We present an atlas of a sample of local ( z < 0.1 ) LIRGs ( 10 ) and ULIRGs ( 7 ) covering the luminosity range log ( L _ { IR } /L _ { \odot } ) = 11.1 - 12.4 . The atlas is based on near-infrared H ( 1.45 - 1.85 { \mu } m ) and K-band ( 1.95 - 2.45 { \mu } m ) VLT-SINFONI integral field spectroscopy ( IFS ) . The atlas presents the ionised , partially ionised , and warm molecular gas two-dimensional flux distributions and kinematics over a FoV of \sim 3 \times 3 kpc ( LIRGs ) and \sim 12 \times 12 kpc ( ULIRGs ) and with average linear resolutions of \sim 0.2 kpc and \sim 0.9 kpc , respectively . The different phases of the gas show a wide morphological variety with the nucleus as the brightest Br \gamma source for \sim 33 % of the LIRGs and \sim 71 % of the ULIRGs , whereas all the LIRGs and ULIRGs have their maximum H _ { 2 } emission in their nuclear regions . In LIRGs , the ionised gas distribution is dominated by the emission from the star-forming rings or giant HII regions in the spiral arms . The Br \gamma and [ FeII ] line at 1.644 \mu m trace the same structures , although the emission peaks at different locations in some of the objects , and the [ FeII ] seems to be more extended and diffuse . The ULIRG subsample is at larger distances and contains mainly pre-coalescence interacting systems . Although the peaks of the molecular gas emission and the continuum coincide in \sim 71 % of the ULIRGs , regions with intense Pa \alpha ( Br \gamma ) emission tracing luminous star-forming regions located at distances of 2–4 kpc away from the nucleus are also detected , usually associated with secondary nuclei or tidal tails . LIRGs have mean observed ( i.e . uncorrected for internal extinction ) SFR surface densities of about 0.4 to 0.9 M _ { \odot } yr ^ { -1 } kpc ^ { -2 } over large areas ( 4–9 kpc ^ { 2 } ) with peaks of about 2 - 2.5 M _ { \odot } yr ^ { -1 } kpc ^ { -2 } in the smaller regions ( 0.16 kpc ^ { 2 } ) associated with the nucleus of the galaxy or the brightest Br \gamma region . ULIRGs do have similar average SFR surface densities for the integrated emitting regions of \sim 0.4 M _ { \odot } yr ^ { -1 } kpc ^ { -2 } in somewhat larger areas ( 100 - 200 kpc ^ { 2 } ) and for the Pa \alpha peak ( \sim 2 M _ { \odot } yr ^ { -1 } kpc ^ { -2 } in 4 kpc ^ { 2 } ) . The observed gas kinematics in LIRGs is primarily due to rotational motions around the centre of the galaxy , although local deviations associated with radial flows and/or regions of higher velocity dispersions are present . The ionised and molecular gas share the same kinematics ( velocity field and velocity dispersion ) to first order , showing slight differences in the velocity amplitudes ( peak-to-peak ) in some cases , whereas the average velocity dispersions are compatible within uncertainties . As expected , the kinematics of the ULIRG subsample is more complex , owing to the interacting nature of the objects of the sample .