There is however one main difference in this chapter compared to many other chapters. All loss and gain coefficients are given for the intensity and not the amplitude and are therefore a factor of 2 larger! l q q t o tal nonsaturable intensity loss coefficient per resonator round-trip (i.e. without the saturable absorber, but includes output coupler loss and any additional parasitic loss also the nonsaturable losses of the saturable absorber s a turable intensity loss coefficient of the saturable absorber per cavity round-trip u n bleached intensity loss coefficient of the saturable absorber per cavity roundtrip (i.e. maximum q at low intensity) g s a turated intensity gain coefficient per resonator round-trip (please note here we use intensity gain and not amplitude gain) g intensity small signal gain coefficient per resonator round-trip (often also simply called small signal gain). For a homogenous gain material applies in steady-state (factor 2 for a linear standing-wave resonator): g g = 1+ 2I I sat
g = rl γ c = lt R Intensität e γ c t ~ e (g l)t/t R ~ 4 8 12 16 2 Zeit, ns
laser crystal A/O Q-switch output coupler diode laser focussing optics coating: HR - laser λ HT - diode λ acoustic transducer partially reflective coating
dn dt = KNn γ cn dn dt = R p γ L N KnN R p = P abs hν pump
dn dt = KNn γ c n dn dt = R p γ L N KnN dn dt 3τ L R p γ L N = R p N τ L () N t nt (), N max = R p τ L R p = const. N t ()= R p τ L 1 exp( t τ L ) ( ) = N max 1 exp t τ L τ L 2τ L t
3τ L nt (), R p = const. dn dt R p γ L N = R p N τ L () N t N max = R p τ L N t ()= R p τ L 1 exp( t τ L ) ( ) = N max 1 exp t τ L τ L 2τ L t E p = const. T rep > 3τ L, or f rep = 1 T rep < 1 3τ L 1 = 3τ L
dn dt = KNn γ c n dn dt = R p γ L N KnN N( t = )= N i nt= ( )= n i 1 dn dt K ( N i N th )n = KN th ( r 1)n = r 1 n τ c () n i exp r 1 nt τ c t τ c =T R l, g =rl = n i exp g l ( ) t T R N() t N i const. r = N i N th = γ c N th K
g = rl γ c = lt R Intensität e γ c t ~ e (g l)t/t R ~ 4 8 12 16 2 Zeit, ns
n max dn dt = KNn γ c n N th = γ c K dn dt = R p γ L N KnN dn dn K ( N N th )n = N N th KnN N dn dt = K ( N N th )n dn KnN dt dn N th N N dn N( t = )= N i = rn th, n( t = )= n i 1 nt () n i dn Nt () N i =rn th N th N N dn nt () N i N() t N i r ln N i N t (), with N i = rn th nt ()= n max for g = l N()= t N th
n max n max N i nt ()= n max for g = l N()= t N th n max r 1 lnr r N i, with N i = rn th P p,out = n maxhν τ c E p,out E p ( N i N f )hν
n max η Q - switched pulse energy stored energy ( = N i N f )hν = N i N f N i hν N i nt ()= n max for g = l N()= t N th n max r 1 lnr r N i, with N i = rn th P p,out = n maxhν τ c E p,out E p ( N i N f )hν E p,out = E p η( r)n i hν
n max τ p E p,out P p,out η( r)n i n max τ c rη ( r) r 1 ln r τ c τ p η( r) P p,out = n maxhν τ c τ c E p,out = E p η( r)n i hν
n max nt ()= n max exp( t τ c ) τ p η( r) P p,out = n maxhν τ c τ c E p,out = E p η( r)n i hν
dr di I > T R τ stim r T R τ L
Nd:LSB microchip laser (25% doped) A-FPSA Copper heat sink 1 % Output coupler 22 μm Cavity length Output @ 162 nm Pump laser @ 88 nm Waist radius: 4 μm Dichroic beamsplitter HT @ 88 nm HR @ 162 nm LT GaAs/InGaAs MQW absorber Sampling Oscilloscope 18 ps -5 5 Time [ps] GaAs Substrate GaAs/AlAs mirror Dielectric top mirror R t I in I out d
