Bibliography
45
=
q
n K
2n n i q i q j
q (ε i q j + ε j q i )
n i K
q i E I,x =
2ε i q j
ε i q j + ε j q i E I,x = F
i→j
xx · E I,x ,
(2.100)
E T (z) + E R (z) =
k x
n K
(T P
− R P
) =
k x
n K
n i
n
2ε j q i
(ε i q j + ε j q i )
I P
=
k x
n K
n i
n
2ε j q i
(ε i q j + ε j q i )
n i K
k x
E I,z =
ε i
ε
2ε j q i
(ε i q j + ε j q i )
E I,z = F
i→j
zz
· E I,z .
(2.101)
S component The y component is derived from the S polarization in the same way.
Using Eqs. (2.64), (2.73), and (2.97),
E T ,y + E R ,y = T S
+ R S
= I S + R S
=
1 +
q i − q j
q i + q j
I S =
2q i
q i + q j E I,y = F
i→j
yy
· E I,y .
(2.102)
Fresnel factor The above equations (2.100), (2.101), and (2.102) derive the Fresnel
factor F i→j ,
F
i→j
=
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
2ε i q j
ε j q i + ε i q j
2q i
q i + q j
2ε i ε j
ε
q i
ε j q i + ε i q j
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
(2.18)
The above derivation clarifies that the Fresnel factor F i→j in Eq. (2.18) for the
three-layer model describes the total (T +R ) electric field inside the thin interfacial
layer.
Bibliography
1. Born M, Wolf E (1999) Principles of optics, 7th edn. Cambridge University Press, Cambridge
2. Heinz TF (1991) Second-order nonlinear optical effects at surfaces and interfaces. In: Ponath
H-E, Stegeman GI (eds) Nonlinear surface electromagnetic phenomena. Elsevier, Amsterdam,
pp 353–416
3. Jackson JD (1998) Classical electrodynamics. Wiley, New York
4. Nihonyanagi S, Mondal JA, Yamaguchi S, Tahara T (2013) Structure and dynamics of interfacial
water studied by heterodyne-detected vibrational sum-frequency generation. Annu Rev Phys
Chem 64:579–603