  Probing optical excitations with high resolution is important for
understanding their dynamics and controlling their interaction with other
photonic elements. This can be done using state-of-the-art electron
microscopes, which provide the means to sample optical excitations with
combined meV--sub-nm energy--space resolution. For reciprocal photonic systems,
electrons traveling in opposite directions produce identical signals, while
this symmetry is broken in nonreciprocal structures. Here, we theoretically
investigate this phenomenon by analyzing electron energy-loss spectroscopy
(EELS) and cathodoluminescence (CL) in structures consisting of magnetically
biased InAs as an instance of gyrotropic nonreciprocal material. We find that
the spectral features associated with excitations of InAs films depend on the
electron propagation direction in both EELS and CL, and can be tuned by varying
the applied magnetic field within a relatively modest sub-tesla regime. The
magnetic field modifies the optical field distribution of the sampled
resonances, and this in turn produces a direction-dependent coupling to the
electron. The present results pave the way to the use of electron microscope
spectroscopies to explore the near-field characteristics of nonreciprocal
systems with high spatial resolution.
