Channel capacity lies at the core of wireless communication, yet determining it typically requires detailed channel information between the transmitter and receiver. For near field MIMO systems, obtaining the detailed native channel is often difficult or expensive. This paper develops a scheme to approximate the near field channel in a Gaussian beam domain. Hermite Gaussian (HG) modes are used to approximate the channel between a pair of square antenna arrays in a free space line of sight (LOS) environment. We show that HG modes efficiently represent the dominant singular modes of the native channel, enabling accurate channel estimation and capacity computation in the HG beam space. An iterative algorithm is proposed to approach the maximal channel capacity by gradually expanding the beam space dimension. Simulation results demonstrate that the method converges rapidly and significantly reduces channel estimation overhead.