  A standard multimode optical fiber can be used as a general purpose
spectrometer after calibrating the wavelength dependent speckle patterns
produced by interference between the guided modes of the fiber. A transmission
matrix was used to store the calibration data and a robust algorithm was
developed to reconstruct an arbitrary input spectrum in the presence of
experimental noise. We demonstrate that a 20 meter long fiber can resolve two
laser lines separated by only 8 pm. At the other extreme, we show that a 2
centimeter long fiber can measure a broadband continuous spectrum generated
from a supercontinuum source. We investigate the effect of the fiber geometry
on the spectral resolution and bandwidth, and also discuss the additional
limitation on the bandwidth imposed by speckle contrast reduction when
measuring dense spectra. Finally, we demonstrate a method to reduce the
spectrum reconstruction error and increase the bandwidth by separately imaging
the speckle patterns of orthogonal polarizations. The multimode fiber
spectrometer is compact, lightweight, low cost, and provides high resolution
with low loss.
