band structure refers to the modification of the propagation properties
of electromagnetic waves travelling through a periodically modulated dielectric.
As an example consider light traveling through a regularly spaced array
of spherical glass beads. The effects of scattering and interference of
the light by the glass beads clearly would result in a change in the propagation
of the waves. The alteration in the propagation properties is particularly
significant when the wavelength of the light is approximately equal to
the spacing between the beads. In this regime photonic band gaps--frequency
intervals in which no photon modes are allowed--can be created for appropriately
designed dielectric arrays. The ability to create volumes of space in which
no photons of a given band of energies can exist has a number of fundamental
and applied consequences. To find out more about the subject you can check
out the special issues of the Journal of the Optical Society of America
B, Volume 10, 1993 and the Journal of Modern Optics, 41, 1994, or the following
internet sites at UCLA,
State University, and Redstone
current projects in the area of photonic band structure center around two
projects. The first is the development and exploration of new analysis
tools for calculating the response of Photonic Band Gap Arrays. My particular
interest is in the temporal response and I am at present using a time domain
simulator based on the transmission line matrix method (TLM) to model electromagnetic
wave propagation in dielectric arrays.
Surface Elelctromagnetic Waves on
One-Dimensional Photonic Band Gap Materials
The second aspect of my
photonic band structure research concerns the use of an attenuated total-internal-reflection
(ATR) configuration capable of measuring optical frequency surface electromagnetic
wave generation at the surface of photonic crystals. The ATR technique
uses a prism in a reflection configuration as shown in the following figure.
I performed the first experiments
that detected surface waves on two-dimensional photonic crystals some years
ago [Optics Letters, 18#7, 528-530, 1993.]. Those experiments used the
ATR method but they were performed at microwave frequencies for which two-
and three-dimensional photonic crystals could be easily fabricated. Making
photonic band gap arrays with fundamental gaps at optical frequencies is
a current challenge to the field of photonic band gap research, but one
that is being met successfully by a number of groups. I hope to have a
novel tool for probing these samples as they become available. For now,
I use a commercially made Bragg reflector--a one-dimensional photonic band
gap material--to verify the performance of the system.
The figure below shows the
experimental ATR reflectivity of a Bragg stack at three different wavelengths.
For clarity, the curves have been offset vertically.
The narrow dip at the highest angle corresponds to the excitation of
surface waves at the air/Bragg stack interface, whereas the other dips
correspond to lossy modes guided within the multilayer stack. The angular
position of the reflectivity minima at each wavelength can be directly
related to the wave vector of the corresponding mode. By varying the wavelength
of the incident light and finding the corresponding angles of coupling,
it is possible to reconstruct the surface wave and guided wave dispersion
relations. In principle, the guided mode dispersion should permit one to
determine the effective index of the photonic band gap material at the
particular wavelength/angle of coupling. This information would permit
the determination of the photonic dispersion relation governing propagation
of radiation in the dielectric array for frequencies outside the forbidden
band gap. The surface modes exist only within the region of the band
Finally, the work described here pertains to electromagnetic waves.
A similar process can occur for acoustic waves, a topic that my student
Jake Rudy and I explored experimentally in the summer months of 1997.
With very simple equipment and home made samples we measured acoustic stop
bands and determined the acoustic band structure in two-dimensional arrays.
This work is described in more details on my acoustic
Acknowledgement: This work is funded by a grant from the Research