Fizika | Lézerek » Keller-Gallmann - Ultrafast Laser Physics

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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 larg e r ! l q q0 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) s a turated intensity gain coefficient per resonator round-trip (please note here we use intensity gain and not amplitude gain) g0 i n t e n s i t y 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= g0 1 + 2I I sat Source: http://www.doksinet  
 
 
 
  γ c = l TR Intensität g0 = rl –γc t ~ e (g 0 – l)t/TR 0 4 ~e 8 Zeit, ns 12 16 20 Source: http://www.doksinet 
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  dn = KNn − γ c n dt dN = Rp − γ L N − KnN dt Rp = Pabs hν pump Source: http://www.doksinet "


 

  dn = KNn − γ c n dt  dN = Rp − γ L N − KnN dt 
 




 


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τL dt  n ( t ) ≈ 0 , Rp = const. N max = Rpτ L N (t ) N ( t ) = Rpτ L ⎡⎣1 − exp ( −t τ L ) ⎤⎦ = N max ⎡⎣1 − exp ( −t τ L ) ⎤⎦ τL 2τ L t Source: http://www.doksinet !#*
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 #$!  N max = Rpτ L N dN ≈ Rp − γ L N = Rp − dt τL N (t ) N ( t ) = Rpτ L ⎡⎣1 − exp ( −t τ L ) ⎤⎦ = N max ⎡⎣1 − exp ( −t τ L ) ⎤⎦ τL E p = const. ⇔ Trep >≈ 3τ L , or frep = 1 1 <≈ Trep 3τ L 1 3τ L )"

  

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 dn = KNn − γ c n dt  dN = Rp − γ L N − KnN dt  N (t = 0 ) = Ni n ( t = 0 ) = ni ≈ 1 
   






  



    



 

 
r −1 dn ≈ K ( N i − N th ) n = KN th ( r − 1) n = n τc dt ⎛ r − 1 ⎞ τ c =TR l, g0 =rl ⎡ t ⎤ n ( t ) ≈ ni exp ⎜ t ⎟ ⎯⎯⎯⎯⎯ = ni exp ⎢( g0 − l ) ⎥ TR ⎦ ⎝ τc ⎠ ⎣ N ( t ) ≈ N i ≈ const. r = N i N th N th = γ c K Source: http://www.doksinet  
 
 
 
  γ c = l TR Intensität g0 = rl –γc t ~ e (g 0 – l)t/TR 0 4 ~e 8 Zeit, ns 12 16 20 Source: http://www.doksinet 


 


  nmax dn = KNn − γ c n dt N th = γ c K  dN = Rp − γ L N − KnN dt    
 
 
 


 
dn K ( N − N th ) n N th − N ≈ = −KnN dN N N −N dn ≈ th dN N n (t ) ≈ Ni − N (t ) − N ( t = 0 ) = N i = rN th , n ( t = 0 ) = ni ≈ 1 dn = K ( N − N th ) n dt dN ≈ −KnN dt n( t ) ∫ ni Ni ⎛ Ni ⎞ , ln ⎜

⎟ r ⎝ N (t ) ⎠ with N i = rN th  dn ≈ N (t ) ∫ N i =rN th N th − N dN N n ( t ) = nmax for g = l ⇔ N ( t ) = N th Source: http://www.doksinet  

 
   
 

  nmax nmax N i n ( t ) = nmax for g = l ⇔ N ( t ) = N th nmax ≈ r − 1 − lnr Ni , r Pp ,out = nmax hν τc with N i = rN th ( ) E p ,out ≈ E p ≈ N i − N f hν Source: http://www.doksinet  

 
   
 

  nmax η≡ ( ) N i − N f hν N i − N f Q - switched pulse energy = = stored energy N i hν Ni n ( t ) = nmax for g = l ⇔ N ( t ) = N th nmax ≈ r − 1 − lnr Ni , r Pp ,out = nmax hν τc with N i = rN th ( ) E p ,out ≈ E p ≈ N i − N f hν E p ,out = E p ≈ η ( r ) N i hν Source: http://www.doksinet  

 
   
 

  nmax τp ≈ E p ,out Pp ,out τp η (r ) Pp ,out = nmax hν τc E p ,out = E p ≈ η ( r ) N i hν τc η ( r ) Ni rη

( r ) ≈ τc ≈ τc nmax r − 1 − ln r Source: http://www.doksinet  

 
   
  
 nmax n ( t ) = nmax exp ( − t τ c ) τp η (r )

 Pp ,out = nmax hν τc E p ,out = E p ≈ η ( r ) N i hν τc Source: http://www.doksinet 



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  MISER: Monolithic Nd:YAG Laser Applying a magnetic field causes unidirectional lasing Evanescent wave coupled nonlinear semiconductor mirror Interface B (see Fig. 1a) Inside MISER (Nd:YAG, n =1.82) Inside nonlinear semiconductor mirror Air C D z B α>α Saturable Absorber or Modulator section Mirror section Τ A 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) Source: http://www.doksinet *"-$0
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4 6 2 4 6 Fsat 100 1000 Fluence on absorber (μJ/cm ) 10 SESAM #1:
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   P - + P=P =P n= P 2L R =2 L c TR ⎯T⎯⎯⎯ = P hν chν + P g q τ , EL L τA , EA AA AL 1 ⎞ dn ⎛ = ⎜ KL NL − KA NA − ⎟ n dt ⎝ τc ⎠  g = Lg T out N NL V =AL Lg σ L ⎯⎯⎯ = L σL V AL W stim = K L n = TR I P σL = σL hν AL hν dg ( t ) g ( t ) − g0 g ( t ) P ( t ) =− − dt τL EL N A − N A0 dN A =− − KA n NA dt τA dq ( t ) q ( t ) − q0 q ( t ) P ( t ) =− − dt τA EA NA σA AA KL = dP ( t ) = ⎡⎣ g ( t ) − l ( t ) − q ( t ) ⎤⎦ P ( t ) dT N dN L = − L − K L n N L + Rp dt τL  
 
  

 
 q= σL AL TR Source: http://www.doksinet  
 
  
 Phase 1 Phase 3 Phase 2 Gain g(t) Phase 4 Intracavity power P(t) l +ΔR Δg   
 
 
  

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