Programmable Photonic Processor - a Seven-cell Hexagonal Topology

In this article, we demonstrate the reconfigurable functionality of a programmable photonic processor based on a 7-cell hexagonal topology. A series of functionalities are implemented herein, including various types of linear optics transformations, by programming the processor at the level of individual tuneable basic units (TBUs).

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Overview

Understand the simulation workflow and key results

A general-purpose programmable photonic processor shares conceptual similarities with a Field Programmable Gate Array (FPGA) in electronics, such as reconfigurability and parallel processing. These photonic processors can be programmed to implement a variety of functions ranging from linear optics transformations, described by N × N unitary matrices, to some advanced level optical filtering. Various designs of a photonic processor have been proposed in the literature, however, configurations based on triangular and hexagonal meshes demonstrate superior performance in several aspects: spatial tuning reconfiguration steps, reconfiguration efficiency, the density of switching elements per unit area, and losses per spatial resolution [1]. Moreover, the hexagonal mesh offers the simplest implementation for both multiport interferometers and traditional FIR and IIR photonic circuits [1]. Here, we use a configuration based on a 7-cell hexagonal topology. In this configuration, each edge of the hexagon represents a tuneable basic unit (TBU), a 2 × 2 optical beam splitting element that can independently control both the power splitting and the relative phase delay [2].

Step 1: Single TBU Simulation

First, we simulate a single TBU to obtain its amplitude response (transmission vs voltage). This response characteristics can then be utilized to program the individual TBUs into either a cross-state, a bar-state, or a tuneable state with a specified power splitting ratio.

The TBU used in this example consists of a balanced MZI with two 3-dB directional couplers (C_1, C_2), two phase-shifters (OM_1, OM_2), and waveguides for connection as shown in figure below along with a dummy layout of the TBU. Adjusting the voltage applied to the phase-shifters controls the accumulated phase in the two arms and the phase difference between them, which in turn regulates/controls the MZI's time delay and splitting ratio.

Step 2: Function Implementation and Verification

Using the information from step 1, the circuit is programmed at individual TBU level for implementing a range of functionalities including several linear optic transformations, basic tuneable MZIs, and FIR filters.

The programmable processor design consists of around 500 optical elements in total. To well organize such a high number of elements and their connections, compound elements are used to enable hierarchical design. The following block (top-level compound element) represents a programmable photonic processor defined in a hierarchal manner. It can be expanded to visualize the underlying circuit consisting of 30 TBUs connected in a 7-cell hexagonal topology. The individual TBUs can be further expanded to visualize the underlying circuit, which is comprises of two 3 dB couplers, two phase shifters, and waveguides/bends for connection as shown in step 1.

With 60 phase shifters (2 for each TBU) used in this design, 60 electrical input ports are necessary for biasing on the top-level. Additionally, there are a total of 24 optical input ports for optical IO.

Figure (a) shows the schematic view of the complete processor in 7-cell hexagonal topology with concise version of the naming conventions. The naming conventions used here can be well understood in terms of the optical interconnection node, composed of three tuneable basic units as shown in the following Figure (b). The naming convention for each TBU starts with ’MZI’ followed by indices m and 𝑛, which represent the column and row number of the optical interconnection node in the full hexagonal topology. Finally, the label ‘left’, ‘top’, or ‘bottom’ is added depending on whether the position of the TBU in optical interconnection node is middle left, top right, or bottom right. For representing the optical ports of the complete processor, the prefix ‘OptPort’ and suffix ‘left’ or ’right’ is added to the naming convention of the TBU depending on whether the port is on the left or right of the TBU [Figure (c)]. To represent an electric port, a suffix ‘btH’ or ‘tpH’ is added to the naming convention of a TBU, denoting whether the port corresponds to the bottom, or top phase shifter within a TBU.

Run and results

Instructions for running the model and discussion of key results

Step 1: Single TBU Simulation

We employ a parameter sweep utility to capture the frequency domain amplitude response. This response is recorded by varying the applied voltage on the bottom phase shifter while maintaining the voltage on the top phase shifter at a fixed DC level of 0 V. At 0 V on the bottom phase shifter, the MZI is balanced, and the phase shifter section does not introduce any additional phase difference, resulting in a cross state through the combination of the two 3 dB directional couplers. Conversely, when the voltage applied to the bottom phase shifter is -3.725 V, the phase shifter section introduces an additional 180-degree phase difference, resulting in a bar state.

