Single mode waveguide with an adiabatic bend
A single mode waveguide with a straight portion and a curved portion, the curved portion having the shape of an adiabatic bend. The single mode waveguide has a curved portion that is shaped according to an adiabatic bend, with a curvature that varies continuously, and that vanishes at a point at which the curved portion is contiguous with a straight portion of the waveguide. The absence of curvature discontinuities avoids the coupling, within the waveguide, of optical power from a fundamental mode into a higher order mode and the curvature of the curved portion results in attenuation of optical power, in higher order modes, that may be coupled into the waveguide at either end.
1. An arrayed waveguide grating having an input waveguide and an output waveguide, the arrayed waveguide grating comprising:
a first star coupler, comprising:
a first input star coupler aperture connected to the input waveguide,
a first free-propagation region, and
a first output star coupler aperture,
a second star coupler, comprising:
a second input star coupler aperture,
a second free-propagation region, and
a second output star coupler aperture connected to the output waveguide; and
an array of waveguides, extending into the first output star coupler aperture and into the second input star coupler aperture and connecting the first output star coupler aperture to the second input star coupler aperture,
the first input star coupler aperture being coupled to the first output star coupler aperture through the first free-propagation region,
the second input star coupler aperture being coupled to the second output star coupler aperture through the second free-propagation region,
each waveguide of the array of waveguides producing a net clockwise change in direction for propagation through the waveguide from the first output star coupler aperture to the second input star coupler aperture,
each waveguide of the array of waveguides having:
a first portion,
a second portion having a first end and a second end,
a third portion,
a fourth portion having a first end and a second end,
a fifth portion, and
a sixth portion,
the first portion of each waveguide of the array of waveguides being within the first output star coupler aperture and having a maximum curvature less than 0.01/mm,
the second portion of each waveguide of the array of waveguides being outside the first output star coupler aperture, the second portion being contiguous, at the first end of the second portion, with the first portion,
the second portion of each waveguide of the array of waveguides having:
at the first end of the second portion, a curvature less than 0.01/mm,
at the second end of the second portion, a curvature less than 0.01/mm, and
at a point between the first end of the second portion and the second end of the second portion, a curvature greater than 0.3/mm, the curvature being counterclockwise for propagation through the waveguide from the first output star coupler aperture to the second input star coupler aperture,
the third portion of each waveguide of the array of waveguides being within the second input star coupler aperture and having a maximum curvature less than 0.01/mm,
the fourth portion of each waveguide of the array of waveguides being outside the second input star coupler aperture, the fourth portion being contiguous, at the first end of the fourth portion, with the third portion,
the fourth portion of each waveguide of the array of waveguides having:
at the first end of the fourth portion, a curvature less than 0.01/mm,
at the second end of the fourth portion, a curvature less than 0.01/mm, and
at a point between the first end of the fourth portion and the second end of the fourth portion, a curvature greater than 0.3/mm, the curvature being counterclockwise for propagation through the waveguide from the first output star coupler aperture to the second input star coupler aperture,
the magnitude of the rate of change of curvature of each waveguide being, everywhere on a segment of the waveguide including the first portion and the second portion, less than 15/mm 2 , the curvature being, everywhere on the segment, less than 2/mm,
the fifth portion of each waveguide of the array of waveguides being contiguous with the second portion of the waveguide, and having a curvature less than 0.01/mm,
the sixth portion of each waveguide of the array of waveguides being contiguous with the fourth portion of the waveguide, and having a curvature less than 0.01/mm,
a centerline of the first star coupler being oblique to the fifth portion of a waveguide of the array of waveguides, and
a centerline of the second star coupler being oblique to the sixth portion of a waveguide of the array of waveguides.
2. The arrayed waveguide grating of claim 1 , wherein
the magnitude of the rate of change of curvature of a first waveguide of the array of waveguide is, everywhere on a segment of the first waveguide including the third portion and the fourth portion of the first waveguide, less than 15/mm 2 .
3. The arrayed waveguide grating of claim 1 , wherein the first output star coupler aperture comprises a plurality of tapered rib waveguides.
4. The arrayed waveguide grating of claim 3 , wherein each of the tapered rib waveguides has a rib having:
a first width at a first end of the first input star coupler aperture adjacent the first free-propagation region, and
a second width at a second end of the first input star coupler aperture, the second end being opposite the first end of the first input star coupler aperture,
the first width being at least 30% greater than the second width.
5. The arrayed waveguide grating of claim 1 , wherein the first output star coupler aperture has a length and comprises:
a first dummy waveguide on a first side of the array of waveguides, the first dummy waveguide extending only along the length of the first output star coupler aperture; and
a second dummy waveguide on a second side of the array of waveguides, opposite the first side, the second dummy waveguide extending only along the length of the first output star coupler aperture.
