Waveguide arrangements based on adiabatic elimination
This disclosure provides systems, methods, and apparatus related to nanophotonics. In one aspect, an arrangement of waveguides includes a substrate and three waveguides. Each of the three waveguides may be a linear waveguide. A second waveguide is positioned between a first waveguide and a third waveguide. The dimensions and positions of the first, the second, and the third waveguides are specified to substantially eliminate coupling between the first waveguide and the third waveguide over a distance of about 1 millimeter to 2 millimeters along lengths of the first waveguide, the second waveguide, and the third waveguide.
1. An arrangement of waveguides comprising:
a substrate;
a first waveguide having a first effective refractive index and being a linear waveguide having cross-sectional dimensions of less than about 1 micron;
a second waveguide being a linear waveguide having cross-sectional dimensions of less than about 1 micron; and
a third waveguide having the first effective refractive index and being a linear waveguide having cross-sectional dimensions of less than about 1 micron, the first, the second, and the third waveguides arranged on the substrate, the first, the second, and the third waveguides being substantially parallel over a specified distance, the second waveguide being positioned between the first waveguide and the third waveguide, the first waveguide being positioned less than about 1 micron from the second waveguide, the third waveguide being positioned less than about 1 micron from the second waveguide, the first waveguide and the third waveguide having substantially the same cross-sectional dimensions, dimensions and positions of the first, the second, and the third waveguides being specified to substantially eliminate coupling between the first waveguide and the third waveguide over a distance of about 1 millimeter to 2 millimeters along lengths of the first waveguide, the second waveguide, and the third waveguide.
2. The arrangement of claim 1 , wherein the first waveguide is positioned less than about 2 microns from the third waveguide.
3. The arrangement of claim 1 , wherein the first waveguide, the second waveguide, and the third waveguide are disposed on the substrate.
4. The arrangement of claim 1 , wherein the first waveguide and the third waveguide comprise a first material, and wherein the first material comprises a first dielectric material or a first semiconductor material.
5. The arrangement of claim 4 , wherein the second waveguide comprises the first material.
6. The arrangement of claim 4 , wherein the cross-sectional dimensions of the first waveguide and the third waveguide are different than the cross-sectional dimensions of the second waveguide.
7. The arrangement of claim 4 , wherein the second waveguide comprises a second material, and wherein the second material is selected from a group consisting of a second dielectric material, a second semiconductor material, and a metal.
8. The arrangement of claim 1 , wherein the second waveguide has a second effective refractive index, and wherein the second effective refractive index is different than the first effective refractive index.
9. The arrangement of claim 1 , wherein the first, second, and third waveguides have a height of about 200 nanometers to 500 nanometers, wherein the first and the third waveguides have a width of about 200 nanometers to 300 nanometers, wherein the second waveguide has a width of about 250 nanometers to 330 nanometers, wherein the first waveguide is positioned about 150 nanometers to 350 nanometers from the second waveguide, and wherein the third waveguide is positioned about 150 nanometers to 350 nanometers from the second waveguide.
10. An arrangement of waveguides comprising:
a substrate;
a first waveguide having a first effective refractive index and being a linear waveguide having cross-sectional dimensions of less than about 1 micron;
a second waveguide having a second effective refractive index and being a linear waveguide having cross-sectional dimensions of less than about 1 micron; and
a third waveguide having the first effective refractive index and being a linear waveguide having cross-sectional dimensions of less than about 1 micron, the first, the second, and the third waveguides arranged on the substrate, the first, the second, and the third waveguides being substantially parallel over a specified distance, the second waveguide being be positioned between the first waveguide and the third waveguide, the first waveguide being positioned less than about 1 micron from the second waveguide, the third waveguide being positioned less than about 1 micron from the second waveguide, the first waveguide and the third waveguide having substantially the same cross-sectional dimensions, dimensions and positions of the first, the second, and the third waveguides being specified such that when the second effective refractive index changes, a coupling between the first and the third waveguides changes.
11. The arrangement of claim 10 , wherein the first waveguide is positioned less than about 2 microns from the third waveguide.
12. The arrangement of claim 10 , wherein the first waveguide, the second waveguide, and the third waveguide are disposed on the substrate.
13. The arrangement of claim 10 , wherein the first waveguide and the third waveguide comprise a first material, wherein the first material comprises a first dielectric material or a first semiconductor material, wherein the second waveguide comprises a second material, and wherein the second material comprises a second dielectric material or a second semiconductor material.
14. The arrangement of claim 13 , wherein the first material is the same as the second material.
15. The arrangement of claim 13 , wherein the cross-sectional dimensions of the first waveguide and the third waveguide are different than cross-sectional dimensions of the second waveguide.
16. The arrangement of claim 13 , wherein the first material and the second material are different materials.
17. The arrangement of claim 10 , wherein the first, second, and third waveguides have a height of about 200 nanometers to 500 nanometers, wherein the first and the third waveguides have a width of about 200 nanometers to 300 nanometers, wherein the second waveguide has a width of about 250 nanometers to 330 nanometers, wherein the first waveguide is positioned about 150 nanometers to 350 nanometers from the second waveguide, and wherein the third waveguide is positioned about 150 nanometers to 350 nanometers from the second waveguide.
18. The arrangement of claim 10 , further comprising:
a first electrode and a second electrode disposed on the second waveguide.
19. The arrangement of claim 18 , wherein the first electrode and the second electrode are spaced about 150 microns to 450 microns from one another on the second waveguide in a direction of light propagation in the second waveguide.
20. The arrangement of claim 18 , wherein the first electrode and the second electrode comprise a metal selected from a group consisting of gold, platinum, and titanium.