An Investigation of Protonic Band Structure for Metallic Protonic Crystals
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Date
2011-05
Authors
LOW, KHEE LAM
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Abstract
Photonic crystals are artificial periodic structures. Their unique properties are one of
the most extensively studied topics in the past 20 years. Researchers believe that this
structure can overcome the challenge that we are facing nowadays in the nano-optics
related research field. In this thesis, the nature of photonic crystals has been
investigated. One of the most important parameters that exhibits the characteristic or
properties of photonic crystals is the photonic band structure.
In this thesis, a plane wave equation (PWE) has been used to calculate the
photonic band structure of photonic crystals. Vacuum, teflon, silicon dioxide, FR-4,
and gallium arsenide are used to mix, match, and study the photonic crystal photonic
band structure. Our results clarify the discrepancies of photonic crystals property in
the literature. In the literature, the band gap tends to appear at high dielectric contrast
of photonic crystals, which was predicted by John D. Joannopoulos and coworkers,
but was not found in this investigation.
Unfortunately, the PWE numerical method is limited to frequencyindependent
dielectric materials. Therefore a new equation for the dielectric
materials containing metallic components (frequency-dependent materials) has been
derived. This equation is much more general compared to the previous studies by
other researchers. The photonic band structures of vacuum, teflon, FR-4, and gallium
arsenide containing copper rods are plotted for E and H polarization. Copper rods in
teflon are not photonic crystals in both square and triangular lattice arrangements for
the E polarization. But all the materials can work as photonic crystals for the H
polarization mode in both square and triangular lattice arrangements including teflon.
In Brillouin zone arrangements, the direction of r-X showed the group velocity
anomaly effect found at the third lowest band for all the materials in H polarization.
Properties of left-handed metamaterials are found for all the materials in all lattice
arrangements in the E polarization. A new analytical model is derived for the
effective plasma frequency of E polarization from the simulation data using
statistical analysis.
By utilizing this new calculation, the plane wave expansion method is used to
calculate the photonic band structure of photonic crystals containing dielectric rods
in metallic media (frequency-dependent materials). Thus a new equation is derived.
This equation is utilized to plot the photonic band structures of copper media
containing vacuum, teflon, FR-4, and gallium arsenide rods forE and H polarization.
FR-4 rods in copper forE polarization in square and triangular lattice arrangements
cannot is not functioning photonic crystals. Other than that, all other materials are
functioning as photonic crystals for E and H polarizations in square and triangular
lattice arrangements. The materials used in this research do not affect the band gap
because the same band gap appears at the same range of the normalized frequency in
H polarization mode. A negative refraction and low effective plasma frequency are
detected for vacuum rods and teflon rods in copper for E polarization mode, which
are the properties of left-handed metamaterials. The group velocity anomaly and the
surface plasmons effect are detected for all the materials in H polarization mode.
Finally, waveguides and microstrips are used for the application ofphotonic crystals.
Description
Keywords
INVESTIGATION OF PROTONIC , METALLIC PROTONIC CRYSTALS