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Chapter I Brief Introduction...
and ω2, a Nonlinear response P2 proportional to (2) E1 E2 , with spectral
components at ω1 ± ω2 , are obtained as follows:
Suppose two travelling waves are,
E1 (z,t)= E1cos(ω1t + k1z) (1.4)
E2 (z,t)= E2cos(ω2t + k2z) (1.5)
Considering the second order Nonlinearity in polarization alone is,
P= (2) E 2 (1.6)
P= (2) [E1 2 cos 2 (ω1t + k1z) + E2 2 cos 2 (ω2t + k2z) +
2 E1cos(ω1t + k1z) E2cos(ω2t + k2z)] (1.7)
However, from above expression it can be found that the polarization consists
of number of component with different frequencies as follows:
Where, first term is =P1 ω1= (2) E1 2 [ cos2(ω1t + k1z)]
And second term is=P2ω2= (2) E2 2 [ cos 2(ω2t + k2z)]
P1 ω1 + P2ω2 = (2) E1 E2[ cos(ω1+ ω2)t + cos(k1 + k2)z]
P1 ω1 - P2ω2 = (2) E1 E2[ cos(ω1- ω2)t + cos(k1 - k2)z]
And steady term, Pdirect = ( (2) /2 ) (E1 2 + E2 2 )
The different components of nonlinear polarization generate electromagnetic
waves having frequency different from those of the incident ones.
Sum Frequency Generation (SFG)
From equation (1.7) the sum of frequency term is obtained which is
ω1+ω2=ω3 (or in form of wavelength 1/λ1+1/λ2=1/λ3). This is shown in figure
(1.6) schematically. It combines two low energy (or low frequency) photons
into a high energy photon.
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