INTERFEROMETER AND METHOD OF DESIGNING AN INTERFEROMETER

• US 20190086610A1
• Filed: 02/24/2017
• Published: 03/21/2019
• Est. Priority Date: 02/25/2016
• Status: Active Grant

• Current Assignee: Oxford University Innovation Limited (University of Oxford)
• Original Assignee: Oxford University Innovation Limited (University of Oxford)
• Inventors: Clements, William, Humphreys, Peter, Metcalf, Benjamin, Kolthammer, Steven, Walmsley, Ian
• Granted Patent: US 10,641,954 B2
• Time in Patent Office: Days
• CPC Class Codes: G02B 6/12007 forming wavelength selective elements, e.g. multiplexer, demultiplexer
• CPC Class Codes: G02B 6/29344 operating by modal interference or beating, i.e. of transverse modes, e.g. zero-gap directional coupler, MMI
• CPC Class Codes: G02B 6/29355 Cascade arrangement of interferometers
• CPC Class Codes: G02B 6/29395 configurable, e.g. tunable or reconfigurable switching G02B6/35
• CPC Class Codes: G02F 1/3136 of interferometric switch type
• CPC Class Codes: G06F 30/00 Computer-aided design [CAD]
• CPC Class Codes: H04B 10/2581 Multimode transmission
• CPC Class Codes: H04B 10/70 Photonic quantum communication

Abstract

A universal interferometer (100) for coupling modes of electromagnetic radiation according to a transformation has N inputs and N outputs for inputting and outputting N modes of electromagnetic radiation into and from the interferometer. Waveguides (101, 102, 103, 104, 105) pass through the interferometer to connect the N inputs to the N outputs and to carry the N modes of electromagnetic radiation. The waveguides provide crossing points between pairs of waveguides and a reconfigurable beam splitter (107) implements a reconfigurable reflectivity and a reconfigurable phase shift at each crossing point. The waveguides and crossing points are arranged such that each of the N modes of electromagnetic radiation is capable of coupling with each of the other modes of electromagnetic radiation at respective reconfigurable beam splitters. The couplings between modes at the reconfigurable beam splitters are configured such that the interferometer implements a transformation of the N modes between the N inputs and the N outputs.

Claims

1. A universal interferometer for coupling a plurality of modes of electromagnetic radiation according to a transformation comprising:

N inputs for inputting N modes of electromagnetic radiation into the interferometer;

N outputs for outputting N modes of electromagnetic radiation from the interferometer; and

a plurality of waveguides arranged to pass through the interferometer to connect the N inputs to the N outputs and for carrying the N modes of electromagnetic radiation through the interferometer;

wherein;

N is a natural number;

the plurality of waveguides are arranged to provide a plurality of crossing points between pairs of the plurality of waveguides, wherein a reconfigurable beam splitter arranged to implement a reconfigurable reflectivity and a reconfigurable phase shift is arranged at each of the plurality of crossing points, such that at each reconfigurable beam splitter the two modes of electromagnetic radiation carried by the two respective waveguides to the crossing point are capable of coupling with each other with a reconfigurable reflection coefficient and a reconfigurable phase shift coefficient, wherein the plurality of waveguides and the plurality of crossing points are arranged such that each of the N modes of electromagnetic radiation is capable of coupling with each of the other modes of electromagnetic radiation at respective reconfigurable beam splitters; and

the plurality of waveguides are arranged such that the plurality of crossing points are arranged into N groups along the plurality of waveguides from the inputs to the outputs through the interferometer, wherein each group contains the maximum number of possible crossing points between pairs of waveguides, and wherein the crossing points in each group involve pairs of adjacent waveguides whose paths were not crossed in the previous group of crossing points; and

the couplings between the pairs of modes at each of the reconfigurable beam splitters are configured such that the interferometer implements a transformation of the N modes between the N inputs and the N outputs.

2. An interferometer as claimed in claim 1, wherein the interferometer comprises an integrated circuit, and wherein the plurality of waveguides and the plurality of crossing points are arranged in the integrated circuit.

3. An interferometer as claimed in claim 1, wherein the modes of electromagnetic radiation each have a wavelength of between 700 nm and 1600 nm.

