Resonant cavities employing two dimensionally periodic dielectric materials

The present invention provides a resonant cavity including a planar two-dimensional periodic dielectric structure which exhibits a photonic band gap and a defect in the periodic dielectric structure which results in an electromagnetic mode within the photonic band gap. The photonic band gap effects an in-plane spacial confinement of electromagnetic radiation generated within the structure. The electromagnetic radiation is vertically confined by total internal reflection.

BACKGROUND OF THE INVENTION 
The invention is directed to resonant cavities employing two dimensional 
periodic dielectric materials. 
In the past decades, the semiconductor laser has come to play a critical 
role in numerous applications including optical information storage and 
retrieval (e.g. CD players), lightwave communication (e.g. optical 
fibers), and computer input/output. In most commercial applications, these 
lasers have been of the buried heterostructure or distributed feed back 
(DFB) varieties. While lasers of this type have been tremendously 
successful, there have recently been attempts at improving the design of 
semiconductor lasers to improve efficiency, power output, linewidth, 
modulation speeds and other device characteristics. In particular, there 
has been recent success at fabricating vertical cavity surface emitting 
lasers (VCSELs), microdisk lasers, and even steps toward a photonic band 
gap (PBG) laser. In each of these systems, the gain is achieved in a 
similar manner, i.e. by injecting carriers across a p-n junction. However, 
in each system the cavity in which the lasing occurs is created in a 
different manner. 
In order to put the cavity of the present invention in perspective, it is 
beneficial to discuss the three conventional cavities which are part of 
the state of the art. All of the aforementioned cavities have a common 
feature in that a cavity must have walls along each dimension which 
reflect electromagnetic radiation. There are two principle ways to reflect 
light at optical frequencies, total internal reflection (TIR) and 
reflection from a periodic dielectric structure. 
TIR occurs at the interface between two dielectrics when it is not possible 
to simultaneously match both the frequency and the phase on both sides of 
the interface. When light is incident from the high dielectric material, 
it is totally reflected back into the material. This only occurs if the 
angle of incidence is greater than the critical angle. Light can also be 
reflected at the interface between a homogeneous dielectric and a periodic 
dielectric. This occurs when multiple scattered waves in the periodic 
medium destructively interfere, thereby prohibiting propagation inside the 
periodic medium. 
When a periodic medium forbids the propagation of light, it is said to have 
a photonic band gap (PBG). It is possible to make PBG structures which 
reflect light along a single axis (a multilayer film) as described in U.S. 
patent. application. Ser. No. 08/318,161 entitled "Resonant Microcavities 
Employing One-Dimensional Periodic Dielectric Waveguides", incorporated 
herein by reference. It is also possible to make PBG structures which 
reflect light incident from any arbitrary direction (3-D PBG), as 
described in U.S. Pat. No. 5,440,421 entitled "Three-Dimensional Periodic 
Dielectric Structures Having Photonic Bandgaps", also incorporated herein 
by reference. The present invention relates to PBG structures which 
reflect light incident in a single plane, thus a two-dimensional PBG. 
Having identified the two ways to reflect light, it is now possible to 
review the conventional cavities which are used in semiconductor lasers 
according to a simple scheme. These cavities are labeled according to how 
light is reflected along each of the three axes. Consider, for example, 
microdisk laser 100 shown in FIG. 1. The microdisk is made of a small 
high-index disk 102 having a gain medium which is made of one or several 
quantum layers in the center of the disk. The dominant resonant (high-Q) 
mode 104 is called a whispering-gallery mode since it propagates around 
the edge of the disk with low losses due to total internal reflection. In 
this case, the light is totally internally reflected along every axis, and 
so it is designated T3. 
The situation is changed when we consider the VCSEL structure 200 of FIG. 2 
(or, equivalently, a DFB laser with phase slip). The VCSEL is made of two 
multilayer dielectric quarter-wave mirrors 202, 204 separated by a cavity 
206 having a gain medium of one or several quantum wells. These periodic 
dielectrics reflect light incident normal to the layers, in the vertical 
direction. Along the other two directions light is guided along the 
dielectric-air boundary by TIR and so this construction is labeled as 
P1T2. In spite of the advantages of the VCSEL over typical semiconductor 
lasers, the most significant drawback of these devices is their vertical 
position and vertical emission 208 on the substrate which limits 
significantly their usefulness in optoelectronic integrated circuits 
(OEICs). 
