Bibliography
199
We notice a slight but significant difference; the third term of the integrand in
Eq. (7.36) is −χ
Q,β
pqrs ((, ω 1 , ω 2 )
k
β
T ,s (ω 1 ) + k
β
T ,s (ω 2 )
, while that in Eq. (7.138)
is −χ
Q,β
pqrs ((, ω 1 , ω 2 )k
β
G,s (().
We could interpret that P B
G in Eq. (7.138) involves both the bulk polarization P B
G
and a part of interfacial polarization attributed to χ IQB . Equation (7.28) shows that
the part of interfacial polarization P I attributed to χ IQB is
P
IQB
p
=
q,r
χ
IQB
pqr ((, ω 1 , ω 2 )L I,q (ω 1 )L I,r (ω 2 )E α
I,q (ω 1 )E α
I,r (ω 2 )
=
q,r
χ
Q,β
pqrz ((, ω 1 , ω 2 )f
β
p (()f
β
q (ω 1 )f
β
r (ω 2 )L I,q (ω 1 )L I,r (ω 2 )E α
I,q (ω 1 )E α
I,r (ω 2 )
= i
0
−∞
dz
q,r,s
δ sz
k
β
T ,s (ω 1 ) + k
β
T ,s (ω 2 ) − k
β
G,s (()
χ
Q,β
pqrz ((, ω 1 , ω 2 )
· f
β
p (()f
β
q (ω 1 )f
β
r (ω 2 )L I,q (ω 1 )L I,r (ω 2 )E α
I,q (ω 1 )E α
I,r (ω 2 )
· exp
i
k
β
T ,z (ω 1 ) + k
β
T ,z (ω 2 ) − k
β
G,z (()
z
,
(7.139)
where the form of χ IQB in Eq. (7.30) has been adopted in the above formula.
Therefore, we can readily see the following relation,
P
B
G,p + P
IQB
p
= P
B
G,p
.
(7.140)
Although either definition for the bulk polarization could be used in principle,
we recommend P B
G in Eq. (7.36) to describe the bulk polarization for the following
reasons. First, P B
G is a well defined quantity with respect to the choice of origin
as described in Sect. 7.4, and can be separately detected from the other terms by
experimental measurements. Second, P B
G allows for distinguishing χ IQB and χ B .
We have argued in Chap. 7 and Figure 7.5 that χ IQB and χ B have different physical
meanings and different dependence on the optical geometry. The role of χ IQB
has been increasingly recognized in the SFG spectroscopy [12, 13]. The former
definition is convenient to examine the effects of χ IQB and χ B separately.
Bibliography
1. Adler E (1964) Nonlinear optical frequency polarization in a dielectric. Phys Rev 134:A728–
A733
2. Bloembergen N, Chang RK, Jha SS, Lee CH (1968) Optical second-harmonic generation in
reflection from media with inversion symmetry. Phys Rev 174:813–822
3. Bloembergen N, Pershan PS (1962) Light waves at the boundary of nonlinear media. Phys Rev
128:606–622
4. Boyd RW (2003) Nonlinear optics. Academic, Amsterdam
199
We notice a slight but significant difference; the third term of the integrand in
Eq. (7.36) is −χ
Q,β
pqrs ((, ω 1 , ω 2 )
k
β
T ,s (ω 1 ) + k
β
T ,s (ω 2 )
, while that in Eq. (7.138)
is −χ
Q,β
pqrs ((, ω 1 , ω 2 )k
β
G,s (().
We could interpret that P B
G in Eq. (7.138) involves both the bulk polarization P B
G
and a part of interfacial polarization attributed to χ IQB . Equation (7.28) shows that
the part of interfacial polarization P I attributed to χ IQB is
P
IQB
p
=
q,r
χ
IQB
pqr ((, ω 1 , ω 2 )L I,q (ω 1 )L I,r (ω 2 )E α
I,q (ω 1 )E α
I,r (ω 2 )
=
q,r
χ
Q,β
pqrz ((, ω 1 , ω 2 )f
β
p (()f
β
q (ω 1 )f
β
r (ω 2 )L I,q (ω 1 )L I,r (ω 2 )E α
I,q (ω 1 )E α
I,r (ω 2 )
= i
0
−∞
dz
q,r,s
δ sz
k
β
T ,s (ω 1 ) + k
β
T ,s (ω 2 ) − k
β
G,s (()
χ
Q,β
pqrz ((, ω 1 , ω 2 )
· f
β
p (()f
β
q (ω 1 )f
β
r (ω 2 )L I,q (ω 1 )L I,r (ω 2 )E α
I,q (ω 1 )E α
I,r (ω 2 )
· exp
i
k
β
T ,z (ω 1 ) + k
β
T ,z (ω 2 ) − k
β
G,z (()
z
,
(7.139)
where the form of χ IQB in Eq. (7.30) has been adopted in the above formula.
Therefore, we can readily see the following relation,
P
B
G,p + P
IQB
p
= P
B
G,p
.
(7.140)
Although either definition for the bulk polarization could be used in principle,
we recommend P B
G in Eq. (7.36) to describe the bulk polarization for the following
reasons. First, P B
G is a well defined quantity with respect to the choice of origin
as described in Sect. 7.4, and can be separately detected from the other terms by
experimental measurements. Second, P B
G allows for distinguishing χ IQB and χ B .
We have argued in Chap. 7 and Figure 7.5 that χ IQB and χ B have different physical
meanings and different dependence on the optical geometry. The role of χ IQB
has been increasingly recognized in the SFG spectroscopy [12, 13]. The former
definition is convenient to examine the effects of χ IQB and χ B separately.
Bibliography
1. Adler E (1964) Nonlinear optical frequency polarization in a dielectric. Phys Rev 134:A728–
A733
2. Bloembergen N, Chang RK, Jha SS, Lee CH (1968) Optical second-harmonic generation in
reflection from media with inversion symmetry. Phys Rev 174:813–822
3. Bloembergen N, Pershan PS (1962) Light waves at the boundary of nonlinear media. Phys Rev
128:606–622
4. Boyd RW (2003) Nonlinear optics. Academic, Amsterdam