Picometer-Scale Resolution Speckle Spectrometer Enabled by a Hybrid Dispersive Fiber-Chip System

Speckle spectrometers reconstruct unknown spectra from single-shot imaging, enabling diverse applications such as chemical sensing, health monitoring, and optical characterization. However, achieving spectral resolution on the picometer scale presents significant challenges, particularly in the pursuit of rapid, scalable, and cost-effective solutions. In this work, we introduce a novel speckle spectrometer based on a passive hybrid dispersive fiber-chip system. Our approach leverages cascaded Mach-Zehnder interferometers featuring randomized arm length differences to generate a noise-like spectral response. This uniquely patterned light then undergoes angular dispersion via a grating antenna array and is coupled into a multimode optical fiber. We experimentally demonstrate that various unknown optical spectra can be accurately reconstructed through a single-shot measurement of the speckle pattern, achieving a resolution of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2\;\text{pm}$</tex-math></inline-formula> and an operational bandwidth of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ 100$</tex-math></inline-formula> nm. Furthermore, we illustrate that this resolution can be dynamically tuned by employing multimode fibers of varying lengths. Our design offers a flexible and rapid solution for high-performance optical spectral analysis.