阅读说明：本技术 基于集成光波导网状结构的可编程光子器件的配置和优化方法 (Configuration and optimization method of programmable photonic device based on integrated optical waveguide mesh structure ) 是由 J·卡普曼尼·弗兰科伊 I·加苏拉·梅斯特雷 D·佩雷斯·洛佩兹 于 2019-10-14 设计创作，主要内容包括：本发明的方法目标使得能够对基于网状结构的可编程光电路执行可扩展配置和性能优化,使得它们可以执行光/量子信号处理功能。本发明的目的可以应用于通过对波导网格编程而实现的具有任意复杂度的电路中。本发明的方法目标不仅能够进行性能的分析和评估,而且能够进行可编程光学器件的后续编程和优化。(The method object of the present invention enables scalable configuration and performance optimization of mesh-based programmable optical circuits so that they can perform optical/quantum signal processing functions. The object of the invention can be applied in circuits of arbitrary complexity realized by programming the waveguide grid. The method of the present invention aims to enable not only the analysis and evaluation of performance, but also the subsequent programming and optimization of programmable optical devices.)

1. A method for configuring and optimizing a programmable optical device based on a mesh optical structure, the mesh optical structure being a highly coupled structure defined by at least three or more Tunable Base Units (TBUs) implemented by two coupled waveguides, providing independent power and phase division values; the method is characterized in that it comprises:

a. the entire mesh is partitioned into Tunable Base Units (TBUs) or subsets of Tunable Base Units (TBUs) in an initial configuration,

b. determining a complete frequency response with an adjustable base unit (TBU) in an initial configuration, wherein the complete response comprises amplitudes and phases of input/output ports of a 2D waveguide grid,

c. calculating at least one parameter of the 2D waveguide grid from the result of the previous step, an

d. Modifying the configuration of at least one Tunable Base Unit (TBU) according to the parameters calculated in the previous step.

2. The method according to claim 1, wherein the frequency response of the complete trellis is obtained by applying an inductive method, wherein the resulting matrix is obtained by defining a matrix of the trellis formed by n-1 subsets of Tunable Base Units (TBUs) and defining additional subsets connected to the trellis formed by n-1 subsets of Tunable Base Units (TBUs).

3. The method of claim 1, wherein the evaluation and modification of the Tunable Base Unit (TBU) is performed using a recursive algorithm.

4. The method of claim 3, wherein the recursive algorithm comprises:

a. the elements constituting the main circuit to be programmed are selected,

b. a subset of Tunable Base Units (TBUs) adjacent to the circuit to be used is selected and its configuration is modified,

c. a complete grid of the system defining the 2D programmable optical grid is evaluated,

d. the state of the parameter to be optimized is checked,

e. calculating a change in configuration of each Tunable Base Unit (TBU) not present in the main circuit, an

f. Steps b-e are repeated recursively until the desired optimization is reached.

5. The method of claim 2, wherein the number of ports to connect and the number of new cavities created after each new subset of Tunable Base Units (TBUs) interconnect define different interconnection scenarios selected from:

a. scenario 0 is defined by the interconnections in a single port,

b. scenario 1 is defined by the interconnection of two ports and the absence of a new cavity,

c. scenario 2 is defined by the interconnection of the two ports and the origin of the new cavity,

scenario 3 is defined by the interconnection of the three ports and the origin of the new cavity.

6. Method according to claim 1, wherein the main circuit is additionally optimized using those Tunable Base Units (TBUs) that do not constitute it, by repeatedly applying the method according to any one of claims 1 to 3.

7. The method of claim 1, wherein the overall evaluation phase of the programmable circuit combines analytical evaluation with experimental monitoring of optical signals in a subset of output ports or interior points of the circuit.

8. Method according to claim 1, wherein the Tunable Base Unit (TBU) is a non-resonant interferometer of the Mach-zehnder (mzi) type.

9. The method of claim 4, wherein the Mach-Zehnder interferometer (MZI) is balanced, i.e., where the two arms making up the interferometer are equal, with a loss of 3 dB.

10. The method of claim 1, wherein the adjustable base unit (TBU) is a double-actuated directional coupler.

11. The method according to claim 1, wherein the Tunable Base Unit (TBU) is a resonance interferometer.

12. Method according to claim 1, wherein said Tunable Base Unit (TBU) has an arbitrary number of ports.

13. The method of claim 1, wherein the Tunable Base Unit (TBU) is configured by tuning elements based on: MEMS, thermo-optic tuning, electro-optic tuning, opto-mechanical or capacitive tuning.

