Curved graded-index waveguides and methods of making the same

1. A method of making a curved polymeric waveguide having a graded refractive index profile with a refractive index spatially varying through a thickness of the polymeric waveguide, the method comprising:

forming a stacked structure comprising at least a layer of a first resin and a layer of a second resin, the first resin having a first refractive index when polymerized and the second resin having a second refractive index when polymerized that is different than the first refractive index;

allowing the first resin and the second resin to diffuse into one another to form a composite resin structure in which a ratio of the second resin to the first resin in the composite resin varies in a thickness dimension of the stacked structure;

polymerizing the composite resin structure; and

forming the polymerized composite resin structure into a pre-defined curved shape;

whereby the curved polymeric waveguide has a refractive index monotonically decreasing through a thickness thereof from a concave surface of the curved polymeric waveguide to a convex surface of the curved polymeric waveguide.

2. The method of claim 1 , wherein forming the stacked structure comprises:

flowing the first resin into a first inlet of a plurality of inlets at a first end of a diffusion channel, the diffusion channel including an outlet at a second end opposite to the first end and separated from the plurality of inlets by a channel length; and

flowing the second resin into a second inlet of the plurality of inlets, the flowing of the second resin being directed along a first periphery of the first resin,

wherein the first resin and the second resin diffuse into one another over the channel length between the plurality of inlets and the outlet.

3. The method of claim 1 , wherein the first resin and the second resin are selected from a group consisting of: a polyacrylate, a polyurethane, a polysilicone, a polyester, a polyolefin, a polyamide, a polycarbonate, copolymers thereof, and mixtures thereof.

4. The method of claim 1 , wherein the pre-defined curved shape includes a portion of a sphere.

5. The method of claim 1 , wherein the pre-defined curved shape includes a portion of a cylinder.

6. The method of claim 1 , further comprising forming a layer of a third resin along a second periphery of the first resin that is opposite the first periphery, such that the first resin is disposed between the second resin and the third resin in the stacked structure, the third resin having a third refractive index when polymerized that is different than the first refractive index.

7. The method of claim 6 , wherein the first refractive index is higher than the third refractive index, and the second refractive index is lower than the first refractive index.

8. The method of claim 7 , wherein the first refractive index is lower than or equal to the third refractive index.

9. A method of making a curved waveguide having a graded refractive index profile with a refractive index spatially varying through a thickness of the curved waveguide, the method comprising:

providing a substrate in a deposition chamber;

introducing a monomer containing vapor into the deposition chamber and depositing material from the monomer containing vapor onto a surface of the substrate over a period of time;

controllably varying a ratio of an amount of a first monomer to an amount of a second monomer in the monomer containing vapor over the period of time, such that a-composition of the material that is deposited on the substrate changes over the period of time,

wherein the first monomer has a first refractive index when polymerized, and the second monomer has a second refractive index when polymerized, the second refractive index being different than the first refractive index; and

polymerizing the material deposited on the substrate;

whereby the curved waveguide has a refractive index monotonically decreasing through a thickness thereof from a concave surface of the curved waveguide to a convex surface of the curved waveguide.

10. The method of claim 9 , wherein the surface of the substrate has a curved shape that includes a portion of a sphere.

11. The method of claim 9 , wherein the surface of the substrate has a curved shape that includes a portion of a cylinder.

12. The method of claim 9 , wherein the monomer containing vapor comprises an initiator.

13. The method of claim 12 , wherein depositing material from the monomer containing vapor onto the substrate further comprises initiating the initiator using an actinic source to provide energy for initiating the initiator to form radicals.

14. The method of claim 12 , wherein depositing material from the monomer containing vapor onto the substrate further comprises initiating the initiator using a thermal source to provide energy for initiating the initiator to form radicals.

15. The method of claim 9 , wherein the surface of the substrate has a convex shape, and wherein the ratio of the amount of the first monomer to the amount of the second monomer in the monomer containing vapor decreases over the period of time.

16. The method of claim 15 , wherein the first refractive index is greater than the second refractive index.