Lasers by zhangyun


                                                    Fast decay
    Stimulated Emission


    Inversion                         Pump           Laser
                                   Transition        Transition
    The Laser

    Four-level System

                                                    Fast decay
    Some lasers

* Light Amplification by Stimulated Emission of Radiation
Stimulated emission leads to a chain
reaction and laser emission.
If a medium has many excited molecules, one photon can become
                          Excited medium

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.
The Laser
A laser is a medium that stores energy, surrounded by two mirrors.
A partially reflecting output mirror lets some light out.

           I0                                          I1

            I3             Laser medium                I2
R = 100%                    with gain, G                    R < 100%

A laser will lase if the beam increases in intensity during a round trip:
that is, if I 3  I 0

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.
Calculating the gain:
Einstein A and B coefficients                              1

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
                                                               Laser medium
Laser gain                                           I(0)                        I(L)
Neglecting spontaneous emission:                                                  z
                                                               0            L
      dI     dI
          c     BN 2 I - BN1I            [Stimulated emission minus absorption]
      dt     dz
                 B  N 2 - N1  I
                                                Proportionality constant is the
The solution is:
                                                absorption/gain cross-section, 

        I ( z )  I (0) exp   N2  N1  z

There can be exponential gain or loss in irradiance.
Normally, N2 < N1, and there is loss (absorption). But if N2 > N1,
there’s gain, and we define the gain, G:

                                                If N2 > N1:        g   N2  N1 
     G  exp   N2  N1  L
                                                If N2 < N1 :          N1  N2 
In order to achieve G > 1, that is, stimulated emission must exceed

             B N2 I > B N1 I                      Inversion

Or, equivalently,


                    N2 > N1                                   temperature”

This condition is called inversion.
It does not occur naturally. It is                     Molecules
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.
Achieving inversion:
Pumping the laser medium
Now let I be the intensity of (flash lamp) light used to pump energy
into the laser medium:

           I0                                        I1

           I3             Laser medium               I2
R = 100%                                                  R < 100%

Will this intensity be sufficient to achieve inversion, N2 > N1?
It’ll depend on the laser medium’s energy level system.
Rate equations for a                                           2            N2
two-level system                                             Pump        Laser

                                                               1            N1
Rate equations for the densities of the two states:

              Stimulated emission   Spontaneous
  dN 2
        BI ( N1  N 2 )  AN 2                       If the total number
   dt                                                 of molecules is N:
                            Pump intensity
  dN1                                                  N  N1  N 2
       BI ( N 2  N1 )  AN 2
   dt                                                N  N1  N 2
    d N                                     2 N 2  ( N1  N 2 )  ( N1  N 2 )
         2 BI N  2 AN 2
      dt                                            N  N
    d N
         2 BI N  AN  AN
Why inversion is impossible                                 2            N2
in a two-level system                                                   Laser

                 d N                                       1            N1
                        2 BI N  AN  AN
In steady-state:    0  2BI N  AN  AN
                    ( A  2BI )N  AN
                    N  AN /( A  2BI )
                    N  N /(1  2BI / A)

                   N                where:    I sat  A / 2 B
         N 
               1  I / I sat        Isat is the saturation intensity.

N is always positive, no matter how high I is!
It’s impossible to achieve an inversion in a two-level system!
Rate equations for a                              3
                                                              Fast decay
three-level system                                2

                                                Pump          Laser
Assume we pump to a state 3 that             Transition       Transition
rapidly decays to level 2.
                           Spontaneous            1
     dN 2
           BIN1  AN 2
      dt                                 The total number       Level 3
                     Absorption          of molecules is N:     decays
                                                                fast and
     dN1                                  N  N1  N 2
           BIN1  AN 2                                        so is zero.
      dt                                 N  N1  N 2
    d N
          2 BIN1  2 AN 2              2N 2  N  N
                                         2N1  N  N
   d N
         BIN  BI N  AN  AN
Why inversion is possible                       2
                                                            Fast decay

in a three-level system
                                              Pump          Laser
                                           Transition       Transition
  d N
          BIN  BI N  AN  AN        1
In steady-state: 0  BIN  BI N  AN  AN