14. The method of claim 1, wherein the subset of Tunable Base Units (TBUs) form a uniform topology of the 2D programmable light circuit.

15. The method of claim 1, wherein the subset of Tunable Base Units (TBUs) form a non-uniform topology of the 2D programmable light circuit.

16. The method of claim 1, wherein the parameters to be calculated and optimized are related to programming of the programmable optical device.

17. The method of claim 16, wherein the parameters to be calculated and optimized are selected from the group consisting of: overall power consumption, reduced losses, reduced interference and crosstalk, isolation between circuits, and reduced area usage.

Technical Field

The invention aims to belong to the technical field of physics.

More specifically, the scope of the invention is in the field of photonics.

Background

There is a great deal of literature on programmable optical integrated structures. We can classify them into two types: the first group of devices provides programming of and access to the subsystems, and the second group is based on a complete discretization of all subsystems and routing systems in the waveguides that make up the mesh. Optical switch matrices can be divided into two types.

Programmable Multifunction Photonics (PMP) aims at designing a general-purpose integrated optical system by hardware configurations that can be programmed to implement various functions. Several authors propose theoretical works based on different configurations and design principles of a splitter cascade or integrated mach-zehnder interferometer (MZI).

By following principles similar to those of Field Programmable Gate Array (FPGA) based electronics development, a more general architecture can be obtained, resulting in a programmable photonic gate array (FPPGA). The main idea is to decompose a complex circuit into a large network of identical single tuning units implemented and interconnected by integrating a two-dimensional (2D) waveguide grid or network. In this way, different functions can be obtained by selecting appropriate paths via the grid and local offsets. Complex functions are therefore synthesized by programming optical interventions that activate the necessary resources within the grid. The integrated 2D grid formed by replicating tuning elements forms uniform cells (square, hexagonal or triangular) providing regular and periodic geometries, where each side of a basic cell is realized by two waveguides coupled by an independently (power and phase division) Tunable Basic Unit (TBU).

Today, configurations have been demonstrated that reduce the number of cells (i.e., up to seven), which suggests that traditional signal processing architectures and commonly used arbitrary linear matrix transformations can be modeled as the basis for most applications for photonic chips. For example, in quantum information, NxN conversion, simulation of bosch sub-sampling circuits and quantum laboratory chips for implementing simple and complex logic gates are supported.

The waveguide grid paves a way for a large-scale reconfigurable integrated quantum information system, and is possible to replace the current static configuration-based method. In computer processor interconnects, reconfigurable broadband interprocessor and computer interconnects are essential in high performance computing and data centers. The linear transformation of photon lines into core processor resource management provides a clean, crosstalk-free high-speed option. In optical signals, the processing and linear transformation compatible with 2D mesh waveguide based PMN processors includes several operations critical to optical signal processing, such as: optical FFT, hilbert transform, integrator, and differentiator. In neurophotonics, unitary (NxM) and non-unitary (NxM) matrix transformations are the basic elements in neural networks prior to nonlinear threshold operations. The availability of PMP processors opens an interesting avenue for research into this emerging area. In biophotonics, PMP supports the implementation of single and multiple input/multiple output (MIMO) sensors that are capable of implementing interferometric structures for lab-on-a-chip capable of detecting a variety of parameters.

Last but not least, in advanced physics, waveguide meshes provide programmable 2D platforms to implement different topological systems, such as multi-ring cavity structures, to support the study of composite dimensions and devices based on the principle of topological isolation.

Expanding the 2D waveguide grid to account for a greater number of TBUs (>80) is essential to achieve more complex structures and to result in Large Scale (LS) or Very Large Scale (VLS) photonic integrated circuits.

Scalability greatly increases the amount of functionality that can be implemented using a given piece of hardware. However, the scalability of the waveguide grid results in the configuration and performance obtained from the programming circuitry being affected by excessive losses, undesirable levels of optical interference, and increased complexity of the system configuration. As the number of TBUs increases, the grid global configuration based on the initial mapping of only the ideal behavior of the assumed TBUs becomes less reliable. Furthermore, poor performance of a single TBU can lead to severe degradation of the overall behavior of the circuit. Furthermore, as with any optical circuit having non-ideal components, performance is degraded by the accumulation of unwanted optical interference. For example, in the practical case of switch matrix synthesis/simulation, part of the output signal may be routed as noise to an unwanted port. The degree of unwanted coupling depends on the degree of optical interference of each component (TBU in the case of a waveguide grid). For the same reason, a waveguide network that simulates both circuits simultaneously would result in unwanted coupling between the two. The physical connection between the two is significant and the level of unwanted interference can again limit the performance achieved.

