ( ) = 0 SAM (self-amplitude modulation) time shift of pulse A out ( t) = exp q( t) A in t ΔA q( t) A( T,t) ( ) q( t) = q A exp A t L σ A A ( t ) A A hν d t q A : unsaturated loss of the absorber Solution: A ( t ) = A sech t Rhodamin 6G: 0 τ τ 4 π Δν g Δν g 4 10 13 Hz With SPM: factor of shorter (Martinez numerically) 1 ΔA 3 = t D H. A. Haus, Theory of modelocking with a slow saturable absorber, IEEE J. Quantum Electron. 11, 736, 1975 d dt A T,t ( ) τ p = 1.76 τ 56 fs

Passive mode locking with an ideally fast saturable absorber loss loss gain gain pulse pulse time time Semiconductor and dye lasers: Dynamic gain saturation G.H.C. New, Opt. Com. 6, 188, 1974 Solid-state lasers (e.g. Ti:sapphire) Kerr lens modelocking (KLM) Ideally fast saturable absorber Opt. Lett. 16, 4, 1991

Ultrashort pulse generation with modelocking dye laser 7 fs with 10 mw FWHM pulse width (sec) 10 ps Ti:sapphire laser 5.5 fs with 00 mw 1 ps 100 fs 10 fs compressed Science 86, 1507, 1999! 1 fs 1960 1960 A. J. De Maria, D. A. Stetser, H. Heynau Appl. Phys. Lett. 8, 174, 1966 1970 1970 1980 1980 # Year 1990 1990 KLM! 000 000 Year# Kerr lens modelocking (KLM): 00 ns/div# 50 ns/div# Nd:glass first passively modelocked laser Q-switched modelocked! discovered - initially not understood ( magic modelocking ) D. E. Spence, P. N. Kean, W. Sibbett, Opt. Lett. 16, 4, 1991 KLM mechanism explained for the first time: U. Keller et al., Opt. Lett. 16, 10, 1991# c

World record pulse duration at ETH Tages Anzeiger 7./8. Juni 1997

How does such a short pulse look like? λ/c =.7 fs @800 nm# The shortest pulses ( 5 fs at 800 nm) in the VIS-IR spectral region are still generated with KLM Ti:sapphire lasers 1.5 µm # speed of light# under laser lab conditions KLM is stable 1 fs 0.3 µm spatial extent of a 5-fs pulse

Kerr Lens Modelocking (KLM) D. E. Spence, P. N. Kean, W. Sibbett, Optics Lett. 16, 4, 1991 Effective Saturable Absorber Fast Self-Amp. Modulation Saturation fluence Loss Gain Loss Pulse fluence on absorber Pulse Time

Kerr Lens Modelocking (KLM) First Demonstration: D. E. Spence, P. N. Kean, W. Sibbett, Optics Lett. 16, 4, 1991 Explanation: U. Keller et al., Optics Lett. 16, 10, 1991 Advantages of KLM very fast thus shortest pulses very broadband thus broader tunability Disadvantages of KLM not self-starting critical cavity adjustments (operated close to the stability limit) saturable absorber coupled to cavity design (limited application)

Kerr Lens Modelocking (KLM) q( t) = q 0 γ A A( t) g( t) = g Ideally fast saturable absorber and cw gain saturation for solid-state lasers (no dynamic pulse-to-pulse gain saturation)

Ideally fast saturable absorber modelocking cw Argon-Ionen Pumplaser f=1.5 cm R=10cm Ti:Saphir, 4mm dick R=10cm Fused Quartz Prismen 60 cm Master equation: T = 3-10 % Auskopplung T R A T = g 1+ 1 Ω g t A l A + γ A 0 A A + id t A iδ A A iψ A = 0

Master equation without SPM and GDD A T R T = g 1+ 1 Ω g t A l A + γ A 0 A A = 0 ( ) = A sech t 0 τ A t τ = 4D g γ A E p Limit of very long pulses (cw limit): g = l 0 1 + 1 Ω g τ g = l 0, for τ H. A. Haus, J. G. Fujimoto, E. P. Ippen, Structures for additive pulse modelocking, J. Opt. Soc. Am. B 8, 068, 1991

