High density optical waveguide using hybrid spiral pattern

1. Apparatus comprising at least one high-density spiral-configured optical waveguide in which an inward-directed spiral arm and an outward-directed spiral arm are coupled together in a central portion of the spiral-configured waveguide, wherein:

the optical waveguide has multiple turns;

the spiral-configured waveguide has an outer region and an inner region;

in the outer region, the arms conform to a spiral of a first type having essentially uniform spacing between adjacent turns;

in the inner region, the arms conform to a spiral of a second type having a curvature that tends toward zero as the central portion is approached; and

each arm asymptotically conforms itself to the first-type spiral in the outer region and to the second-type spiral in the inner region;

wherein for each of the respective arms, a radius r is defined by the relation

r

=

a

⁡

(

1

+

k

θ

)

c

⁢

θ

,

and α represents a constant and k and c are factors selected in combination with a known waveguide length L to define a minimum bend radius.

2. The apparatus of claim 1 , wherein the at least one high-density spiral-configured optical waveguide is a partially-etched silicon rib waveguide.

3. The apparatus of claim 1 , wherein, at an operating wavelength, coupling between the inward-directed spiral arm and the outward-directed spiral arm is effectuated with less than 0.5 dB of bend loss.

4. The apparatus of claim 1 , wherein the type-1 spiral is an Archimedean spiral of the form r=aθ, r represents a radius, θ represents a rotational angle, and a represents a constant.

5. The apparatus of claim 1 , wherein:

the type-1 spiral is an Archimedean spiral of the form r=aθ;

the type-2 spiral is a Fermat spiral of the form r=bθ 1/2 ; and

r represents a radius, θ represents a rotational angle, and a and b represent constants.

6. The apparatus of claim 1 , further comprising at least one phase-control element, wherein:

the at least one phase-control element comprises a thermo-optic phase shifter disposed entirely within the inner region of the at least one high-density spiral-configured optical waveguide; and

the thermo-optic phase shifter is formed of a doped portion of silicon disposed alongside the at least one high-density spiral-configured optical waveguide.

7. The apparatus of claim 1 , formed as a photonic lightwave circuit (PLC) component.

8. The apparatus of claim 1 , wherein the inward-directed spiral arm and the outward-directed spiral arm each have at least eight turns, and wherein the outer region of essentially uniform spacing between adjacent waveguides is reached by the outward-directed spiral arm within six turns spiraling outward from the central portion.

9. The apparatus of claim 8 , wherein the outer region where the spacing between adjacent waveguides is essentially uniform contains at least eight turns of the inward-directed spiral arm and at least eight turns of the outward-directed spiral arm.

10. The apparatus of claim 1 , wherein the at least one high-density spiral-configured optical waveguide is a partially etched silicon rib waveguide, said waveguide has a waveguide density ρ of at least 0.15 μm −1 , and ρ represents waveguide length per unit area of a circumscribing square.

11. The apparatus of claim 1 , wherein:

the at least one high-density spiral-configured optical waveguide is a partially etched silicon rib waveguide;

said waveguide has a location of greatest curvature; and

at said location, said waveguide has a bend radius in the range 35-100 μm.

12. The apparatus of claim 1 , wherein:

the at least one high-density spiral-configured optical waveguide is a fully etched silicon ridge waveguide;

said waveguide has a location of greatest curvature; and

at said location, said waveguide has a bend radius in the range 6-12 μm.

13. The apparatus of claim 1 , constituted as a high-density arrayed waveguide grating (AWG) structure comprising:

one or more input waveguides;

an input free space region;

an output free space region;

a plurality of output waveguides; and

a plurality of the high-density spiral-configured optical waveguides, wherein:

each of the high-density spiral-configured optical waveguides is disposed between the input free space region and the output free space region;

each of the high-density spiral-configured optical waveguides has a length; and

the lengths are stepped up incrementally over the said waveguide plurality.

14. The apparatus of claim 13 , wherein the plurality of high-density spiral-configured optical waveguides comprises at least eight said waveguides arranged in an array.

15. The apparatus of claim 13 , wherein the plurality of high-density spiral-configured optical waveguides comprises at least thirty-two said waveguides arranged in an array.

16. Apparatus comprising at least one high-density spiral-configured optical waveguide in which an inward-directed spiral arm and an outward-directed spiral arm are coupled together in a central portion of the spiral-configured waveguide, wherein:

the optical waveguide has multiple turns;

the spiral-configured waveguide has an outer region and an inner region;

in the outer region, the arms conform to a spiral of a first type having essentially uniform spacing between adjacent turns;

in the inner region, the arms conform to a spiral of a second type having a curvature that tends toward zero as the central portion is approached; and

each arm asymptotically conforms itself to the first-type spiral in the outer region and to the second-type spiral in the inner region;

and wherein the apparatus further comprises a phase-control element disposed entirely within the inner region of the at least one high-density spiral-configured optical waveguide.

17. The apparatus of claim 16 , constituted as a high-density arrayed waveguide grating (AWG) structure comprising:

one or more input waveguides;

an input free space region;

an output free space region;

a plurality of output waveguides; and

a plurality of the high-density spiral-configured optical waveguides, wherein:

each of the high-density spiral-configured optical waveguides is disposed between the input free space region and the output free space region;

each of the high-density spiral-configured optical waveguides has a length; and

the lengths are stepped up incrementally over the said waveguide plurality;

and wherein a respective phase shifter element is centrally disposed entirely within the inner region of each of the high-density spiral-configured optical waveguides.

18. The apparatus of claim 17 , wherein each of the respective phase shifter elements comprises a thermo-optic phase shifter.

19. Apparatus comprising at least one high-density spiral-configured optical waveguide in which an inward-directed spiral arm and an outward-directed spiral arm are coupled together in a central portion of the spiral-configured waveguide, wherein:

the optical waveguide has multiple turns;

the spiral-configured waveguide has an outer region and an inner region;

in the outer region, the arms conform to a spiral of a first type having essentially uniform spacing between adjacent turns;

in the inner region, the arms conform to a spiral of a second type having a curvature that tends toward zero as the central portion is approached; and

each arm asymptotically conforms itself to the first-type spiral in the outer region and to the second-type spiral in the inner region;

and wherein the at least one high-density spiral-configured optical waveguide is a fully etched silicon ridge waveguide, said waveguide has a waveguide density ρ of at least 0.2 μm −1 , and ρ represents waveguide length per unit area of a circumscribing square.