Optical waveguides – Optical fiber waveguide with cladding – Utilizing nonsolid core or cladding
Reexamination Certificate
2002-07-10
2004-04-27
Sanghavi, Hemang (Department: 2874)
Optical waveguides
Optical fiber waveguide with cladding
Utilizing nonsolid core or cladding
C385S015000, C385S039000, C385S050000, C359S321000
Reexamination Certificate
active
06728457
ABSTRACT:
FIELD OF INVENTION
The present invention relates generally to the field of photonic crystals and more particularly to two-dimensional photonic crystal apparatus.
BACKGROUND OF INVENTION
Photonic crystals (PC) are periodic dielectric structures which can prohibit the propagation of light in certain frequency ranges. Photonic crystals have spatially periodic variations in refractive index and with a sufficiently high contrast in refractive index, photonic bandgaps can be opened in the structure's optical spectrum. The “photonic bandgap” is the frequency range within which propagation of light through the photonic crystal is prevented. A photonic crystal that has spatial periodicity in three dimensions can prevent light having a frequency within the crystal's photonic bandgap from propogating in any direction. However, fabrication of such a structure is technically challenging. A more attractive alternative is to utilize photonic crystal slabs that are two-dimensionally periodic dielectric structures of finite height that have a band gap for propagation in the plane and use index-confinement in the third dimension. In addition to being easier to fabricate, two-dimensional photonic crystal slabs provide the advantage that they are compatible with the planar technologies of standard semiconductor processing.
An example of a two-dimensional photonic crystal structure periodic in two dimensions and homogeneous in the third may be fabricated from a bulk material having a periodic lattice of circular air filled columns extending through the bulk material in the height direction and periodic in the planar direction. The propagation of light in two-dimensional photonic crystals is determined by a number of parameters, including radius of the cylindrical columns, the lattice spacing, the symmetry of the lattice and the refractive indices of the bulk and column material.
Introducing defects in the periodic structure of a photonic crystal allows the existence of localized electromagnetic states that are trapped at the defect site and that have resonant frequencies within the bandgap of the surrounding photonic crystal material. By providing a line of such defects in the photonic crystal, a waveguiding structure is created that can be used in the control and guiding of light (see, for example, J. D. Joannopoulos, R. D. Meade, and J. N. Winn, “Photonic Crystals”, Princeton University Press, Princeton, N.J., 1995). Light of a given frequency that is prevented from propagating in the photonic crystal may propagate in the defect region.
A two-dimensional photonic crystal slab waveguide usually comprises a two-dimensional periodic lattice in the form of an array of dielectric rods or air holes incorporated in a slab body. High guiding efficiency can be achieved only in a narrow frequency region close to the upper or lower edge (for dielectric rods or air holes, respectively) of the waveguide band, where there are no leaky modes. Typically, high guiding efficiency is achieved only in a narrow frequency region that is only a few percent of the center frequency of the waveguide band and existing configurations suffer from low group velocities in the allowed waveguide band. Low group velocity increases the unwanted effects of disorder and absorption. (see S. G. Johnson, S. Fan, P. R. Villeneuve, L. Kolodziejski and J. D. Joannopoulos, Phys. Rev. B 60,5751, 1999 and S. G. Johnson, P. R. Villeneuve, S. Fan and J. D. Joannopoulos, Phys. Rev. B 62,8212,2000).
FIG. 1
shows an xy view of prior art two-dimensional photonic crystal slab apparatus
100
. Photonic crystal slab
115
has circular holes
110
arranged to from a periodic triangular lattice with a lattice spacing equal to a. Circular holes
110
are filled with air. Region of defects
125
is created by replacing circular holes
110
of the lattice with larger circular holes
120
along a line in the x direction. Ridge waveguide
175
couples light into photonic crystal slab apparatus
100
that may have its edge at line A′, line B′ or line C′ in FIG.
1
.
FIG. 2
shows the transmission coefficient for two-dimensional crystal slab apparatus
100
as a function of frequency expressed in fractions of c/a—where c—is the speed of light—and a is the lattice spacing. The radius for circular holes
120
is about 0.45 a and the radius for circular holes
110
is about 0.3 a. Curve
210
represents the unguided case which has low transmission in the bandgap and high transmission in the allow band. Curve
201
represents the case where ridge waveguide
175
is attached to photonic crystal slab
15
at the edge defined by line A in FIG.
1
. Curve
202
represents the case where ridge waveguide
175
is connected to photonic crystal slab
115
at the edge defined by line B in FIG.
1
. Curve
203
represents the case where ridge waveguide
175
is connected to photonic crystal slab
115
at the edge defined by line C′ in FIG.
2
. The transmission for curve
203
is a maximum for a frequency of about 0.253 c/a and the waveguide band is narrow. Increasing the radius of circular holes
120
to 0.5 a causes circular holes
120
to touch and start to overlap. This results in rapid deterioration of the transmission properties of two-dimensional crystal slab apparatus
100
as the light wave becomes less confined due to the decrease of the average dielectric constant of two-dimensional crystal slab
100
.
SUMMARY OF INVENTION
In accordance with the invention, noncircular holes such as elliptical holes or rectangular holes are introduced as defects in the guiding direction of the photonic-crystal slab to create wide wave guiding bands covering more than 10% of the center frequency portion of the waveguide band. The elliptical or rectangular holes form a line of defects in the photonic crystal slab. Because low group velocities occur at the edges of the waveguide bands where the band becomes flat there is a wider range of frequencies with high group velocities available. Elliptical and rectangular holes provide significantly wider waveguide bandwidth and higher group velocity than circular holes. Over 10% of guiding bandwidth is achieved for a wide range of elliptical and rectangular shapes. The presence of a wider range of operating frequencies gives more forgiving fabrication tolerance for practical waveguide and allows more design flexibility when stub tuners, add-drop filters, bends and splitters are added. Higher group velocity will also lower the propagation loss of the waveguide.
REFERENCES:
patent: 6483640 (2002-11-01), Tonucci et al.
patent: 6643439 (2003-11-01), Notomi et al.
patent: 2002/0048422 (2002-04-01), Cotteverte et al.
patent: 2003/0174993 (2003-09-01), Tomaru
patent: 2003/0202764 (2003-10-01), Lee et al.
Johnson, S.G. et al., “Linear Waveguides in Photonic-Crystal Slabs”, Physical Review B, vol. 62, No. 12, Sep. 15, 2000, pp. 8212-8221.
Johnson, S. G. et al., “Guided Modes in Photonic Crystal Slabs”, Physical Review B, vol. 60, No. 8, Aug. 15, 1999, pp. 5751-5758.
Chow Kai Cheung
Sigalas Mihail M.
Agilent Technologie,s Inc.
Juergen Krause Polstorff
Sanghavi Hemang
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