To overcome these physical and design limitations, scalable performance configurations and optimization methods must be provided. This method is also essential for performing an optimal technical mapping of the circuit to be simulated on the hardware resources provided by the grid. The core of this method requires the correct spectral signature to be represented by the overall dispersion matrix of the system. Once obtained, different optimization algorithms should modify the parameters of each TBU to achieve the desired configuration and performance improvements by evaluating the dispersion matrix. The large number of input/output ports and internal interconnections that enable propagation and re-feeding in multiple directions in a two-dimensional structure means that conventional configuration and optimization techniques cannot be used. In fact, the difference between pure mathematical analysis techniques of 2D structures and the proposed optimization process is that. Although it is necessary firstly only to be able to characterize the influence of the resources used on the transmission between the input and output ports of the useful signal, the influence of all resources on all possible input and output configurations needs to be taken into account in the optimization process, since the optimization of the operation of the architecture requires information about the resources used and also, in principle, the resources which remain static.

Currently, there is evidence for:

US2015086203a1 "Method and apparatus for optical node construction using field programmable photonics" and US2018139005a1, respectively, describe apparatus for routing optical signals. It is not a programmable signal processor but a device that routes/amplifies a channel from one port to another, the wavelength being selectable. These devices are known in the art as optical switch matrices.

US2018234177a1, which describes a matrix of programmable integrated circuits for optical testing, which is defined by a fixed structure to test signal transmitting/receiving devices. It can modify the modulation type, power and speed.

WO2016028363a2, in which a programmable photonic integrated circuit is described that implements arbitrary linear optical transformations in spatial modes with high fidelity. Under a realistic manufacturing model, a CNOT gate, a CPHASE gate, an iterative phase estimation algorithm, state preparation and a programming implementation of a quantum random path are analyzed. Programmability greatly increases the tolerance of the device to manufacturing defects and enables a single device to perform a wide range of experiments for quantum and classical linear optics. The results show that existing fabrication processes are sufficient to build such devices on silicon photonics platforms. This document may be understood to relate to an interferometric measuring device which performs a linear optical transformation. The device is only capable of performing progressive combining of signals, i.e. signals cannot be recycled or combined in simultaneous nodes or nodes of previous levels.

WO2004015471a2, wherein reference is made to a set of functional blocks interconnected by an optical routing/switching matrix. A device is described whose functional blocks are physically customized before being programmed. The user selects whether to access or not by means of a circuit switch.

Similarly, a document entitled "Reconfigurable lattice grid designs for programmable Optical processors and general couplers", published by Perez Daniel, Gasula Ivana, Capmany Jose, Soref Richard A on 201618 th International Conference on Transparent Optical Networks (ICTON) (18 th Transparent Optical network International Conference (ICTON) 2016), is known in which two lattice design geometries, hexagonal and triangular lattices, are described for implementing a core in programmable Optical processors and general couplers. Comparing them with the previously proposed square mesh topology, in terms of considering a series of figures of merit for the metrics related to on-chip integration of the mesh, a hexagonal mesh was found to be the most suitable choice. Also, a document entitled "Multi-purpose silicon Photonic processor core" (https:// www.nature.com/optics/s 41467-017-00714-1) by Perez Daniel, Gasula Ivana, Caphany Jose, et al, published in Nature Communications at 11/27/2017, describes application specific photonic integrated circuits in which specific circuits/chips are designed to perform specific functions in an optimal manner. Another approach inspired by the electronic field programmable gate matrix is a programmable optical processor in which generic hardware implemented by a two-dimensional photonic waveguide grid is programmed to perform different functions. More than 20 different functions are disclosed by the simple structure of seven hexagonal cells, applicable to different fields including communication, chemical and biomedical detection, signal processing, multi-processor networks and quantum information systems. Although both documents refer to mesh geometry when proposing and comparing physical architecture and simple configuration examples. However, no method is discussed or proposed for its efficient configuration and performance optimization of grids with arbitrarily high number of TBUs. For example, analytical analysis of the presented grid may be resolved over several days. However, from 4 cells to 20 cells makes it impractical to analyze and develop them by conventional methods. As are the configuration, programming and optimization of their circuits. Therefore, a method applicable to all types of mesh structures is required.

