Interferometer and method of designing an interferometer

• US 10,641,954 B2
• Filed: 02/24/2017
• Issued: 05/05/2020
• 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
• Primary Examiner(s): Kianni, Kaveh C
• Application Number:
  US16/080,037
• Publication Number:
  US 20190086610A1
• Time in Patent Office: 1,166 Days
• Field of Search: 385 14
• 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, the 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;

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; and

a plurality of reconfigurable beam splitters, wherein each reconfigurable beam splitter of the plurality of reconfigurable beam splitters is arranged to implement a reconfigurable reflectivity and a reconfigurable phase shift;

wherein;

N is a natural number;

the plurality of waveguides is arranged to provide a plurality of crossing points between pairs of adjacent waveguides of the plurality of waveguides,

each crossing point of the plurality of crossing points comprises a reconfigurable beam splitter of the plurality of reconfigurable beam splitters,

wherein each reconfigurable beam splitter of the plurality of reconfigurable beam splitters permits two modes of electromagnetic radiation carried by the respective pair of adjacent waveguides to the crossing point to be coupled 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 mode of the N modes of electromagnetic radiation is capable of coupling with each of the other modes of the N modes of electromagnetic radiation at respective reconfigurable beam splitters of the plurality of reconfigurable beam splitters; and

the plurality of waveguides is arranged such that the plurality of crossing points are arranged into N sequential groups of crossing points along the plurality of waveguides from the inputs to the outputs through the interferometer,

wherein each group of the N sequential groups of crossing points contains the maximum possible number of crossing points between pairs of adjacent waveguides, and

wherein the crossing points in each group of the N sequential groups of crossing points involve pairs of adjacent waveguides that were not crossed in the immediately previous group of crossing points; and

couplings between pairs of modes at each reconfigurable beam splitter 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 each mode of the N modes of electromagnetic radiation has 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 pairs of modes at each reconfigurable beam splitter of the plurality of 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 each transformation matrix of the plurality of transformation matrices used to decompose the unitary matrix represents the coupling between a pair of modes at a crossing point of a pair of adjacent 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 of electromagnetic radiation at each crossing point of the plurality of crossing points.

6. An interferometer as claimed in claim 5, wherein each transformation matrix of the plurality of 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 of electromagnetic radiation at the respective crossing point, and the couplings between the pairs of modes of electromagnetic radiation at each of the reconfigurable beam splitters are further determined by:

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

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

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

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

9. An interferometer as claimed in claim 5, wherein the couplings between pairs of modes of electromagnetic radiation at each reconfigurable beam splitter 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 annihilation operators of the N modes of electromagnetic radiation of the interferometer that the unitary matrix represents, wherein the annihilation operators and the unitary matrix satisfy the equation;

a_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 of electromagnetic radiation and all the N output modes of electromagnetic radiation respectively.

11. An interferometer as claimed in claim 5, wherein each transformation matrix of the plurality of transformation matrices 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 forma 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 of electromagnetic radiation at each reconfigurable beam splitter 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 pairs of modes of electromagnetic radiation at each reconfigurable beam splitter 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 a 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 a 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;