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We analyze the possibilities of constructing a novel metamaterial with the arrangement of structural layers as in quantum cascade laser. The starting point is the Lorentz model of atomic electrical susceptibility. Within this model, the total permittivity consists of two terms: the first term is the averaged permittivity of the background material, while the second one is proportional to the difference of electron occupation densities of corresponding energy levels. In case of a passive configuration (where upper levels are less occupied than the lower ones), the imaginary part of this second term of permittivity is always positive. However, if the occupation of levels is inverse (active configuration), the total permittivity could be made negative (both the real and the imaginary part), which is important for design of photonic heterostructures and effective manipulation of light. A favorable candidate for illustration of these effects of advanced dispersion engineering is the quantum cascade laser in a strong magnetic field. Considerable (negative) values of the second term of permittivity may be achieved even by low carrier charge sheet densities (on the order of 109 cm−2), owing to narrow absorption linewidths and large matrix elements. Numerical results obtained for GaAs/AlGaAs quantum cascade lasers illustrate significant potential for tuning of the sign and magnitude of the real and the imaginary part of the total permittivity with magnetic field.

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In order to avoid losses in metamaterial unit cells at frequencies of interest, caused by metallic inclusions, an active medium design has been proposed. As candidate structures for this active medium, we have chosen quantum cascade lasers because of their high output gain. Here we analyze and compare two quantum cascade structures that emit at 4.6 THz and 3.9 THz, respectively, placed under the influence of a strong magnetic field. We first solve the full system of rate equations for all relevant Landau levels, and obtain the necessary information about carrier distribution among the levels, after which we are able to evaluate the permittivity component along the growth direction of the structure. With these data one can determine the conditions under which negative refraction occurs, and calculate the values of the refractive index of the structure, as well as the range of frequencies at which the structure exhibits negative refraction for a predefined total electron sheet density.

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