Negative refractive index (NRI) has been reported to be the requirement for negative refraction of electromagnetic waves in isotropic media. Such discussions have assumed that the material is lossless. Mctamaterials have been used to create effective media with NRI by exciting plasmon-like resonances. In reality, there are no lossless metamatcrials. In this paper, we derive the conditions for negative refraction of electromagnetic waves in isotropic and lossy media. The angles for phase refraction and energy refraction are different in lossy media. NRI is required for the negative refraction of phase but is not a requirement for achieving negative refraction of energy in lossy media. Negative permittivity or negative permeability is required for negative energy refraction at TM polarization and TE polarization, respectively. NRI is not necessary for negative energy refraction in lossy media.
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