  The ~1700 year old PSR B0540-69 in the LMC is considered the twin of the Crab
pulsar because of its similar spin parameters, magnetic field, and energetics.
Its optical spectrum is fit by a power-law, ascribed to synchrotron radiation,
like for the young Crab and Vela pulsars. nIR observations, never performed for
PSR B0540-69, are crucial to determine whether the optical power-law spectrum
extends to longer wavelengths or a new break occurs, like it happens for both
the Crab and Vela pulsars in the mIR, hinting at an even more complex particle
energy and density distribution in the pulsar magnetosphere. We observed PSR
B0540-69 in the J, H, and Ks bands with the VLT to detect it, for the first
time, in the nIR and characterise its optical-to-nIR spectrum. To disentangle
the pulsar emission from that of its pulsar wind nebula (PWN), we obtained
high-spatial resolution adaptive optics images with NACO. We could clearly
identify PSR B0540-69 in our J, H, and Ks-band images and measure its flux
(J=20.14, H=19.33, Ks=18.55, with an overall error of +/- 0.1 magnitudes in
each band). The joint fit to the available optical and nIR photometry with a
power-law spectrum gives a spectral index alpha=0.70 +/-0.04. The comparison
between our NACO images and HST optical ones does not reveal any apparent
difference in the PWN morphology as a function of wavelength. The PWN
optical-to-nIR spectrum is also fit by a single power-law, with spectral index
alpha=0.56+/- 0.03, slightly flatter than the pulsar's. Using NACO at the VLT,
we obtained the first detection of PSR B0540-69 and its PWN in the nIR. Due to
the small angular scale of the PWN (~4") only the spatial resolution of the
JWST will make it possible to extend the study of the pulsar and PWN spectrum
towards the mid-IR.
