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We present a detailed multi-wavelength study (from rest-frame UV to far-IR)of narrow-band (NB) selected, star-forming (SF) H$\alpha$ emitters (HAEs) at $z\sim 2.23$ taken from the High Redshift(Z) Emission Line Survey (HiZELS). Wefind that HAEs have similar SED-derived properties and colors to $sBzK$galaxies and probe a well-defined portion of the SF population at $z \sim 2$.This is not true for Ly$\alpha$ emitters (LAEs), which are strongly biasedtowards blue, less massive galaxies (missing a significant percentage of the SFpopulation). Combining our H$\alpha$ observations with matched, existingLy$\alpha$ data we determine that the Ly$\alpha$ escape fraction ($f_{\rmesc}$) is low (only $\sim$ 4.5\% of HAEs show Ly$\alpha$ emission) anddecreases with increasing dust attenuation, UV continuum slope, stellar mass,and star formation rate (SFR). This suggests that Ly$\alpha$ preferentiallyescapes from blue galaxies with low dust attenuation. However, a smallpopulation of red and massive LAEs is also present in agreement with previousworks. This indicates that dust and Ly$\alpha$ are not mutually exclusive.Using different and completely independent measures of the total SFR we showthat the H$\alpha$ emission is an excellent tracer of star formation at $z \sim2$ with deviations typically lower than 0.3 dex for individual galaxies. Wefind that the slope and zero-point of the HAE main-sequence (MS) at $z \sim 2$strongly depend on the dust correction method used to recover SFR, althoughthey are consistent with previous works when similar assumptions are made.

On the nature of H$\alpha$ emitters at $z \sim 2$ from the HiZELS survey: physical properties, Ly$\alpha$ escape fraction, and main sequence