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Optics Lasers

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  • Lasers* Laser

    Transition

    Pump

    Transition

    Fast decay

    Fast decay

    * Light Amplification by Stimulated Emission of Radiation

  • The Ruby Laser

    1960

    1965

  • THE LARGEST LASER IN THE WORLD

    National Ignition Facility

    192 beams,

    4 MJ per pulse

  • "Experimental realization of a one-atom laser in the

    regime of strong coupling," J. McKeever, A. Boca, A.

    D. Boozer, J. R. Buck and H. J. Kimble, Nature 425,

    268 (2003).

    SINGLE ATOM LASER

  • NANOLASERS

    Zinc oxide wires on a sapphire substrate self organized nano-wire forest

    Pumped by 266 nm beamed at a slight angle laser wavelength 385 nm

    The first room temperature UV nanowire lasers

    P. Yang, UC Berkeley 2001

  • Courtesy A. Siegman

  • Charles Townes (and Mrs Townes) - 2006

  • Interaction of light with excited media

    Excited media? Matter which has energy in excited energy levels

    Process of excitations

    Eg

    Eexcited

    Excitation

    Absorption

    De-excitation

    Emission

    Assumptions - quantized energy levels - electronic, vibrational rotational

    Limitations Optical processes only

    Energy levels

  • Emission and Absorption Basic ideas

    Restrict ourselves to two level system

    E1

    E

    2

    E2 E1 = hn = hc/l

    E1

    E

    2

    E1

    E

    2

    E1

    E

    2

    Three basic processes

    ground state

    rest state

    excited state

    temporary state

    Absorption Spontaneous

    Emission Stimulated

    Emission

    N2

    N1

    Number of atoms (or molecules) / unit volume

    N = number density N = N1 + N2

    N1,2 = population of levels 1 & 2

  • Spontaneous emission

    Probability that the process occurs can be defined by

    Rate of decay of the upper state population E1

    E

    2

    N 2

    N1

    22 AN

    dt

    dN

    sp

    rate of spontaneous decay (units = 1/ time) Einstein A Coefficient

    Asp

    1 = spontaneous emission lifetime ( radiative lifetime)

    Note: Rate of spontaneous decay defined for a specific transition

  • Absorption and Stimulated Emission

    We can write the rate of change of population

    2212 NW

    dt

    dN

    st

    E1

    E

    2

    Stimulated

    Emission

    N2

    N1

    E1

    E2

    Absorption

    N2

    N1

    However, now the rate of stimulated emission

    is dependent on the intensity of the EM wave

    FW 2121

    stimulated emission

    cross-section (units = area)

    Photon flux

    (number of photons/ unit area/unit time)

    Similarly for Absorption

    1121 NW

    dt

    dN

    ab

    FW 1212

    absorption cross-section

  • Stimulated emission leads to a chain

    reaction and laser emission.

    Excited medium

    If a medium has many excited molecules, one photon can become

    many.

    This is the essence of the laser. The factor by which an input beam is

    amplified by a medium is called the gain and is represented by G.

  • Usually, additional losses in intensity occur, such as absorption, scat-

    tering, and reflections. In general, the laser will lase if, in a round trip:

    Gain > Loss This called achieving Threshold.

    The Laser

    A laser is a medium that stores energy, surrounded by two mirrors.

    A partially reflecting output mirror lets some light out.

    A laser will lase if the beam increases in intensity during a round trip:

    that is, if 3 0I I

    R = 100% R < 100%

    I0 I1

    I2 I3 Laser medium with gain, G

  • Calculating the gain:

    Einstein A and B coefficients

    In 1916, Einstein considered the various transition rates between

    molecular states (say, 1 and 2) involving light of irradiance, I:

    Absorption rate = B N1 I

    Spontaneous emission rate = A N2

    Stimulated emission rate = B N2 I

    2

    1

  • Laser gain

    Neglecting spontaneous emission:

    2 1

    2 1

    dI dIc BN I - BN I

    dt dz

    B N - N I

    2 1( ) (0)expI z I N N z

    2 1expG N N L

    [Stimulated emission minus absorption]

    Proportionality constant is the

    absorption/gain cross-section,

    2 1g N N

    1 2N N

    If N2 > N1:

    If N2 < N1 :

    There can be exponential gain or loss in irradiance.

    Normally, N2 < N1, and there is loss (absorption). But if N2 > N1,

    theres gain, and we define the gain, G:

    The solution is:

    Laser medium

    I(0)

    z L 0

    I(L)

  • Inversion

    In order to achieve G > 1, that is, stimulated emission must exceed

    absorption:

    B N2 I > B N1 I

    Or, equivalently,

    This condition is called inversion.

