Physics | Lasers » Keller-Gallmann - Ultrafast Laser Physics

Source: http://www.doksinet   
 
  


 
    

 
 
    


 

  
 Source: http://www.doksinet 
  



  


 
 
 


 


 
 
  
 

 


! 
  
   

 
 !
!

 Source: http://www.doksinet  
  
 
   $     
  

 "
 

 
 
" %

 "
  

  #

# #  
  

 

 
 
 "


  
 
"
! 



 


" 

 
#


 




 Source: http://www.doksinet 


  
 

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 
),!* 
!&+$
))#)( laser crystal A/O Q-switch output coupler diode laser focussing optics  


)

"-
   


)

"-
 
#))$%%
*
#
 acoustic transducer coating: HR - laser λ HT - diode λ 

"
 

$
 

.
 
  

partially reflective coating 

"
 

$
 

.
 
  Source: http://www.doksinet "*
!
"(&""#
"("%
"%& - "(&
%%%
%$(!+
"(

,
.
, - )!
"
"(&
*) - %"!
!
% !
+
%
"!"!
 
&"(%
# *!! -

!
"(&
*)
&
#%&!

"&&&
(
"
%"!
!"
& "%% - *
"(&
)
"!
!
"

&%
&
#(&
%#"!
%

%#

"(& Source: http://www.doksinet   

  
  
 

 

   
 

 
  

 
 
  Source: http://www.doksinet 

  •    
 " %
 

$





# 
•    
 
 
 

!


 
#" $




 
 


 
 
! 
 
%
 
Source: http://www.doksinet %*
$(%
# !
$# &
% 

#*# % %
$(%
*
$% %
#*# %
#$ 
#"&*


&%

%
# !
)
  % 
#$


$%
(%

 
## # 

* ($
%



 
  



  Source: http://www.doksinet ),
&*
%"#
&% 

,"*&



 

 
  (!
"!

%,%" )
&*!
,
&! 
%,%"
%&"!!
%$(!,
!
!
"(
"

%"#
+
" "!
%&"!!
&
*
!
%""#
 
#&

&"%&
#(&&
*
) &*! Source: http://www.doksinet   
 
 
  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 
 




 


  ≈ 3τ L 














 
 !
 N dN ≈ Rp − γ L N = Rp −

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 !#*
!#
%
$(% 
&&"
"$ n ( t ) ≈ 0 , Rp = const. &&"
"$

!$$

 
$ 
%#$!
!%
# ≈ 3τ L %
$












%!
#
)&
 #$!  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 )"

  

&""#
$%%
%

,$












 +
= 2τ L t Source: http://www.doksinet 



 


 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 



   Source: http://www.doksinet *#-
.#+"#&! +,)$
*))
#&+!)+
#&+

%#)))
+,)$
) $+) &#+#&
)
*.#+"#&! TR TR dR I> ≈r dI τ stim τL 

/)+&)


)-$$#

( 

%(

$*
&

$$)



 
 Source: http://www.doksinet ##%
#&$
" !
#" 
!#

) 

$

 
  



 
!#

)

( 

 &#
$

 
 

  
 Source: http://www.doksinet Sampling Oscilloscope 


 180 ps -500 0 Time [ps] 500 




 


 Source:

http://www.doksinet 


  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
."+!
")!"(
*) μJ-pulses with ≈ 10 kHz repetition rates
≈ 10 mW average powers 

(1!$)

*!++

$,#

),&

)

!& 

"&"
&

$$)


/()"%&+$$0
&")%
*" &
,"$"&
)
("-$0
."+!
%")!"(
$*)
,*"&
%"&,+)
+,)$
))

 
 
 

-$

((
  
 Source: http://www.doksinet !$
"

 Microchip crystal SESAM Output coupler Laser output Diode pump laser Copper heat sink Cavity length 
 !$
%
$ & 
 & 
# & 
  Dichroic beamsplitter HT @ pump wavelength HR @ laser wavelength & 



 & 
!$

 
 
"
  & 
 

 & 

 $ Source: http://www.doksinet    
 
  
 
