Optical waveguides – Planar optical waveguide – Thin film optical waveguide
Reexamination Certificate
2001-08-06
2003-07-22
Juba, John (Department: 2874)
Optical waveguides
Planar optical waveguide
Thin film optical waveguide
C359S332000, C257S021000
Reexamination Certificate
active
06597851
ABSTRACT:
BACKGROUND OF THE INVENTION
The invention relates to the field of periodic dielectric structures, and in particular to such structures with complete or omnidirectional photonic band gaps.
Much research in recent years has been focused on photonic crystals: periodic dielectric (or metallic) structures with a photonic band gap (PBG), a range of frequencies in which light is forbidden to propagate. Photonic crystals provide an unprecedented degree of control over light, introducing the possibility of many novel optical devices and effects. One important area for potential applications is that of integrated optics; here, the band gap allows miniaturization to the ultimate wavelength scale while eliminating the inefficiencies and complexities caused by radiation losses in such devices.
Generally speaking, there have been two main categories of study regarding photonic-crystal systems for integrated optics: first, analyzing the phenomena and potential devices that a PBG makes possible; and second, figuring out how to realize these effects in practice. There is a need to bridge the gap between these two categories. It is therefore desirable to achieve a three-dimensional crystal, amenable to layer-by-layer lithographic fabrication, which permits the direct realization of theoretical results from two dimensions.
In order to understand PBG phenomena and to propose useful optical components that photonic crystals might make possible, researchers have often focused on two-dimensional systems. Working in two dimensions has many advantages, in addition to the substantial computational savings versus 3D. The electromagnetic fields are completely TE or TM polarized, with the electric or magnetic field, respectively, entirely in the plane. This reduces the vectorial Maxwell's equations to a scalar problem in terms of the field (magnetic or electric, respectively) perpendicular to the plane. As a result of this scalar, two-dimensional nature, visualization and understanding of theory and simulation are greatly simplified. Band gaps are achieved with uncomplicated structures, and symmetries are obvious. Another attraction of two dimensions that is particularly relevant in device design: when trapping light in linear defects (waveguides) and point defects (microcavities), the fixed polarization and simple geometries make it easy to predict, analyze, and manipulate the character of the localized modes introduced by the defects.
In two dimensions, photonic band gaps have been shown to make possible a number of useful optical components, some of which are shown in FIGS.
1
A-
1
D: sharp bends, efficient waveguide splitters and intersections, and channel-dropping filters.
FIGS. 1A-1D
are top views of block diagrams of photonic-crystal devices in a two-dimensional crystal (square lattice of dielectric rods in air), showing the TM electric field value. All four devices have essentially 100% transmission, with no reflections or losses.
FIG. 1A
shows a 90° waveguide bend
100
,
FIG. 1B
shows a channel-dropping filter
102
,
FIG. 1C
shows an intersection
104
of two waveguides without crosstalk, and
FIG. 1D
shows a waveguide splitter/junction
106
.
All of these devices are designed by combining a few well-understood elements (waveguides and cavities) and by employing general principles of resonance, symmetry, and coupled-mode theory. The attainable device characteristics are thereby known a priori, and minimal tuning is required to push the precise numerical results to the desired values. What makes all of this possible is the photonic band gap: it forces the light to exist only in one of a few states or channels, and transforms a problem with infinitely many directions of propagation into a one-dimensional system with a small number of variables. Although the same ideas can be then applied to conventional waveguides employing total internal reflection, the inevitable radiation losses of those systems spoil the perfection of the theory (and the devices). Such losses generally require ad hoc tuning to minimize, and greatly complicate the design, usage, and understanding of any component.
For example, consider the case of the waveguide bend in FIG.
1
A. Because of the photonic band gap, light can do only one of two things when it hits the bend: go forward, or go back. The radiation that would plague any sharp bend in a conventional waveguide is completely absent, since light cannot propagate in the bulk crystal. Moreover, if the waveguide and bend region support only single-mode propagation, the problem can be described effectively as transmission through a one-dimensional potential well. If the bend/well is symmetric, a well-known result predicts resonant frequencies with 100% transmission, and nearly the exact transmission curve can be calculated via this model. Significantly, these predictions are independent of the exact crystal or waveguide structure, and depend only upon their symmetry and single-modality.
In order to realize two-dimensional photonic-crystal designs in three dimensions, one would ideally like to use the same 2D pattern for the 3D structure. That is, use a two-dimensionally-periodic slab, consisting of a two-dimensionally periodic dielectric structure with constant cross-section in the vertical direction and finite height, as depicted in
FIGS. 2A and 2B
for two typical structures.
FIGS. 2A and 2B
are perspective views of block diagrams of two-dimensionally-periodic slabs. By themselves, they can form photonic-crystal slabs, which use a combination of in-plane photonic band gaps and vertical index-guiding.
FIG. 2A
shows a triangular lattice
200
of dielectric rods
201
in air.
FIG. 2B
shows a triangular lattice
202
of air holes
203
in dielectric.
It will be appreciated that the exact shape of the rods/holes are of little importance; the key feature is their topology: a high/low dielectric region surrounded by low/high dielectric, respectively. In fact, such slabs form the building blocks of the new 3D crystal that is described herein.
With the slab alone, however, one encounters the obvious difficulty of how light is confined in the third dimension and the question of whether if one takes into account the third dimension, is there any longer a band gap. One possible answer to these questions, dubbed photonic-crystal slabs, uses index-guiding (total internal reflection) to confine light vertically. In this case, the higher index of the slab (compared to the material above and below) produces guided modes confined to the vicinity of the slab, and the periodicity creates a band gap where no guided modes exist. Although this is not a complete gap due to the presence of radiating modes at all frequencies (the light cone), it can be used to losslessly confine light in linear waveguides and to imperfectly trap light in resonant cavities.
The lack of a complete band gap leads to a number of difficulties, however. First, whenever translational symmetry is broken, e.g., by a bend or a cavity, radiation losses are inevitable. Although such losses can often be minimized, they must be continually taken into account, just as for conventional waveguides. A second limitation is that the need for waveguide modes to be index-guided, and thus to lie underneath the light line, produces a limited bandwidth and low group velocities in a periodic slab (compared to two-dimensional crystals or to conventional waveguides). Nevertheless, because of their relative ease of fabrication, slab structures continue to attract considerable experimental and theoretical attention. Another interesting system with somewhat different tradeoffs uses in-plane resonant modes above the light line, i.e., not guided, which more closely model the two-dimensional modes at the expense of large aspect ratios required everywhere to minimize radiation losses.
A full realization of a photonic band gap requires a crystal periodic in all three dimensions, and many such structures have been proposed. Some of the most attractive systems for integrated optics are planar-layer structures. These systems have pie
Joannopoulos John D.
Johnson Steven G.
Povinelli Michelle L.
Boutsikaris Leo
Juba John
Massachusetts Institute of Technology
Samuels , Gauthier & Stevens, LLP
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