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We present a computationally efficient spectral ray tracing (SRT) method that requires one spectral domain integration step for each observation point. We compare the SRT method with the finite element method (FEM) and geometrical optics (GO) via simulation of terahertz Gaussian beam propagation through a hemispherical lens. The SRT was able to accurately solve the problem 30 times faster than FEM. The matrix formulation of SRT is promising for solving complex electrically large problems with high accuracy and 2 orders of magnitude reduction in computation time through parallel processing.