Optimized 2×2 3dB multi-mode interference coupler

1. A 2×2 multi-mode interference coupler, comprising:

a multi-mode interference region having a length L MMI and having a plurality of segments having widths W 1 , . . . , W N , . . . , W 1 , where N in an integer greater than one, with at least five of said widths W 1 to W 5 between the first end and the central distance L MMI /2 being different one from the other, said widths varying in a symmetric pattern relative to the central distance L MMI /2 along said length; and

four ports p1, p2, p3 and p4, two of said ports in optical communication with said multi-mode interference region at a first end thereof and spaced apart by a distance Dgap and the other two of said ports in optical communication with said multi-mode interference region at a second end thereof, at least one of said four ports configured as an input port and two others of said four ports configured as output ports.

2. The 2×2 multi-mode interference coupler of claim 1 , wherein each of said two of said ports in optical communication with said multi-mode interference region at the first end thereof is connected to said multi-mode interference region by a taper connector having a length L taper .

3. The 2×2 multi-mode interference coupler of claim 2 , wherein said length L taper is tuned to reduce optical loss.

4. The 2×2 multi-mode interference coupler of claim 1 , configured to be operable in a wavelength in a band selected from an O band, an E band, an S band, a C band, an L band, and a U band.

5. A plurality of the 2×2 multi-mode interference couplers of claim 1 in cascade, wherein one of said output ports of a first of said plurality of the 2×2 multi-mode interference couplers is connected in serial connection with one of said input ports of a second of said plurality of the 2×2 multi-mode interference couplers.

6. The 2×2 multi-mode interference coupler of claim 1 , wherein the widths W 1 to W N are at equally spaced locations along the length L MMI .

7. The 2×2 multi-mode interference coupler of claim 1 , wherein the multi-mode interference region is symmetrical about W 5 , whereby the 2×2 multi-mode interference coupler works the same way in either direction.

8. The 2×2 multi-mode interference coupler of claim 1 , wherein W 2 and W 4 are greater than W 3 and W 5 .

9. An N×M multi-mode interference coupler, comprising:

a multi-mode interference region having a length L MMI and having a plurality of segments having widths W 1 , . . . , W N , . . . , W 1 , where N in an integer greater than one, with at least five of said widths W 1 to W 5 between the first end and the central distance L MMI /2 being different one from the other, said widths varying in a symmetric pattern relative to the central distance L MMI /2 along said length; and

N×M ports, N of said ports in optical communication with said multi-mode interference region at a first end thereof and spaced apart by a distance Dgap and the other M of said ports in optical communication with said multi-mode interference region at a second end thereof, at least one of said N×M ports configured as an input port and two or more of said N×M ports configured as output ports, where N and M are positive integers each greater than zero.

10. The N×M multi-mode interference coupler of claim 9 , wherein the widths W 1 to W N are at equally spaced locations along the length L MMI .

11. The N×M multi-mode interference coupler of claim 9 , wherein the multi-mode interference region is symmetrical about W 5 , whereby the N×M multi-mode interference coupler works the same way in either direction.

12. The N×M multi-mode interference coupler of claim 9 , wherein W 2 and W 4 are greater than W 3 and W 5 .

13. A method of making a 2×2 multi-mode interference coupler, comprising the steps of:

providing a multi-mode interference region having a length L MMI and having a plurality of segments having widths W 1 , . . . , W N , . . . , W 1 , where N in an integer greater than one, with at least five of said widths W 1 to W 5 between the first end and the central distance L MMI /2 being different one from the other, said widths varying in a symmetric pattern relative to the central distance L MMI /2 along said length; and

providing four ports p1, p2, p3 and p4, two of said ports in optical communication with said multi-mode interference region at a first end thereof and spaced apart by a distance Dgap and the other two of said ports in optical communication with said multi-mode interference region at a second end thereof, at least one of said four ports configured as an input port and two others of said four ports configured as output ports;

said widths W 1 , . . . , W N calculated by application of the particle swarm optimization algorithm.

14. The method of making a 2×2 multi-mode interference coupler of claim 13 , further comprising the step of providing a taper connector having a length L taper to connect each of said two of said ports to said first end of said multi-mode interference region.

15. The method of making a 2×2 multi-mode interference coupler of claim 13 , wherein said 2×2 multi-mode interference coupler is configured to be operable in a wavelength in a band selected from an O band, an E band, an S band, a C band, an L band, and a U band.

16. A method of using a 2×2 multi-mode interference coupler, comprising the steps of:

providing a multi-mode interference region having a length L MMI and having a plurality of segments having widths W 1 , . . . , W N , . . . , W 1 , where N is an integer greater than one, with at least five of said widths W 1 to W 5 between the first end and the central distance L MMI /2 being different one from the other, said widths varying in a symmetric pattern relative to the central distance L MMI /2 along said length; and

providing four ports p1, p2, p3 and p4, two of said ports in optical communication with said multi-mode interference region at a first end thereof and spaced apart by a distance Dgap and the other two of said ports in optical communication with said multi-mode interference region at a second end thereof, at least one of said four ports configured as an input port and two others of said four ports configured as output ports;

said widths W 1 , . . . , W N calculated by application of the particle swarm optimization algorithm;

applying an input optical signal to one of said four ports configured as an input port; and

recovering two optical output signals, one each at each of said two others of said four ports configured as output ports, at least one of said two optical output signals differing from said input optical signal at least one of a mode and a phase.

17. The method of using a 2×2 multi-mode interference coupler of claim 16 , wherein said 2×2 multi-mode interference coupler is configured to be operable in a wavelength in a band selected from an O band, an E band, an S band, a C band, an L band, and a U band.