, , (7.66)where, (7.65)and, :duetoaslightdifference,intheabsorptionsForsmallphaseshift, with (7.64)#Intensitydifferencebetweentwoprobebeams, measuringtheinterferencebetweentwoprobebeams(saturatedandunsaturatedbeams)#onepumpbeam+twoprobebeams+Jamininterfer

7 .6 S pe c i al T e c hn iqu e s of N olin e ar S pe c tro s c opy

7 .6 .1 S atu rat e d In t e rf ere n c e S pe ctro s c opy

m easuring the interference betw een tw o probe beam s

(s atur ated and un s atur ated beam s )

# one pump beam + t w o probe beam s + J amin int erferom et er

=> w ithout the s atur ating beam , t w o beam s int erfer e destructiv ely

# the s atur ation by the pump beam introduces a ph ase shift , r esultin g inten sity at the det ect or ,

I = I₁ + I₂ - 2 I₁I₂cos (7.64)

# Inten sity difference betw een tw o probe beam s ,

I₁ = I₂( 1 + ) w ith 1

: du e to a slight difference, in the ab sorption s

F or sm all ph as e shift ,

I ( 1 4

2 + ²) I2 (7.65)

and, ( ) = ⁰

1 + x² , ( ) = 1 2 ⁰

x

1 + x² (7.66)

w here, 0 = ( 0), x = 2 ( - 0) /

< ( ) = 0 condition >

* Piezo cry st al is m odulat ed by a sine fun ction ,

( ) = ₀( ) + a s in ( 2 f₁t)

* lock - in feedb ack to piezo cry st al t o bring the ph ase difference

0 b ack to zero

==> I ( ) = 1

4 ( )²I₂ = 1 4

2 0 I²

( 1 + x²)² (7.68)

# h alf w idth : ' = ( 2 - 1)^{1 / 2} 0 . 64

** Contr ary to the situ ation in polarization spectroscopy , pure Loren t zi an/ D i s p ers ion profile can be obt ain ed !!

7 .6 .2 D opple r - F re e L as er - In du c e d D ic h roi s m an d B ire fre n g e n c e Pump w av e : linear polarization , Pr obe w av e : cir cular polarization

# probe beam (circular polarization )

=> tw o orthog on al lin ear polarization s (par allel / perpendicular )

# , , n , n => ch ange of the pr obe beam polarization

F or L 1 , n ( L / ) 1, tr an smitt ed int en sity is giv en by

It( ) = I

2

(

2 cos 2 - L

c n s in 2

)

w ith = - , n = n - n

differen ce of tw o tr an smitted inten sities ,

1 = It( = 0^o) - It( = 90^o) = I L / 2

: pure dichroism sign al

2 = I_t( = 45^o) - I_t( = - 45^o) = I ( L / c) n

: pure Birefringence sign al

ex ample)

7 .6 .3 H e t erody n e P ol ariz ati on S pe c tro s c opy

M ajor contribution t o the noise in s atur ation or polarization spectr oscopy => inten sity fluctu ation of probe laser => noise pow er spectr al den sity decr eas es w ith in creasing fr equen cy (1/ f - noise )

m odulation of las er frequency at higher frequ ency (～MHz region )

7 .6 .4 Com bin ati on of D if f ere n t N on lin e ar T e c h ni qu e s

Doppler - free t w o- photon spectr os copy + Polarization spectroscopy

# 486 nm : Balm er β- line (2S^{1/ 2} - 4P^{1/ 2})

# 243 nm : tw o- phot on (1S^{1/ 2} - 2S^{1/ 2})

In the simple Bohr m odel, ( 1S_{1/ 2} - 2 S_{1/ 2}) = 4 ( 4 S_{1/ 2} - 4P_{1/ 2})

=> measured frequency difference,

= ( 1S_{1/ 2} - 2 S_{1/ 2}) - 4 ( 4 S_{1/ 2} - 4P_{1/ 2}) : Lamb shift giv en by

L( 1 S ) = - _L( 2 S ) - _{f s}( 4 S_{1 / 2} - 4 P_{1 / 2}) - ( 2 S )

* _L ( 2 S ) is know n ,

* _{f s}( 4 S_{1/ 2} - 4P_{1/ 2}) can be calculat ed by Dir ac theory