Similarly, in a document entitled "All-optical programmable photonic integrated circuit" by the authors of dependen Mao, Peng Liu, Liang Dong, and entitled "All-optical programmable photonic analogue to electronic FPGA" (published in 2011 16 th International Solid-State Sensors, Actuators and subsystems reference (TRANSDUCERS 2011); Beijing, China; 2011 6 months 5-9), a fully programmable photonic platform utilizing programmable integrated circuits of three technologies is described: two-dimensional silicon photonic crystals, digital micromirror devices, and photosensitive liquid crystals. This document basically proposes a "programmable" photonic platform for integrated circuits. It is actually a mask programming device (with a large lab facility or chip manufacturing company, rather than a field programming device. specifically, it is an efficient index to modify a waveguide based on the photosensitivity of the component, describing the mechanism of the tuning method or platform.

Summary of The Invention

The object of the present invention is a scalable method of configuration and performance optimization of programmable optical circuits based on a mesh structure, so that they can perform optical/quantum signal processing functions; in the following, the method of the invention or the method object of the invention is referred to.

The method of the present invention first includes discretizing/partitioning the grid into smaller TBU cells or sets of replicated TBUs forming the grid. Secondly, the core of the method object of the invention requires the correct spectral characterization represented by the dispersion matrix of the system, i.e. the complete frequency response (angle and phase of all input/output ports) of the high coupling structure. Once obtained, different optimization algorithms modify one or more parameters of each TBU to produce the desired configuration and performance improvements; the parameter to be optimized is related to the programming of the programmable optical device and may be selected, for example, from: overall power consumption, reduced loss, reduced interference and crosstalk, isolation between circuits, and reduced footprint. For example, inactive TBUs that do not belong to the primary target may be modified to reduce optical interference and provide the best signal-to-noise ratio by minimizing the corresponding values of the system matrix. Furthermore, the system may be partially optimized by performing optimization on only a subset of the inactive TBUs to take into account the trade-off between overall power consumption and optimization. The application of this method makes possible the feasibility of highly coupled (gridded) programmable photonic structures (hereinafter referred to as grids) and thus achieves technical advantages.

In order to obtain a dispersion matrix that characterizes the system, the large number of input/output ports and internal interconnections enables multi-directional propagation and feedback in a two-dimensional structure, which means that conventional configuration and optimization techniques cannot be used.

As a non-limiting descriptive explanation, applying the method object of the invention to a grid of hexagonal topology, the grid of two-dimensional hexagonal waveguides is divided into elementary blocks n-1, each block being formed by three TBUs (hereinafter tri-TBUs). After the segmentation, an analytical dispersion matrix defining a complete mesh is recursively obtained from a matrix defining the mesh with n-1 tri-TBUs and a dispersion matrix defining a new tri-TBU to be merged. As a result, an analytical dispersion matrix for any integrated photonic waveguide grid circuit composed of any number of TBUs is obtained. The value of each TBU is then modified and the process repeated to achieve the desired performance improvement (relative to a specific or general purpose operation, such as reducing optical interference, power consumption, or cumulative loss in a complex programmable photonic circuit).

Again, the method of the present invention enables the design of unused areas (TBUs) of the waveguide grid so that they can be used to manage the unwanted contribution of reflected and interfering signals, thereby optimizing the performance of the chip; it is also possible to study all input/output responses as internal parameters of the Tunable Base Unit (TBU) change, thereby achieving error optimization through multi-parameter optimization and in combination with machine learning algorithms for circuit self-correction.

The approach proposed here was developed for hexagonal waveguide meshes, however, it can be applied to any uniform and non-uniform 2D mesh topology; the core of the method starts with the application of Mathematical Induction (MI), a technique that can be used to test specific rules or patterns, generally infinite or arbitrarily large, and is based on two steps, the basic step in which simple cases are built and an inductive step that involves proving that arbitrarily large instances are logically derived from a slightly smaller instance. In mathematical terms, the induction principle determines that for a fixed integer b and each integer n ≧ b, S (n) is a statement containing n. If (i) S (b) is true and (ii) for any integer k ≧ b, S (k) → S (k +1), then for all n ≧ b, it is stated that S (n) is true. This seemingly simple principle effectively hides a very powerful testing technique that may find application in a variety of fields, including probability, geometry, game theory, graph theory, system complexity, and manual systems.

