  The supernova remnant SNR 0540-69.3, twin of the Crab Nebula, offers an
excellent opportunity to study the continuum emission from a young pulsar and
pulsar-wind nebula (PWN). We present observations taken with the VLT
instruments MUSE and X-shooter in the wavelength range 3000-25,000 \r{A}, which
allow us to study spatial variations of the optical spectra, along with the
first near-infrared (NIR) spectrum of the source. We model the optical spectra
with a power law (PL) $F_\nu\propto\nu^{-\alpha}$ and find clear spatial
variations (including a torus-jet structure) in the spectral index across the
PWN. Generally, we find spectral hardening toward the outer parts, from
$\alpha\sim1.1$ to $\sim0.1$, which may indicate particle reacceleration by the
PWN shock at the inner edge of the ejecta or alternatively time variability of
the pulsar wind. The optical-NIR spectrum of the PWN is best described by a
broken PL, confirming that several breaks are needed to model the full spectral
energy distribution of the PWN, suggesting the presence of more than one
particle population. Finally, subtracting the PWN contribution from the pulsar
spectrum we find that the spectrum is best described with a broken-PL model
with a flat and a positive spectral index, in contrast to the Crab pulsar that
has a negative spectral index and no break in the optical. This might imply
that pulsar differences propagate to the PWN spectra.
