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 0 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 0 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 0 g = 1+ 2I I sat
g 0 = rl γ c = lt R Intensität 0 e γ c t ~ e (g l)t/t R ~ 0 4 8 12 16 20 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 cn 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 () 0, 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 () 0, 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 cn dn dt = R p γ L N KnN N( t = 0)= N i nt= ( 0)= 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 0 =rl = n i exp g 0 l ( ) t T R N() t N i const. r = N i N th = γ c N th K
g 0 = rl γ c = lt R Intensität 0 e γ c t ~ e (g l)t/t R ~ 0 4 8 12 16 20 Zeit, ns
n max dn dt = KNn γ cn 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 = 0)= N i = rn th, n( t = 0)= 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
Sampling Oscilloscope 180 ps -500 0 500 Time [ps]
MISER: Monolithic Nd:YAG Laser Applying a magnetic field causes unidirectional lasing D C Evanescent wave coupled nonlinear semiconductor mirror B Interface B (see Fig. 1a) Inside MISER (Nd:YAG, n =1.82) Air z Inside nonlinear semiconductor mirror Saturable Absorber or Modulator section Mirror section A α > α Τ Pump-Laser: cw Ti:Sapphire laser @ 809 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 10 khz repetition rates 10 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 1.00 substrate GaAs Refractive Index index 4 3 2 1 0 0 Pump probe signal Bragg mirror AlAs/GaAs 1 8 0.1 6 4 2 8 6 0 5 10 z (μm) 100 top reflector HfO2/SiO2 τ A = 120 ps 200 15 Time delay pump-probe (ps) 4 3 2 1 0 incoming light Field intensity (rel. units) Field Intensity (Rel. Units) Reflectivity 0.96 0.92 0.88 ΔR = 10.3% 2 4 6 2 4 6 10 F sat 100 1000 Fluence on absorber (μj/cm ) SESAM #1: R = 10.3% F sat = 36 μj/cm 2 Reflectivity 1.00 0.98 0.96 0.94 0.92 0.90 2 4 ΔR = 7.3% 2 4 10 F sat 100 1000 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 0 τ L gt ()P() t E L dn A dt = N A N A0 τ A K A nn A dq() t dt = qt () q 0 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 -600-400 -200 0 200 400 600 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 0 ΔR R): Δg 2ΔR
l +ΔR l l -ΔR Phase 1 Phase 2 Phase 3 Phase 4 Gain g(t) Loss q(t)+l Intracavity power P(t) Δg -600-400 -200 0 200 400 600 Time (ps) Peak power (kw) 100 80 60 40 20 0 0 Unsaturated loss Gain g(t) r=3 Power P(t) 10 20 Time (μs) l + ΔR Gain g(t) r=2 No pulse for r=2 30 20 15 10 5 0 40 Gain, Loss (%)
E p hν L σ L E p A τ p 3.52T R ΔR A ΔR η out f rep g 0 (L tot + ΔR) 2ΔRτ L L L + abs L
τ p 3.52T R ΔR 1.5 1.0 0.5 37 ps 0.0-100 0 100 Time (ps) 200