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Novel concepts of nonmagnetic nonlinear-optical (NLO) photonic metamaterials (MMs) are proposed. They concern with coherent NLO energy exchange between ordinary and backward waves (BWs) through the frequency-conversion processes. Two different classes of materials which support BWs are considered: MMs with specially engineered spatial dispersion and crystals that support optical phonons with negative group velocity. The possibility to replace plasmonic NLO MMs enabling magnetic response at optical frequencies, which are very challenging to engineer, by the ordinary readily available crystals, are discussed. The possibility to mimic extraordinary NLO frequency-conversion propagation processes attributed to negative-index MMs is shown in some of such crystals, if optical phonons with negative group velocity and a proper phase-matching geometry are implemented. Here, optical phonons are used as one of the coupled counterparts instead of backward electromagnetic wave (BEMWs). The appearance of BEMWs in metaslabs made of carbon nanotubes, the possibilities and extraordinary properties of BW second harmonic generation in such a MM is another option of nonmagnetic NIMs which is described too. The possibility of creation of a family of unique BW photonic devices is discussed.

negative-index metamaterials, nonlinear optics