Photonic waveguide mesh arrangements and field programmable photonic gate array (FPPGA) comprising the same

Abstract

The present invention relates to a photonic waveguide mesh arrangement for a field programmable photonic gate array (FPPGA) that comprises a plurality of hexagonal or quadrangular cells and a plurality of defective cells or a plurality of divided cells. The length of the sides of the defective cells or the divided cells is greater than or less than L.

Description

[0001] PHOTONIC WAVEGUIDE MESH ARRANGEMENTS AND FIELD PROGRAMMABLE PHOTONIC GATE ARRAY (FPPGA) COMPRISING THE SAME

[0002] DESCRIPTION

[0003] OBJECT OF THE INVENTION

[0004] The invention relates to the field of integrated circuits and, more particularly, to the field of programmable integrated photonics (PIP).

[0005] An object of the invention is photonic waveguide mesh arrangements for improving the properties of a field-programmable photonic gate array (FPPGA).

[0006] Another object of the invention is a field-programmable photonic gate array (FPPGA) comprising the photonic waveguide mesh arrangements.

[0007] BACKGROUND OF THE INVENTION

[0008] Programmable Integrated Photonics (PIP) is a new emerging paradigm that aims to design common configurations of integrated optical hardware resources, capable of implementing an unlimited variety of functionalities through appropriate programming.

[0009] A field-programmable photonic gate array (FPPGA) has recently been introduced into the state of the art.

[0010] The FPPGA has a similar logic to the FPGA in electronics; that is, common hardware is designed to provide various resources that can be used to implement different functionalities programmatically. However, the FPPGA differs from the FPGA in that it does not perform digital logic operations, but rather exploits optical interference to perform very high-speed analog operations that affect the phase and amplitudes of optical signals in a controlled environment.

[0011] Figure 1 shows the overall design of the FPPGA device. A detailed description of the technology stack and the programmable silicon photonic core is also shown in Figure 1.

[0012] The FPPGA has a programmable photonic core driven and monitored by RF control and electronics, optical ports, and RF input / output ports. Software algorithms and programming layers give the user access to the photonic functionality.

[0013] However, the typical achievable length and propagation delay in a unit cell of a programmable photonic waveguide array of an FFPGA are fixed and limit the flexibility in the spectral and time domain responses of the circuits that can be implemented.

[0014] DESCRIPTION OF THE INVENTION

[0015] An FFPGA has a programmable photonic waveguide mesh. The photonic waveguide mesh has a regular, periodic geometry, formed by replicated unit cells.

[0016] Typically, these cells take the form of rectangles or hexagons, where each side of the cell is formed by two integrated waveguides connected by a balanced Mach-Zehnder interferometer (MZI). This can be operated by an output control signal as a crossbar switch or as a variable coupler with independent power division ratio and phase shifting. Additional elements of the photonic core are the high-performance blocks (HPBs), specific circuits that cannot be incorporated into the mesh, such as sources, modulators, and detectors.

[0017] A typical cell that can be achieved in silicon photonics has a side length L sabout 450 mm providing a propagation delay T s of about 11.5 psec. These values ​​are fixed and limit the flexibility in the spectral and time domain responses of the circuits that can be implemented. Therefore, the present invention is directed to developing and demonstrating solutions that overcome the limited flexibility in spectral period and sampling time values ​​that FPPGAs can provide by providing a photonic waveguide mesh arrangement for implementing the photonic core that overcomes such limitations and that can be readily incorporated into existing mesh designs.

[0018] Therefore, the proposed solution consists of embedding defective cells in a uniform 2D hexagonal or rectangular waveguide mesh. These defective cells are compatible and easily integrated into the uniform waveguide mesh.

[0019] The present invention relates to photonic waveguide mesh arrays incorporating defective cells. Four different approaches are defined.

[0020] In a first approach, the photonic waveguide mesh arrangement of the invention comprises a plurality of hexagonal cells and a plurality of defective cells.

[0021] Hexagonal cells comprise two right sides of length L, one top side of length L, one bottom side of length L, and two left sides of length L.

[0022] The defective cells comprise two right sides of length L each parallel to each of the two right sides of the hexagonal cells or to each of the two left sides of the hexagonal cells, an upper side parallel to the upper side of the hexagonal cells, a lower side parallel to the lower side of the hexagonal cells and two left sides of length L each parallel to each of the two right sides of the hexagonal cells or to each of the two left sides of the hexagonal cells.

[0023] In defective cells, the length of the upper side and lower side of the defective cells could be greater or less than L, thus solving the problem of spectral limitation.

