waveguide at a speed that depends in part on the refractive index of the
area within ~100 nm of the sensing waveguide surface (i.e., within the
evanescent field). Hence, any thin films or molecules that are adsorbed to
the sensing waveguide surface change the speed at which the light travels
through the sensing waveguide (because the adsorbed molecules change
the refractive index of the sensing region within the evanescent field). On
the other hand, light always travels through the reference waveguide
at the same speed because the cladding regions on either side are fixed.
Since the relative speeds of the light emerging from the two waveguides
affects the interference pattern produced, the interference pattern changes
as a thin film is adsorbed to the sensor surface. More specifically, the
relative positions of the light and dark bands (or fringes) shift as the film
adsorbs to the surface. By using Maxwell’s equations of electromagnetism
and after applying some rather complex mathematics, the shifts in the
fringe pattern can be used to calculate the refractive index of the film
adsorbed to the surface of the sensing waveguide. Thus, a waveguide
interferometer is able to characterize a thin nanofilm.
The refractive index measured by an interferometer such as described
above is not the true refractive index of the film, but rather the effective
refractive index, which is a complicated function of both the absolute
refractive index and the thickness of the film. In this way, DPI is similar to
SPR and ellipsometry in that it measures an optical parameter related to
thickness or refractive index instead of directly measuring the thickness or
refractive index. However, DPI has an advantage over single-wavelength
ellipsometry or SPR in that it obtains the effective refractive index for two
different polarizations of light. These two measurements can be used to
mathematically obtain the thickness and refractive index in a manner
similar to that used in spectroscopic ellipsometry.
8.4.3.3 Principles of dual polarization interferometry
DPI uses a waveguide interferometer setup as described above, only the
light source is modified such that it alternately produces two different
types of linearly polarized light via a polarizer switch (see Figure 8.17).
One type of polarized light, named the transverse magnetic (TM) polarized mode, is composed of light waves with an electric field that oscillates
perpendicular to the direction of the waveguide core, as shown in Figure
8.17. The other type, called the transverse electric (TE) mode, has light
waves with an electric field that oscillates parallel to the direction of the
waveguide. If we define the waveguide core as the plane of incidence,
then the TM and TE modes directly correspond to the s- and p-polarized
OTHER TECHNIQUES FOR MEASURING THICKNESS AND REFRACTIVE INDEX 287
area within ~100 nm of the sensing waveguide surface (i.e., within the
evanescent field). Hence, any thin films or molecules that are adsorbed to
the sensing waveguide surface change the speed at which the light travels
through the sensing waveguide (because the adsorbed molecules change
the refractive index of the sensing region within the evanescent field). On
the other hand, light always travels through the reference waveguide
at the same speed because the cladding regions on either side are fixed.
Since the relative speeds of the light emerging from the two waveguides
affects the interference pattern produced, the interference pattern changes
as a thin film is adsorbed to the sensor surface. More specifically, the
relative positions of the light and dark bands (or fringes) shift as the film
adsorbs to the surface. By using Maxwell’s equations of electromagnetism
and after applying some rather complex mathematics, the shifts in the
fringe pattern can be used to calculate the refractive index of the film
adsorbed to the surface of the sensing waveguide. Thus, a waveguide
interferometer is able to characterize a thin nanofilm.
The refractive index measured by an interferometer such as described
above is not the true refractive index of the film, but rather the effective
refractive index, which is a complicated function of both the absolute
refractive index and the thickness of the film. In this way, DPI is similar to
SPR and ellipsometry in that it measures an optical parameter related to
thickness or refractive index instead of directly measuring the thickness or
refractive index. However, DPI has an advantage over single-wavelength
ellipsometry or SPR in that it obtains the effective refractive index for two
different polarizations of light. These two measurements can be used to
mathematically obtain the thickness and refractive index in a manner
similar to that used in spectroscopic ellipsometry.
8.4.3.3 Principles of dual polarization interferometry
DPI uses a waveguide interferometer setup as described above, only the
light source is modified such that it alternately produces two different
types of linearly polarized light via a polarizer switch (see Figure 8.17).
One type of polarized light, named the transverse magnetic (TM) polarized mode, is composed of light waves with an electric field that oscillates
perpendicular to the direction of the waveguide core, as shown in Figure
8.17. The other type, called the transverse electric (TE) mode, has light
waves with an electric field that oscillates parallel to the direction of the
waveguide. If we define the waveguide core as the plane of incidence,
then the TM and TE modes directly correspond to the s- and p-polarized
OTHER TECHNIQUES FOR MEASURING THICKNESS AND REFRACTIVE INDEX 287