Optical parametric amplification controlled by the auxiliary electromagnetic field enables transparency, amplification, and oscillation with no cavity in strongly absorbing negative-index metamaterials. The opposite directions of the wave vector and the Poynting vector in such materials result in extraordinary optical properties, including "backward" phase matching and the generation of entangled pairs of left-and right-handed counterpropagating photons. © 2006 Optical Society of America OCIS code: 190.4410. Metamaterials with a negative refractive index (NIMs), also referred to as left-handed metamaterials (LHMs), exhibit highly unusual electromagnetic properties and promise a variety of novel applications, particularly for nonlinear optical phenomena. As shown recently, NIMs that include structural elements with nonsymmetric current-voltage characteristics can possess a nonlinear magnetic response at optical frequencies 1-3 and thus combine unprecedented linear and nonlinear electromagnetic properties. The opposite directions of the wave and Poynting vectors inherent for NIMs lead to extraordinary properties for basic optical processes in such metamaterials. The possibility of exact phase matching for waves with counterpropagating energy flows has been shown in Ref. 4 for the case of secondharmonic generation (SHG), when the fundamental wave is in the negative-index frequency domain while the SH wave is in the positive-index domain (PID). As seen from our considerations, phase matching of forward and backward waves is inherent for the nonlinear optics of NIMs. Important advantages of the interaction schemes involving counterdirected Poynting vectors in the process of optical parametric amplification for conventional right-handed materials (RHMs), also referred to as positive-index materials (PIMs), were discussed in early papers.5-7 However, in RHMs such schemes impose severe limitations on the frequencies of the coupled waves, because one of the waves must be in the far-infrared range in this case. [5][6][7] Absorption is one of the largest problems that needs to be addressed to enable applications of NIMs. 8,9 A transfer of the near-field image into the SH frequency domain, where absorption is typically much less, was proposed in Refs. 10 and 11 as a means to overcome dissipative losses and thus enable the NIM-based superlens. This Letter proposes an alternative means for compensating losses, by producing entire transparency amplification, or even lasing without a cavity in NIMs, with the aid of only one control auxiliary electromagnetic field. The underlying physical mechanism is based on optical parametric amplification (OPA), where a positive-index control field enables a loss-balancing OPA for a negativeindex signal wave. We also predict the possibility of the generation of entangled pairs of counterpropagating right-and left-handed photons.We assume a negative-index wave at 1 (signal; n 1 Ͻ 0) has a wave vector k 1 , which is directed along the z axis, and an energy flow S 1 , which is directed agai...