[0024] The inclusion of defective cells solves the problem of spectral period limitation by exploiting the Vernier effect. The individual cavities in uniform and defective cells have slightly different spectral periods, or free spectral range. When coupled, only the resonances common to both cavities are enabled, allowing the spectral period to be extended to a value given by:

[0025] FSR ± • FSR2

[0026] FSR T =

[0027] \FSR1- FSR2\

[0028] The defective cells of the photonic waveguide mesh arrangement of the invention could be connected to the hexagonal cells, could be connected to each other, or could be connected to both hexagonal cells and defective cells.

[0029] In preferred embodiments, the defective cells are connected to each other forming at least one row or at least one column.

[0030] In such a case, a row or column of defective cells could be connected to a row or column of hexagonal cells or to another row or column of defective cells.

[0031] Additionally, one or more rows or columns of defective cells could periodically connect to one or more rows or columns of hexagonal cells.

[0032] The defective cells in each of the rows or columns of defective cells could be defective cells with the length of the top and bottom sides greater than L or with the length of the top and bottom sides less than L.

[0033] Additionally, defective cells in at least one row or column of defective cells could have:

[0034] - the two right sides parallel to the two left sides of the hexagonal cells; and

[0035] - the two left sides parallel to the two right sides of the hexagonal cells, thus forming an hourglass shape.

[0036] In such cases, the row or column of defective cells could be connected to a row or column of hexagonal cells or a row or column of defective cells.

[0037] In a second approach, the photonic waveguide mesh arrangement for a field-programmable photonic gate array (FPPGA) of the invention could comprise:

[0038] - a plurality of quadrangular cells comprising two lateral sides of length L, an upper side of length L and a lower side of length L; and

[0039] - a plurality of defective cells comprising two lateral sides of length L parallel to the lateral sides of the quadrangular cells, an upper side and a lower side parallel to the upper side and a lower side of the quadrangular cells wherein the length of the upper side and the lower side of the defective cells could be greater or less than L, thus forming a rectangular shape.

[0040] As explained above, in this case, the defective cells could also be connected to each other, forming at least one row or at least one column.

[0041] Rows or columns of defective cells could be connected to a row or column of quadrangular cells or to another row or column of defective cells.

[0042] In a third approach, the photonic waveguide mesh arrangement of the invention comprises:

[0043] - a plurality of hexagonal cells; and

[0044] - a plurality of divided hexagonal cells comprising six sides of length L and six vertices, wherein the sides connect consecutive vertices.

[0045] In this approach, the divided hexagonal cells further comprise one or more internal edges connecting non-consecutive vertices.

[0046] For example, split hexagonal cells may comprise an internal edge connecting two non-consecutive vertices, forming a triangle and a pentagon, or two quadrilaterals. Alternatively, split hexagonal cells may comprise two internal edges that do not intersect. In this case, each internal edge connects two non-consecutive vertices, forming two triangles and one quadrilateral.

[0047] In this approach, the inner edge causes the perimeter of the divided hexagonal cells to vary. The divided hexagonal cell functions as two or three different cells, and therefore the total perimeter is the sum of the perimeters of each of the different cells. Consequently, each inner edge increases the perimeter of the divided hexagonal cell by twice the length of that inner edge.

[0048] The split hexagonal cells could be connected to the hexagonal cells or to each other at different positions, so that each position results in a different free spectral range value.

[0049] In a fourth approach, the photonic waveguide mesh arrangement comprises:

[0050] - a plurality of quadrangular cells; and

[0051] - one or more divided quadrangular cells comprising four sides of length L and four vertices, where the sides connect consecutive vertices.

[0052] In this approach, the divided quad cells further comprise an internal edge that connects non-consecutive vertices.

[0053] In this approach, the inner edge also changes the perimeter of the divided quadrangular cells. The divided quadrangular cell functions as two triangular cells, and therefore the total perimeter is the sum of the perimeters of each of the triangular cells. Consequently, the inner edge increases the perimeter of the divided quadrangular cell by a value equal to (2^2)L.

[0054] Preferably, in the photonic waveguide mesh arrangements of the invention, each side and each inner side of the hexagonal cells, defective cells and split cells comprises two integrated waveguides connected by means of a balanced Mach-Zehnder interferometer (MZI).

[0055] The invention also relates to a field-programmable photonic gate array (FPPGA) comprising the described photonic waveguide mesh arrangements.

