Waveguide facet interface
A photonic integrated circuit. In some embodiments, the photonic integrated circuit includes: a waveguide; and a waveguide facet, a first end of the waveguide being at the waveguide facet, a first angle being an angle between: the waveguide at the first end of the waveguide and the normal to the waveguide facet, the first angle being at least 5 degrees, a first section of the waveguide having a first end at the waveguide facet and a second end, the first section having: a curvature of less than 0.01/mm at the first end of the first section, a curvature of less than 0.01/mm at the second end of the first section, and a curvature of at least 0.1/mm at a point between the first end and the second end.
1. A photonic integrated circuit, comprising:
a waveguide; and
a waveguide facet,
a first end of the waveguide being at the waveguide facet,
a first angle being an angle between:
the waveguide at the first end of the waveguide, and
the normal to the waveguide facet,
the first angle being at least 5 degrees,
a first section of the waveguide having a first end at the waveguide facet and a second end,
the first section having:
a curvature of less than 0.01/mm at the first end of the first section,
a curvature of less than 0.01/mm at the second end of the first section, and
a curvature of at least 0.1/mm at a point between the first end and the second end,
wherein the maximum value of the magnitude of the rate of change of curvature within the first section is less than 15/mm 2 .
2. The photonic integrated circuit of claim 1 , further comprising a dicing edge, wherein a second angle is an angle between the waveguide facet and the dicing edge, the second angle being greater than 20 degrees.
3. The photonic integrated circuit of claim 2 , wherein the second angle is within 2 degrees of the inverse sine of 3.5 times the sine of the first angle.
4. The photonic integrated circuit of claim 1 , wherein the first angle is less than 13 degrees.
5. The photonic integrated circuit of claim 1 , wherein the length of the first section is less than 4 mm.
6. The photonic integrated circuit of claim 5 , wherein the first section has a curvature of at least 0.2/mm at a point between the first end and the second end.
7. The photonic integrated circuit of claim 5 , wherein the first section attenuates a fundamental transverse mode by less than 0.1 dB.
8. The photonic integrated circuit of claim 5 , wherein the first section attenuates a higher order transverse mode by at least 3 dB.
9. The photonic integrated circuit of claim 5 , comprising a doped region on one side of the first section.
10. The photonic integrated circuit of claim 5 , wherein the length of the first section is less than 2 mm.
11. The photonic integrated circuit of claim 10 , wherein the first section has a curvature of at least 0.3/mm at a point between the first end and the second end.
12. The photonic integrated circuit of claim 10 , wherein the first section attenuates a fundamental transverse mode by less than 0.1 dB.
13. A photonic integrated circuit, comprising:
a waveguide; and
a waveguide facet,
a first end of the waveguide being at the waveguide facet,
a first angle being an angle between:
the waveguide at the first end of the waveguide, and
the normal to the waveguide facet,
the first angle being at least 5 degrees,
a first section of the waveguide having a first end at the waveguide facet and a second end,
the first section having:
a curvature of less than 0.01/mm at the first end of the first section,
a curvature of less than 0.01/mm at the second end of the first section, and
a curvature of at least 0.1/mm at a point between the first end and the second end,
wherein:
the first section comprises:
a second section of waveguide having a first end and a second end, and
a third section of waveguide, having a first end abutting against the second end of the second section, and a second end;
the curvature at the second end of the second section of waveguide is at least 0.1/mm;
the curvature at the first end of the third section of waveguide is at least 0.1/mm; and
the rate of change of curvature is, everywhere within the second section or everywhere within the third section, within 20% of a constant.
14. The photonic integrated circuit of claim 13 , wherein the rate of change of curvature is, everywhere within the second section, within 20% of a constant.
15. The photonic integrated circuit of claim 13 , wherein the rate of change of curvature is, everywhere within the third section, within 20% of a constant.
16. A photonic integrated circuit, comprising:
a waveguide; and
a waveguide facet,
a first end of the waveguide being at the waveguide facet,
a first angle being an angle between:
the waveguide at the first end of the waveguide, and
the normal to the waveguide facet,
the first angle being at least 5 degrees,
a first section of the waveguide having a first end at the waveguide facet and a second end,
the first section having:
a curvature of less than 0.01/mm at the first end of the first section,
a curvature of less than 0.01/mm at the second end of the first section, and
a curvature of at least 0.1/mm at a point between the first end and the second end,
wherein:
the first section comprises:
a second section of waveguide having a first end and a second end, and
a third section of waveguide, having a first end abutting against the second end of the second section, and a second end;
the curvature at the second end of the second section of waveguide is at least 0.1/mm;
the curvature at the first end of the third section of waveguide is at least 0.1/mm; and
each point of a centerline of the second section is within 5 microns of a curve defined by a set of points, each point having, for a value of a parameter L:
an x coordinate equal to a product of a constant of proportionality and the integral, over a first variable of integration ranging from zero to L, of the cosine of the square of the first variable of integration, and
a y coordinate equal to a product of the constant of proportionality and the integral, over a second variable of integration ranging from zero to L, of the sine of the square of the second variable of integration.
17. A photonic integrated circuit, comprising:
a waveguide; and
a waveguide facet,
a first end of the waveguide being at the waveguide facet,
a first angle being an angle between:
the waveguide at the first end of the waveguide, and
the normal to the waveguide facet,
the first angle being at least 5 degrees,
a first section of the waveguide having a first end at the waveguide facet and a second end,
the first section having:
a curvature of less than 0.01/mm at the first end of the first section,
a curvature of less than 0.01/mm at the second end of the first section, and
a curvature of at least 0.1/mm at a point between the first end and the second end,
wherein the first section attenuates a fundamental transverse mode by less than 0.1 dB, and
wherein the length of the first section is less than 4 mm.
18. A photonic integrated circuit, comprising:
a waveguide; and
a waveguide facet,
a first end of the waveguide being at the waveguide facet,
a first angle being an angle between:
the waveguide at the first end of the waveguide, and
the normal to the waveguide facet,
the first angle being at least 5 degrees,
a first section of the waveguide having a first end at the waveguide facet and a second end,
the first section having:
a curvature of less than 0.01/mm at the first end of the first section,
a curvature of less than 0.01/mm at the second end of the first section, and
a curvature of at least 0.1/mm at a point between the first end and the second end,
wherein the photonic integrated circuit comprises a doped region on one side of the first section.
19. The photonic integrated circuit of claim 18 , wherein the length of the first section is less than 4 mm.