  The Hermite-Gaussian (HG) modes, sometimes also referred to as transverse
electromagnetic modes in free space, form a complete and orthonormal basis that
have been extensively used to describe optical fields. In addition, these modes
have been shown to be helpful to enhance information capacity of optical
communications as well as to achieve super-resolution imaging in microscopy.
Here we propose and present the realization of an efficient, robust mode sorter
that can sort a large number of HG modes based on the relation between HG modes
and Laguerre-Gaussian (LG) modes. We experimentally demonstrate the sorting of
16 HG modes, and our method can be readily extended to a higher-dimensional
state space in a straightforward manner. We expect that our demonstration will
have direct applications in a variety of fields including fiber optics,
classical and quantum communications, as well as super-resolution imaging.
