We present the results of a near-infrared imaging survey of z \sim 3 Lyman Break Galaxies ( LBGs ) .
The survey covers a total of 30 arcmin ^ { 2 } and includes 118 photometrically selected LBGs with K _ { s } band measurements , 63 of which also have J band measurements , and 81 of which have spectroscopic redshifts .
Using the distribution of optical { \cal R } magnitudes from previous work and { \cal R } - K _ { s } colors for this sub-sample , we compute the rest-frame optical luminosity function of LBGs .
This luminosity function is described by an analytic Schechter fit with a very steep faint end slope of \alpha = -1.85 \pm 0.15 , and it strikingly exceeds locally determined optical luminosity functions at brighter magnitudes , where it is fairly well constrained .
The V -band luminosity density of only the observed bright end of the z \sim 3 LBG luminosity function already approaches that of all stars in the local universe .

For the 81 galaxies with measured redshifts , we investigate the range of LBG stellar populations implied by the photometry which generally spans the range 900–5500 Å in the rest-frame .
The parameters under consideration are the star-formation rate as a function of time , the time since the onset of star-formation , and the degree of reddening and extinction by dust .
While there are only weak constraints on the parameters for most of the individual galaxies , there are strong trends in the sample as a whole .
With a wider wavelength baseline than most previous studies at similar redshifts , we confirm the trend that intrinsically more luminous galaxies are dustier .
We also find that there is a strong correlation between extinction and the age of the star-formation episode , in the sense that younger galaxies are dustier and have much higher star-formation rates .
The strong correlation between extinction and age , which we show is unlikely to be an artifact of the modeling procedure , has important implications for an evolutionary sequence among LBGs .
A unified scenario which accounts for the observed trends in bright LBGs is one in which a relatively short period of very rapid star-formation ( hundreds of M _ { \sun } yr ^ { -1 } ) lasts for roughly 50–100 Myr , after which both the extinction and star-formation rate are considerably reduced and stars are formed at a more quiescent , but still rapid , rate for at least a few hundred Myr .
In our sample , a considerable fraction ( \sim 20 % ) of the LBGs have best-fit star-formation ages \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 1 Gyr , implied stellar masses of \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 10 ^ { 10 } M _ { \sun } , and are still forming stars at \sim 30 M _ { \sun } yr ^ { -1 } .