24
2 Electrodynamics at Interface
This is the general formula of SFG intensity I i (() emitted into the medium i, as
a function of the incident visible and infrared intensities in the media i1 and i2,
I i1 (ω 1 ) and I i2 (ω 2 ), respectively [2, 5].
2.3 Summary of Factors in SFG Spectra
The general formula of Eq. (2.25) allows us to summarize the following factors to
determine the SFG spectra, (A)–(C).
(A) Surface nonlinear susceptibility tensor χ (2) ((, ω 1 , ω 2 ).
This quantity reflects the molecular species as well as their orientation at the
interface. This is the most important factor to govern the features of SFG
spectra. The χ (2) depends on the incident frequencies ω 1 and ω 2 , and its
dependence on the infrared frequency ω 2 is essential for the application of SFG
to the vibrational spectroscopy. The next section will focus on the microscopic
interpretation of this quantity.
(B) Dielectric constants ε i (ω).
Equation (2.25) involves the dielectric constants of three regions (bulk 1, bulk
2, and interface) at three frequencies (, ω 1 , and ω 2 );
ε
α (ω), ε
β (ω), ε
(ω), where ω = ω 1 , ω 2 .
These values are also incorporated in the Fresnel factors and the vectors, e((),
e(ω 1 ), and e(ω 2 ). The dielectric constants in the bulk media, ε α (ω) and ε β (ω),
are measurable quantities, whereas the dielectric constant at the interface,
ε (ω), needs some modeling to be determined. This issue will be discussed
in Sect. 5.3.
(C) Spatial geometry of lights.
The SFG measurement includes the following three factors, (c1)–(c3), about
the light geometry.
(c1) Light Polarization.
Since the light wave is transverse, each light wave may have either S or P
polarization. In the geometry illustrated in Fig. 2.1 where the wave vector
lies on the xz plane, the S polarization means the case that the electric
field oscillates along the y direction (perpendicular to the xz plane), while
the P means the case that the electric field is in the xz plane. In the SFG
measurements, the complete set of polarization specifies those of three
lights, i.e. SFG, visible and infrared, and is thereby designated with three
letters, such as SSP, PPP, SPS, etc. The three letters correspond to the
polarizations of SFG, visible and infrared, respectively, in order.
2 Electrodynamics at Interface
This is the general formula of SFG intensity I i (() emitted into the medium i, as
a function of the incident visible and infrared intensities in the media i1 and i2,
I i1 (ω 1 ) and I i2 (ω 2 ), respectively [2, 5].
2.3 Summary of Factors in SFG Spectra
The general formula of Eq. (2.25) allows us to summarize the following factors to
determine the SFG spectra, (A)–(C).
(A) Surface nonlinear susceptibility tensor χ (2) ((, ω 1 , ω 2 ).
This quantity reflects the molecular species as well as their orientation at the
interface. This is the most important factor to govern the features of SFG
spectra. The χ (2) depends on the incident frequencies ω 1 and ω 2 , and its
dependence on the infrared frequency ω 2 is essential for the application of SFG
to the vibrational spectroscopy. The next section will focus on the microscopic
interpretation of this quantity.
(B) Dielectric constants ε i (ω).
Equation (2.25) involves the dielectric constants of three regions (bulk 1, bulk
2, and interface) at three frequencies (, ω 1 , and ω 2 );
ε
α (ω), ε
β (ω), ε
(ω), where ω = ω 1 , ω 2 .
These values are also incorporated in the Fresnel factors and the vectors, e((),
e(ω 1 ), and e(ω 2 ). The dielectric constants in the bulk media, ε α (ω) and ε β (ω),
are measurable quantities, whereas the dielectric constant at the interface,
ε (ω), needs some modeling to be determined. This issue will be discussed
in Sect. 5.3.
(C) Spatial geometry of lights.
The SFG measurement includes the following three factors, (c1)–(c3), about
the light geometry.
(c1) Light Polarization.
Since the light wave is transverse, each light wave may have either S or P
polarization. In the geometry illustrated in Fig. 2.1 where the wave vector
lies on the xz plane, the S polarization means the case that the electric
field oscillates along the y direction (perpendicular to the xz plane), while
the P means the case that the electric field is in the xz plane. In the SFG
measurements, the complete set of polarization specifies those of three
lights, i.e. SFG, visible and infrared, and is thereby designated with three
letters, such as SSP, PPP, SPS, etc. The three letters correspond to the
polarizations of SFG, visible and infrared, respectively, in order.