MISER: Monolithic Nd:YAG Laser Applying a magnetic field causes unidirectional lasing D C Evanescent wave coupled nonlinear semiconductor mirror Interface B (see Fig. 1a) Inside MISER (Nd:YAG, n =1.82) Air Inside nonlinear semiconductor mirror Saturable Absorber or Modulator section B z Mirror section A α > α Τ Pump-Laser: cw Ti:Sapphire laser @ 89 nm Output: Without nonlinear mirror -> cw output, single mode due to unidirectional ring laser With nonlinear mirror-> single mode Q-switched Airgap: Coupling through evanescent waves: Frustrated total internal reflection (FTIR)
μj-pulses with 1 khz repetition rates 1 mw average powers
Microchip crystal SESAM Output coupler Laser output Diode pump laser Copper heat sink Cavity length Dichroic beamsplitter HT @ pump wavelength HR @ laser wavelength
absorber: InGaAs/GaAs quantum wells 1. substrate GaAs Refractive Index index 4 3 2 1 Pump probe signal Bragg mirror AlAs/GaAs 1 8.1 6 4 2 8 6 5 1 z (μm) 1 top reflector HfO2/SiO2 τ A = 12 ps 2 15 Time delay pump-probe (ps) 4 3 2 1 incoming light Field intensity (rel. units) Field Intensity (Rel. Units) Reflectivity.96.92.88 ΔR = 1.3% 2 4 6 2 4 6 1 F sat 1 1 Fluence on absorber (μj/cm ) SESAM #1: R = 1.3% F sat = 36 μj/cm 2 Reflectivity 1..98.96.94.92.9 2 4 ΔR = 7.3% 2 4 1 F sat 1 1 Fluence on absorber (μj/cm ) SESAM #2: R = 7.3% F sat = 47 μj/cm 2
longitudinal section L g crosssection mode area A SESAM Gain R, F sat,a material Output coupler T out L, F sat,l Parasitic losses L p Total losses L tot = T out + L p out = L out /(L out + L p ) F sat,a << F sat,l = hν L 2σ L A > p
g q P - P + P + = - P = P T out n = P hν T R g = L g N L V σ L T R =2 Lc = 2L chν P V =A L L g = N L A L σ L q = N A A A σ A τ, E L L A L τ A, EA A A W stim = K L n = I hν σ L = P A L hν σ L K L = σ L A L T R dn dt = K L N L K A N A 1 τ c n dp () t T R dt = gt () l () t qt () P() t dn L dt = N L τ L K L nn L + R p dg() t dt = gt () g τ L gt ()P() t E L dn A dt = N A N A τ A K A nn A dq() t dt = qt () q τ A qt ()P() t E A
l +ΔR l l -ΔR Phase 1 Phase 2 Phase 3 Phase 4 Gain g(t) Loss q(t)+l -6-4 -2 2 4 6 E stored = E L g tot Time (ps) Intracavity power P(t) Δg T out + L p ΔR E released = E L Δg l l p q ΔR R): Δg 2ΔR
l +ΔR l l -ΔR Peak power (kw) 1 8 6 4 2 Phase 1 Phase 2 Phase 3 Phase 4 Gain g(t) Loss q(t)+l Intracavity power P(t) Δg -6-4 -2 2 4 6 Time (ps) Unsaturated loss Gain g(t) r=3 Power P(t) 1 2 Time (μs) l + ΔR Gain g(t) r=2 No pulse for r=2 3 2 15 1 5 4 Gain, Loss (%)
E p hν L σ L E p A τ p 3.52T R ΔR A ΔR η out f rep g (L tot + ΔR) 2ΔRτ L L L + abs L
E stored = AL g N 2 hν L g = 2σ L N 2 L g E stored = hν L 2σ L Ag = E L g E released = E L Δg η out = Δg 2ΔR L out L out + L p E p hν L σ L AΔRη out
E p /E L (%) 2 15 1 5 γ = L p = γδr γ =.2 γ =.4 L tot + ΔR = 2% γ =.6 L tot + ΔR =1% Gain reduction Δg (%) 3 25 2 15 1 5 ΔR =15% ΔR =1% ΔR = 5% 5 1 15 2 Total nonsaturable losses L tot (%) 25 5 1 15 2 Total nonsaturable losses L tot (%) 25 R R L tot g 2 R
E p hν L σ L AΔRη out L L abs
