TABLE OF CONTENTS Pierre R. Villeneuve [*]
Department of Physics
Massachusetts Institute of Technology
Cambridge, Massachusetts
| lattice constant of the periodic structure | a | |
| speed of light in vacuum | c | |
| energy | E | |
| electric field | E | |
| frequency | f | |
| center frequency of the cavity resonance | f 0 | |
| magnetic field | H | |
| wavevector | k | |
| cavity length | L | |
| index of refraction | n | |
| power | P | |
| quality factor | Q | |
| position vector | r | |
| modal volume | V m | |
| frequency width of the cavity resonance | ? f | |
| macroscopic dielectric function | ? | |
| enhancement factor of the spontaneous emission rate | ? | |
| wavelength in vacuum | ? | |
| angular frequency | ? | |
| differential operator | ? |
[*]Current address: Clarendon Photonics, Inc., Boston, Massachusetts.
Electromagnetic waves inside quarter-wave dielectric stacks undergo partial reflection at the different dielectric interfaces. The destructive interference of the waves leads to the formation of bands of forbidden electromagnetic states. When light is incident at frequencies lying within the forbidden bands, it is prevented from propagating inside the stack; instead it is reflected and its amplitude decays exponentially through successive layers.
The operational principle behind fiber Bragg gratings1, interference filters2, and distributed feedback lasers3 is also based on the multiple scattering that occurs inside periodic dielectric materials. The range of frequencies over which light is reflected (i.e., over which wave propagation is forbidden) defines a stop band, or bandgap, the size of which is proportional to the grating strength (i.e., to the effective...
