Nested waveguide fan-out structure and methods for forming the same

A device structure comprising an optical beam splitter, wherein the optical beam splitter comprises a multi-stage nested network of waveguide bifurcation branches that comprise, for each of at least two consecutive positive integers i that includes 1 and 2:

• (2i−1)-th-stage waveguide bifurcation branches each comprising a pair of (2i−1)-th-stage waveguide segments, wherein each pair of (2i−1)-th-stage waveguide segments comprises a (2i−1)-th common end and a pair of (2i−1)-th split ends and a pair of (2i−1)-th interconnection portions connecting the (2i−1)-th common end to a respective (2i−1)-th split end within the pair of (2i−1)-th split ends, wherein each (2i−1)-th common end of the optical beam splitter points toward a first widthwise direction of the optical beam splitter, and each (2i−1)-th interconnection portion of the optical beam splitter comprises a respective (2i−1)-th outer convex sidewall segment that generally faces a second widthwise direction that is an opposite direction of the first widthwise direction;
• and
• 2i-th-stage waveguide bifurcation branches each comprising a pair of 2i-th-stage waveguide segments, wherein each pair of 2i-th-stage waveguide segments comprises a 2i-th common end and a pair of 2i-th split ends and a pair of 2i-th interconnection portions connecting the 2i-th common end to a respective 2i-th split end within the pair of 2i-th split ends, wherein each of the 2i-th split ends of the optical beam splitter is connected to a respective (2i−1)-th common end of the (2i−1)-th-stage waveguide bifurcation branches, wherein each 2i-th common end and each 2i-th split end of the optical beam splitter point toward the second widthwise direction of the optical beam splitter.

A method of forming a device structure, the method comprising:

• forming a waveguide material layer over a dielectric material layer;
• and
• patterning the waveguide material layer into a multi-stage nested network of waveguide bifurcation branches, which comprises:
• first-stage waveguide bifurcation branches each comprising a pair of first-stage waveguide segments, wherein each pair of first-stage waveguide segments comprises a first common end and a pair of first split ends and a pair of first interconnection portions connecting the first common end to a respective first split end within the pair of first split ends, wherein each first common end and each first split end of the optical beam splitter point to a first widthwise direction of the optical beam splitter, and each first interconnection portion of the optical beam splitter comprises a respective first outer convex sidewall segment that generally faces a second widthwise direction that is an opposite direction of the first widthwise direction;
• and
• second-stage waveguide bifurcation branches each comprising a pair of second-stage waveguide segments, wherein each pair of second-stage waveguide segments comprises a second common end and a pair of second split ends and a pair of second interconnection portions connecting the second common end to a respective second split end within the pair of second split ends, wherein each of the second split ends of the optical beam splitter is connected to a respective first common end of the first-stage waveguide bifurcation branches, wherein each second common end and each second split end of the optical beam splitter point to the second widthwise direction of the optical beam splitter.