Wavelength multiplexed matrix-matrix multiplier

1. The method of optically performing matrix-matrix multiplications comprising the steps of:

(a) providing spatially coherent light;

(b) separating the light by wavelength in a first dimension of space;

(c) spreading the light in a second dimension of space;

(d) applying first-matrix values to amplitude of the separated and spread light wherein different wavelengths are modulated by different matrix rows;

(e) combining the modulated light by wavelength over the first dimension;

(f) spreading the modulated light over the first dimension;

(g) applying second-matrix values to the combined and spread modulated light wherein matrix rows are applied across the second dimension and matrix columns are applied across the first dimension;

(h) adding amplitudes of the light from step (g) over the second dimension;

(i) filtering out light that is not part of the added amplitudes of light; and

(j) separating the added amplitudes of light by wavelength in the second dimension.

2. The method of claim 1 wherein the first dimension is the vertical dimension and the second dimension is the horizontal dimension.

3. The method of claim 1 wherein, for at least one of the matrices, one of the dimensions is a coarsely-spaced sparse-array rastered horizontically and vertically and the second dimension is a series of offset copies of the sparse-array.

4. The method of claim 3 further including the step of obtaining data for at least one of either first-matrix values or second-matrix values comes from a backplane with a local memory.

5. The method of claim 1 wherein, for at least one of the matrices, one of the dimensions is a rastered array of rastered subarrays.

6. The method of claim 5 further including the step of obtaining data for at least one of either first-matrix values or second-matrix values comes from a backplane with a local memory.

7. The method of claim 1 wherein step (i) is performed by a space variant spectral filter.

8. The method of claim 1 wherein step (i) is performed using a slit.

9. The method of claim 1 wherein step (i) is performed using a pinhole array.

10. The method of claim 1 wherein step (d) and step (g) are performed by some combination of the following:

transmissive spatial light modulators;

reflective spatial light modulators;

multi-quantum-well spatial light modulators.

11. The method of claim 1 wherein at least one of step (b) and step (e) are performed by a grating.

12. The method of claim 1 further including the steps of applying a polarization to the light and using the polarization to route the light.

13. The method of claim 1 further including the step of using the matrix-matrix multiplier in an artificial neural network.

14. Apparatus for optically performing matrix-matrix multiplications comprising:

a source of spatially coherent light;

a first dimension separator configured to separate the light by wavelength in a first dimension of space;

a second dimension spreader configured to spread the light in a second dimension of space;

a first matrix modulator configured to apply first-matrix values to amplitude of the first-dimension separated and second-dimension spread light wherein different wavelengths are modulated by different matrix rows;

a combiner configured to combine the first matrix modulated light by wavelength over the first dimension;

a first dimension spreader configured to spread the first-matrix-modulated light over the first dimension;

a second matrix modulator configured to modulate the combined and first-dimension spread modulated light such that matrix rows are applied across the second dimension and matrix columns are applied across the first dimension;

an adder configured to add amplitudes of the second-matrix-modulated light over the second dimension;

a filter element configured to filter out light that is not part of the added amplitudes of light; and

a second dimension separator configured to separate the added amplitudes of light by wavelength in the second dimension.

15. The apparatus of claim 14 wherein the filter element is a space variant spectral filter.

16. The apparatus of claim 14 wherein the filter element is a slit.

17. The apparatus of claim 14 wherein the filter element is a pinhole array,

the first matrix modulator and the second matrix are chosen from among the following the following:

transmissive spatial light modulators;

reflective spatial light modulators;

multi-quantum-well spatial light modulators.

18. The apparatus of claim 14 implemented using only two cylindrical lenses.

19. The apparatus of claim 14 further comprising a polarizer configured to polarize the light and optics configured to route the light based on polarization.

20. The apparatus of claim 14 wherein the second-dimension spreader comprises a grating.