In FIG. 3, a resonant cavity constructed in a threedimensional periodic 
dielectric structure 300 with PBG is shown. This cavity is surrounded by a 
dielectric crystal which is periodic along all three directions, thus the 
periodicity reflects light along all three directions. Such a structure is 
labeled P3. U.S. Pat. No. 5,187,461 entitled "Low-loss Dielectric 
Resonator Having a Lattice Structure With a Resonant Defect", incorporated 
herein by reference, describes a three-dimensional dielectric lattice with 
a defect. 
It is therefore an object of the present invention to provide a new 
technique of producing high Q resonant cavities. These cavities may be 
employed in a laser, as filters, or in any other application which 
requires a resonant cavity. 
It is a further object of the present invention to provide a resonant 
cavity which achieves in-plane (x-y) localization of electromagnetic 
radiation using a two-dimensional periodic dielectric, and vertical 
confinement of electromagnetic radiation using TIR. Such a cavity is 
designated as P2T1 and will work at any frequency between ultraviolet and 
microwave. 
SUMMARY OF THE INVENTION 
The present invention provides a resonant cavity including a planar 
two-dimensional periodic dielectric structure and a defect in the periodic 
dielectric structure which results in a photonic band gap. The photonic 
band gap effects an in-plane spacial confinement of electromagnetic 
radiation generated within the structure. The electromagnetic radiation is 
vertically confined by total internal reflection.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS 
With reference now to FIG. 4A, a high Q resonant cavity 400 in accordance 
with the present invention is shown schematically in block diagram form. 
The cavity 400 is constructed in a two-dimensional periodic dielectric 
structure 402 having a PBG. As is known in the art, the existence of a PBG 
results in a range of frequencies where electromagnetic energy is not 
permitted to exist in the periodic structure. A defect 404 introduced to 
the structure results in the structure exhibiting an electromagnetic mode 
within the PBG. Since the mode is not normally allowed within the PBG, the 
mode exists only localized to the defect. In accordance with the present 
invention, the mode is confined because the dielectric structure is 
periodic along two directions, and so it can reflect light if it is 
propagating in the plane of the underlying substrate. Moreover, the mode 
is also confined in the vertical direction by TIR. Accordingly, this 
cavity is classified as P2T1. 
It is understood that the energy developed within the cavity is captured 
within the cavity. However, the energy leaks out exponentially from the 
cavity with respect to distance to the cavity. In other words, there is an 
exponential decay of intensity of the mode into the surrounding regions of 
the cavity. Accordingly, it is desirable to recapture this escaped energy. 
If a waveguide is positioned in the vicinity of the cavity, the energy can 
be recaptured and channeled through the waveguide. FIG. 4B shows a 
periodic structure with an integrated waveguide 406 which can be used to 
couple energy out of the cavity. As will be discussed hereinafter, it will 
be desirable to couple into the cavity using a waveguide in close 
proximity to the defect. Under these circumstances, the waveguide is a 
linear defect in an otherwise periodic dielectric structure. 
The 2D PBG cavity of the present invention has the two important features 
of in-plane confinement of light employing a two-dimensional photonic band 
gap material, and vertical confinement of light via TIR. Each of these 
features will be discussed in detail hereinafter. 
According to the present invention, the in-plane confinement of 
electromagnetic radiation is achieved employing a two-dimensional periodic 
dielectric array. Such a structure can be produced with a photonic band 
gap, which reflects light from all in-plane directions. In particular, 
square, triangular and honeycomb lattices have adequate electromagnetic 
properties. Moreover, such dielectric arrays may be constructed, for 
example, either from air in dielectric as achieved by resonant cavity 500 
of FIG. 5, or dielectric in air as achieved by resonant cavities 600 and 
700 of FIGS. 6 and 7, respectively. It will be appreciated by those of 
skill in the art that other configurations of dielectric arrays are 
possible without the use of air, in particular it is desirable to obtain a 
structure with sufficient dielectric contrasts. While the subject of two 
dimensional dielectric lattices has received some attention as reflected 
in Meade et al., "Novel Applications of Photonic Band Gap Materials: 
Low-loss Bends and High Q Cavities", incorporated herein by reference, 
however, in accordance with the present invention, the electromagnetic 
energy is vertically confined by TIR in a 2D PBG structure. 
