Bending Waveguide
An optical waveguide of the present disclosure proposes a configuration of a bent waveguide having a novel configuration. For proposed four types of curves A, B, C, and D, a value obtained by differentiating a curvature along a waveguide is 0 at one end 1=0 and the other end 1=L of a bent waveguide. It is possible to suppress optical loss and inter-mode crosstalk occurring in the bent waveguide. Even in a bent waveguide having a waveguide width under a multimode condition, excellent inter-mode crosstalk characteristics and low loss are achieved as compared with the clothoid curve of the prior art.
1 . A bent waveguide, wherein
a curvature radius r gradually varies from a first value (R1) at a first end to a second value (R2) at a second end,
a curvature is represented by the reciprocal 1/r of the curvature radius, and
a differential coefficient obtained by differentiating the curvature with a length 1 along the waveguide is 0 at the first end and the second end.
2 . The bent waveguide according to claim 1 , wherein a width of the waveguide is a width satisfying a multimode condition.
3 . The bent waveguide according to claim 1 , wherein the differential coefficient is represented by:
d
dl
(
1
r
)
=
π
2
RL
sin
π
l
L
where L denotes a total length of a curve and R denotes a minimum bending radius.
4 . The bent waveguide according to claim 1 , wherein the differential coefficient is represented by:
d
dl
(
1
r
)
=
1
RL
(
1
-
cos
2
π
l
L
)
where L denotes a total length of a curve and R denotes a minimum bending radius.
5 . The bent waveguide according to claim 1 , wherein the differential coefficient is represented by:
d
dl
(
1
r
)
=
6
l
RL
2
(
1
-
l
L
)
where L denotes a total length of a curve and R denotes a minimum bending radius.
6 . The bent waveguide according to claim 1 , wherein the differential coefficient is represented by:
d
dl
(
1
r
)
=
4
l
RL
2
(
l
≦
L
2
)
and
d
dl
(
1
r
)
=
4
(
L
-
l
)
RL
2
(
l
>
L
2
)
where L denotes a total length of a curve and R denotes a minimum bending radius.
7 . A direction conversion circuit, comprising:
a first linear waveguide;
a first bent waveguide according to claim 1 , the bent waveguide being connected to the first linear waveguide at the first end; and
a second bent waveguide connected to the second end of the first bent waveguide and having a shape obtained by inverting the first bent waveguide; and
a second linear waveguide connected at a first end of the second bent waveguide.
8 . The direction conversion circuit according to claim 7 , wherein the first bent waveguide and the second bent waveguide each correspond to a direction conversion of 45° and achieve a bending of 90°θ in total.