Transcript
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 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
q s a turable intensity loss coefficient of the saturable absorber per cavity round-trip q0 u n bleached intensity loss coefficient of the saturable absorber per cavity round-
trip (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)
g0 i n t ens 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 = g01+ 2I Isat
0 20161284Zeit, ns
Inte
nsitä
t
~~ e(g – l)t/TR0 e–γ tc
γ c = l TRg0 = rl
focussingoptics coating:
HR - laser λHT - diode λ
partiallyreflectivecoating
lasercrystal
diodelaser
A/O Q-switch
acoustictransducer
outputcoupler
•
•
dndt = KNn − γ cn
dNdt = Rp − γ LN − KnN
Rp =Pabshν pump
dndt = KNn − γ cn
dNdt = Rp − γ LN − KnN
dNdt ≈ Rp − γ LN = Rp −
Nτ L
N t( ) = Rpτ L 1− exp −t τ L( )⎡⎣ ⎤⎦= Nmax 1− exp −t τ L( )⎡⎣ ⎤⎦
Nmax = Rpτ L
2τ Lτ L t
N t( )
n t( ) ≈ 0 , Rp = const.≈ 3τ L
≈ 3τ LdNdt ≈ Rp − γ LN = Rp −
Nτ L
N t( ) = Rpτ L 1− exp −t τ L( )⎡⎣ ⎤⎦= Nmax 1− exp −t τ L( )⎡⎣ ⎤⎦
Nmax = Rpτ L
2τ Lτ L t
N t( )
n t( ) ≈ 0 , Rp = const.
Ep = const. ⇔ Trep >≈ 3τ L , or frep =1Trep
<≈ 13τ L
13τ L
=
dndt = KNn − γ cn
dNdt = Rp − γ LN − KnN
N t = 0( ) = Ni
n t = 0( ) = ni ≈ 1
N t( ) ≈ Ni ≈ const.
r = Ni Nth
Nth = γ c K
dndt ≈ K Ni − Nth( )n = KNth r −1( )n = r −1
τ cn
n t( ) ≈ niexpr −1τ c
t⎛⎝⎜
⎞⎠⎟
τ c=TR l, g0=rl⎯ →⎯⎯⎯⎯ = niexp g0 − l( ) tTR⎡
⎣⎢
⎤
⎦⎥
0 20161284Zeit, ns
Inte
nsitä
t
~~ e(g – l)t/TR0 e–γ tc
γ c = l TRg0 = rl
dndt = KNn − γ cn
dNdt = Rp − γ LN − KnN
Nth = γ c K
dndt = K N − Nth( )ndNdt ≈ −KnNdn
dN ≈K N − Nth( )n
−KnN = Nth − NN
dn ≈ Nth − NN dN N t = 0( ) = Ni = rNth , n t = 0( ) = ni ≈ 1 dn
ni
n t( )
∫ ≈ Nth − NN dN
Ni=rNth
N t( )
∫
n t( ) ≈ Ni − N t( ) − Nir ln
NiN t( )
⎛⎝⎜
⎞⎠⎟
, with Ni = rNth n t( ) = nmax for g = l ⇔ N t( ) = Nth
nmax
n t( ) = nmax for g = l ⇔ N t( ) = Nth
nmax ≈r −1− lnr
r Ni , with Ni = rNth
nmax Ni
Pp,out =nmaxhντ c
Ep,out ≈ Ep ≈ Ni − N f( )hν
nmax
n t( ) = nmax for g = l ⇔ N t( ) = Nth
nmax ≈r −1− lnr
r Ni , with Ni = rNth
Pp,out =nmaxhντ c
Ep,out ≈ Ep ≈ Ni − N f( )hν
η ≡ Q - switched pulse energystored energy =
Ni − N f( )hνNihν
=Ni − N f
Ni
Ep,out = Ep ≈ η r( )Nihν
nmax
Pp,out =nmaxhντ c
Ep,out = Ep ≈ η r( )Nihν
τ p ≈Ep,out
Pp,out≈η r( )Ni
nmaxτ c ≈
rη r( )r −1− ln r τ c
η r( )
τ p
τ c
nmax
τ p
τ c
n t( ) = nmaxexp − t τ c( )
Pp,out =nmaxhντ c
Ep,out = Ep ≈ η r( )Nihν
η r( )
nmax
dRdI I > TR
τ stim≈ r TR
τ L
Sam
plin
g O
scillo
scop
e
-500 0 500Time [ps]
180 ps
Evanescent wave coupled nonlinear semiconductor mirror
B
CD