Master equation without SPM and GDD A T R T = g 1+ 1 Ω g t A l A + γ A 0 A A = 0 ( ) = A sech t 0 τ A t τ = 4g Ω g γ A E p = 4D g γ A E p Comparison with active modelocking: τ 4 = g M 1 ω m Ω g E p = P ( t) dt = A dt = A0 Mω m γ A A 0 τ t sech τ dt = A 0 τ H. A. Haus, J. G. Fujimoto, E. P. Ippen, Structures for additive pulse modelocking, J. Opt. Soc. Am. B 8, 068, 1991

Master equation with SPM and GDD T R A T = g 1 + 1 Ω g t A l A + γ A 0 A A + id t A iδ A A iψ A = 0

Linearized operators: self-phase modulation (SPM) n > 0 I(t) ( ) I t φ ( t) = kn I ( t) L K = kn L K A( t) δ A( t) leading edge SPM: red Pulsfront Gaussian Pulse Zeitabhängige Intensität trailing Pulsflanke edge SPM: blue ( ) t ω ( t) t Verbreiterung des Spektrums Spectral broadening ω t ω 0 0 t δ kn L K ( ) = dφ ( t ) dt = δ di ( t) dt E ( L K,t) = A 0,t ( )exp iω 0 t + iφ ( t) = A( 0,t)exp iω 0t ik n ω 0 A( L K,t) = e iδ A A( 0,t)e ik n ω 0 ( )L K δ A <<1 ( ( ) ) A 0,t 1 iδ A t ( ) L K iδ A( t) ( )e ik n ω 0 ( )L K ΔA SPM iδ A( T,t)

Linearized operators: group delay dispersion (GDD) A ( z,δω ) = A ( 0,Δω )e iδknz = A 0,Δω ( )e i k n ω 0 +Δω ( ) k n ω 0 ( ) z k n ( ω ) k n ( ω 0 ) + k n Δω + 1 k Δω n +... A ( z, Δω ) A 0, Δω Δ AGDD ( )exp i 1 k nδω k n Δω <<1 A 0, Δω ( Δω ) i 1 k nδω A ( Δω ) idδω A ( Δω ) ( ) 1 i 1 D 1 k n k nδω ω i t ω t = i t Fourier transformation: Δω t ΔA GDD id t

Master equation with SPM and GDD T R A T = g 1 + 1 Ω g t A l A + γ A 0 A A + id t A iδ A A iψ A = 0 Here normalize pulse envelope as follows: P ( t) = A( t) Therefore: δ δ δ A L γ A γ A γ A A A

Master equation with SPM and GDD T R A T = g 1 + 1 Ω g t A l A + γ A 0 A A + id t A iδ A A iψ A = 0 ( ) = A sech t 0 τ A t g l 0 + 1 β τ g Ω g 1 τ = γ A A 0 g β Ω g 1+iβ βd τ = 0 ( ) 3βD β = 1 3 D g D ± 9 D g D + 8 + 4 δ A 0τ D no SPM and GDD: ( ) = A sech t 0 τ A t g l 0 + g Ω g τ = 4g Ω g γ A E p D δ = D g γ A 1 τ = 0 = 4D g γ A E p β = 0 H. A. Haus, J. G. Fujimoto, E. P. Ippen, Structures for additive pulse modelocking, J. Opt. Soc. Am. B 8, 068, 1991

Master equation with SPM and GDD T R A T = g 1 + 1 Ω g t A l A + γ A 0 A A + id t A iδ A A iψ A = 0 ( ) = A sech t 0 τ A t 1+iβ β = 3 χ ± 3 χ + H. A. Haus, J. G. Fujimoto, E. P. Ippen, J. Opt. Soc. Am. B 8, 068, 1991 τ n E p D g τ D n D g Ω = D 3β g D g β = δ + γ D A n δ D n γ A 1 χ

