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