Although there is a general consensus on the fact that pulsars ’ radio emission is coherent in nature , whereas the emission from the optical to high-energy \gamma -rays is due to incoherent processes , it has not been established yet at which wavelengths the transition occurs , a key information for all emission models of pulsar magnetospheres . Of course , to address this issue covering the spectral region between the GHz radio frequencies and the mid-infrared ( IR ) is crucial . We used the Atacama Large Millimetre Array ( ALMA ) to observe the Vela pulsar ( PSR B0833 - 45 ) , one of the very few observed in radio and from the mid-IR up to the very high-energy \gamma -rays . We detected Vela at frequencies of 97.5 , 145 , 233 , and 343.5 GHz , which makes it the first pulsar ever detected with ALMA . Its energy density spectrum follows a power-law of spectral index \alpha = -0.93 \pm 0.16 . This corresponds to very high brightness temperatures - from 10 ^ { 17 } to 10 ^ { 15 } K - suggesting that a coherent radiative process still contributes to the mm/sub-mm emission . Therefore , this is the first indication of coherent emission in pulsars extending to the sub-mm range . At the same time , we identified an extended structure , preliminarily detected in ground-based near-IR observations , at a distance of \sim 1 \farcs 4 from the pulsar , possibly interpreted as a counter-jet protruding from the pulsar .