Photonic filter bank system and method of use

1. A method for optical computation comprising:

throughout a time period, controlling a filter bank based on a plurality of weights, comprising:

based on a first weight of the plurality, determining a first control signal;

based on a second weight of the plurality, determining a second control signal;

providing the first control signal to a first optical filter of the filter bank, wherein the first optical filter is associated with a first optical characteristic; and

providing the second control signal to a second optical filter of the filter bank, wherein the second optical filter is associated with a second optical characteristic different from the first optical characteristic;

during the time period, receiving an optical input signal at an input waveguide of the filter bank, wherein the optical input signal comprises:

a first portion having the first optical characteristic; and

a second portion having the second optical characteristic; and

during the time period, in response to receiving the optical input signal at the input waveguide:

at the first optical filter, based on the first control signal, coupling a first signal subportion of the first portion from the input waveguide to an output waveguide of the filter bank;

at the second optical filter, based on the second control signal, coupling a second signal subportion of the second portion from the input waveguide to the output waveguide;

at the second optical filter, coupling a first leakage subportion of the first portion from the input waveguide to the output waveguide; and

at the output waveguide, outputting the first signal subportion, the second signal subportion, and the first leakage subportion, wherein the first signal subportion is phase-shifted with respect to the first leakage subportion.

2. The method of claim 1 , wherein:

the first optical characteristic is a first optical wavelength;

the second optical characteristic is a second optical wavelength;

the first optical filter comprises a first wavelength-selective filter; and

the second optical filter comprises a second wavelength-selective filter.

3. The method of claim 2 , wherein:

the first wavelength-selective filter comprises a first microresonator;

the second wavelength-selective filter comprises a second microresonator;

providing the first control signal to the first optical filter alters a first resonance wavelength of the first microresonator; and

providing the second control signal to second first optical filter alters a second resonance wavelength of the second microresonator.

4. The method of claim 3 , wherein:

the first wavelength-selective filter is a first even-pole filter; and

the second wavelength-selective filter is a second even-pole filter.

5. The method of claim 1 , wherein the first signal subportion and the first leakage subportion define a phase difference, wherein a magnitude of the phase difference is between π/4 radians and 3π/4 radians.

6. The method of claim 5 , wherein the phase difference is substantially equal to ±π/2 radians.

7. The method of claim 1 , further comprising:

throughout a second time period after the time period, controlling the filter bank based on a second plurality of weights, comprising:

based on a third weight of the second plurality, determining a third control signal;

based on a fourth weight of the second plurality, determining a fourth control signal;

providing the third control signal to the first optical filter; and

providing the fourth control signal to the second optical filter;

during the second time period, receiving a second optical input signal at the input waveguide, wherein the second optical input comprises:

a third portion having the first optical characteristic; and

a fourth portion having the second optical characteristic; and

during the second time period, in response to receiving the second optical input signal at the input waveguide:

at the first optical filter, based on the third control signal, coupling a third signal subportion of the third portion from the input waveguide to the output waveguide;

at the second optical filter, based on the fourth control signal, coupling a fourth signal subportion of the fourth portion from the input waveguide to the output waveguide;

at the second optical filter, coupling a third leakage subportion of the third portion from the input waveguide to the output waveguide; and

at the output waveguide, outputting the third signal subportion, the fourth signal subportion, and the third leakage subportion, wherein the third signal subportion is phase-shifted with respect to the third leakage subportion by a phase difference;

wherein the first signal subportion is phase-shifted with respect to the first leakage subportion substantially by the phase difference.

8. The method of claim 7 , wherein:

a first amplitude ratio of the first signal subportion to the first portion is substantially equal to the first weight; and

a third amplitude ratio of the third signal subportion to the third portion is substantially equal to the third weight.

9. The method of claim 1 , wherein:

the filter bank further comprises a third optical filter associated with a third optical characteristic different from the first and second optical characteristics;

the optical input signal further comprises a third portion having the third optical characteristic;

controlling the filter bank based on the plurality of weights further comprises:

based on a third weight of the plurality, determining a third control signal; and

providing the third control signal to the third optical filter; and

the method further comprises, during the time period, in response to receiving the optical input signal at the input waveguide:

at the third optical filter, based on the third control signal, coupling a third signal subportion of the third portion from the input waveguide to the output waveguide;

at the third optical filter, coupling a second leakage subportion of the second portion from the input waveguide to the output waveguide; and

at the output waveguide, outputting the third signal subportion and the second leakage subportion, wherein the second signal subportion is phase-shifted with respect to the second leakage subportion.

10. The method of claim 9 , further comprising, during the time period, in response to receiving the optical input signal at the input waveguide:

at the first optical filter, coupling a fourth leakage subportion of the second portion from the input waveguide to the output waveguide; and

at the output waveguide, outputting the fourth leakage subportion, wherein the second signal subportion is phase-shifted with respect to the fourth leakage subportion.

11. The method of claim 1 , wherein:

the input waveguide defines a first propagation vector, wherein the optical input signal propagates along the first propagation vector;

the output waveguide defines a second propagation vector, wherein the first signal subportion and the second signal subportion propagate along the second propagation vector; and

a dot product of the first and second propagation vectors is greater than zero.

12. The method of claim 1 , wherein:

the first optical filter couples the first signal subportion from a first point of the input waveguide to a second point of the output waveguide;

the second optical filter couples the second signal subportion and the first leakage subportion from a third point of the input waveguide to a fourth point of the output waveguide;

the first signal subportion propagates along a first input waveguide section from the third point to the first point;

the second signal subportion and the first leakage subportion propagate along a second input waveguide section from the fourth point to the second point; and

an optical path length difference between the first input waveguide section and the second input waveguide section is substantially non-zero.