The object of the present invention is applicable to programmable photonics, which has applications in countless fields, to name a few:

radiofrequency photonics: reconfigurable filter, adjustable real-time delay line, arbitrary phase shift, waveform generator, ADC, frequency measurement.

Quantum: the implementation supports logic gate operation, random circuit simulation and general NxN unitary transformation of quantum labs on a chip.

Telecommunication: switch, add/drop multiplexer, mode converter in SDM system.

Interconnection: reconfigurable broadband interconnects and computer interconnects.

Optical signal processing: optical FFT, Hilbert transform, integrator, differentiator.

Neurophotonics: unitary (NxM) and non-unitary (NxM) matrix transforms for neural network, spike, and reservoir computations.

The sensor: simple interferometric architectures and MIMO for lab-on-a-chip and multi-parameter detection applications are supported.

High-level physics: a multi-ring cavity structure is implemented to support the stereosynthetic material.

Drawings

To supplement the description which is being made and to help better understand the characteristics of the invention according to its preferred practical exemplary embodiments, a set of drawings is attached as an integral part of said description, in which the following is described in an illustrative and non-limiting way:

figure 1 shows different mesh circuits and splitting options in a TBU or a subset of TBUs. All of these, and any circuit that can be discretized in the same tuning unit, are eligible for application of the disclosed method. (a) Square mesh application, (b) hexagonal mesh application, (c) triangular mesh application.

Fig. 2 shows TBU discretization for different mesh circuit topologies (a) hexagonal uniformity, (b) square uniformity, (c) triangular uniformity, (d) one-way propagation uniform interferometer, and (e) non-uniformity, where each TBU can have different orientations and sizes.

Figure 3 shows the tri-TBU building blocks for a 2D hexagonal waveguide grid and the magnification between the number of optical nodes and ports and the number of cells. (a) A tri-TBU consisting of three TBUs and associated symbols, (b) two tri-TBUs interconnected by an optical node P1, (c) three tri-TBUs creating a closed hexagonal cell, (d) eight tri-TBUs interconnected to obtain a waveguide grid formed by four cells. (e) The number of optical nodes and ports in the web waveguide IC integrated photonic circuit (ON) and the number of closed cells (C).

FIG. 4 depicts an generalized method for obtaining the dispersion matrix H (n) for a two-dimensional hexagonal waveguide grid of n basic tri-TBU units by adding one tri-TBU unit H (1) to the two-dimensional hexagonal waveguide grid of n basic tri-TBU units H (n-1) and a general signal flow diagram for deriving H (n) as a function of H (n-1) and H (1). a, interconnect scenario 0. b, interconnect scenario 1. c, interconnect scenario 2. d, interconnect scenario 3.

Fig. 5 depicts scenario 0. (a) A connection graph of grid n-1, (b) an interconnection graph with tag contributions, (c) a result portion of the matrix. S1: x is P-1. Direct contributions within the network N ports are not included in the figure.

Fig. 6 depicts scenario 1. (a) A connection graph of grid n-1, (b) an interconnection graph with tag contributions, (c) a result portion of the matrix. S1: x is P-1 and y is P. Direct contributions within the network N ports are not included in the figure.

For graphs showing signal flow, connections N, M, X, Y, F, DE ', F', Q, R, C ', D', A ', B', S, U, I, J, B, F, hyy, hzz, hxx represent signal flow paths whose transfer functions are given by the coefficients of the dispersion matrix H (n-1). Connection K, L, O, P, A, H, C, E, T, G, V, W represents the additional signal flow path generated by the additional tri-TBU.

Fig. 7 depicts scenario 2. (a) A connection graph with an n-1 grid, (b) an interconnection graph with contributing labels, (c) a result portion of the matrix. x is P-1 and y is P. Note that the figure does not include direct contributions within the network N ports.

Fig. 8 depicts scene 3. (a) A connection graph with grid n-1, (b) an interconnection graph with label contribution, and (c) a result portion of the matrix. x is P-2, y is P-1, and z is P. Direct contributions within the network ports are not included in the figure.