[0056] DESCRIPTION OF THE DRAWINGS

[0057] To complement the description being made and in order to help better understand the characteristics of the invention, according to a preferred practical example of its realization, said description is accompanied, as an integral part thereof, by a set of drawings where, for illustrative and non-limiting purposes, the following has been represented:

[0058] Figure 1 shows an example of a field-programmable photonic gate array (FPPGA) according to the invention.

[0059] Figure 2 shows a detail of a photonic core of the field-programmable photonic gate array (FPPGA) shown in Figure 1.

[0060] Figure 3 shows an example of a first preferred embodiment of the invention in which multiple different defective cells are connected to multiple quadrangular cells.

[0061] Figure 4 shows an example of a first preferred embodiment of the invention in which multiple rows of defective cells are connected to a row of quadrangular cells.

[0062] Figure 5 shows an example of a second preferred embodiment of the invention in which a first defective cell is connected to a hexagonal cell.

[0063] Figure 6 shows an example of a second preferred embodiment of the invention in which a second defective cell is connected to a hexagonal cell.

[0064] Figure 7 shows an example of a second preferred embodiment of the invention, in which a row of defective cells is connected to multiple rows of hexagonal cells. Figure 8 shows an example of a second preferred embodiment of the invention, in which multiple rows of defective cells are connected to multiple rows of hexagonal cells in a periodic manner.

[0065] Figure 9 shows an example of a second preferred embodiment of the invention in which multiple rows of defective cells are connected to each other, forming a first group, and said first group is connected to multiple rows of hexagonal cells, forming a second group.

[0066] Figure 10 shows an example of a second preferred embodiment of the invention in which multiple rows of different defective cells are connected to multiple rows of hexagonal cells.

[0067] Figure 1 1. Shows an example of a second preferred embodiment of the invention in which a first type of hourglass-shaped defect cell is connected to a hexagonal cell.

[0068] Figure 12 shows an example of a second preferred embodiment of the invention in which a second type of hourglass-shaped defect cell is connected to a hexagonal cell.

[0069] Figure 13 shows a comparison between the spectral domain response of a hexagonal cell, a defective cell and a combination of a hexagonal and a defective cell, in a second preferred embodiment of the invention.

[0070] Figure 14 shows a connection of a hexagonal cell with a divided hexagonal cell comprising an inner side forming two trapezoids.

[0071] Figure 15 shows a first connection of a hexagonal cell with a divided hexagonal cell comprising an inner side forming a triangle and a quadrilateral.

[0072] Figure 16 shows a second connection of a hexagonal cell with a divided hexagonal cell comprising an inner side forming a triangle and a quadrilateral.

[0073] Figure 17 shows a connection of a hexagonal cell with a split hexagonal cell comprising two internal sides forming two triangles and a rectangle.

[0074] Figure 18 shows a connection of a hexagonal cell with a divided hexagonal cell comprising two internal sides forming two triangles and a trapezoid.

[0075] Figure 19 shows a photonic waveguide mesh arrangement comprising four types of split hexagonal cells.

[0076] Figure 20 shows an example of a divided quadrangular cell.

[0077] PREFERRED EMBODIMENT OF THE INVENTION

[0078] The invention relates to a field-programmable photonic gate array (FPPGA) characterized in that it comprises photonic waveguide mesh arrangements comprising defective cells.

[0079] Figure 1 shows an example of a field-programmable gate array (FPPGA) according to the invention, comprising photonic I / O ports, a photonic core, RF electronics, RF I / O ports, and control electronics. The photonic core is connected to the photonic I / O ports, the control electronics, and the RF electronics, which are in turn connected to the RF I / O ports.

[0080] Figure 2 shows a detail of the photonic core shown in Figure 1. The photonic core comprises connections to the photonic I / O ports, high-performance external blocks, and a waveguide mesh, which connects the photonic I / O ports to the high-performance external blocks.

[0081] Figure 3 shows an example of a first preferred embodiment of a photonic waveguide mesh arrangement of the invention. In such a photonic waveguide mesh arrangement, multiple different defective cells are connected to multiple quadrangular cells. The quadrangular cells each have four sides of length L.

[0082] Defective cells are rectangular cells comprising a top side and a bottom side that may be larger or smaller than L.

[0083] As shown in Figure 4, defective cells could be combined to form a row of defective cells. Thus, Figure 4 shows multiple rows of defective cells connected to a row of rectangular cells. The multiple rows of defective cells in Figure 4 include rectangular cells comprising a top and a bottom side of lengths: L+(AL / 2), L+(AL), and L+(3AL / 2).