    It does not occur naturally. It is

    inherently a non-equilibrium state.

    In order to achieve inversion, we must hit the laser medium very

    hard in some way and choose our medium correctly.

    N2 > N1

    En

    erg

    y

    Inversion

    Molecules

    Negative temperature

  • Achieving inversion:

    Pumping the laser medium

    Now let I be the intensity of (flash lamp) light used to pump energy

    into the laser medium:

    R = 100% R < 100%

    I0 I1

    I2 I3 Laser medium

    I

    Will this intensity be sufficient to achieve inversion, N2 > N1?

    Itll depend on the laser mediums energy level system.

  • Rate equations for a

    two-level system

    Rate equations for the densities of the two states:

    21 2 2( )

    dNBI N N AN

    dt

    12 1 2( )

    dNBI N N AN

    dt

    22 2d N

    BI N ANdt

    Absorption Stimulated emission Spontaneous

    emission

    1 2N N N

    1 2N N N

    If the total number

    of molecules is N:

    2 1 2 1 22 ( ) ( )N N N N N

    N N

    2d N

    BI N AN A Ndt

    2

    1

    N2

    N1

    Laser Pump

    Pump intensity

  • Why inversion is impossible

    in a two-level system

    0 2BI N AN A N

    1 / sat

    NN

    I I

    / 2satI A B

    In steady-state:

    ( 2 )A BI N AN

    where:

    N is always positive, no matter how high I is!

    Its impossible to achieve an inversion in a two-level system!

    2d N

    BI N AN A Ndt

    /( 2 )N AN A BI

    /(1 2 / )N N BI A

    Isat is the saturation intensity.

    2

    1

    N2

    N1

    Laser

  • Rate equations for a

    three-level system

    Assume we pump to a state 3 that

    rapidly decays to level 2.

    21 2

    dNBIN AN

    dt

    11 2

    dNBIN AN

    dt

    1 22 2d N

    BIN ANdt

    Absorption

    Spontaneous

    emission

    1 2N N N

    1 2N N N

    The total number

    of molecules is N:

    22N N N

    d NBIN BI N AN A N

    dt

    Fast decay

    Laser

    Transition

    Pump

    Transition

    1

    2

    3

    Level 3

    decays

    fast and

    so is zero.

    12N N N

  • Why inversion is possible

    in a three-level system

    1 /

    1 /

    sat

    sat

    I IN N

    I I

    /satI A B

    In steady-state:

    ( ) ( )A BI N A BI N

    where:

    Now if I > Isat, N is negative!

    ( ) /( )N N A BI A BI

    Isat is the saturation intensity.

    d NBIN BI N AN A N

    dt

    0 BIN BI N AN A N

    Fast decay

    Laser

    Transition

    Pump

    Transition

    1

    2

    3

  • Rate equations for a

    four-level system

    Now assume the lower laser level 1

    also rapidly decays to a ground level 0.

    20 2

    dNBIN AN

    dt

    1 0,N

    22 2( )

    dNBI N N AN

    dt

    2N N

    Laser

    Transition

    Pump

    Transition

    Fast decay

    Fast decay

    1

    2

    3

    0 As before:

    Because 0 2N N N

    The total number

    of molecules is N :

    0 2N N N

    d NBIN BI N A N

    dt

    At steady state: 0 BIN BI N A N

  • Why inversion is easy

    in a four-level system

    (contd)

    0 BIN BI N A N

    /

    1 /

    sat

    sat

    I IN N

    I I

    /satI A Bwhere:

    Isat is the saturation intensity.

    Now, N is negativealways!

    Laser

    Transition

    Pump

    Transition

    Fast decay

    Fast decay

    1

    2

    3

    0

    ( / ) /(1 / )N BIN A BI A

    /( )N BIN A BI

    ( )A BI N BIN

  • What about the

    saturation intensity?

    A is the excited-state relaxation rate: 1/

    /satI A B

    Laser

    Transition

    Pump

    Transition

    Fast decay

    Fast decay

    1

    2

    3

    0

    B is the absorption cross-section, , divided by the energy per photon, w: / w

    satIw

    The saturation intensity plays a key role in laser theory.

    Both and depend on the

    molecule, the

    frequency, and

    the various

    states involved.

    w ~10-19 J for visible/near IR light

    ~10-12 to 10-8 s for molecules

    ~10-20 to 10-16 cm2 for molecules (on resonance)

    105 to 1013

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