4. An interferometer as claimed in claim 1, wherein N is greater than 3.

5. An interferometer as claimed in claim 1, wherein the couplings between the pairs of modes at each of the reconfigurable beam splitters are determined by:

receiving a unitary matrix describing a desired transformation to be performed by the interferometer;

operating on the unitary matrix with a plurality of transformation matrices to decompose the unitary matrix into a diagonal matrix, wherein the transformation matrices used to decompose the unitary matrix each represent the coupling between a pair of modes at a crossing point of a pair of waveguides, and wherein the transformation matrices are arranged to operate on the unitary matrix in an order that matches a sequence in which the crossing points in the interferometer may be arranged; and

determining, using the transformation matrices, the coupling for the pair of modes at each of the plurality of crossing points.

6. An interferometer as claimed in claim 5, wherein each of the transformation matrices comprises one or more elements that are representative of a reflectivity and a phase shift of the coupling between the pair of modes at the respective crossing point, and the couplings between the pairs of modes at each of the reconfigurable beam splitters are further determined by:

determining a reflectivity coefficient and a phase shift coefficient from each of the transformation matrices; and

determining, using the reflectivity coefficient and the phase shift coefficient, the reflectivity and phase shift for the coupling of each of the pairs of modes at the respective crossing points.

7. An interferometer as claimed in claim 6, wherein a beam splitter is arranged at each of one or more of the crossing points, and each beam splitter is configured to couple the respective pair of modes according to the determined reflectivity coefficient and the determined phase shift coefficient at each of the plurality of crossing points.

8. An interferometer as claimed in claim 7, wherein each of the beam splitters is adjustable.

9. An interferometer as claimed in claim 5, wherein the couplings between the pairs of modes at each of the reconfigurable beam splitters are further determined by defining a unitary matrix describing the desired transformation to be performed by the interferometer.

10. An interferometer as claimed in claim 5, wherein the unitary matrix is defined by an N×

N unitary matrix that describes the transformation of the annihilation operators of the N modes of the interferometer that the unitary matrix represents, wherein the annihilation operators and the unitary matrix satisfy the equation;

â

_out=Û

â

_in, where â

_out=(â

_out,1, â

_out,2, . . . , â

_out,N) and â

_in=(â

_in,1, â

_in,2, . . . , â

_in,N) are column vectors representing the annihilation operators of all the N input modes and all the N output modes respectively.

11. An interferometer as claimed in claim 5, wherein each transformation matrix is defined as an N×

N matrix T_m,n (θ

, ϕ

), which is identity except for the (m,m), (m,n), (n,m) and (n,n) elements, that form a 2×

2 sub-matrix that performs the transformation;

12. An interferometer as claimed in claim 11, wherein the unitary matrix Û

is decomposed into a product of a plurality of T_m,n matrices that satisfy

13. An interferometer as claimed in claim 5, wherein the couplings between the pairs of modes at each of the reconfigurable beam splitters are further determined by operating on the unitary matrix with the plurality of transformation matrices, wherein the operation of each transformation matrix on the unitary matrix nulls a respective different non-diagonal element of the unitary matrix.

14. An interferometer as claimed in claim 5, wherein the couplings between the pairs of modes at each of the reconfigurable beam splitters are further determined by operating on the unitary matrix with the plurality of transformation matrices, wherein the operation of each transformation matrix on the unitary matrix nulls the elements of the lower or upper triangle of the unitary matrix to decompose the unitary matrix.

15. An interferometer as claimed in claim 14, wherein the elements of the lower or upper triangle of the unitary matrix are nulled in an order such that a triangle of increasing size of nulled elements is formed until the whole of the lower or upper triangle has been nulled.

16. An interferometer as claimed in claim 13, wherein the initial element nulled is the bottom left hand corner element in the lower triangle or the top right hand corner element in the upper triangle of the unitary matrix.

17. An interferometer as claimed in claim 13, wherein when the initial element nulled is the bottom left hand corner element in the lower triangle of the unitary matrix, the order in which the elements of the unitary matrix are nulled, for an N×

N unitary matrix Û

is;

18. An interferometer as claimed in claim 13, wherein when the initial element nulled is the bottom left hand corner element in the lower triangle of the unitary matrix, the order in which the transformation matrices are applied to the unitary matrix, for an N×

N unitary matrix Û

is;

19. A method of designing an interferometer for coupling a plurality of modes of electromagnetic radiation, the method comprising:

for an interferometer comprising;

N inputs for inputting N modes of electromagnetic radiation into the interferometer,

N outputs for outputting N modes of electromagnetic radiation from the interferometer, and

a plurality of waveguides arranged to pass through the interferometer to connect the N inputs to the N outputs and for carrying the N modes of electromagnetic radiation through the interferometer,

wherein;