[0084] Figure 5 shows an example of a second preferred embodiment of the invention in which the defective cell is connected to a hexagonal cell.

[0085] The hexagonal cell has six sides of length L: two right sides, two left sides, one top side, and one bottom side. In this case, the defective cell also has six sides, four of which have exactly the same length L as the sides in the uniform hexagonal mesh.

[0086] The defective cell also has two sides with a different length L-(AL / 2), namely, the top face and the bottom face.

[0087] The defective cell also has two sides facing opposite directions compared to the hexagonal cell. Thus, the two left sides are each parallel to the two right sides of the hexagonal cell and, consequently, also to the two right sides of the defective cell.

[0088] This defect cell is compatible and easily integrated into the uniform hexagonal waveguide mesh.

[0089] Figure 6 also shows an example of a second preferred embodiment of the invention. In this case, the defective cell is similar to the defective cell shown in Figure 5, but the top and bottom sides of the defective cell have a length equal to L+(AL / 2). The defective cell is also connected to a hexagonal cell.

[0090] Figure 7 shows an example of the second preferred embodiment of the invention defined previously in which a row of defective cells is connected to multiple rows of hexagonal cells, the row of defective cells being incorporated into the waveguide mesh.

[0091] In Figure 8, multiple rows of defective cells are connected to multiple rows of hexagonal cells in a periodic manner, thus alternating groups of rows of defective cells with groups of rows of hexagonal cells.

[0092] Figure 9 shows another example of the photonic waveguide mesh arrangement of the invention, in which multiple rows of defective cells are connected to each other, forming a first group, and said first group is connected to multiple rows of hexagonal cells, forming a second group.

[0093] Figure 10 shows another example in which multiple rows of different defective cells are connected to multiple rows of hexagonal cells, thus alternating rows of hexagonal cells with rows of defective cells, which have a top and bottom side of different lengths. In particular, in the case shown in Figure 10, the top and bottom sides of the rows of defective cells have lengths equal to L+(AL / 2) and L-(AL / 2), respectively.

[0094] Alternatively, cells could be connected to form columns instead of rows.

[0095] Figure 11 shows an example of a defective cell according to the second preferred embodiment of the invention, wherein the defective cell is hourglass-shaped. Thus, in this case, the defective cell has its two right sides parallel to the two left sides of the hexagonal cell, and its two left sides parallel to the two right sides of the hexagonal cell. The defective cell shown in Figure 11 is connected to a hexagonal cell. In Figure 11 , the left sides of the defective cell are connected to the right sides of the defective cell.

[0096] In contrast, Figure 12 shows a second type of hourglass-shaped defective cell, in which the left sides of the defective cell are not connected to the right sides of the defective cell.

[0097] Figure 13 shows a comparison between the spectral domain response of a hexagonal cell, a defective cell, and a combination of a hexagonal and a defective cell.

[0098] Figure 13 shows how the Vernier effect allows to solve the problem of the limitation of the spectral period by including the defective cells.

[0099] The individual cavities in hexagonal and defective cells have slightly different spectral periods or free spectral range values ​​(FSRi and FSR2). When coupled, only the resonances common to both cavities are enabled, allowing the spectral period to be extended to a value given by:

[0100] FSR, • FSR-, F SRt ~ \FSR1- FSR21

[0101] A typical cell that can be achieved in silicon photonics has a side length L s about 450 mm providing a propagation delay T sof about 11.5 psec. These values ​​are fixed and limit the flexibility in the spectral and time domain responses of the circuits that can be implemented.

[0102] For example, cavities of minimum length L=6L S provide a round trip of about 69 ps, resulting in a spectral period in the range of 14.8 GHz, which is not sufficient for broadband applications requiring at least 40 GHz or more. Similarly, the achievable sampling rate is given by T s , which is not sufficient for applications requiring delay accuracies in the range of less than 10 ps. However, using the photonic waveguide mesh arrangements according to the invention: if FSR1= 0.75 • FSR2 then FSR T = 3FSR1

[0103] In practice, this corresponds to increasing a typical FSR of 14.8 GHz of a 2D uniform hexagonal waveguide mesh to 45 GHz in the photonic waveguide mesh arrangement of the invention.

[0104] This is achieved by reducing the lengths of the "short" sides of the defective cell by 12.5% ​​(i.e., from 450 mm to 394 mm), which is technologically very affordable.

