Biomedical Engineering Reference
In-Depth Information
Fig. 7.5.
Gap size (as a fraction of the mid-gap frequency) versus Si slab (
n
=3
.
45)
thickness for PhC slabs with air hole radius to periodicity ratio r/a of 0.3 and 0.45,
respectively. The optimum slab thickness is different for these two cases because of
the difference in slab effective refractive index
of frequencies for which no guided modes exist. For a slab surrounded by
identical top and bottom layers, two categories of slab modes [even (TE-like)
and odd (TM-like)] are then defined according to the reflection symmetry
with respect to the horizontal plane of midthickness of the slab.
The slab thickness plays an important role in determining whether a PhC
slab has a bandgap. For example, if the slab is too thin (i.e., less than half
a wavelength), the mode cannot be confined within the slab. As shown in
Fig. 7.5, the photonic bandgap width depends on the slab thickness, and the
optimal slab thickness varies with different
r/a
- or different effective slab
refractive index. However, the bandgap width is not be the only consideration
in selecting the slab thickness. With the microcavities to be discussed later,
longer photon decay times or higher quality factors Q can be achieved by
using slightly thicker slabs.
7.1.3 Microcavities: Breaking the Periodicity
By intentionally introducing a defect in the PhC, localized electromagnetic
states can arise inside the photonic bandgap. These localized modes are the
optical analog of the donor or acceptor states produced inside the bandgap
of semiconductor crystals. Figure 7.6 illustrates the electric field distribution
of a fundamental mode in a PhC microcavity. Instead of staying inside the
high refractive index Si, the electric field concentrates in lower refractive index
air holes. This property makes it possible for the E-field to interact with the
analyte infiltrated inside the air holes.