Master equation with SPM and GDD T R A T = g 1 + 1 Ω g t A l A + γ A 0 A A + id t A iδ A A iψ A = 0 ( ) = A sech t 0 τ A t 1+iβ τ n = β 3βD n γ A = D n + D n β 3β δ H. A. Haus, J. G. Fujimoto, E. P. Ippen, J. Opt. Soc. Am. B 8, 068, 1991 τ n E p D g τ D n D g Ω = D 3β g D g β = δ + γ D A n δ D n γ A 1 χ

Master equation with SPM and GDD T R A T = g 1 + 1 Ω g t A l A + γ A 0 A A + id t A iδ A A iψ A = 0 ( ) = A sech t 0 τ A t 1+iβ Stability of solution (a simple criteria): l cw > g g l cw < 0 l cw > 1 T R T R 0 l ( t)dt l cw l 0 g l 0 = ( 1 β ) g Ω g τ + βd < 0 τ S ( 1 β ) βd n > 0 τ n E p D g τ D n D g Ω = D 3β g D g β = δ + γ D A n δ D n γ A 1 χ

Master equation with SPM and GDD T R A T = g 1 + 1 Ω g t A l A + γ A 0 A A + id t A iδ A A iψ A = 0 ( ) = A sech t 0 τ A t 1+iβ S ( 1 β ) βd n > 0 H. A. Haus, J. G. Fujimoto, E. P. Ippen, J. Opt. Soc. Am. B 8, 068, 1991 τ n E p D g τ D n D g Ω = D 3β g D g β = δ + γ D A n δ D n γ A 1 χ

Master equation with SPM and GDD H. A. Haus, J. G. Fujimoto, E. P. Ippen, J. Opt. Soc. Am. B 8, 068, 1991

Self-starting modelocking? Fast Absorber without Dynamic Gain Saturation Modelocking Driving Force Active Modelocking Slow Absorber with dynamic gain saturation Dispersion Limit ( 1 / Pulse width ) shorter pulse width E. P. Ippen, Principles of passive modelocking, Appl. Phys. B 58, 159, 1994

Ultrashort pulse generation with modelocking A. J. De Maria, D. A. Stetser, H. Heynau Appl. Phys. Lett. 8, 174, 1966 Q-switching instabilities continued to be a problem until 199" SESAM# 00 ns/div# First passively modelocked (diode-pumped) solid-state laser without Q-switching 50 ns/div# Nd:glass first passively modelocked laser Q-switched modelocked! KLM! IEEE JSTQE, 435, 1996 Nature 44, 831, 003 # # 1960 1970 Flashlamp-pumped solid-state lasers! 1980 Year# U. Keller et al. Opt. Lett. 17, 505, 199 1990 000 Diode-pumped solid-state lasers (first demonstration 1963)#

SESAM modelocking U. Keller et al. Opt. Lett. 17, 505, 199 IEEE JSTQE, 435, 1996# Progress in Optics 46, 1-115, 004" Nature 44, 831, 003# SESAM solved Q-switching problem for diode-pumped solid-state lasers Gain! Output coupler! SESAM SEmiconductor Saturable Absorber Mirror # self-starting, stable, and reliable # modelocking of diode-pumped ultrafast solid-state # lasers

KLM vs. Soliton modelocking loss loss gain gain pulse pulse time Kerr lens modelocking (KLM) Fast saturable absorber D. E. Spence, P. N. Kean, W. Sibbett Opt. Lett. 16, 4, 1991 time Soliton modelocking not so fast saturable absorber F. X. Kärtner, U. Keller, Opt. Lett. 0, 16, 1995

Passive mode locking with slow saturable absorbers loss loss gain gain pulse pulse time Semiconductor lasers: Dynamic gain saturation G.H.C. New, Opt. Com. 6, 188, 1974 time Ion-doped solid-state lasers: Constant gain saturation: soliton modelocking F. X. Kärtner, U. Keller, Opt. Lett. 0, 16, 1995

