Documents
Resources
Learning Center
Upload
Plans & pricing Sign in
Sign Out

Interaction of radiation with atoms and ions

VIEWS: 9 PAGES: 7

									     Interaction of radiation with atoms and ions (I)
   Absorption- Stimulated emission
                                           2 2
                          | a2 (t ) |2           I | 21 |2  (  0 ) t
E2                                       3n 0ch2
    E2  E1  h 0
E1                                                  W12 =W21
        E  E0 sin(t ) h                             (  0 )  g (  0 )

                              W
More definitions                     Cross section
                              F
                       ( N1  N 2 )   Absorption        ( N 2  N1 )   Gain
                                       coefficient
                                      16 3 3n
 Spontaneous emission              A           | 21 |2
                                       3 0c3h
     Interaction of radiation with atoms and ions (II)

Line broadening        Homogeneous                    Inhomogeneous
                       (Lorentz)                         (Gauss)
                                              1
                                    0 
                       Collisions            c       Doppler
                       Spont. emission                             0  2 0
                                                                                2kT ln( 2)
                                              1                                   Mc 2
                                    0 
                                            2 sp
                       Phonons                         Local field

Saturation
                                                             0
 2                2                                  
                                                          1 I / Is
 1                1
     High             Reduced
     absorption       absorption
Ray and wave propagation through optical media
Matrix- formulation of Geometric Optics
                                                1         0                                                1 L / n
        r2   A B  r1           lens      
                                                1/ f                   Material with                             
        
          C D  
                                                       1
                                                                         index n
                                                                                                             0
                                                                                                                1  
        2         1 
Gaussian Beam                                              
                                                             x2  y 2                    x2  y 2
           ~           w                                                          ik
           Em (r )  A 0 H  ( w(2zx) ) H m ( w(2zy) )e     w( z ) 2
                                                                        e ikz e         2R( z )
                                                                                                    e i (   m1) ( z )
                       w( z )
             z  2   1/ 2
                                                                          1  z                                w02
                                                                                                            zR 
                                                2
w( z )  w0 1  2                            z              ( z )  tan  
                                                                             z 
             z                R( z )  z     R
                                                                              R                                 
                R                             z
                               1      1       i
 ABCD law                                 
                             q ( z ) R( z ) w( z ) 2

               Aq1  B                         1 C  D / q1
          q2                                    
               Cq1  D                         q2 A  B / q1
                                   Stable resonators
                                      Stability condition
      General case                                     Two-mirror resonator
                                  A D                                L
 Round trip matrix         1         1                    gi  1                             0  g1 g 2  1
      A B                        2
     C D
         
                                                                      Ri
                                       Gaussian beam                                 R( z1 )   R1
                                            solution                                                                   1/ 4
                                                                        L                
   Single passage                                                                      1/ 2
                                                                                     g2
   matrix                                                         w1         g (1  g g ) 
                                                                                           
                        qi 
                              B1 D1                                        1        1 2 
     A1     B1 
    
    C                       A1C1                                                                            Lg 2 (1  g1 )
             D1 
                                                                                              1/ 4
                                                          L   g 2 g1 (1  g1 g 2 ) 
                                                               1/ 2
     1                                            w0                                          z1 
                                                                 g  g  2 g g 2 
                                                             1                                          g1  g 2  2 g1 g 2
                                                                         2       1 2   

                                             Frequencies                         c  1   m                   
           c  1   m                                               mn         n       cos 1 ( g1 g 2 )
 mn         n       cos 1 ( A1 D1 )                                      2L 
                                                                                                              
          2L 
                                                                                                               g2
                                                  B1 D1
                                             Spectral width
                                                                                   L                        1
                                                                          c              c 
                        ln R1R2 (1  Ti ) 2 
                            1
                                                                                  c                    2 c
                            2
           Continuous Wave Laser Behavior
                                                                c                Le
                     dN               N                B                   c 
Rate equations           R p  BN                        Va Le                  c
                     dt               
                                                                        
                     d           
                         BNVa 
                     dt           c
                                                     2c              Va      Ab
             N (0), (0)  N (t ), (t )    Put           h
                                                    2 Le
cw-laser
                                                          N ,
Threshold    Nc             Rcp 
                                                      Nc
Stationary
                 N0  Nc    0  Va c ( R p  Rcp )
solution                                                                                Rp
                                                dP                    Rcp
                   Ab I s 2  Pp          s  ut
             Put              1
                      2  Pth 
                                                dPp
                                 
               Transient Laser Behavior

Q-switching:     High losses High population inversion               N   R p
                    Switching of losses    Pulse (ns)
Mode-locking      Frequency domain: Modes “in phase”
                  Time domain: Pulse train, periodicity: 2 L
                                                                 c
                         p  L  1 (0.44 ) Gaussian

                          c                                  d
Phase velocity   v ph            Group velocity        vg 
                          n                                  d  L
                          d
Group delay    d                 ' (L )
                      vg   d      L




 Group delay      d d    d 2                                 d d
                                         " ( L )    d       L
 dispersion       d      d 2     L
                                                               d
                     Properties of Laser beams
          Temporal coherence                            Spatial coherence
 (r , r , )  E (r , t   ) E (r , t ) 
  (1)                             *             (1) (r1 , r2 ,0)  E (r1 , t ) E * (r2 , t ) 

        Measurement: Michelson                 Measurement: Young’s
        interferometer                         double slit interferometer
Temporal coherence:                       1    Spatial coherence:                            
                                   co                                              
monochromaticity                             directionality                                d
Laser: good temporal                           Laser: good spatial coherence
coherence if monomode                          if one transverse mode
                  P                                                        L
Brightness: B                                 Thermal light: d coh  0.32
                 A                                                        d
                                      4P       Laser and thermal light have different
For a Gaussian beam           B               statistical properties
(high brightness)                     2                 different high-order coherence

								
To top