Step 2: Function Implementation and Verification

We initialize the processor to execute the following range of functionalities and conduct the functional verification.

Linear Optic Transformations

Linear optic transformations, described by N × N unitary matrices, find applications in signal processing tasks and include operations like switching, mode combining and splitting, and quantum logic gates. Here, we demonstrate various linear optic transformations including:

• A 3 × 3 column swapper between inputs 1 and 3 leaving column 2 invariant.
• Backward input swapper where input 1 is routed to output 3, input 2 to output 1 and input 3 to output 2.
• A C-NOT gate, which is a universal gate in quantum information processing and can be described by a unitary 4 × 4 matrix.

The unitary matrix representation of the above three linear optic transformations is shown below.

In the following figures, we show the schematic with color-coded representation of the individual TBU states, the circuit layout, and the corresponding transmission as a function of wavelength for the above mentioned linear optic transformations. With the project file linear_optic_trans_3x3.icp loaded, running the script linear_optic_trans_3x3.lsf performs programming and verification as a 3 × 3 column swapper between inputs 1 and 3 or a 3 × 3 backward input swapper. Similarly, the script file linear_optic_trans_4x4.lsf programs the processor in the project file linear_optic_trans_4x4.icp as a CNOT gate and performs the functional verification.

Note: For the following three linear optic transformations, the couplers only need to be set to either a cross state or a bar state and do not require an arbitrary splitting ratio. The acronyms used for the color-coded representation of the individual TBU states are as follows: cross state (CS), available (AV), bar state (BS), and tuneable coupler (TC).

Basic Tuneable MZIs and FIR Filters

Unbalanced Mach-Zehnder interferometers (UMZIs) find applications in a lot of areas ranging from optical filtering to biosensing. We model UMZI devices with path imbalances of 4 BULs (configuration 1) and 8 BULs (configuration 2), where BULs represents the basic unit lengths.

For configuration 1 and 2, the input and output TBUs are used as tuneable couplers, for which the splitting ratio can be controlled. All the other participating TBUs are set in either cross state or bar state. By adjusting parameters κ_1 and κ_2 through variations in the applied voltage to the bottom phase shifters of the input and output TBUs, the splitting ratio of these TBUs can be modified. This enables control over the broadness and amplitude of the notch. Changing the path imbalance (for example, between configuration 1 and 2), changes the free spectral range (FSR).

We also show the implementation of a 3-tap transversal filter (configuration 3) through parallel UMZI cascade. In this configuration, 4 TBUs (including two input/output TBUs) are used as tuneable couplers while the remaining are either set to cross state or bar state. The user can adjust the parameters κ of the tuneable couplers by applying voltage variations to the bottom phase shifters. This allows for precise tuning of the zero positions and reconfiguration of the transfer function.

Important model settings

Description of important objects and settings used in this model

The insertion loss for both directional couplers in the TBU is set to zero, thus functioning as ideal directional couplers.

The element used to model phase shifter ( Optical Modulator Measured (OM) - INTERCONNECT Element – Ansys Optics ) shifts the phase of an optical signal based on an electrical signal input. The relationship between the electrical input and the phase shift can be defined using either polynomial coefficients or a table of values. A dummy data is used here for demonstrating the functionality. Ideally, this element is used together with a waveguide to represent a modulated waveguide. This way, the waveguide element is given the properties of the unmodulated waveguide whereas the OMM element takes care of the perturbation in effective index or phase/absorption due to the modulation.

Updating the model with your parameters

Instructions for updating the model based on your device parameters

The non-idealities in the directional coupler can be introduced by changing the insertion loss to a non-zero value. For the phase shifter, the "measurement type" is set to "effective index" and requires data in the form of voltage and the corresponding changes in the real and imaginary parts of the effective refractive index. The user can replace this data with their own simulation or measurement data. Additionally, the measurement type can be changed to "absorption & phase," allowing the user to directly provide absorption and phase data.

Taking the model further

Information and tips for users that want to further customize the model

The usage of the photonic processor based on a hexagonal mesh can be extended beyond above implemented functionalities. From basic tuneable ring cavities and IIR filters to complex tuneable and reconfigurable filters can be implemented using the hexagonal topology [1].

Additional resources

Additional documentation, examples and training material

Related publications

1. D. Pérez et al., “Multipurpose silicon photonics signal processor core,” Nat Commun, vol. 8, no. 1, pp. 636, 2017.
2. W. Bogaerts et al., “Programmable photonic circuits,” Nature, vol. 586, no. 7828, Oct. 2020.

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