Pulse-shaping VECSEL KLM Solid-state and SESAM Gain window can be up to 0 times longer than the pulse before mode locking becomes unstable fast/broadband sat. abs.# critical cavity adjustment: KLM better at cavity stability limit # typically not self-starting not so fast sat. abs absorber independent of cavity design self-starting For stable pulse generation it was initially assumed that we need g T < 0 at both beginning and end of the pulse. This is however not the case! See SESAM modelocking with slow saturable absorber and soliton modelocking

Slow saturable absorber modelocking R. Paschotta, U. Keller, Appl. Phys. B 73, 653, 001 absorber delays pulse! loss Fully saturated absorber:# leading edge of pulse# negligible loss for# has significant loss from # trailing edge of pulse# the saturable absorber# time Dominant stabilization process:! Picosecond domain: absorber delays pulse# The pulse is constantly moving backward and # can swallow any noise growing behind itself# Femtosecond domain: dispersion in soliton modelocking#

Soliton modelocking: GDD negative, n > 0 Outputcoupler Group Delay Velocity Dispersion Self- Phase- Modulation Gain Slow Absorber A out ( T,t) = e q(t ) A in ( T,t) Master equation: ( ) = 1 q( t) A in ( T,t) ( ) = q( t) A( T,t) A out T,t ΔA T,t T R T A T,t ( ) = id ( ) iδ A T,t t A T,t ( ) + g l + D g t q t ( ) A T,t ( ) = 0 ( ) = A sech t 0 τ A T,t exp iφ 0 T T R + continuum τ = 4 D δ F p,l

Soliton modelocking: GDD negative, n > 0 F. X. Kärtner, U. Keller, Optics Lett. 0, 16, 1995 Invited Paper: F. X. Kärtner, I. D. Jung, U. Keller, IEEE JSTQE,, 540, 1996 Soliton # Perturbation # Theory:# A(T,t) = Asech t τ T exp i Φ 0 T R { soliton + small perturbations { continuum only GDD & SAM (no SPM) Continuum Loss GDD Continuum spreading GDD Gain Gain Pulse Pulse Frequency Time Frequency domain Time domain Stabilization: Dispersion spreads continuum out where it sees more loss

A T,t Soliton modelocking: GDD negative, n > 0 Solution: stable soliton pulses ( ) = A sech t 0 τ exp iφ 0 T T R 0 τ = 4 D + continuum δ F p,l Continuum Loss GDD Continuum GDD Gain Gain Pulse Pulse Frequency Frequency domain Time Time domain Stabilization: Dispersion spreads continuum out where it sees more loss

Experimental confirmation: example Ti:sapphire laser T=3% output coupler SF 10 prism 45 cm 5 µm etalon SF 10 prism ROC 10cm Ti:sapphire 4mm, 0.15% doping 40cm ROC 10cm Argon pump d R=10cm Absorber (A-FPSA) SESAM SESAM: LT-GaAs Impulse response measured with 300 fs pulses clearly a slow saturable absorber No KLM: cavity operated in the middle of cavity stability regime (and use etalon for bandwidth limitation) Reflection, % 98.4 98. 98.0 97.8 97.6 97.4 97. 0 A = 10 ps 10 0 30 Time delay, ps 40 50 I. D. Jung, F. X. Kärtner, L. R. Brovelli, M. Kamp, U. Keller, "Experimental verification of soliton modelocking using only a slow saturable absorber," Opt. Lett., vol. 0, pp. 189-1894, 1995

Experimental confirmation: example Ti:sapphire laser Solution: soliton pulse A s ( T,t) = F p,l soliton phase per resonator roundtrip φ 0 = D τ = δ F p,l 4τ Stability (soliton perturbation theory): continuum loss l c is larger than soliton loss l s Normalized abs. recovery lc/q0, ls/q0 1.0 0.8 0.6 0.4 0. τ sech t τ e iφ 0 Kontinuumverluste continuum loss soliton loss Solitonverluste T T R τ FWHM stabiles stable regime Regime τ FWHM = 1.76 τ = 1.76 4 D δ F p,l unstabiles unstable regime Regime 1000 800 600 400 Pulse Width τ FWHM, fs w = τ A τ q 0 φ 0 = τ A q 0 D 1 D 0.0 0 10 0 30 Normalized Absorber Recovery Time w 40 00 I. D. Jung, F. X. Kärtner, L. R. Brovelli, M. Kamp, U. Keller, "Experimental verification of soliton modelocking using only a slow saturable absorber," Opt. Lett., vol. 0, pp. 189-1894, 1995

