  This paper considers a scenario in which the Terahertz (THz) transmitter
equipped with a linear antenna array wishes to focus its beam to a desired
spatial region in the array near-field. The goal is to compute the achievable
spatial region and determine how the system parameters such as the carrier
frequency, the array dimension and the user's location affect its beam focusing
performance. First, based on a theorem from analytic geometry, we show that the
achievable focusing spatial region constitutes a rotated ellipse, with the x
and y coordinates denoting the range and angle, respectively. In this way, the
determination of the spatial region is reduced to a problem of deriving the
coverage of an ellipse. The achievable coverage is then obtained in closed
form, and the construction of carrier frequency offsets that can analytically
control the beam focusing performance is provided. Numerical results validate
the theoretical findings and demonstrate the performance of the proposed
method.
