Arrayed waveguide grating with free propagation region matching

1. An array mode converter for coupling to a free propagation region of a star coupler, the array mode converter comprising:

a high-index layer on a low-index layer, the high-index layer having:

a first region, having a first height above the low-index layer;

a second region, having a second height above the low-index layer, the second height being less than the first height; and

a third region, having a third height above the low-index layer, the third height being less than the second height,

the first region, the second region, and the third region defining a first waveguide,

the first waveguide having a sidewall height decreasing, with decreasing distance, along the first waveguide, from the free propagation region, to a sidewall height of less than 1.2 microns at the free propagation region, and

the second region forming a slab on both sides of the first waveguide, the slab having a width, on each side of each sidewall of the first waveguide, tapering, at a taper angle, in a direction, along the first waveguide, of increasing distance from the free propagation region, from a width of more than three microns to a width of less than 0.5 microns, the taper angle being, at a point along a length of the slab, less than 2 degrees.

2. The array mode converter of claim 1 , wherein:

the first region, the second region, and the third region further define a second waveguide; and

a trench width between the first waveguide and the second waveguide, at the free propagation region, is less than 1.5 microns.

3. The array mode converter of claim 2 , wherein a trench width between the first waveguide and the second waveguide, at the free propagation region, is less than 0.7 microns.

4. The array mode converter of claim 1 , wherein the first region has a height, above the low-index layer, that is within 20% of 3.0 microns.

5. The array mode converter of claim 4 , wherein the second region has a height, above the low-index layer, that is less than the height, above the low-index layer, of the first region, by an amount that is within 20% of 0.6 microns.

6. The array mode converter of claim 1 , wherein the third region has a height that is within 20% of 1.8 microns.

7. The array mode converter of claim 1 , wherein the taper angle is, at a point along the length of the slab, less than 1 degree.

8. The array mode converter of claim 1 , further comprising a fourth region, having a fourth height above the low-index layer, the fourth height being less than the third height.

9. The array mode converter of claim 8 , wherein the fourth height is greater than or equal to zero microns and less than 0.5 microns.

10. A star coupler, comprising:

the array mode converter of claim 1 ;

the free propagation region; and

a second waveguide,

wherein:

the first region, the second region, and the third region define:

an array of first waveguides, including the first waveguide, terminating at a first aperture of the star coupler, each of the first waveguides having a fundamental transverse electric mode, a superposition of the modes defining a first field pattern at the first aperture of the star coupler, and

the second waveguide,

the second waveguide terminates at a second aperture of the star coupler and has a fundamental transverse electric mode defining a second field pattern at the first aperture of the star coupler, and

an overlap integral of the first field pattern with the second field pattern over the first aperture of the star coupler is at least 0.8 times as great as an overlap integral of the first field pattern with the first field pattern.

11. The star coupler of claim 10 , wherein each of the first waveguides comprises a shallow rib mode converter forming a transition between a first rib waveguide section and second rib waveguide section, the second rib waveguide section being nearer the star coupler than the first rib waveguide section and having a rib height less than a rib height of the first rib waveguide section.

12. The star coupler of claim 11 , wherein the shallow rib mode converter is capable of transforming a fundamental transverse electric mode of the first rib waveguide section to a fundamental transverse electric mode of the second rib waveguide section with a loss of less than 0.5 dB.

13. An arrayed waveguide grating, comprising:

a first star coupler,

a second star coupler,

an array of waveguides connecting the first star coupler and the second star coupler, and

an array mode converter, in the array of waveguides, at the first star coupler,

each of the waveguides having four bends, each of the bends having a change of direction of at least 80 degrees,

wherein a first waveguide of the array of waveguides has, along the first waveguide in a direction from the first star coupler to the second star coupler:

a first clockwise bend,

a first counterclockwise bend following the first clockwise bend,

a second counterclockwise bend following the first counterclockwise bend, and

a second clockwise bend following the second counterclockwise bend, and

wherein the array mode converter comprises:

a high-index layer on a low-index layer, the high-index layer having:

a first region, having a first height above the low-index layer;

a second region, having a second height above the low-index layer, the second height being less than the first height; and

a third region, having a third height above the low-index layer, the third height being less than the second height,

a first waveguide of the array of waveguides having, within the array mode converter, a sidewall height decreasing, with decreasing distance, along the first waveguide, from a free propagation region of the first star coupler, to a sidewall height of less than 1.2 microns at the free propagation region of the first star coupler, and

the second region forming a slab on both sides of the first waveguide, the slab having a width, on each side of each sidewall of the first waveguide, tapering, at a taper angle, in a direction, along the first waveguide, of increasing distance from the free propagation region of the first star coupler, from a width of more than three microns to a width of less than 0.5 microns, the taper angle being, at a point along a length of the slab, less than 2 degrees.

14. The array mode converter of claim 13 , wherein a trench width between the first waveguide and a second waveguide of the array of waveguides, at the free propagation region of the first star coupler, is less than 0.7 microns.

15. The array mode converter of claim 13 , wherein the second region has a height, above the low-index layer, that is less than the height, above the low-index layer, of the first region, by an amount that is within 20% of 0.6 microns.

16. The array mode converter of claim 13 , wherein the taper angle is, at a point along the length of the slab, less than 1 degree.

17. The array mode converter of claim 13 , further comprising a fourth region, having a fourth height, above the low-index layer, the fourth height being less than the third height.

18. The array mode converter of claim 17 , wherein the fourth height is greater than or equal to zero microns and less than 0.5 microns.