            ( A  BI )N  ( A  BI ) N

            N  N ( A  BI ) /( A  BI )

             1  I / I sat      where:     I sat  A / B
     N  N
             1  I / I sat      Isat is the saturation intensity.

             Now if I > Isat, N is negative!
Rate equations for a                            3
                                                          Fast decay
four-level system                               2

                                              Pump         Laser
Now assume the lower laser level 1         Transition      Transition
also rapidly decays to a ground level 0.
              dN 2                                         Fast decay
As before:          BIN 0  AN 2               0
       dN 2                                    The total number
             BI ( N  N 2 )  AN 2            of molecules is N :
                                                 N  N0  N2
Because   N1  0,    N   N 2
                                                 N0  N  N2
      d N
           BIN  BI N  AN
At steady state:    0  BIN  BI N  AN
Why inversion is easy                                      Fast decay
in a four-level system
(cont’d)                                     Pump

    0  BIN  BI N  AN                      1
                                                           Fast decay
     ( A  BI )N   BIN

     N   BIN /( A  BI )

     N  ( BIN / A) /(1  BI / A)

                  I / I sat     where:     I sat  A / B
      N   N
                1  I / I sat   Isat is the saturation intensity.

            Now, N is negative—always!
What about the                                                      Fast decay
saturation intensity?
                                                   Pump              Laser
                                                Transition           Transition
             I sat  A / B
                                                                    Fast decay
A is the excited-state relaxation rate: 1/t           0
B is the absorption cross-section, , divided by
the energy per photon, ħw:  / ħw
                                          ħw ~10-19 J for visible/near IR light
Both  and t
depend on the                      w      t ~10-12 to 10-8 s for molecules
molecule, the           I sat   
frequency, and                    t       ~10-20 to 10-16 cm2 for molecules (on
the various                               resonance)
states involved.    105 to 1013 W/cm2

The saturation intensity plays a key role in laser theory.
   Two-, three-, and four-level systems
    It took laser physicists a while to realize that four-level systems are

        Two-level                   Three-level                   Four-level
         system                       system                       system

                                                                         Fast decay
                                             Fast decay
   Pump         Laser                                      Transition     Laser
Transition      Transition                                                Transition
                                                                         Fast decay

    At best, you get
                                  If you hit it hard,
   equal populations.                                           Lasing is easy!
                                   you get lasing.
       No lasing.
Achieving Laser Threshold
An inversion isn’t enough. The laser output and additional losses in
intensity due to absorption, scattering, and reflections, occur.

           I0                                    I1
                          Laser medium
            I3         Gain, G = exp(gL), and    I2
R = 100%              Absorption, A = exp(-L)        R < 100%

The laser will lase if the beam increases
                                                 Gain > Loss
in intensity during a round trip, that is, if:

This called achieving Threshold. It means: I3 > I0. Here, it means:

   I 3  I 0 exp( gL) exp( L) R exp( gL) exp(  L)  I 0
                    2( g   ) L  ln(1/ R)
Types of Lasers
Solid-state lasers have lasing material distributed in a solid matrix
  (such as ruby or neodymium:yttrium-aluminum garnet "YAG"). Flash
  lamps are the most common power source. The Nd:YAG laser
  emits infrared light at 1.064 nm.
Semiconductor lasers, sometimes called diode lasers, are pn
  junctions. Current is the pump source. Applications: laser printers or
  CD players.
Dye lasers use complex organic dyes, such as rhodamine 6G, in liquid
  solution or suspension as lasing media. They are tunable over a
  broad range of wavelengths.
Gas lasers are pumped by current. Helium-Neon lases in the visible
  and IR. Argon lases in the visible and UV. CO2 lasers emit light in
  the far-infrared (10.6 mm), and are used for cutting hard materials.
Excimer lasers (from the terms excited and dimers) use reactive
  gases, such as chlorine and fluorine, mixed with inert gases such as
  argon, krypton, or xenon. When electrically stimulated, a pseudo
  molecule (dimer) is produced. Excimers lase in the UV.
The Ruby Laser

Invented in 1960 by Ted Maiman
at Hughes Research Labs, it was
the first laser.

