  Context. Lyman alpha emitting galaxies (LAEs) are used to probe the distant
universe and are therefore important for galaxy evolution studies and for
providing clues to the nature of the epoch of reionization, but the exact
circumstances under which Lyman alpha escapes a galaxy are still not fully
understood.
  Aims. The Trident project is designed to simultaneously examine Lyman alpha,
H-alpha and Lyman Continuum emission from galaxies at redshift z~2, thus
linking together these three aspects of ionising radiation in galaxies. In this
paper, we outline the strategy of this project and examine the properties of
LAEs in the GOODS North field.
  Methods. We performed a narrowband LAE survey in GOODS North using existing
and two custom made filters at the Nordic Optical Telescope with MOSCA. We use
complementary broad band archival data in the field to make a careful candidate
selection and perform optical to near-IR SED fitting. We also estimate
far-infrared luminosities by matching our candidates to detections in
Spitzer/MIPS 24{\mu}m and Herschel/PACS catalogs.
  Results. We find a total of 25 LAE candidates, probing mainly the bright end
of the LAE luminosity function with L_Ly {\alpha} ~ 1-15e42 erg/s. They display
a range of masses of ~0.5-50e9 M_solar, and average ages from a few tens of Myr
to 1 Gyr when assuming a constant star formation history. The majority of our
candidates also show signs of recent elevated star formation. Three candidates
have counterparts in the GOODS-Herschel far-IR catalogue, with luminosities
consistent with ultra-luminous infrared galaxies (ULIRGs).
  Conclusions. The wide range of parameters derived from our SED fitting, as
well as part of our sample being detected as ULIRGs, seems to indicate that at
these Lyman alpha luminosities, LAEs do not necessarily have to be young
dwarfs, and that a lack of dust is not required for Lyman alpha to escape.
