γ c = rl = lt R ~ e (g l)t/t R Intensität 0 e γ c t Zeit, ns

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4 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

5 g = rl γ c = lt R Intensität e γ c t ~ e (g l)t/t R ~ Zeit, ns

6 laser crystal A/O Q-switch output coupler diode laser focussing optics coating: HR - laser λ HT - diode λ acoustic transducer partially reflective coating

12 dn dt = KNn γ cn dn dt = R p γ L N KnN R p = P abs hν pump

13 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

14 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

15 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

16 g = rl γ c = lt R Intensität e γ c t ~ e (g l)t/t R ~ Zeit, ns

17 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

18 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

19 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

20 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

21 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

23 dr di I > T R τ stim r T R τ L

25 Nd:LSB microchip laser (25% doped) A-FPSA Copper heat sink 1 % Output coupler 22 μm Cavity length 162 nm Pump 88 nm Waist radius: 4 μm Dichroic beamsplitter 88 nm 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

26 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 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)

27 μj-pulses with 1 khz repetition rates 1 mw average powers

28 Microchip crystal SESAM Output coupler Laser output Diode pump laser Copper heat sink Cavity length Dichroic beamsplitter pump wavelength laser wavelength

$absorber: InGaAs/GaAs quantum wells 1. substrate GaAs Refractive Index index 4 3 2 1 Pump probe signal Bragg mirror AlAs/GaAs 1 8.$

29 absorber: InGaAs/GaAs quantum wells 1. substrate GaAs Refractive Index index Pump probe signal Bragg mirror AlAs/GaAs z (μm) 1 top reflector HfO2/SiO2 τ A = 12 ps 2 15 Time delay pump-probe (ps) incoming light Field intensity (rel. units) Field Intensity (Rel. Units) Reflectivity ΔR = 1.3% F sat 1 1 Fluence on absorber (μj/cm ) SESAM #1: R = 1.3% F sat = 36 μj/cm 2 Reflectivity ΔR = 7.3% F sat 1 1 Fluence on absorber (μj/cm ) SESAM #2: R = 7.3% F sat = 47 μj/cm 2

30 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

31 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

32 l +ΔR l l -ΔR Phase 1 Phase 2 Phase 3 Phase 4 Gain g(t) Loss q(t)+l 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

33 l +ΔR l l -ΔR Peak power (kw) Phase 1 Phase 2 Phase 3 Phase 4 Gain g(t) Loss q(t)+l Intracavity power P(t) Δg 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= Gain, Loss (%)

34 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

36 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

37 E p /E L (%) γ = L p = γδr γ =.2 γ =.4 L tot + ΔR = 2% γ =.6 L tot + ΔR =1% Gain reduction Δg (%) ΔR =15% ΔR =1% ΔR = 5% Total nonsaturable losses L tot (%) Total nonsaturable losses L tot (%) 25 R R L tot g 2 R

38 E p hν L σ L AΔRη out L L abs

39 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 Time (ps) g i l q q g f l q = q Δg q q / T R

40 τ p 3.52T R ΔR ps Time (ps) 2

41 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

42 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

43 f rep g (L tot + ΔR) 2ΔRτ L g 2ΔRτ L L g f rep σ L g f rep

44 τ p 3.5T R ΔR 185 μm Nd:YVO 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** = 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 MHz

45 l + ΔR l l - ΔR Phase 1 Phase 2 Phase 3 Phase 4 Gain Loss 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.

46 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% Pump power (mw) Rep. rate (khz) Pulse width (ps) Fluence (mj/cm 2 ) 25 T out = 4.8 % 2 15 T out = 9 % T out = 9 % T out = 4.8 % 6 T out = 9 % 4 2 T out = 4.8 % Pump power (mw)

47 R Pulse width (ps) Fluence (mj/cm ) 2 Pulse energy (nj) Experiment Theory Theory Experiment linear fit without additive constant A (μm 2 )

48 Pulse width (ps) 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 ) ΔR = 1.3% ΔR = 7.3% Pump power (mw) E p A hν L σ L ΔR η out

49 Pulse width (ns) SESAM Crystal Variable cavity length Output Coupler Output beam τ p 3.5T R ΔR R R Cavity length (mm)

52 Cross-section (x 1-2 cm 2 ) pumping emission absorption Wavelength (nm) 15 11

53 Pulse energy # : E p hν L σ L AΔRη out Pulse duration *# : τ 3.52T R p ΔR

54 2% Yb:YAG SEmiconductor Saturable Absorber Mirror SESAM 2 μm copper heat sink 4.8% output coupler 13 nm 968 nm 968 nm 13 nm Pump: 3 μm single emitter P pump,max = nm w px = 56 μm; w py = 27 μm substrate GaAs Refractive Index index 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 Field Intensity intensity (Rel. Units) (rel. u.)

55 2. P pump = 485 mw Power (kw) 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

56 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 cm cm 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

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