COMPACT MODE-SIZE TRANSITION USING A FOCUSING REFLECTOR
Disclosed herein are techniques, methods, structures and apparatus for optically coupling optical waveguides and optical structures exhibiting different widths in which In which a focusing reflector is used to optically couple a relatively wide optical waveguide to a relatively narrow optical waveguide. An exemplary method according to the present disclosure comprises the steps of: providing the first waveguide that is 5 or more wavelengths in width; providing the second waveguide that is 3 or less wavelengths in width; coupling light emanating from the first waveguide to the second waveguide through the effect of a slab waveguide having a curved edge.
1 . A method of optically coupling a first waveguide to a second waveguide comprising the steps of:
providing the first waveguide that is 5 or more wavelengths in width;
providing the second waveguide that is 3 or less wavelengths in width;
coupling light emanating from the first waveguide to the second waveguide through the effect of a slab waveguide having a curved edge.
2 . The method according to claim 1 wherein said first waveguide comprises an optical grating.
3 . The method according to claim 1 wherein said first waveguide comprises a 2-D optical grating and said slab waveguide comprises a plurality of curved edges, one for each of the edges of the 2-D optical grating.
4 . The method according to claim 1 wherein said curved edge of the slab waveguide is defined by:
y
=
y
0
-
y
0
2
+
2
x
(
x
0
-
x
0
2
+
y
0
2
)
where x, y represents the origin of the coordinate system and is the point on the reflector closest to the first waveguide and the second waveguide inlet is represented by (x 0 , y 0 ) and the set of (x, y) define the shape of the curved edge.
5 . The method according to claim 4 wherein the maximum maximum angle of all lightwaves striking the curved edge with respect to a local normal is less than a critical angle and defined by:
y
0
>
x
0
tan
(
2
sin
-
1
η
clad
η
wg
)
where η wg is the effective waveguide refractive index and η clad is the cladding refractive index.
6 . A apparatus that optically couples a first waveguide to a second waveguide comprising:
the first waveguide that is 5 or more wavelengths in width;
the second waveguide that is 3 or less wavelengths in width;
a slab waveguide having a curved edge interposed between the first waveguide and the second waveguide and configured such that light emanating from the first waveguide is coupled to the second waveguide through the effect of the curved edge.
7 . The apparatus according to claim 6 wherein said first waveguide comprises an optical grating.
8 . The apparatus according to claim 6 wherein said first waveguide comprises a 2-D optical grating and said slab waveguide comprises a plurality of curved edges, one for each of the edges of the 2-D optical grating.
9 . The apparatus according to claim 6 wherein said curved edge of the slab waveguide is defined by:
y
=
y
0
-
y
0
2
+
2
x
(
x
0
-
x
0
2
+
y
0
2
)
where x, y represents the origin of the coordinate system and is the point on the reflector closest to the first waveguide and the second waveguide inlet is represented by (x 0 , y 0 ) and the set of (x, y) define the shape of the curved edge.
10 . The apparatus according to claim 9 wherein the maximum maximum angle of all lightwaves striking the curved edge with respect to a local normal is less than a critical angle and defined by:
y
0
>
x
0
tan
(
2
sin
-
1
η
clad
η
wg
)
where η wg is the effective waveguide refractive index and η clad is the cladding refractive index.
11 . A method of optically coupling an optical grating to an optical waveguide comprising the steps of:
coupling light emanating from the optical grating to the optical waveguide through the effect of a slab waveguide having a curved edge.
12 . The method according to claim 11 wherein the side of the grating emitting the light exhibits a width that is 5 or more wavelengths in width and the optical waveguide exhibits a width that is 3 or less wavelengths in width wherein said width dimension is measured at the point where the light is emitted and received, respectively.
13 . The method according to claim 11 wherein said grating is a 2-D optical grating and said slab waveguide comprises a plurality of curved edges, one for each of the edges of the 2-D optical grating, and the optical waveguide is one of a plurality of waveguides optically connected to a respective side of the 2-D grating by the effect of a respective curved edge.
14 . The method according to claim 1 wherein a curved edge of the slab waveguide is defined by:
y
=
y
0
-
y
0
2
+
2
x
(
x
0
-
x
0
2
+
y
0
2
)
where x, y represents the origin of the coordinate system and is the point on the reflector closest to the first waveguide and the second waveguide inlet is represented by (x 0 , y 0 ) and the set of (x, y) define the shape of the curved edge.
15 . The method according to claim 14 wherein the maximum angle of all lightwaves striking the curved edge with respect to a local normal is less than a critical angle and defined by:
y
0
>
x
0
tan
(
2
sin
-
1
η
clad
η
wg
)
where η wg is the effective waveguide refractive index and η clad is the cladding refractive index.