Higher order mode filter
A waveguide mode filter. In some embodiments, the waveguide mode filter includes a first section of waveguide. The first section may have: a first end; a second end; a rate of change of curvature having a magnitude not exceeding 15/mm 2 within the first section; a curvature having a magnitude of at most 0.03/mm at the first end; and a curvature having a magnitude of at least 0.1/mm at the second end.
1. A waveguide mode filter, comprising:
a first section of waveguide, the first section having:
a first end,
a second end,
a rate of change of curvature having a magnitude not exceeding 15/mm 2 within the first section,
a curvature having a magnitude of at most 0.03/mm at the first end, and
a curvature having a magnitude of at least 0.1/mm at the second end;
a second section of waveguide, the second section having:
a first end abutting the second end of the first section,
a second end,
a curvature having a magnitude of less than 0.01/mm at the second end; and
a third section of waveguide, the third section having:
a first end abutting the second end of the second section,
a second end, and
a curvature having a magnitude of at least 0.1/mm at the second end,
wherein each of the first section, the second section, and the third section has a maximum magnitude of curvature between 0.1/mm and 1/mm.
2. The waveguide mode filter of claim 1 , wherein the curvature of the first section is, at each point on the first section, within 1/mm of a linear function of distance along a length of the first section.
3. The waveguide mode filter of claim 1 , wherein each point of a centerline of the first 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 an 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 an integral, over a second variable of integration ranging from zero to L, of the sine of the square of the second variable of integration.
4. The waveguide mode filter of claim 1 , comprising a doped region on one side of the first section of waveguide.
5. The waveguide mode filter of claim 1 , wherein the first section has a length less than 200 microns.
6. The waveguide mode filter of claim 1 , wherein the first section attenuates a fundamental transverse mode by at most 0.5 dB.
7. The waveguide mode filter of claim 1 , wherein the first section attenuates a higher order transverse mode by at least 3 dB.
8. The waveguide mode filter of claim 1 , wherein the magnitude of the curvature of the waveguide, at the first end of the first section, is less than 0.01/mm.
9. The waveguide mode filter of claim 1 , further comprising:
a fourth section of waveguide, the fourth section having:
a first end abutting the second end of the third section, and
a second end;
wherein:
the first end of the second section has a curvature equal to the curvature at the second end of the first section; and
the first end of the fourth section has a curvature having a magnitude of at least 0.1/mm.
10. The waveguide mode filter of claim 9 , wherein the magnitude of the curvature of the fourth section, at the second end of the fourth section, is less than 0.01/mm.
11. The waveguide mode filter of claim 10 , wherein the waveguide, at the second end of the fourth section, is parallel, to within 0.5 degrees, to the waveguide, at the first end of the first section.
12. The waveguide mode filter of claim 9 , wherein an angle between the waveguide, at the second end of the second section, and the waveguide, at the first end of the first section, is greater than 0.5 degrees and less than 2 degrees.
13. The waveguide mode filter of claim 9 , wherein, at each of a set of four points within the first section, the second section, the third section, and the fourth section, respectively, the rate of change of curvature is greater than 1/mm 2 .
14. The waveguide mode filter of claim 9 , wherein a fifth section of waveguide, consisting of the first section, the second section, the third section, and the fourth section, has a length of less than 600 microns.
15. The waveguide mode filter of claim 14 , wherein everywhere within the fifth section the rate of change of curvature is less than 15/mm 2 .
16. The waveguide mode filter of claim 15 , wherein the fifth section of waveguide attenuates a fundamental transverse mode by at most 1 dB.
17. The waveguide mode filter of claim 15 , wherein the fifth section of waveguide attenuates a higher order transverse mode by at least 10 dB.
18. The waveguide mode filter of claim 14 , comprising a doped region on one side of the fifth section of waveguide.
19. A waveguide mode filter, comprising:
a first section of waveguide; and
a doped region on a side of the first section of waveguide,
the first section having:
a first end;
a second end;
a rate of change of curvature having a magnitude not exceeding 15/mm 2 within the first section;
a curvature having a magnitude of at most 0.03/mm at the first end; and
a curvature having a magnitude of at least 0.1/mm at the second end, and
a length of the doped region, measured in a direction parallel to an optical path of the waveguide, being greater than a length of the first section of waveguide.
20. The waveguide mode filter of claim 19 , wherein the length of the doped region is at least twice the length of the first section of waveguide.