Design of a fast speckle wavemeter with optical processing

We present a design concept for a speckle-based wavemeter that combines high spectral resolution and fast response times. Our device uses a fixed disperse medium with small coherence length as an optical pre-processor and a series of programmable optical elements as a post-processor. The pre-processor generates a complex speckle pattern with a given correlation length, and then the post-processor transforms the optical field to a simple binary pattern with intensity proportional to the wavelength deviation from a reference value. We show how to construct a device that can be trained to produce an electrical signal on a balanced detector proportional to the wavelength. Also, we demonstrate that the device can operate from sub-picometer up to nanometer resolution using a pre-processor with correlation length in the picometer range. More generally, our results show how the use of a programmable optical post-processor with low spectral resolution can be enhanced by a fixed pre-processor with a higher one.