Abstract: Under one aspect, a method for performing an operation is provided. The method can include receiving, by different physical locations of a multi-mode waveguide, an input signal and a plurality of coefficients imposed on laser light. The method also can include generating, by the multi-mode waveguide, a speckle pattern based on the different physical locations, the input signal, and the plurality of coefficients. The method also can include adjusting at least one of the coefficients based on the speckle pattern.

Abstract: Under one aspect, a method for performing an operation is provided. The method can include receiving, by different physical locations of a multi-mode waveguide, an input signal and a plurality of coefficients imposed on laser light. The method also can include generating, by the multi-mode waveguide, a speckle pattern based on the different physical locations, the input signal, and the plurality of coefficients. The method also can include adjusting at least one of the coefficients based on the speckle pattern.

Abstract: A nanopillar photonic crystal laser includes a plurality of nanopillars and a support structure in contact with at least a portion of each of the nanopillars. Each nanopillar has an axial dimension and two mutually orthogonal cross dimensions. The axial dimension of each of the nanopillars is greater than the two mutually orthogonal cross dimensions, where there mutually orthogonal cross dimensions are less than about 1 ?m and greater than about 1 nm. The support structure holds the plurality of nanopillars in preselected relative orientations and displacements relative to each other to form an array pattern that confines light of a preselected wavelength to a resonance region that intercepts at least one nanopillar of the plurality of nanopillars. The at least one nanopillar includes a lasing material to provide an output laser beam of light at the preselected wavelength.

Abstract: A nanopillar photonic crystal laser includes a plurality of nanopillars and a support structure in contact with at least a portion of each of the nanopillars. Each nanopillar has an axial dimension and two mutually orthogonal cross dimensions. The axial dimension of each of the nanopillars is greater than the two mutually orthogonal cross dimensions, where there mutually orthogonal cross dimensions are less than about 1 ?m and greater than about 1 nm. The support structure holds the plurality of nanopillars in preselected relative orientations and displacements relative to each other to form an array pattern that confines light of a preselected wavelength to a resonance region that intercepts at least one nanopillar of the plurality of nanopillars. The at least one nanopillar includes a lasing material to provide an output laser beam of light at the preselected wavelength.