Having created a reflecting two-dimensional dielectric lattice, it is then 
necessary to embed a defect in this lattice to localize the light. This 
process is similar in spirit to that described in U.S. Pat. No. 5,187,461 
entitled "Low-loss Dielectric Resonator Having a Lattice Structure With a 
Resonant Defect", incorporated herein by reference, in which a 
three-dimensional dielectric lattice is created and a defect introduced. 
In accordance with the present invention, the 2D periodicity is 
responsible for 2D (in-plane) localization. For example, with reference to 
FIGS. 8A and 8B, a localized mode created by a cavity 800 surrounded by 2D 
reflecting walls is shown. In FIG. 8A, the cavity is centrally located 
with a surrounding periodic lattice 802 of reflecting dielectric. The 
electric fields 804 associated with the localized cavity mode are shown in 
the contour plot of FIG. 8B. As in the 3D PGP structure, by varying the 
defect size the cavity resonance can be tuned to any frequency in the band 
gap, as shown in the plot of FIG. 8C. 
In accordance with the present invention, the vertical confinement of 
electromagnetic radiation is achieved by creating a high dielectric layer 
surrounded by layers of lower dielectric constant. With reference back to 
FIG. 5, one exemplary embodiment of this implementation is shown. The 
resonant cavity structure 500 includes a layer of material 502 having a 
predetermined dielectric constant with a periodic array of air holes 504 
disposed therethrough. The cavity is formed by breaking the perfect 
periodicity along the x and y axes, hence forming a local defect 506 which 
can lead to strong spacial confinement of the radiation around the defect 
in order to generate an electromagnetic mode. In this embodiment, the TIR 
occurs between the dielectric material and air on both sides of the 
cavity. 
A straightforward way to produce the cavity 500 at microwave frequencies is 
to take a plane of high dielectric material and drill the periodic series 
of holes with conventional machine tools, thus resulting in the 2D PBG 
structure. At optical frequencies, such a cavity can be fabricated 
employing techniques similar to those used to fabricate the microdisk 
laser. For example, photolithography, x-ray lithography, electron beam 
lithography, and reactive ion beam etching. 
Another exemplary embodiment of a P2T1 cavity 600 is shown in FIG. 6. In 
this embodiment, a layer 602 of high index material such as GaAs is grown 
on a low index substrate 604, such as GaA1As. Thereafter, a periodic 
series of columns, for example, are formed by etching. A defect 606 is 
provided at a selected position. The defect is formed, for example, by 
removing the high index material from a selected column or any other 
process which would interrupt the periodicity of the surrounding material. 
The column structures are produced, for example, by utilizing reactive ion 
beam etching or electron beam lithography. At the top surface, the index 
contrast between the GaAs and air is large and so the reflections are 
quite strong, while at the bottom surface the index contrast between the 
GaAs and GaA1As is small, thus the reflections are weaker. 
A further exemplary embodiment of a resonant cavity 700 which achieves 
inplane confinement of electromagnetic radiation is shown in FIG. 7. The 
cavity 700 includes a high index layer 702 of, for example, GaAs, 
positioned between lower index material layers 704, 705 such as GaA1As. 
Through conventional chemical etching, a periodic array of columns are 
formed. The defect 706 which breaks the periodicity of the structure in 
the illustrated example is formed by the creation of an oversized column. 
In this embodiment, light is confined to the high index GaAs layer 
surrounded by low index GaAs on either side. It will be appreciated by 
those of skill in the art that while the illustrated embodiments are shown 
utilizing GaAs/eGaA1As epilayers, in fact any two dielectric materials of 
differing dielectric constant can be used. For example, an alternative 
construction can include a layer of GaInAsP between layers of InP. 