MISER: Monolithic Nd:YAG LaserApplying a magnetic field causes unidirectional lasing
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
A
z
α > α Τ
Saturable Absorber orModulator section
Mirror section
Interface B (see Fig. 1a)
Inside MISER(Nd:YAG, n =1.82)
Airgap:Coupling through evanescent waves:Frustrated total internal reflection (FTIR)
Inside nonlinear semiconductor mirror
Air
μJ-pulses with ≈ 10 kHz repetition rates ≈ 10 mW average powers
Output coupler
Laser output
Diode pump laser
Dichroic beamsplitterHT @ pump wavelengthHR @ laser wavelengthCopper
heat sink
Cavitylength
SESAM
Microchip crystal
6
80.1
2
4
6
81
Pum
p pr
obe
sign
al
2001000
Time delay pump-probe (ps)
τA = 120 ps
SESAM #1: R = 10.3%Fsat = 36 μJ/cm2
1.00
0.96
0.92
0.88
Refle
ctivi
ty
102 4 6
1002 4 6
1000Fluence on absorber (μJ/cm )
R = 10.3%Δ
F sat
SESAM #2: R = 7.3%Fsat = 47 μJ/cm2
1.000.980.960.940.920.90
Refle
ctivi
ty
102 4
1002 4
1000Fluence on absorber (μJ/cm )
Fsat
R = 7.3%Δ
4
3
2
1
0
Refra
ctiv
e In
dex
151050z (μm)
4
3
2
1
0
Field Intensity (Rel. Units)
absorber: InGaAs/GaAs quantum wells
top reflectorHfO2/SiO2
Bragg mirrorAlAs/GaAs
substrateGaAs
incoming light
Field intensity (rel. units)
Refra
ctive
inde
x
• A > p
Fsat,A << Fsat,L = hνL2σL
SESAM R, Fsat,A
Gainmaterial L, Fsat,L
OutputcouplerTout
mode area A
longitudinalsection
cross-section
Parasitic losses Lp
Lg
Total losses Ltot = Tout + Lp
out = Lout/(Lout + Lp)
P-
P+P+ P = P-=
T out
τ , ELL
q
τ , EA AAL AA
g
dndt = KL NL − KA NA −
1τ c
⎛⎝⎜
⎞⎠⎟n
dNLdt = − NL
τ L− KL n NL + Rp
dNAdt = − NA − NA0
τ A− KA n NA
n = Phν TR
TR=2L c⎯ →⎯⎯⎯ = 2Lchν P
g = LgNLV σ L
V=ALLg⎯ →⎯⎯ = NLAL
σ L
TRdP t( )dT = g t( ) − l t( ) − q t( )⎡⎣ ⎤⎦ P t( )
W stim = KLn =Ihν σ L =
PALhν
σ L KL =σ LALTR
dg t( )dt = −
g t( ) − g0τ L
−g t( ) P t( )
EL
dq t( )dt = −
q t( ) − q0τ A
−q t( ) P t( )
EA
q = NAAA
σ A
-600 -400 -200 0 200 400 600
Time (ps)
l
Gain g(t)
Loss q(t)+L
Intracavitypower P(t)
gΔ
Phase 1 Phase 2 Phase 3 Phase 4
l +ΔR
RΔ-l tot
Estored = ELg
Ereleased = ELΔg
R):Δg ≈ 2ΔRTout + Lp ≈ ΔR
llp
q0 ≈ ΔR
••
••
••
•
•
-600 -400 -200 0 200 400 600
Time (ps)
l
Gain g(t)
Loss q(t)+l
Intracavitypower P(t)
gΔ
Phase 1 Phase 2 Phase 3 Phase 4
l +ΔR
RΔ-l
100
80
60
40
20
0
Pe
ak
po
we
r (k
W)
403020100
Time (μs)
20
15
10
5
0
Ga
in, L
oss (%
)
Unsaturated loss l + ΔR
Gain g(t)r=3
Gain g(t)r=2
Power P(t) No pulse for r=2
Ep ≈hνLσ L
AΔRηout
τ p ≈3.52TRΔR
Ep A
frep ≈g0 − (Ltot + ΔR)
2ΔRτ L
L L + Labs
τ p ≈3.52TRΔR
1.5
1.0
0.5
0.02001000-100
Time (ps)
37 ps
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