INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY
VOL.1, NO. 2, AUGUST 2006
IJMOT-2006-6-153 © ISRAMT 2006
Large Frequency Range of Omnidirectional Reflection in
Si-based One-Dimensional Photonic Crystals
S. K. Singh*, Khem B. Thapa and S. P. Ojha
Department of Applied Physics, Institute of Technology, Banaras Hindu University,
Varanasi-221005, INDIA
Tel: +91-542-2307040; Fax: +91-542-2368428; E–mail: sks_m2002@yahoo.co.in, spojha@yahoo.com
Abstract: We study the omnidirectional photonic
band gap in one dimensional photonic crystal of
Si/SiO
2
structures. Three structures of Si/SiO
2
multilayer have been studied. The first structure
has filling factor 0.333 and the second structure has
filling factor 1.50. The third photonic structure is a
combination of first and second structures. Using
transfer matrix method, the reflectivities of
photonic crystals are plotted as a function of
normalized frequency and omnidirectional PBGs
are measured. We found that the large frequency
range of omnidirectional PBG can be obtained
from Si/SiO
2
system by combination of 1D photonic
band gap structures. For obtaining this large
omnidirectional PBG, the directional PBGs of
constituent 1D PCs should overlap each other.
Index Terms: Omnidirectional PBG, photonic
crystal, transfer matrix.
I. INTRODUCTION
Yablonovitch [1] in 1987 pointed out the
possibility of the realization of photonic band gap,
localized defect modes, and their applications to
various optoelectronic devices. In the same year,
John [2] discussed the strong localization of
electromagnetic waves in disordered photonic
crystals. Ojha et al. [3] observed filtering
properties in PBG materials and extended the
idea for constructing monochromators [4].
Photonic crystals are periodic dielectric or
metallic structures in which propagation of
electromagnetic wave is forbidden within a
certain frequency. This frequency range is called
the photonic band gap which is analogous to the
electronic band gap in ordinary materials. These
materials have many potential applications in
optoelectronics and optical communications, such
as resonant cavities [5], optical waveguides [6],
light emitting diodes [1], superfast optical
switches and detectors [7], etc. Three
dimensional (3D) photonic crystals may exhibit
absolute photonic band gap in which propagation
of light is prohibited regardless of the direction of
the wave vector and all polarization. There is a
significant progress in the fabrication of 3D
photonic crystals to obtain complete band gap
from microwave to visible. However, due to
technological problem and high cost, the
applications of the 3D photonic crystals are
limited. The 1D photonic crystals are attractive
since their production is more feasible at any
wavelength scale and their analytical and
numerical calculations are simpler.
Besides 2D and 3D photonic crystals, 1D
periodic structure such as superlattices can also
exhibit the property of omnidirectional reflection
[8-10] provided the optical indices of
supperlattice constituents are chosen
appropriately. Metallic mirrors reflect light over a
broad range of frequencies incident from
arbitrary angles (i.e. omnidirectional reflector).
However, at infrared and optical frequencies,
they absorb a small fraction of incident optical
power. An omnidirectional dielectric mirror i.e.
1D PC has low loss. These properties make
omnidirectional dielectric mirrors ideal candidate
for applications in which a beam of light with an
unknown polarization is to arrive from any
direction and in which loss of power, although
very small, is not desirable. In 1998 Fink et al.
[8] first reported that one dimensional dielectric
lattice displays total omnidirectional reflection
for incident light under certain conditions. They
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