[0105] Furthermore, the insertion of defective cells allows changing trajectories within the mesh with propagation differences in time D T « Ts, thus also solving the sampling time resolution limitation of the uniform waveguide mesh (in the example from 1 1 .5 to 1 .5 ps).

[0106] Additionally, a similar effect can be achieved by introducing split hexagonal cells and split quadrangular cells.

[0107] Divided hexagonal cells and divided quadrangular cells have the same shape and size as a defect-free cell, making them compatible and easily integrated into the uniform hexagonal waveguide mesh. Because of this, a mesh comprising one or more of the divided hexagonal cells or divided quadrangular cells would also have the same shape and size as the equivalent mesh of completely defect-free cells.

[0108] Figure 14 shows a connection of a hexagonal cell with a divided hexagonal cell comprising an inner side forming two equal trapezoids. In this case, the length of the inner side is 2L and the perimeter of the divided hexagonal cell would be equal to the sum of the perimeters of the two equal trapezoids: 5L.

[0109] In this case, the free spectral range (FSR) of the combination of the hexagonal cell and the split hexagonal cell would be equal to: being 6 times greater than the free spectral range (FSR) of a single hexagonal cavity.

[0110] Figure 15 shows a first type of connection between a hexagonal cell and a split hexagonal cell, comprising an inner side forming a triangle and a quadrilateral. In this case, the connection is made between the triangle of the split hexagonal cell and the hexagonal cell.

[0111] The length of the inner side is equal to 3L. Thus, the perimeter of the divided hexagonal cell would be the sum of the perimeters of the triangle and the quadrilateral. The perimeter of the triangle would be (2 + 3)L, and the perimeter of the quadrilateral would be (4 + 3)L.

[0112] In this case, the free spectral range (FSR) of the combination of the hexagonal cell and the split hexagonal cell would be equal to: being 2.64 times larger than the free spectral range (FSR) of a single hexagonal cavity.

[0113] Figure 16 shows a second type of connection between a hexagonal cell and a split hexagonal cell, comprising an inner side forming a triangle and a quadrilateral. In this case, the connection is made between the quadrilateral of the split hexagonal cell and the hexagonal cell.

[0114] The length of the inner side is equal to 3L. Thus, the perimeter of the divided hexagonal cell would be the sum of the perimeters of the triangle and the quadrilateral. The perimeter of the triangle would be (2 + 3)L, and the perimeter of the quadrilateral would be (4 + 3)L.

[0115] In this case, the free spectral range (FSR) of the combination of the hexagonal cell and the split hexagonal cell would be equal to: being 22.7 times greater than the free spectral range (FSR) of a single hexagonal cavity.

[0116] Figure 17 shows a connection between a hexagonal cell and a split hexagonal cell comprising two internal sides forming two triangles and a rectangle. This cell has two parallel internal sides.

[0117] The perimeter of the divided hexagonal cell would be the sum of the perimeters of the triangles and the rectangle. The perimeter of each of the triangles is (2 + 3)L, and the perimeter of the rectangle is (2 + 2^3) L.

[0118] In this case, the free spectral range (FSR) of the combination of the hexagonal cell and the split hexagonal cell would be equal to: being 11.2 times greater than the free spectral range (FSR) of a single hexagonal cavity.

[0119] Figure 18 shows a connection of a hexagonal cell with a split hexagonal cell comprising two inner sides forming two triangles and a trapezoid.

[0120] The perimeter of the divided hexagonal cell would be the sum of the perimeters of the triangles and the trapezoid. The perimeter of the trapezoid would be 5L, the perimeter of a first triangle would be (3 + 3)L, and the perimeter of a second triangle would be (2 + 3)L.

[0121] In this case, the free spectral range (FSR) of the combination of the hexagonal cell and the split hexagonal cell would be equal to: being 4.76 times greater than the free spectral range (FSR) of a single hexagonal cavity.

[0122] Figure 19 shows a photonic waveguide mesh arrangement comprising four split hexagonal cells representing the four types of split hexagonal cells already defined. Figure 20 shows an example of a split quadrangular cell. In this case, the split quadrangular cell comprises an inner side, having a length equal to 2L, which divides the split quadrangular cell into two equal triangles. Therefore, the perimeter of the split quadrangular cell would be equal to the sum of the equal triangles. The perimeter of each triangle would be (2 + 2)L.