N is a natural number,

the plurality of waveguides are arranged to provide a plurality of crossing points between pairs of the plurality of waveguides such that at each crossing point the two modes of electromagnetic radiation carried by the two respective waveguides are capable of coupling with each other, wherein the plurality of waveguides and the plurality of crossing points are arranged such that each of the N modes of electromagnetic radiation is capable of coupling with each of the other modes of electromagnetic radiation at respective crossing points, and

the plurality of waveguides are arranged such that the plurality of crossing points are arranged into N groups along the plurality of waveguides from the inputs to the outputs through the interferometer, wherein each group contains the maximum number of possible crossing points between pairs of waveguides, and wherein the crossing points in each group involve pairs of adjacent waveguides whose paths were not crossed in the previous group of crossing points;

receiving a unitary matrix describing a desired transformation to be performed by the interferometer;

operating on the unitary matrix with a plurality of transformation matrices to decompose the unitary matrix into a diagonal matrix, wherein the transformation matrices used to decompose the unitary matrix each represent the coupling between a pair of modes at a crossing point of a pair of waveguides, and wherein the transformation matrices are arranged to operate on the unitary matrix in an order that matches a sequence in which the crossing points in the interferometer may be arranged;

determining, using the transformation matrices, the coupling for the pair of modes at each of the plurality of crossing points for use in designing the interferometer.

35. A method as claimed in claim 19, comprising outputting the determined couplings for the pairs of modes at each of the plurality of crossing points.

36. A method as claimed in claim 19, comprising designing and manufacturing the interferometer using the determined couplings for the pair of modes at each of the plurality of crossing points.

20-34. -34. (canceled)

37. A non-transient computer readable storage medium storing computer software code which when executing on a data processing system performs a method of designing an interferometer for coupling a plurality of modes of electromagnetic radiation, the method comprising:

for an interferometer comprising;

N inputs for inputting N modes of electromagnetic radiation into the interferometer,

N outputs for outputting N modes of electromagnetic radiation from the interferometer, and

a plurality of waveguides arranged to pass through the interferometer to connect the N inputs to the N outputs and for carrying the N modes of electromagnetic radiation through the interferometer,

wherein;

N is a natural number,

the plurality of waveguides are arranged to provide a plurality of crossing points between pairs of the plurality of waveguides such that at each crossing point the two modes of electromagnetic radiation carried by the two respective waveguides are capable of coupling with each other, wherein the plurality of waveguides and the plurality of crossing points are arranged such that each of the N modes of electromagnetic radiation is capable of coupling with each of the other modes of electromagnetic radiation at respective crossing points, and

the plurality of waveguides are arranged such that the plurality of crossing points are arranged into N groups along the plurality of waveguides from the inputs to the outputs through the interferometer, wherein each group contains the maximum number of possible crossing points between pairs of waveguides, and wherein the crossing points in each group involve pairs of adjacent waveguides whose paths were not crossed in the previous group of crossing points;

receiving a unitary matrix describing a desired transformation to be performed by the interferometer;

operating on the unitary matrix with a plurality of transformation matrices to decompose the unitary matrix into a diagonal matrix, wherein the transformation matrices used to decompose the unitary matrix each represent the coupling between a pair of modes at a crossing point of a pair of waveguides, and wherein the transformation matrices are arranged to operate on the unitary matrix in an order that matches a sequence in which the crossing points in the interferometer may be arranged;

determining, using the transformation matrices, the coupling for the pair of modes at each of the plurality of crossing points for use in designing the interferometer.

38-40. -40. (canceled)

41. A method of determining the physical couplings between a plurality of modes in a system, the method comprising:

for a system comprising;

N modes,

a plurality of interaction points at which pairs of the plurality of modes couple with each other,

wherein;

N is a natural number,

the plurality of interaction points are arranged such that each of the N modes is capable of coupling with each of the other modes respective interaction points, and

the plurality of interaction points are arranged into N groups, wherein each group contains the maximum number of possible interactions points between pairs of modes, and wherein the interaction points in each group involve pairs of adjacent modes that were not interacted in the previous group of interaction points;

receiving a unitary matrix describing a desired overall transformation to be performed by the system;

operating on the unitary matrix with a plurality of transformation matrices to decompose the unitary matrix into a diagonal matrix, wherein the transformation matrices used to decompose the unitary matrix each represent the coupling between a pair of modes at an interaction point, and wherein the transformation matrices are arranged to operate on the unitary matrix in an order that matches a sequence in which the interaction points in the system may be arranged; and

determining, using the transformation matrices, the coupling for the pair of modes at each of the plurality of interaction points for use in designing the system.