light modes described in our discussion of ellipsometry. Both of these
polarization modes generate evanescent fields that extend into the cladding or sensing regions, but the fields produced by each mode are of different intensities and decay at different rates. Therefore, each polarized
mode generates its own interference pattern on the detection screen and
consequently each polarized mode provides a separate calculation of the
effective refractive index.
It is important not to be misled by the direction of oscillation of the two
polarized modes into thinking that no evanescent field would be generated by the TE mode, which oscillates parallel to the direction of the
waveguide core. Regardless of polarization, the light waves still undergo
total internal reflection (meaning the light beams still “bounce” off the
cladding and/or sensing regions) and the two polarized modes still
generate evanescent fields in the surrounding regions.
For the effective refractive index determined by each polarized mode, a
large number of absolute refractive index and thickness values can be
calculated that could possibly yield the observed effective refractive index,
as shown in Figure 8.18. However, there is only one unique pair of absolute refractive index and thickness values that may generate the observed
effective refractive index for both polarized modes. This pair represents
the actual value of the absolute refractive index and the thickness of the
film on the sensing waveguide surface. Therefore, by using two different
polarized modes of light and by calculating the unique solution pair, DPI
can be used to determine the actual refractive index and thickness of thin
nanofilms. The technique is so sensitive that thickness changes of less
than 1 Å are detectable. Furthermore, if one can assume that the
refractive index of the thin film is a linear function of the density of its
contents (a good assumption for many thin films), then the refractive
index can be manipulated to yield density d of the film according to
d =
n film − n buffer
dn film =dc
(8.25)
where dn film /dc is the change in refractive index of the film per change in
content density and n film and n buffer are the refractive indexes of the film
and buffer (or solvent), respectively. In order to get the mass per unit area
of the film, one need merely multiply the calculated density value by the
average thickness of the film. Thus, DPI can be used to calculate the
average density, mass, and thickness of the film simultaneously.
CHAPTER 8: Surface Characterization and Imaging Methods
288
polarization modes generate evanescent fields that extend into the cladding or sensing regions, but the fields produced by each mode are of different intensities and decay at different rates. Therefore, each polarized
mode generates its own interference pattern on the detection screen and
consequently each polarized mode provides a separate calculation of the
effective refractive index.
It is important not to be misled by the direction of oscillation of the two
polarized modes into thinking that no evanescent field would be generated by the TE mode, which oscillates parallel to the direction of the
waveguide core. Regardless of polarization, the light waves still undergo
total internal reflection (meaning the light beams still “bounce” off the
cladding and/or sensing regions) and the two polarized modes still
generate evanescent fields in the surrounding regions.
For the effective refractive index determined by each polarized mode, a
large number of absolute refractive index and thickness values can be
calculated that could possibly yield the observed effective refractive index,
as shown in Figure 8.18. However, there is only one unique pair of absolute refractive index and thickness values that may generate the observed
effective refractive index for both polarized modes. This pair represents
the actual value of the absolute refractive index and the thickness of the
film on the sensing waveguide surface. Therefore, by using two different
polarized modes of light and by calculating the unique solution pair, DPI
can be used to determine the actual refractive index and thickness of thin
nanofilms. The technique is so sensitive that thickness changes of less
than 1 Å are detectable. Furthermore, if one can assume that the
refractive index of the thin film is a linear function of the density of its
contents (a good assumption for many thin films), then the refractive
index can be manipulated to yield density d of the film according to
d =
n film − n buffer
dn film =dc
(8.25)
where dn film /dc is the change in refractive index of the film per change in
content density and n film and n buffer are the refractive indexes of the film
and buffer (or solvent), respectively. In order to get the mass per unit area
of the film, one need merely multiply the calculated density value by the
average thickness of the film. Thus, DPI can be used to calculate the
average density, mass, and thickness of the film simultaneously.
CHAPTER 8: Surface Characterization and Imaging Methods
288