  We present the Texas Euclid Survey for Lyman-Alpha (TESLA), a spectroscopic
survey in the 10 square degree of the Euclid North Ecliptic Pole (NEP) field.
Using TESLA, we study how the physical properties of Lyman-alpha emitters
(LAEs) correlate with Lyman-alpha emission to understand the escape of Lyman
alpha from galaxies at redshifts 2 -- 3.5. We present an analysis of 43 LAEs
performed in the NEP field using early data from the TESLA survey. We use
Subaru Hyper Suprime-Cam imaging in the grizy-bands, Spitzer/IRAC channels 1
and 2 from the Hawaii 20 square degree (H20) survey and spectra acquired by the
Visible Integral-Field Replicable Unit Spectrograph (VIRUS) on the Hobby-Eberly
Telescope. We perform spectral energy distribution (SED) fitting to compute the
galaxy properties of 43 LAEs, and study correlations between stellar mass, star
formation rate (SFR), and dust, to the Lyman-alpha rest-frame equivalent widths
(EW). We uncover marginal (1 sigma significance) correlations between stellar
mass and Lyman-alpha EW, and star formation rate (SFR) and Lyman-alpha EW, with
a Spearman correlation coefficient of -0.$34_{-.14}^{+.17}$ and
-0.$37_{-.14}^{+.16}$ respectively. We show that the Lyman-alpha distribution
of the 43 LAEs is consistent with being drawn from an exponential distribution
with an e-folding scale of 150 Angstrom. Once complete the TESLA survey will
enable the study of ~ thousands of LAEs to explore correlations between galaxy
properties and Lyman-alpha EW. The large sample size will allow the
construction of a predictive model for the Lyman-alpha EW as a function of
SED-derived galaxy properties, which could be used to improve Lyman-alpha based
constraints on reionization.