6. The arrayed waveguide grating of claim 1 , wherein the array of waveguides has a first L bend portion and a second L bend portion,
wherein:
within the first L bend portion, each waveguide of the array of waveguides has a bend, resulting in a change of direction of more than 60 degrees and less than 120 degrees, and
within the second L bend portion, each waveguide of the array of waveguides has a bend, resulting in a change of direction of more than 60 degrees and less than 120 degrees.
7. The arrayed waveguide grating of claim 6 , wherein:
within the first L bend portion, each waveguide of the array of waveguides is a strip waveguide, and
within the second L bend portion, each waveguide of the array of waveguides is a strip waveguide.
8. The arrayed waveguide grating of claim 7 , wherein each waveguide of the array of waveguides has a straight portion between the first L bend portion and the second L bend portion.
9. The arrayed waveguide grating of claim 6 , wherein the array of waveguides has a rib to strip converter portion between the first output star coupler aperture and the first L bend portion,
the rib to strip converter having a rib end and a strip end,
each waveguide of the array of waveguides being
a rib waveguide at the rib end of the rib to strip converter, and
a strip waveguide at the strip end of the rib to strip converter, and
having, within the rib to strip converter, a cross section varying continuously from a cross section of a rib waveguide to a cross section of a strip waveguide.
10. The arrayed waveguide grating of claim 9 , where, within the rib to strip converter, each waveguide of the array of waveguides has a curvature of less than 0.01/mm.
11. The arrayed waveguide grating of claim 9 wherein each waveguide of the array of waveguides has, along its length, a rate of change of curvature with a magnitude of less than 15/mm 2 .
12. The arrayed waveguide grating of claim 1 , wherein the second portion is configured to transmit, from the first end of the second portion, to the second end of the second portion:
with an attenuation of less than 1 dB:
a fundamental transverse electric mode, and
a fundamental transverse magnetic mode, and
with an attenuation of more than 10 dB:
a first-order transverse electric mode, and
a first-order transverse magnetic mode.
13. An arrayed waveguide grating having an input waveguide and an output waveguide, the arrayed waveguide grating comprising:
a first input star coupler aperture connected to the input waveguide;
a first free-propagation region;
a first output star coupler aperture;
a second input star coupler aperture;
an array of waveguides, extending into the first output star coupler aperture and into the second input star coupler aperture and connecting the first output star coupler aperture to the second input star coupler aperture;
a second free-propagation region; and
a second output star coupler aperture connected to the output waveguide,
the first input star coupler aperture being coupled to the first output star coupler aperture through the first free-propagation region,
the second input star coupler aperture being coupled to the second output star coupler aperture through the second free-propagation region,
each waveguide of the array of waveguides having:
a first portion, and
a second portion having a first end and a second end,
the first portion being within the first output star coupler aperture and having a maximum curvature less than 0.01/mm,
the second portion being outside the first output star coupler aperture, the second portion being contiguous, at the first end of the second portion, with the first portion,
the second portion having:
at the first end of the second portion, a curvature less than 0.01/mm,
at the second end of the second portion, a curvature less than 0.01/mm, and
at a point between the first end of the second portion and the second end of the second portion, a curvature greater than 0.3/mm, and
the magnitude of the rate of change of curvature of each waveguide being, everywhere on a segment of the waveguide including the first portion and the second portion, less than 15/mm 2 ,
the curvature being, everywhere on the segment, less than 2/mm,
each waveguide being, within the second portion, a rib waveguide having a rib width of about 3.0 microns and a rib height of about 1.2 microns.
14. An arrayed waveguide grating having an input waveguide and an output waveguide, the arrayed waveguide grating comprising:
a first input star coupler aperture connected to the input waveguide;
a first free-propagation region;
a first output star coupler aperture;
a second input star coupler aperture;
an array of waveguides, extending into the first output star coupler aperture and into the second input star coupler aperture and connecting the first output star coupler aperture to the second input star coupler aperture;
a second free-propagation region; and
a second output star coupler aperture connected to the output waveguide,
the first input star coupler aperture being coupled to the first output star coupler aperture through the first free-propagation region,
the second input star coupler aperture being coupled to the second output star coupler aperture through the second free-propagation region,
a first waveguide of the array of waveguides having:
a first portion,
a second portion having a first end and a second end, and
an L bend,
the first portion being within the first output star coupler aperture and having a maximum curvature less than 0.01/mm,
the second portion being outside the first output star coupler aperture, the second portion being contiguous, at the first end of the second portion, with the first portion,
the second portion having:
at the first end of the second portion, a curvature less than 0.01/mm,
at the second end of the second portion, a curvature less than 0.01/mm, and
at a point between the first end of the second portion and the second end of the second portion, a curvature greater than 0.3/mm,
the magnitude of the rate of change of curvature of the first waveguide being, everywhere on a segment of the first waveguide including the first portion and the second portion, less than 15/mm 2 ,
the curvature being discontinuous at one end of the L bend.