Ruby is a three-level system, so
you have to hit it hard.
The Helium-
Neon Laser
Energetic electrons in a
glow discharge collide with
and excite He atoms,
which then collide with and
transfer the excitation to
Ne atoms, an ideal 4-level
Carbon Dioxide Laser
The CO2 laser operates analogously. N2 is pumped, transferring
the energy to CO2.
CO2 laser in the
Martian atmosphere

                                     The atmosphere is thin
                                     and the sun is dim, but
                                     the gain per molecule is
                                     high, and the
                                     pathlength is long.
   Detuning from line center (MHz)
The Helium Cadmium Laser

The population inversion scheme in HeCd is similar to
that in HeNe’s except that the active medium is
Cd+ ions.

The laser transitions occur in the blue and the
ultraviolet at 442 nm, 354 nm and 325 nm.

The UV lines are useful for applications that require
short wavelength lasers, such as high precision
printing on photosensitive materials. Examples include
lithography of electronic circuitry and making
master copies of compact disks.
The Argon
Ion Laser

Argon lines:

Wavelength     Relative Power   Absolute Power
454.6 nm             .03             .8 W
457.9 nm             .06            1.5 W
465.8 nm             .03             .8 W
472.7 nm             .05            1.3 W
476.5 nm             .12            3.0 W
488.0 nm             .32            8.0 W
496.5 nm             .12            3.0 W
501.7 nm             .07            1.8 W
514.5 nm             .40           10.0 W
528.7 nm             .07            1.8 W
The Krypton Ion Laser

      Krypton lines

      Wavelength      Power
      406.7 nm         .9 W
      413.1 nm        1.8 W
      415.4 nm        .28 W
      468.0 nm         .5 W
      476.2 nm         .4 W
      482.5 nm         .4 W
      520.8 nm         .7 W
      530.9 nm        1.5 W
      568.2 nm        1.1 W
      647.1 nm        3.5 W
      676.4 nm        1.2 W
Dye lasers

Dye lasers are an ideal four-level system, and a given dye will lase
over a range of ~100 nm.
A dye’s energy levels

The lower laser level can be almost any level in the S0 manifold.

              S1: 1st excited
             electronic state

                       Pump Transition             Laser Transitions

                 S0: Ground
             electronic state

Dyes are so ideal that it’s often difficult to stop them from lasing in all
Dyes cover the visible, near-IR, and
near-UV ranges.
Titanium: Sapphire (Ti:Sapphire)

                              Absorption and emission
                               spectra of Ti:Sapphire

                                Upper level lifetime:
                                     3.2 msec

   Al2O3 lattice   oxygen
                                Ti:Sapphire lases from
                                ~700 nm to ~1000 nm.
Diode Lasers
Some everyday applications of diode

    A CD burner           Laser Printer
Laser Safety Classifications
Class I - These lasers are not hazardous.
Class IA - A special designation that applies only to lasers that are
"not intended for viewing," such as a supermarket laser scanner. The
upper power limit of Class IA is 4 mW.
Class II - Low-power visible lasers that emit above Class I levels but at
a radiant power not above 1 mW. The concept is that the human
aversion reaction to bright light will protect a person.
Class IIIA - Intermediate-power lasers (cw: 1-5 mW), which are
hazardous only for intrabeam viewing. Most pen-like pointing lasers
are in this class.
Class IIIB - Moderate-power lasers (~ tens of mW).
Class IV - High-power lasers (cw: 500 mW, pulsed: 10 J/cm2 or the
diffuse reflection limit), which are hazardous to view under any
condition (directly or diffusely scattered), and are a potential fire
hazard and a skin hazard. Significant controls are required of Class IV
laser facilities.

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