Experimental confirmation: example Ti:sapphire laser 1.0 1000 τ FWHM = 1.76 τ = 1.76 4 D δ F p,l lc/q0, ls/q0 0.8 0.6 0.4 0. τ FWHM stabiles Kontinuumverluste stable continuum loss Regime regime Solitonverluste soliton loss unstabiles unstable regime Regime 800 600 400 Pulse Width τ FWHM, fs 0.0 0 10 0 30 40 00 Normalized Absorber Recovery Time w Autocorrelation, a. u. - D = 00 fs - D = 300 fs - D = 500 fs - D = 800 fs - D = 1000 fs - D = 100 fs -000-1000 0 1000 000 Time, fs FWHM = 31 fs FWHM =391 fs FWHM = 469 fs I. D. Jung, F. X. Kärtner, L. R. Brovelli, M. Kamp, U. Keller, "Experimental verification of soliton modelocking using only a slow saturable absorber," Opt. Lett., vol. 0, pp. 189-1894, 1995 Intensity, a. u. - D = 00 fs - D = 300 fs - D = 500 fs - D = 800 fs - D = 1000 fs - D = 100 fs f =.68THz 80 804 806 808 Wavelength, nm f =.97 THz f =.85 THz 810 81

Experimental confirmation: example Ti:sapphire laser 1.0 1000 τ FWHM = 1.76 τ = 1.76 4 D δ F p,l lc/q0, ls/q0 0.8 0.6 0.4 0. τ FWHM stabiles Kontinuumverluste stable continuum loss Regime regime Solitonverluste soliton loss unstabiles unstable regime Regime 800 600 400 Pulse Width τ FWHM, fs 0.0 0 10 0 30 40 00 Normalized Absorber Recovery Time w Autocorrelation, a. u. - D = 00 fs - D = 300 fs - D = 500 fs - D = 800 fs - D = 1000 fs - D = 100 fs -000-1000 0 1000 000 Time, fs FWHM = 31 fs FWHM =391 fs FWHM = 469 fs High dynamic range autocorrelation: 330 fs Opt. Lett. 0, 1889, 1995 I. D. Jung, F. X. Kärtner, L. R. Brovelli, M. Kamp, U. Keller, "Experimental verification of soliton modelocking using only a slow saturable absorber," Opt. Lett., vol. 0, pp. 189-1894, 1995 Autocorrelation, a.u. 10 0 10-1 10-10 -3 10-4 10-5 10-6 -3 - -1 0 1 3 Time, ps

Coupled cavity modelocking Chapter 8.5: for historical reasons summarized here - not used much anymore The soliton laser L. F. Mollenauer, R. H. Stolen, "The soliton laser," Optics Lett., vol. 9, pp. 13-15, 1984. Additive pulse modelocking (APM) K. J. Blow and D. Wood, "Modelocked lasers with nonlinear external cavities," J. Opt. Soc. Am B, vol. 5, pp. 69-63, 1988 P. N. Kean, X. Zhu, D. W. Crust, R. S. Grant, N. Landford, W. Sibbett, "Enhanced modelocking of color center lasers," Optics Lett., vol. 14, pp. 39-41, 1989 9 E. P. Ippen, H. A. Haus, L. Y. Liu, "Additive Pulse Modelocking," J. Opt. Soc. Am. B, vol. 6, pp. 1736-1745, 1989 Resonant passive modelocking (RPM) U. Keller, W. H. Knox, and H. Roskos, "Coupled-Cavity Resonant Passive Modelocked Ti:Sapphire Laser," Optics Lett., vol. 15, pp. 1377-1379, 1990 H. A. Haus, U. Keller, and W. H. Knox, "Theory of Coupled-Cavity Modelocking with a Resonant Nonlinearity," J. Opt. Soc. Am. B, vol. 8, pp. 15-158, 1991