Lasing and Amplified Spontaneous Emission in Periodic and Quasi-Periodic
Photonic Band Gap Materials


Julian Kuerti



	Photonic Band Gap materials (or PBGs) were first fabricated less
than 20 years ago, and currently enjoy considerable popularity among a
growing number of quantum optic experimentalists and theorists. In the
upcoming 'conference', I will present the theory and experimental results
regarding the construction of lasers in periodic and quasi-periodic
photonic band gap materials. 
	The simplest PBG is fabricated by creating cylindrical air 'wells'
in a thin substrate such as silicon or aluminum oxide. These holes are
usually of the order of ~ 1 micron in diameter, ~ 100 microns in length
and with lattice constant ~ 1 micron, and are usually arranged in a
hexagonal lattice structure. Viewed from the side, the structure presents
a 2-D photonic lattice, which, depending on the difference in refractive
index between the air and the substrate material (and further geometrical
considerations), may exhibit a photonic band gap. Quasi-periodic PBG
materials are similar to periodic PBGs, the difference being that the
lattice is not macroscopically ordered, but on a microscopic scale
approximates its periodic cousin fairly closely. 
	These materials have many applications in the construction of
ultra low-loss optical wave guides, photonic filters/polarizers and other
optical devices. One such application (which, strangely enough does not
explicitly utilize the band gap properties) is the construction of a 2-D
lasing medium. 
	By filling the pores with a fluorescing dye, and pumping the
material from the top, lasing was observed in the periodic lattice (as
per Inoue et al, IQEC'98/Tuesday Morning). 
	Recently, the experimental and theoretical results of amplified
spontaneous emission have been detailed (see Lawandy et al, Optics
Letters, Vol. 20 No. 11, June 1, 1995 and Nature, Vol. 368, March 31, 1994
as well as S. John and G. Pang, Phys. Rev. A, Vol. 54 No. 4, October 1996)
in the case of a 3-D non-periodic scattering medium (dubbed 'laser
paint'). 
	Finally, the outline of the current experiment involving 
quasi-periodic lasing in a 2-D substrate will be given and discussed.