We present stellar population modeling results for 10 newly discovered Lyman alpha emitting galaxies ( LAEs ) , as well as four previously known LAEs at z \sim 4.5 in the Chandra Deep Field – South . We fit stellar population models to these objects in order to learn specifically if there exists more than one class of LAE . Past observational and theoretical evidence has shown that while many LAEs appear to be young , they may be much older , with Ly \alpha EWs enhanced due to resonant scattering of Ly \alpha photons in a clumpy interstellar medium ( ISM ) . Our results show a large range of stellar population age ( 3 – 500 Myr ) , stellar mass ( 1.6 \times 10 ^ { 8 } – 5.0 \times 10 ^ { 10 } M _ { \odot } ) and dust extinction ( A _ { 1200 } = 0.3 – 4.5 mag ) , broadly consistent with previous studies . With such a large number of individually analyzed objects , we have looked at the distribution of stellar population ages in LAEs for the first time , and we find a very interesting bimodality , in that our objects are either very young ( < 15 Myr ) or old ( > 450 Myr ) . This bimodality may be caused by dust , and it could explain the Ly \alpha duty cycle which has been proposed in the literature . We find that eight of the young objects are best fit with a clumpy ISM . We find that dust geometry appears to play a large role in shaping the SEDs that we observe , and that it may be a major factor in the observed Ly \alpha equivalent width distribution in high redshift Ly \alpha galaxies , although other factors ( i.e . outflows ) may be in play . We conclude that 12 out of our 14 LAEs are dusty star-forming galaxies , with the other two LAEs being evolved galaxies .