Abstract
A 4 × 4 reconfigurable Mach–Zehnder interferometer (MZI)-based linear optical processor is investigated through its theoretical analyses and characterized experimentally. The linear transformation matrix of the structure is theoretically determined using its building block, which is a 2 × 2 reconfigurable MZI. To program the device, the linear transformation matrix of a given application is decomposed into that of the constituent MZIs of the structure. Thus, the required phase shifts for implementing the transformation matrix of the application by means of the optical processor are determined theoretically. Due to random phase offsets in the MZIs resulting from fabrication process variations, they are initially configured through an experimental protocol. The presented calibration scheme allows to straightforwardly characterize the MZIs to mitigate the possible input phase errors and determine the bar and cross states of each MZI for tuning it at the required sate before programming the device. After the configuration process, the device can be programmed to construct the linear transformation matrix of the application. In this regard, using the required bias voltages, the phase shifts obtained from the decomposition process are applied to the phase shifters of the MZIs in the device.
Highlights
T HE interest in reconfigurable multiport linear optical interferometers is growing rapidly, due to their high speed and low power consumption
A theoretical analysis was developed in detail to extract the required phase shifts from the corresponding linear transformation matrix by decomposing it into that of the Mach–Zehnder interferometer (MZI) in the SU(4) section of the device
The calculated phase shifts can be used to programme the device through an experimental protocol
Summary
T HE interest in reconfigurable multiport linear optical interferometers is growing rapidly, due to their high speed and low power consumption. The linear transformation matrix of a reconfigurable multi-port optical processor can be obtained by the product of the unitary transformation matrices of its constituent MZIs. The main section of the 4 × 4 structure is an SU(4) of which linear transformation matrix can be calculated by the successive multiplications of that of its MZIs. The programming process of the SU(4) for a given application is equivalent to the decomposition of its linear transformation matrix into that of its constituent MZIs. We show how the decomposition process of a linear transformation matrix is used to determine the required phase shifts to implement it in optics. We show how to determine the required phase shifts and their corresponding bias voltages to program the optical processor experimentally
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