Fig. 9-11 illustrate a practical embodiment using the method and the technical advantages obtained. In the first case, a structure has been configured that implements an interference cavity-based filter, and the response thereof has been evaluated for each combination of TBU configurations explored. For the second case (fig. 10), the grid is programmed to implement a complex optical circuit formed by 4 resonant cavities loaded in a balanced MZI interferometer. Optimization was performed to evaluate the performance (extinction range, loss and ripple in the pass band) related to the filtering. For the third case (fig. 11), the grid implements two independent circuits. The first is based on three coupled cavities and the second is an unbalanced MZI type double sample filter. The figure shows that the application of the proposed method is improved in terms of reducing optical interference between circuits, improving both performances.

Detailed Description

In a preferred exemplary embodiment of the object of the invention, the starting point is a 2D waveguide grid formed by a replica of the basic tuning element realized by two waveguides coupled by independent (in power and phase division) Tunable Base Units (TBUs) configured by tuning elements based on: MEMS, thermo-optic tuning, electro-optic tuning, or opto-mechanical or capacitive tuning.

The Tunable Base Unit (TBU) can preferably be realized by a balanced, tunable Mach-Zehnder interferometer (MZI) or by a double-actuated directional coupler and can be realized by H_TBU2x2 transport matrix. Depending on the orientation and interconnection of the TBUs, if each TBU has an arbitrary length and orientation, a uniform (square, hexagonal, triangular, etc.) or non-uniform topology results. Next, theoretical segmentation is performed in TBUs or subsets of TBUs of the target mesh to apply the implementation of Mathematical Induction (MI). In the case of a hexagonal waveguide grid, the choice of basic or tri-TBU building blocks consists of three TBUs (A, B and C) connected in a Y configuration, as shown in fig. 3. a. the tri-TBU set is described by a 6x6 dispersion matrix from three H's describing their respective internal TBUs_TBUThe dispersion matrix is calculated. To help illustrate the method we will use triangle symbols to represent tri-TBUs where each port has in principle up to four opposite ports (i.e. port 1 to port 3, 4, 5, 6, etc.). The Tri-TBUs can be replicated and distributed N times to generate any size hexagonal grid arrangement desired. For example, FIGS. 3b and 3c show the process of constructing a single hexagonal cell consisting of three tri-TBUs (we areThe symbols Ai, Bi, Ci will be used to identify the TBUs that make up the tri-TBU i).

Even for the simplest structure represented by a unit cell, the calculation of a 12 × 12 transfer matrix (i.e., 144 elements) already requires 12 input/output ports and 6 intermediate auxiliary nodes. The above numbers show a sharp increase as the number of cells increases. For example, the quad-cell structure shown in fig. 3.d is still a low complexity structure with 20 input/output ports, 38 internal nodes and a dispersion matrix of 20x20 (i.e., 400 elements). Fig. 3.e provides the exact number of input/output ports and internal nodes in terms of the number of hexagonal cells and clearly shows that even for very low cell numbers, the analytical derivation of the dispersion matrix of the 2D grid seems to be difficult to access.

Furthermore, numerical methods for analyzing circuit responses, such as FDTD (finite difference time domain) and eigenmode based solutions, do not scale well with the number of components in photonic circuits.

Formally, the method object of the invention is expressed as follows, the 2D structure formed by tri-TBUs is described by a unitary dispersion matrix H (1) with known coefficients. Then, if a two-dimensional structure consisting of n-1 ≧ 1 tri-TBUs is described by the unitary dispersion matrix H (n-1) of known coefficients, the structure consisting of n tri-TBUs obtained by adding an additional H (1) tri-TBU to the first one is described by the unitary dispersion matrix H (n) of known coefficients.

The method can use the dispersion matrix sequence of the low-order grid dispersion matrix H (n-1) and the newly added dispersion matrix sequence of H (1) tri-TBU to derive the dispersion matrix of any n-order hexagonal waveguide grid. The final calculation will depend on how the additional tri-TBUs are connected to the low-order mesh. Four different interconnection scenarios can be determined, as shown in fig. 2a, 4.a to 4.d, depending on the number of interconnection ports and the number of new complete hexagonal cells that appear after the new tri-TBU is merged.

In the first scenario, scenario 0 refers to the simplest case representing the starting point of a new mesh design, with only one of the 6 ports defining the triple frame connected to the port of the previous mesh. Adding a new tri-TBU increases the number of trellis ports by 4, correspondingly increasing the number of rows and columns in the dispersion matrix.

In the second scenario, scenario 1, adding a new tri-TBU increases the number of trellis ports by 2, but the number of complete hexagonal cells is not increased.

In the third scenario, scenario 2, adding a new tri-TBU increases the number of ports by 2 and the number of complete cells by 1.

