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 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

    nsit

    t

    ~~ e(g l)t/TR0 e tc

    c = l TRg0 = rl

  • focussingoptics coating:

    HR - laser HT - diode

    partiallyreflectivecoating

    lasercrystal

    diodelaser

    A/O Q-switch

    acoustictransducer

    outputcoupler

  • dndt = KNn cn

    dNdt = Rp LN KnN

    Rp =Pabsh pump

  • dndt = KNn cn

    dNdt = Rp LN KnN

    dNdt Rp LN = Rp

    N L

    N t( ) = Rp L 1 exp t L( ) = Nmax 1 exp t L( )

    Nmax = Rp L

    2 L L t

    N t( )

    n t( ) 0 , Rp = const. 3 L

  • 3 LdNdt Rp LN = Rp

    N L

    N t( ) = Rp L 1 exp t L( ) = Nmax 1 exp t L( )

    Nmax = Rp L

    2 L L t

    N t( )

    n t( ) 0 , Rp = const.

    Ep = const. Trep > 3 L , or frep =1Trep

  • dndt = KNn cn

    dNdt = Rp LN KnN

    N t = 0( ) = Nin t = 0( ) = ni 1

    N t( ) Ni const.

    r = Ni Nth

    Nth = c K

    dndt K Ni Nth( )n = KNth r 1( )n =

    r 1 c

    n

    n t( ) niexpr 1 c

    t

    c=TR l, g0=rl = niexp g0 l( ) tTR

  • 0 20161284Zeit, ns

    Inte

    nsit

    t

    ~~ e(g l)t/TR0 e tc

    c = l TRg0 = rl

  • dndt = KNn cn

    dNdt = Rp LN KnN

    Nth = c K

    dndt = K N Nth( )ndNdt KnN

    dndN

    K N Nth( )nKnN =

    Nth NN

    dn Nth NN dNN t = 0( ) = Ni = rNth , n t = 0( ) = ni 1 dn

    ni

    n t( )

    Nth NN dNNi=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 =nmaxh c

    Ep,out Ep Ni N f( )h

    nmax

  • n t( ) = nmax for g = l N t( ) = Nth

    nmax r 1 lnr

    r Ni , with Ni = rNth

    Pp,out =nmaxh c

    Ep,out Ep Ni N f( )h

    Q - switched pulse energystored energy =Ni N f( )hNih

    =Ni N fNi

    Ep,out = Ep r( )Nih

    nmax

  • Pp,out =nmaxh c

    Ep,out = Ep r( )Nih

    p Ep,outPp,out

    r( )Ninmax

    c r r( )

    r 1 ln r c

    r( )

    p c

    nmax

  • p c

    n t( ) = nmaxexp t c( )

    Pp,out =nmaxh c

    Ep,out = Ep r( )Nih

    r( )

    nmax

  • dRdI I >

    TR stim

    r TR 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

    >

    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

  • J-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

  • 68

    0.1

    2

    4

    68

    1

    Pump

    pro

    be si

    gnal

    2001000Time delay pump-probe (ps)

    A = 120 ps

    SESAM #1: R = 10.3%Fsat = 36 J/cm2

    1.00

    0.96

    0.92

    0.88

    Refle

    ctivi

    ty

    102 4 6

    1002 4 6

    1000Fluence on absorber (J/cm )

    R = 10.3%

    F sat

    SESAM #2: R = 7.3%Fsat = 47 J/cm2

    1.000.980.960.940.920.90

    Refle

    ctivi

    ty

    102 4

    1002 4

    1000Fluence on absorber (J/cm )

    Fsat

    R = 7.3%

    4

    3

    2

    1

    0

    Refra

    ctiv

    e In

    dex

    151050z (m)

    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

  • P-

    P+P+ P = P-=

    T out

    , ELL

    q

    , EA AAL AA

    g

    dndt = KL NL KA NA

    1 c

    n

    dNLdt =

    NL L

    KL n NL + Rp

    dNAdt =

    NA NA0 A

    KA n NA

    n = Ph TRTR=2L c = 2Lch P

    g = LgNLV L

    V=ALLg = NLAL L

    TRdP t( )dT = g t( ) l t( ) q t( ) P t( )

    W stim = KLn =Ih L =

    PALh

    L KL = LALTR

    dg t( )dt =

    g t( ) g0 L

    g t( ) P t( )

    EL

    dq t( )dt =

    q t( ) q0 A

    q t( ) P t( )

    EA

    q = NAAA A

  • -600 -400 -200 0 200 400 600Time (ps)

    l

    Gain g(t)

    Loss q(t)+L

    Intracavitypower P(t)

    g

    Phase 1 Phase 2 Phase 3 Phase 4

    l +R

    R-l tot

    Estored = ELg

    Ereleased = ELg

    R):g 2RTout + Lp R

    llp

    q0 R

  • -600 -400 -200 0 200 400 600Time (ps)

    l

    Gain g(t)

    Loss q(t)+l

    Intracavitypower P(t)

    g

    Phase 1 Phase 2 Phase 3 Phase 4

    l +R

    R-l

    100

    80

    60

    40

    20

    0

    Peak

    powe

    r (kW

    )

    403020100Time (s)

    20

    15

    10

    5

    0

    Gain, Loss (%)

    Unsaturated loss l + R

    Gain g(t)r=3

    Gain g(t)r=2

    Power P(t) No pulse for r=2

  • Ep hL L

    ARout

    p 3.52TRR

    Ep A

    frep g0 (Ltot + R)

    2R L

    L L + Labs

  • p 3.52TRR

    1.5

    1.0

    0.5

    0.02001000-100

    Time (ps)

    37 ps

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