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The development of optical fibers has revolutionized telecommunications by enabling long-distance broad-band transmission with minimal loss. In turn, the ubiquity of high-quality low-cost fibers enabled a number of additional applications, including fiber sensors, fiber lasers, and imaging fiber bundles. Recently, we showed that a mutlimode optical fiber can also function as a spectrometer by measuring the wavelength-dependent speckle pattern formed by interference between the guided modes. Here, we reach a record resolution of 1 pm at wavelength 1500 nm using a 100 meter long multimode fiber, outperforming the state-of-the-art grating spectrometers. we also achieved broad-band operation with a 4 cm long fiber, covering 400 nm - 750 nm with 1 nm resolution. The fiber spectrometer, consisting of the fiber which can be coiled to a small volume and a monochrome camera that records the speckle pattern, is compact, lightweight, and low cost while providing ultrahigh resolution, broad bandwidth and low loss.
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