One important aspect of designing a P2T1 cavity in accordance with the 
present invention is the choice of width of the high dielectric layer, 
which must be neither too large nor too small. For a laser application, 
the vertical mode profile at a given frequency .omega..sub.0 (the 
frequency of the cavity mode which is chosen to be the frequency of the 
laser light) is of the greatest interest. In particular, the dependence of 
the vertical mode profile with the width of the layer in order to 
determine the number of guided modes is of interest. This dependence is 
shown in the graph of FIG. 9, which plots the effective index, n.sub.eff 
=k/.omega..sub.0, versus layer width, where k is the wave vector of the 
propagating mode. This graph shows that there are a number of critical 
widths w.sub.c,n above which a mode with n nodes becomes guided (solid 
lines) and below which the mode is a resonance (dashed-dotted lines). To 
create a high-Q cavity, it is important to have exactly one guided mode. 
If there are no guided modes then there is no high-Q cavity mode. However, 
if there are several guided modes then there will be several high-Q 
cavities which may have similar frequencies. Therefore, it is necessary to 
choose the layer width w.sub.c,0 &lt;w&lt;w.sub.c,1. Although the illustrated 
embodiments are considered with respect to only the simple case of a 
single layer of high dielectric material in the absence of the 2D PBG, the 
variation with width has the same qualitative behavior when the 2D PBG is 
accounted for. FIGS. 10A-10C respectively show electric field intensity 
schematics for modes with zero, one and two nodes. 
Another important aspect of designing a P2T1 cavity in accordance with the 
present invention is the proper consideration of polarization effects. For 
simplicity, the difference between polarizations in the description of 
layer widths is ignored. In fact, the critical widths w.sub.c,n, of a 
single layer of high dielectric material is slightly different for TE 
(E-field parallel to the surface of the substrate) and TM (H-field 
parallel to the surface of the substrate) modes. This difference is 
magnified by the presence of the 2D PBG because in this case, the TE and 
TM modes have very different propagation properties. However, polarization 
considerations can be dealt with easily by choosing a 2D periodic lattice 
which has a gap only for either TE or TM modes. 
One exemplary application of the resonant cavity of the present invention 
is for the production of semiconductor lasers. The 2D laser geometry is 
particularly useful for integrated optoelectronics. The utility arises 
from the ease of coupling the laser light into a nearby inplane waveguide 
as schematically shown in FIG. 11. FIG. 11 shows a two-dimensional 
periodic dielectric structure 1100 having laser cavity 1102 in close 
proximity to a waveguide 1104. Because the dielectric is reflecting, the 
principle exit port for the electromagnetic radiation is into the 
waveguide. This configuration eliminates substrate radiation as a source 
of loss. 
Another exemplary application of the resonant cavity of the present 
invention is for use in semiconductor device filters. The 2D geometry is 
also particularly useful for integrated optoelectronics. The utility 
similarly arises from the ease of coupling electromagnetic energy into and 
out of a resonant cavity as schematically shown in FIG. 12. FIG. 12 shows 
a two-dimensional periodic dielectric structure 1200 having a resonant 
cavity 1202 in close proximity to an input waveguide 1204. Accordingly, 
electromagnetic energy can be transported to the resonant cavity to induce 
the generation of further electromagnetic energy. Thereafter, because the 
dielectric is reflecting, the principle exit port for the electromagnetic 
radiation generated by the cavity is into an output waveguide 1206. This 
configuration can operate as a filter by designing the cavity to include a 
defect which creates a desired electromagnetic mode, thus only specified 
portions of the generated electromagnetic energy are allowed to pass 
through to the output waveguide. It will be appreciated that the 
embodiment of FIG. 12 can be modified to include one or more input 
waveguides as well as one or more output waveguides, depending on the 
desired filtering operation. 
The foregoing description has been set forth to illustrate the invention 
and is not intended to be limiting. Since modifications of the described 
embodiments incorporating the spirit and substance of the invention may 
occur to persons skilled in the art, the scope of the invention should be 
limited solely with reference to the appended claims and equivalents 
thereof.