Docstoc

Optics_Lasers

Document Sample
Optics_Lasers Powered By Docstoc
					Lasers*                                    Fast decay




                                Pump         Laser
                             Transition      Transition




                                            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
        SINGLE ATOM LASER
"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).
NANOLASERS The first room temperature UV nanowire lasers




      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
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

                                    Eexcited
                                                              De-excitation
                                               Excitation
                                                              Emission
                                               Absorption
                                     Eg
                             Energy levels


     Assumptions - quantized energy levels - electronic, vibrational rotational

     Limitations – Optical processes only
Emission and Absorption – Basic ideas

                                                                 excited state
    Restrict ourselves to two level system         N2
                                                           E     temporary state
                E2 – E1 = hn = hc/l                        2


                                               N1          E1
Number of atoms (or molecules) / unit volume                     ground state
N = number density N = N1 + N2                                  rest state
N1,2 = population of levels 1 & 2


  Three basic processes

                      E                        E                     E
                      2                        2                     2


                      E1                     E1                      E1
                                  Spontaneous           Stimulated
             Absorption
                                    Emission             Emission
Spontaneous emission
                                                             N2
                                                                           E
Probability that the process occurs can be defined by                      2


Rate of decay of the upper state population                   N1           E1

            dN 2 
                    AN2
            dt  sp

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

              1
        sp       = spontaneous emission lifetime ( radiative lifetime)
              A


  Note:     Rate of spontaneous decay defined for a specific transition
  Absorption and Stimulated Emission
We can write the rate of change of population
                                                         N2
     dN 2                                                              E
            W21 N 2
     dt  st                                                            2


                                                         N1              E1
   However, now the rate of stimulated emission
   is dependent on the intensity of the EM wave            Stimulated
                                                            Emission
                W21   21F
                                   Photon flux
            stimulated emission (number of photons/ unit area/unit time)
           cross-section (units = area)


   Similarly for Absorption
        dN1 
              W12 N1                                      N2                E2
        dt  ab
              W12   12 F
                                                              N1                E1
            absorption cross-section                               Absorption
Stimulated emission leads to a chain
reaction and laser emission.
If a medium has many excited molecules, one photon can become
many.
                          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.
                                                           2
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 
Inversion
In order to achieve G > 1, that is, stimulated emission must exceed
absorption:

             B N2 I > B N1 I                      Inversion

Or, equivalently,

                                                              “Negative




                                         Energy
                    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:



                                I
           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
 Absorption
                                    emission
  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
      dt
Why inversion is impossible                                 2            N2
in a two-level system                                                   Laser

                 d N                                       1            N1
                        2 BI N  AN  AN
                   dt
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
                           emission
     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
      dt
                                         2N1  N  N
   d N
         BIN  BI N  AN  AN
     dt
                                                3
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
    dt
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.
                                                1
              dN 2                                         Fast decay
As before:          BIN 0  AN 2               0
               dt
       dN 2                                    The total number
             BI ( N  N 2 )  AN 2            of molecules is N :
        dt
                                                 N  N0  N2
Because   N1  0,     N   N 2
                                                 N0  N  N2
      d N
           BIN  BI N  AN
        dt
At steady state:    0  BIN  BI N  AN
                                               3
Why inversion is easy                                      Fast decay
                                               2
in a four-level system
(cont’d)                                     Pump
                                          Transition
                                                           Laser
                                                           Transition

    0  BIN  BI N  AN                      1
                                                           Fast decay
                                               0
     ( 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!
                                                      3
What about the                                                      Fast decay
                                                      2
saturation intensity?
                                                   Pump              Laser
                                                Transition           Transition
             I sat  A / B
                                                      1
                                                                    Fast decay
A is the excited-state relaxation rate: 1/           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 
depend on the                      w       ~10-12 to 10-8 s for molecules
molecule, the           I sat   
frequency, and                           ~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
    best.

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

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


    At best, you get
                                  If you hit it hard,
   equal populations.                                           Lasing is easy!
                                   you get lasing.
       No lasing.
  GAIN IN AN OPTICAL RESONATOR
           pumping




 R2        l            R1
        gain/m = g
 Round trip Gain (Loss) = egl R1 egl R2 = R1 R2 e2gl
      Threshold R1 R2 e2gl = 1
If round trip gain is > 1, then G = R1 R2 e2gl . Note this is inherently
unstable….it will gain exponentially until …...
                                       Saturation occurs…gain saturation...
 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 (minimum pump power of a laser
required for laser emission). 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) where R  R R
                                                                   1   2
Example:
Consider that both ends of ruby laser rod of 5 cm length are coated to have
a reflectance of R=0.9. what is the minimum fraction of excited Cr ions
achieving the threshold condition of oscillation? Assume that the
concentration of Cr ions is N  11019 cm 3, the induced-emission cross-section
is   2 1020 cm2 , and the effective loss constant of the rod is 0.011 cm 1

                          1
         2 g   L  ln  
                          R
                           1 
         2 g   5  ln          0.21072
                           0.81 
         g    0.021072  g  0.021072  0.011  0.032072
                               0.032072
         N 2  N1  g /                  1.6036 1018
                                2 10 20
         N 2  N1  N  11019
          2 N 2  1.160361019  N 2  5.8018 1018
           N 2 5.8018 1018
                           0.58 or 58%
           N      110 19
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.
Laser light properties:



Laser light has a number of very special properties:
• It is usually emitted as a laser beam which can propagate over
  long lengths without much divergence and can be focused to
  very small spots.
• It can have a very narrow bandwidth, while e.g. most lamps emit
  light with a very broad spectrum.
• It may be emitted continuously, or alternatively in the form of
  short or ultrashort pulses, with durations from microseconds
  down to a few femtoseconds.
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
      system.
http://en.wikipedia.org/wiki/Helium-neon_laser
Carbon Dioxide Laser
The CO2 laser operates analogously. N2 is pumped, transferring
the energy to CO2.
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
                    manifold

                       Pump Transition             Laser Transitions

                 S0: Ground
             electronic state
                    manifold



Dyes are so ideal that it’s often difficult to stop them from lasing in all
directions!
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
                   aluminum
                                ~700 nm to ~1000 nm.
Diode Lasers
Some everyday applications of diode
lasers




    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.

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:2
posted:5/18/2012
language:English
pages:46
fanzhongqing fanzhongqing http://
About