Claims

CLAIMS 1. Photonic waveguide mesh arrangement for a field-programmable photonic gate array (FPPGA) comprising: - a plurality of hexagonal cells comprising two right sides of length L, an upper side of length L, a lower side of length L and two left sides of length L; and - one or more defective cells comprising two right sides of length L each parallel to each of the two right sides of the hexagonal cells or to each of the two left sides of the hexagonal cells, an upper side parallel to the upper side of the hexagonal cells, a lower side parallel to the lower side of the hexagonal cells and two left sides of length L each parallel to each of the two right sides of the hexagonal cells or to each of the two left sides of the hexagonal cells; wherein the length of the upper side and the lower side of the defective cells is greater or less than L.

2. Photonic waveguide mesh arrangement according to claim 1, wherein each side of the hexagonal cells and the defective cells comprises two integrated waveguides connected by means of a balanced Mach-Zehnder interferometer (MZI).

3. Photonic waveguide mesh arrangement according to any of claims 1 to 2, wherein the defective cells are connected to the hexagonal cells and / or to each other.

4. Photonic waveguide mesh arrangement according to claim 3, wherein the defective cells are connected to each other forming at least one row or column.

5. Photonic waveguide mesh arrangement according to claim 4, wherein a row or column of defective cells is connected to a row or column of hexagonal cells.

6. Photonic waveguide mesh arrangement according to claim 4, wherein a row or column of defective cells is connected to another row or column of defective cells.

7. Photonic waveguide mesh arrangement according to claim 4, wherein one or more rows or columns of defective cells are connected to one or more rows or columns of hexagonal cells in a periodic manner.

8. Photonic waveguide grid arrangement according to any one of claims 4 to 7, wherein the defective cells in each of the rows or columns of defective cells are defective cells with the length of the top side and the bottom side greater than L or with the length of the top side and the bottom side less than L.

9. Photonic waveguide grid arrangement according to any one of claims 4 to 8, wherein the defective cells of at least one row or column of defective cells have: - the two right sides parallel to the two left sides of the hexagonal cells and - the two left sides parallel to the two right sides of the hexagonal cells; and where the row or column of defective cells is connected to a row or column of hexagonal cells or a row or column of defective cells.

10. Photonic waveguide mesh arrangement for a field programmable photonic gate array (FPPGA) comprising: - a plurality of quadrangular cells comprising two lateral sides of length L, an upper side of length L and a lower side of length L; and - one or more defective cells comprising two lateral sides of length L parallel to the lateral sides of the quadrangular cells, an upper side and a lower side parallel to the upper side and the lower side of the quadrangular cells; where the length of the top side and the bottom side of the defective cells is greater or less than L.

11. Photonic waveguide mesh arrangement according to claim 10, wherein the defective cells are connected to each other forming at least one row or at least one column.

12. Photonic waveguide mesh arrangement according to claim 11, wherein a row or column of defective cells is connected to a row or column of quadrangular cells.

13. Photonic waveguide mesh arrangement according to claim 11, wherein a row or column of defective cells is connected to another row or column of defective cells.

14. Photonic waveguide mesh arrangement for a field-programmable photonic gate array (FPPGA) comprising: - a plurality of hexagonal cells; and - one or more divided hexagonal cells comprising six sides of length L and six vertices, where the sides connect consecutive vertices; and where the divided hexagonal cells further comprise one or more internal sides connecting non-consecutive vertices.

15. Photonic waveguide mesh arrangement according to claim 14, wherein the divided hexagonal cells comprise an inner side connecting two non-consecutive vertices, forming a triangle and a pentagon or two quadrilaterals.

16. Photonic waveguide mesh arrangement according to claim 14, wherein the divided hexagonal cells comprise two internal sides, which do not intersect each other, and where each internal side connects two non-consecutive vertices, forming two triangles and a quadrilateral.

17. Photonic waveguide mesh arrangement according to claim 14, wherein the divided hexagonal cells are connected to the hexagonal cells or connected to each other at different positions, each position resulting in a different free spectral range (FSR) value.

18. Photonic waveguide mesh arrangement according to claim 1, wherein each side of the hexagonal cells and the divided hexagonal cells and each inner side of the divided hexagonal cells comprise two integrated waveguides connected by means of a balanced Mach-Zehnder interferometer (MZI).

19. Photonic waveguide mesh arrangement for a field-programmable photonic gate array (FPPGA) comprising: - a plurality of quadrangular cells; and - one or more divided quadrangular cells comprising four sides of length L and four vertices, where the sides connect consecutive vertices; and where the divided quadrangular cells further comprise an internal side connecting non-consecutive vertices.

20. Field-programmable photonic gate array (FPPGA) comprising a photonic waveguide mesh arrangement according to any one of claims 1 to 19.

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