94
S. Roy et al.
Fig. 3 Energy level diagram of the coherent interaction between ω I R and ω V I S , leading to the
generation of SFG at ω SF = ω V I S + ω I R . For ω I R = ω v , i.e., the incident IR is in resonance
with the vibrational transition of interfacial molecules, the SFG intensity is resonantly enhanced.
Dashed horizontal lines indicate virtual states
χ
(2)
i jk , in addition to the resonant component discussed above, contains a nonresonant component (χ
(2)
N R ), which is invariant with respect to the IR frequency, and
hence, appears as a constant background.
χ
(2)
i jk = χ
(2)
N R +
N s
o
A v
(ω v − ω I R − iΓ v )
(17)
In that case the sum frequency intensity,
I SFG ∝
χ
(2)
N R +
N s A v
ω v − ω I R − iΓ v
2
(18)
For multiple vibrational transitions, the resonant component is generally considered as the sum of all possible vibrational modes such that,
I SFG ∝
χ
(2)
N R +
v
N s A v
ω v − ω I R − iΓ v
2
(19)