Context : Multi-wavelength , optical to IR/sub-mm observations of strongly lensed galaxies identified by the Herschel Lensing Survey are used to determine the physical properties of high-redshift star-forming galaxies close to or below the detection limits of blank fields .

Aims : We aim to constrain their stellar and dust content , determine star formation rates and histories , dust attenuation and extinction laws , and other related properties .

Methods : We study a sample of 7 galaxies with spectroscopic redshifts z \sim 1.5 - 3 , which are well detected thanks to gravitational lensing , and whose SED is well determined from the rest-frame UV to the IR/mm domain .
For comparison , our sample includes two previously well-studied lensed galaxies , MS1512-cB58 and the Cosmic Eye , for which we also provide updated Herschel measurements .
We perform SED-fits of the full photometry of each object as well for the optical and infrared parts separately , exploring various star formation histories , using different extinction laws , and exploring the impact of nebular emission .
The IR luminosity , in particular , is predicted consistently from the stellar population model .
The IR observations and emission line measurements , where available , are used as a posteriori constraints on the models .
We also explore “ energy conserving models ” , that we create by using the observed IR/UV ratio to estimate the extinction .

Results : Among the models we have tested , models with exponentially declining star-forming histories including nebular emission and assuming the Calzetti attenuation law best fit most of the observables .
SED fits assuming constant or rising star formation histories predict in most cases too much IR luminosity .
The SMC extinction law underpredicts the IR luminosity in most cases , except for 2 out of 7 galaxies , where we can not distinguish between different extinction laws .
Our sample has a median lensing-corrected IR luminosity \sim 3 \times 10 ^ { 11 } L _ { \odot } , stellar masses between 2 \times 10 ^ { 9 } and 2 \times 10 ^ { 11 } M _ { \odot } , and IR/UV luminosity ratios spanning a wide range .
The dust masses of our galaxies are in the range [ 2 - 17 ] \times 10 ^ { 7 } M _ { \odot } , extending previous studies at the same redshift down to lower masses .
We do not find any particular trend of the dust temperature T _ { dust } with L _ { IR } , suggesting an overall warmer dust regime at our redshift regardless of IR luminosity .

Conclusions : Gravitational lensing enables us to study the detailed physical properties of individual IR-detected z \sim 1.5 - 3 galaxies up to a factor \sim 10 fainter than achieved with deep blank field observations .
We have in particular demonstrated that multi-wavelength observations combining stellar and dust emission can constrain star formation histories and extinction laws of star-forming galaxies , as proposed in an earlier paper .
Fixing the extinction based on the IR/UV observations successfully breaks the age-extinction degeneracy often encountered in obscured galaxies .