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Most electromagnetic problems deal with media with unit permeability. However, recent interest in metamaterials necessitated studies of wave characteristics in media with arbitrary permittivity and permeability whose real parts can be positive or negative. This paper presents analysis of wave characteristics on semiinfinite metamaterials. Waves are excited by electric or magnetic line sources, and the problem is separated into the p (TM) and the s (TE) polarization, showing symmetries. The Fourier spectra of the reflection and transmission coefficients are examined and the poles, branch points, and zeros are shown in the real μ-real ε diagram. We clarify the location of poles in proper and improper Riemann Surfaces, and the excitation of forward and backward surface waves, forward and backward Lateral waves, and Zenneck waves, and the relations between Brewster's angle and Sommerfeld poles. We include the behaviors of the backward surface waves and the temporal backward Lateral waves.