14
H. Kaur et al.
internal reflection (TIR) is observed for the non-absorbing IR wavenumber (solid
curve), whereas due to the absorption of the evanescent field in the rarer medium,
the maximum value of reflectance is less than unity, hence ATR is observed for the
absorbing IR wavenumber (dotted curves). Along with this, it has been observed
that before the critical angle has been reached, the solid and dotted curves in the
reflectance plots Fig. 6a, b are not completely overlapped. This can be understood
from the dispersion in refractive index values for water samples at two different IR
wavenumbers 2700 and 1630 cm
−1 , which we have considered here while plotting
the reflectance curves in s- and p-polarizations. Also, unlike the s-polarization, the
reflectance in p-polarization mode has reached to zero value for a certain angle of
incidence at which the numerator in the expression for the reflection coefficient r
p
12
(Eq. 12) becomes zero and is termed as Brewster’s angle of incidence.
The IR radiation absorbed in the sample medium through the generated evanescent
wave gets weaker with respect to the penetration depth. The electric field component
of this IR radiation (E) decays exponentially along the distance z from the interface
and is given by [1, 2, 6, 7, 22, 27]:
E(z) = E 0 exp
−
z
d p
(15)
Here, E 0 represents the amplitude of the electric field of IR radiation in the initial
stage of the generated evanescent wave at the interface, whereas d p indicates the
penetration depth of the evanescent wave in the sample. The penetration depth can
be defined as the distance at which the amplitude of the electric field of IR radiation
drops down by
1
e
times of the E 0 i.e., and it can be given as [1, 6, 7, 27, 31]:
d p =
⎡
⎣ 2π n 1 ω I R
sin
2
θ −
n 2
n 1
2
⎤
⎦
−1
(16)
where, ω I R is the wavenumber of the incident IR radiation, θ is the effective angle of
incidence, while n 1 and n 2 are the respective refractive indices of ATR crystal and the
sample medium. Figure 7 (panel a) represents the evanescent field penetration profile
in water medium at two different interfaces; Ge/water and ZnSe/water interface with
45° angle of incidence of IR beam at 1000 cm
−1 wavenumber. We have also plotted
the variation in penetration depth at the ATR crystal/water interface as a function of
angle of incidence, shown in Fig. 7 (panel b). From the plot, it has been observed that
the penetration depth has a decreasing profile with the increase in angle of incidence.
Owing to the refractive index contrast between Ge and ZnSe [22, 24, 25], it has
been observed that the evanescent field has a higher penetration depth of 1.31 μm
at the ZnSe/water interface in comparison to the 0.62 μm value at the Ge/water
interface. This implies that the incident IR field has a strong tendency to interact
with molecules lying more towards the bulk water medium at the ZnSe/water crystal
H. Kaur et al.
internal reflection (TIR) is observed for the non-absorbing IR wavenumber (solid
curve), whereas due to the absorption of the evanescent field in the rarer medium,
the maximum value of reflectance is less than unity, hence ATR is observed for the
absorbing IR wavenumber (dotted curves). Along with this, it has been observed
that before the critical angle has been reached, the solid and dotted curves in the
reflectance plots Fig. 6a, b are not completely overlapped. This can be understood
from the dispersion in refractive index values for water samples at two different IR
wavenumbers 2700 and 1630 cm
−1 , which we have considered here while plotting
the reflectance curves in s- and p-polarizations. Also, unlike the s-polarization, the
reflectance in p-polarization mode has reached to zero value for a certain angle of
incidence at which the numerator in the expression for the reflection coefficient r
p
12
(Eq. 12) becomes zero and is termed as Brewster’s angle of incidence.
The IR radiation absorbed in the sample medium through the generated evanescent
wave gets weaker with respect to the penetration depth. The electric field component
of this IR radiation (E) decays exponentially along the distance z from the interface
and is given by [1, 2, 6, 7, 22, 27]:
E(z) = E 0 exp
−
z
d p
(15)
Here, E 0 represents the amplitude of the electric field of IR radiation in the initial
stage of the generated evanescent wave at the interface, whereas d p indicates the
penetration depth of the evanescent wave in the sample. The penetration depth can
be defined as the distance at which the amplitude of the electric field of IR radiation
drops down by
1
e
times of the E 0 i.e., and it can be given as [1, 6, 7, 27, 31]:
d p =
⎡
⎣ 2π n 1 ω I R
sin
2
θ −
n 2
n 1
2
⎤
⎦
−1
(16)
where, ω I R is the wavenumber of the incident IR radiation, θ is the effective angle of
incidence, while n 1 and n 2 are the respective refractive indices of ATR crystal and the
sample medium. Figure 7 (panel a) represents the evanescent field penetration profile
in water medium at two different interfaces; Ge/water and ZnSe/water interface with
45° angle of incidence of IR beam at 1000 cm
−1 wavenumber. We have also plotted
the variation in penetration depth at the ATR crystal/water interface as a function of
angle of incidence, shown in Fig. 7 (panel b). From the plot, it has been observed that
the penetration depth has a decreasing profile with the increase in angle of incidence.
Owing to the refractive index contrast between Ge and ZnSe [22, 24, 25], it has
been observed that the evanescent field has a higher penetration depth of 1.31 μm
at the ZnSe/water interface in comparison to the 0.62 μm value at the Ge/water
interface. This implies that the incident IR field has a strong tendency to interact
with molecules lying more towards the bulk water medium at the ZnSe/water crystal