Convolutions with optical finite impulse response filters
A method of processing data and related apparatuses. The method relies on an optical finite impulse response (FIR) filter. This optical FIR filter comprises several delay stages having weights set in accordance with parameters of a transformation to be applied by the optical FIR filter. Each of the delay stages is configured to impose a delay matched to a given input data period corresponding to a given input sample rate. According to the method, an optical signal is coupled into the optical FIR filter. The optical signal carries a data stream of input samples encoded at the given input sample rate; the data stream represents the data to be processed. Next, output samples are collected from an output data stream carried by an output optical signal obtained in output of the optical FIR filter. A set of output samples are obtained, which are representative of processed data.
1. A method of processing data, wherein the method comprises:
providing an optical finite impulse response (FIR) filter, wherein the optical FIR filter comprises several delay stages having weights set in accordance with parameters of a transformation to be applied by the optical FIR filter, the delay stages configured to impose a delay matched to a given input data period corresponding to a given input sample rate, and wherein the optical FIR filter is a lattice filter in two-port lattice form, the delay stages being four-terminal lattice filter stages that are optically connected in series, and the four-terminal lattice filter stages comprising two waveguides and two phase shifters, the two phase shifters formed at respective portions of the two waveguides;
coupling an optical signal into the optical FIR filter, wherein the optical signal carries a data stream of input samples encoded at the given input sample rate, the data stream representing data to be processed; and
collecting output samples in an output data stream carried by an output optical signal obtained in output of the optical FIR filter to obtain a set of output samples that are representative of processed data.
2. The method according to claim 1 , wherein the method further comprises;
reconstructing transformed data based on the set of the output samples obtained.
3. The method according to claim 1 , wherein
the output samples are collected by sub-sampling the output samples in the output data stream, at a sub-sampling rate determined in accordance with the parameters of the transformation applied by the optical FIR filter.
4. The method according to claim 1 , wherein
the transformation to be applied is an r-dimensional convolution, r≥1, having a kernel of size k r with given kernel values.
5. The method according to claim 4 , wherein
r≥2,
the optical FIR filter comprises at least k r −1 delay stages, the weights of which are set in accordance with the given kernel values, and
the output samples are collected by sub-sampling the output samples in the output data stream at a sub-sampling rate of k 1-r , whereby the set of output samples obtained is a selection of the output samples carried in the output data stream, the selection including every k r-1 -th sample of at least a subset of the output samples in the output data stream.
6. The method according to claim 4 , wherein
data to be transformed are d-dimensional data, d≥2,
the method further comprises, prior to coupling the optical signal into optical input of the optical FIR filter, scanning through the d-dimensional data according to a predetermined scan path, and
the weights of the delay stages are set in accordance with the given kernel values, consistently with the predetermined scan path.
7. The method according to claim 1 , wherein
the method further comprises, prior to coupling the optical signal into optical input of the optical FIR filter, setting the weights in accordance with the parameters of the transformation to be applied.
8. The method according to claim 1 , wherein
the method further comprises, prior to setting the weights, mapping the weights in accordance with the parameters of the transformation to be applied, whereby the weights are set in accordance with the mapping of the weights.
9. The method according to claim 1 , wherein
the four-terminal lattice filter stages comprise optical phase shifters, and
the method further comprises, prior to coupling the optical signal into optical input of the optical FIR filter, tuning the optical phase shifters to set the weights in accordance with the parameters of the transformation to be applied.
10. An apparatus for processing data, wherein the apparatus comprises:
an optical finite impulse response (FIR) filter comprising several delay stages having weights set in accordance with parameters of a transformation to be applied by the optical FIR filter, the delay stages configured to impose a delay matched to a given input data period corresponding to a given input sample rate, wherein the optical FIR filter is a lattice filter, and the lattice filter is in two-port lattice form, the delay stages being four-terminal lattice filter stages that are optically connected in series, the four-terminal lattice filter stages comprising two waveguides and two phase shifters, the two phase shifters formed at respective portions of the two waveguides;
a transmitter connected to an optical input of the optical FIR filter and configured to couple an optical signal into the optical FIR filter, wherein, in operation, the optical signal carries a data stream of input samples encoded at the given input sample rate, the data stream representing data to be processed; and
a receiver connected to an optical output of the optical FIR filter and configured to collect output samples in an output data stream carried by an output optical signal obtained in output of the optical FIR filter to obtain a set of the output samples that are representative of the transformation.
11. The apparatus according to claim 10 , wherein
the apparatus further comprises a data reconstruction unit connected to the receiver and configured to reconstruct transformed data based on the set of the output samples obtained.
12. The apparatus according to claim 10 , wherein the receiver is further configured to collect the output samples by sub-sampling the output samples in the output data stream, at a sub-sampling rate determined in accordance with the parameters of the transformation applied by the optical FIR filter.
13. The apparatus according to claim 10 , wherein
in the four-terminal lattice filter stages,
the two waveguides are arranged so as to form two directional couplers, and
a length difference between optical paths enabled by the two waveguides is such that a propagation delay difference between the optical paths corresponds to the given input data period.
14. The apparatus according to claim 13 , wherein, in the four-terminal lattice filter stages,
the two waveguides correspond to a first waveguide and a second waveguide;
the respective portions of the two waveguides correspond to a first portion of the first waveguide and a second portion of the second waveguide, respectively;
a first phase shifter of the two phase shifters is arranged at the first portion of the first waveguide between the two directional couplers;
a second phase shifter of the two phase shifters is arranged at the second portion of the second waveguide, the second portion being in output of the second waveguide; and
the four-terminal lattice filter stages are connected in an alternated fashion, such that the first waveguide and the second waveguide of one of the four-terminal lattice filter stages each connects to the second waveguide and the first waveguide, respectively, of a next one of the four-terminal lattice filter stages.
15. The apparatus according to claim 14 , wherein
the first waveguide is a longest one of the two waveguides, and
the two directional couplers and the first phase shifter are configured as a phase-tunable Mach-Zehnder interferometer.
16. The apparatus according to claim 14 , wherein
the two phase shifters are thermo-optic phase shifters;
the apparatus further comprises an electrical circuit, which includes heaters that form part of the thermo-optic phase shifters;
the heaters are in thermal communication with said respective portions of the two waveguides; and
the electrical circuit is configured to apply an electrical current to the heaters of the delay stages, so as to be able to set the weights of the delay stages.
17. The apparatus according to claim 16 , wherein
the apparatus comprises a silicon photonic chip including the optical FIR filter.
18. The apparatus according to claim 17 , wherein
the silicon photonic chip has a layer structure, which includes:
a silicon-insulator-silicon layer stack, including a silicon handle wafer, an oxide layer on top of the silicon handle wafer, and a topmost silicon layer on top of the oxide layer, the topmost silicon layer structured so as to form the two waveguides of the four-terminal lattice filter stages;
an electrically insulating layer cladding the topmost silicon layer, the heaters arranged on top of the electrically insulating layer, and arranged at the respective portions of the two waveguides; and
electrical leads and electrical pads arranged on top of the electrically insulating layer, wherein the electrical leads connect the heaters to the electrical pads.