We study the transmission properties of structures with one or two kinds of lossy single-negative (permittivity-negative and permeability-negative) material. Analytic results show that the transmission of the structure depends on the material absorption and reflection. In sharp contrast to lossy dielectrics, the reflection of the lossy single-negative material(s) can decrease as the dissipation coefficient increases. As a result, the transmission of the lossy single-negative material(s) will be nonmonotonic as the dissipation coefficient varies. In particular, the transmission can be enhanced even when the dissipation coefficient increases.
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