We provide the most accurate estimate yet of the bright end of the infrared (IR) luminosity functions (LFs) and the abundance of hyperluminous IR galaxies (HLIRGs) with IR luminosities > 10^13 L_solar, thanks to the combination of the high sensitivity, angular resolution, and large area of the LOFAR Deep Fields, which probes an unprecedented dynamic range of luminosity and volume. We cross-match Herschel sources and LOFAR sources in Bootes (8.63 deg^2), Lockman Hole (10.28 deg^2), and ELAIS-N1 (6.74 deg^2) with rms sensitivities of around 32, 22, and 20 mJy per beam, respectively. We divide the matched samples into unique and multiple categories. For the multiple matches, we de-blend the Herschel fluxes using the LOFAR positions and the 150-MHz flux densities as priors. We perform spectral energy distribution (SED) fitting, combined with multi-wavelength counterpart identifications and photometric redshift estimates, to derive IR luminosities. The depth of the LOFAR data allows us to identify highly complete (around 92% completeness) samples of bright Herschel sources with a simple selection based on the 250 micron flux density (45, 40, and 35 mJy in Bootes, Lockman Hole, and ELAIS-N1, respectively). Most of the bright Herschel sources fall into the unique category (i.e. a single LOFAR counterpart). For the multiple matches, there is excellent correspondence between the radio emission and the far-IR emission. We find a good agreement in the IR LFs with a previous study out to z around 6 which used de-blended Herschel data. Our sample gives the strongest and cleanest indication to date that the population of HLIRGs has surface densities of around 5 to 18 / deg^2 (with variations due to a combination of the applied flux limit and cosmic variance) and an uncertainty of a factor of 2. In comparison, the GALFORM semi-analytic model significantly under-predicts the abundance of HLIRGs.
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