l +ΔR l l -ΔR Phase 1 Phase 2 Phase 3 Phase 4 Gain g(t) Loss q(t)+l tot Intracavity power P(t) Δg τ p 3.52 T R q l q l < q -6-4 -2 2 4 6 Time (ps) g i l q q g f l q = q Δg q q / T R
τ p 3.52T R ΔR 1.5 1. 37 ps.5. -1 1 Time (ps) 2
L, R L, R P p ( ΔR) 2 P peak E p τ p L hν σ L AΔRη out 3.52T R ΔR ( ΔR)2 A η out T R σ L
P av = η s (P P P P,th ) f rep = P av E p = η s(p P P P,th ) E p r 1 P p P p,th E p r g l + q P P = P P,th = hν P A 2σ L τ L η P g hν P A ( l + q ) 2σ L τ L η P f rep = g (l + q ) Δgτ L g (l + q ) 2q τ L q ΔR
f rep g (L tot + ΔR) 2ΔRτ L g 2ΔRτ L L g f rep σ L g f rep
τ p 3.5T R ΔR 185 μm Nd:YVO 4 1.5 1..5. -1 1 Time (ps) 37 ps 2 f rep = 16 khz E p = 53 nj R 13 % p =37ps E p hν L σ L A ΔR η out 2 μm Yb:YAG* =1.3μm f rep = 12 khz E p = 1.1 μj p = 53 ps.5 mm Er:Yb:glass** = 1.535 μm f rep = 1.4 khz E p = 11.2 μj p = 84 ps f rep g Different crystals and SESAMs Varying pump power 2ΔRτ L f rep = 32 Hz - 7.8 MHz
l + ΔR l l - ΔR Phase 1 Phase 2 Phase 3 Phase 4 Gain Loss -6-4 -2 2 4 6 Time (ps) Intracavity power E p hν L σ L 2F sat,l A ΔR η out τ p 3.5T R ΔR f rep g 2ΔRτ L g
Rep. rate (khz) Pulse width (ps) Fluence (mj/cm 2 ) R R 3 ΔR 7.3% 2 ΔR 1.3% 1 ΔR 7.3% 4 ΔR 1.3% 2 6 ΔR 1.3% 4 2 ΔR 7.3% 1 2 3 4 Pump power (mw) Rep. rate (khz) Pulse width (ps) Fluence (mj/cm 2 ) 25 T out = 4.8 % 2 15 T out = 9 % 1 5 5 4 T out = 9 % 3 2 1 T out = 4.8 % 6 T out = 9 % 4 2 T out = 4.8 % 1 2 3 4 Pump power (mw)
R Pulse width (ps) Fluence (mj/cm ) 2 Pulse energy (nj) 3 2 1 4 3 2 1 12 8 4 Experiment Theory Theory Experiment linear fit without additive constant 36 4 44 48 A (μm 2 )
Pulse width (ps) 3 2 1 ΔR = 7.3% ΔR = 1.3% τ p 3.5T R ΔR Rep. rate (khz) 4 2 ΔR = 7.3% ΔR = 1.3% f rep g 2ΔRτ L Fluence (mj/cm 2 ) 6 4 2 ΔR = 1.3% ΔR = 7.3% 1 2 3 4 Pump power (mw) E p A hν L σ L ΔR η out
Pulse width (ns) 8 6 4 2 SESAM Crystal Variable cavity length Output Coupler Output beam τ p 3.5T R ΔR R R 2 4 6 8 1 12 14 Cavity length (mm)
Cross-section (x 1-2 cm 2 ) 2.5 2. 1.5 1..5 pumping emission absorption. 85 9 95 1 Wavelength (nm) 15 11
Pulse energy # : E p hν L σ L AΔRη out Pulse duration *# : τ 3.52T R p ΔR
2% Yb:YAG SEmiconductor Saturable Absorber Mirror SESAM 2 μm copper heat sink 4.8% output coupler output @ 13 nm pump @ 968 nm HT @ 968 nm HR @ 13 nm Pump: 3 μm single emitter P pump,max =.7 W @ 968 nm w px = 56 μm; w py = 27 μm substrate GaAs Refractive Index index 4 3 2 1 absorber: 9 InGaAs/GaAs quantum wells Bragg mirror AlAs/GaAs 5 1 z (μm) z (μm) top reflector HfO2/SiO2 small penetration depth (a few μm) short pulses adjustable device parameters 15 incoming light 4 3 2 1 Field Intensity intensity (Rel. Units) (rel. u.)
2. P pump = 485 mw Power (kw) 1.5 1..5. -2-1 1 2 Time (ps) 53 ps R 1.6% (R top = 75%) R ( R top ) R E p R top = % 3 mj/cm 2 R top = 75% 2 mj/cm 2 E p = 1.1 μj F p 1 mj/cm 2 p = 53 ps P peak = 2.1 kw P avg = 13.2 mw f rep = 12 khz
absorption length absorption bandwidth gain bandwidth Nd(3%):YVO 4 9 μm 1.5 nm 1 nm Nd(1.1%):YAG 12 μm.8 nm.5 nm Yb(2%):YAG 435 μm 2 nm 8.5 nm gain cross-section 25 1-2 cm 2 25 1-2 cm 2 2.5 1-2 cm 2 typical pulse energies * typical pulse durations * 7 nj <1 ps 1 nj < 1 ns 1 μj < 1 ns good for single mode operation and short pulse generation good for large pulse energies