 1.00 top reflector HfO2/SiO2 4 incoming light 4 3 3 2 2 1 1 0 0 5 10 15 z (μm) Pump probe signal 1 8 6 τA = 120 ps 4 ΔR = 10.3% 0.92 2

4 6 2 4 6 Fsat 100 1000 Fluence on absorber (μJ/cm ) 10 SESAM #1:
R = 10.3% Fsat = 36 μJ/cm2 1.00 0.98 0.96 Δ R = 7.3% 0.94 0.92 0.90 2 2 4 2 4 Fsat100 1000 Fluence on absorber (μJ/cm ) 10 0.1 8 6 0 0.96 0.88 Reflectivity Bragg mirror AlAs/GaAs Field intensity (rel. units) Field Intensity (Rel. Units) Refractive index Refractive Index substrate GaAs Reflectivity absorber: InGaAs/GaAs quantum wells 0 100 200 Time delay pump-probe (ps) SESAM #2:
R = 7.3% Fsat = 47 μJ/cm2 Source: http://www.doksinet  " $
 !
  longitudinal section crosssection % 
 

! Lg mode area A % 

"

" $ % 


!  



# % Fsat,A << Fsat,L Output coupler Tout SESAM Gain
R, Fsat,A material L, Fsat,L h νL = 2σ L %  
#$

  
  Parasitic losses Lp Total losses Ltot = Tout + Lp
out = Lout/(Lout + Lp) %    $ 
 

&
  •  A > p Source: http://www.doksinet  

 
   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   
 
 
  

  Ereleased = EL Δg l l - ΔR Loss q(t)+Ltot l 

 
 lp



  
 
 -600 -400 -200 0 Time (ps) 
  Estored = EL g 200 400 600 q0 ≈ ΔR 

 

 


 
 Tout + Lp ≈ ΔR 
    
 
R): Δg ≈ 2ΔR Source: http://www.doksinet !
  
 •  
#
  • !
!
#

 
 



  • •  
  
 

#
 
  "
 

 
!
 
 

  
 Phase 3 Phase 2 Gain g(t) Phase 4 Intracavity power P(t) l +ΔR Δg l l - ΔR Loss q(t)+l -600 -400 -200 0 200 400 600 Time (ps) l + ΔR Unsaturated loss 100 20 80 15 60 40 Gain g(t) r=3 Gain g(t) r=2 20 Power P(t) No pulse for r=2 0 0 10 20 Time (μs) 30 10 5 40 0 Gain, Loss (%)  
 • !
 # • #


" 

   #
 Phase 1 Peak power (kW)  
 •  
   •

!
!
!
 
 
 


 

  

!
!
 # Source: http://www.doksinet %" hν L Ep ≈ A ΔR ηout σL *"(
$-
Ep A *"(
) $&$$)
%
&*#&
&%, 3.52 TR τp ≈ ΔR %$
$&$$)
%
&*#&
&%, frep &) ) %$
) g0 − (Ltot + ΔR) ≈ 2ΔRτ L &*#& $

#%
&"((
%
(#
, )
(&
$
"$ )"+"
"((
&"
L -
L +
Labs 
&."
)
"
 


 
 
-%,(!
)
"


 
 


  
Source: http://www.doksinet %1)-
3)$%+)-%1 (.02
/3+1%1 9 1(.02
#!4)26
  3.52 TR τp ≈ 9 +!0%
,.$3+!2)-
$%/2(

 ΔR 9 +!0%
!)-
#0.111%#2)-

$  
1,!++
!"1.0/2)-
+%-2(
()(
!)/8(+%0
%2
!+
 


  
 

7
1!,/+)-
.1#)++1#/%
20!#% 1.5 1(.02%12
15)2#(%$
/3+1%1
&0.,
!
1+)$
12!2%
+!1%0

1.0 37 ps 0.5 0.0 -100 0 100 Time (ps) 200 
;,
$  /3,/ 

, 
*7 0%/ 
/ 

-
 <

 1.
&!0

 +),)2%$
"6
!4!)+!"+%

 !-$
!4!)+!"+%
#0612!+
2()#*-%11
-.2
"6
!)-