In a fourth scenario, scenario 3, adding a new tri-mesh network does not increase the number of ports, because it connects 3 ports to the previous mesh, and the number of complete cells increases by 1.

Fig. 5-8 depict a more general signal flow diagram for each scene that must be considered to derive the overall dispersion matrix H (n) from H (n-1) and H (1). The nodes s, r shown on the left represent any pair of input and output ports, respectively (the range of variation allowed for s, r is also shown according to the scenario, where P is the number of input/output ports H (n-1) before the additional tri-TBU is connected). The nodes x, y, z identify the input/output ports of H (n-1) for connecting this mesh to the newly added tri-TBU (the allowable values of x, y, z are also shown depending on the scenario). In FIGS. 5-8, the connection

N，M，X，Y，F，DE′，F′，Q，R，C′，D′，A′，B′，S，U，I，J，B，F，hyy，hzz，hxx

Representing the signal flow path, the transfer function is given by the coefficients of the dispersion matrix H (n-1). And connection K, L, O, P, A, H, C, E, T, G, V, W represents the additional signal flow path generated by the additional tri-TBU. The transfer functions (additional matrix coefficients) of these connections have to be calculated to obtain the overall dispersion matrix h (n).

For the above derivation, the above four scenarios are used, so we have:

in scenario 0, only one of the 6 ports of the new tri-TBU (Latt N) added to H (n-1) is connected to the order trellis n-1. As shown in fig. 4.a, adding a tri-tbu (latt n) increases the number of grid ports by 4, and correspondingly, the number of rows and columns in the dispersion matrix h (n) increases. The interconnection diagram shown in fig. 5b describes the possibility of signal flow within the hierarchical trellis n-1 and between this trellis and the newly added tri-TBU via the interface node x ═ P. The interconnection diagram defines a set of equations relating to node x that can be solved, yielding the following equations (equation 1) that provide the matrix coefficients characterizing the new waveguide mesh ports:

where IntCon represents the internal connection given by the dispersion matrix of the three frame additional unitary cells latt n.

Scene 1: here, adding a new tri-TBU latt n increases the number of trellis ports by two, but not the number of complete hexagonal cells, as shown in FIGS. 6.a, 6.b, and 6.c, which depict the correlation interconnection diagram to be solved and the resulting matrix n of the order trellis, respectively. In this case, the resulting equation is more complex since two interface nodes are required ((x-P-1 ey-P), the solving of the node-dependent set of equations x-P-1 and y-P equation (equation 2) is obtained, which provides the matrix coefficients characterizing the new waveguide mesh ports and the four sub-matrices:

in scenario 2, adding a new tri-TBU increases the number of ports by 2 and the number of complete hexagonal cells by 1, as shown in FIG. 7. a. In this case the signal flow diagram is shown in fig. 7.b, which includes the possibility of recycling between the interface nodes x-P-1 and y-P and the newly added tri-TBU unit latt n, as shown by connection V, W. The process is similar to the two scenarios 0 and 1 described above, solving the system of equations associated with nodes y, x; in this way, the system of equations associated with the nodes x-P-1 and y-P equations (equation 3) are solved, which provide dispersion matrix coefficients that characterize the new waveguide grid ports and the four sub-matrices:

in a third scenario, as shown in fig. 8.a, adding a new tri-TBU does not increase the number of ports, since it connects three ports to the previous mesh, and the number of complete cells is increased by one. Here, the interconnect diagram relates to three interface nodes x, y, z (represented in fig. 8 b). The process of obtaining the different sub-matrix coefficients is similar to the previous three scenarios, but considering the complexity of the addition result, the complexity is higher, which results in:

this completes the complete set of analytical expressions, making the core of the algorithm responsible for evaluating the dispersion matrix that defines the system given each TBU value to be implemented. The core of the method is then used recursively to configure and optimize grid performance.

By way of example, in this document a series of experimental results are provided which reinforce the previous assertions of flexibility and advantages with respect to the object of the present invention.

In this way, the method of the present invention is applied to configure, optimize and evaluate circuits of different complexity achieved by programming a 40 input/40 output waveguide grid. This involves calculating the 40x 40-1600 matrix coefficients, which are affected by the different conditions imposed by the large number of possible individual configuration combinations of each TBU parameter. Furthermore, for each wavelength, the method object of the present invention makes it possible to evaluate the 40 × 40 matrix for each iteration of the optimization/configuration process in a few seconds.