## 4 Discussion
We showed that, at least in some cases, the samples studied could serve for this purpose. On the other hand, one could also try to use samples with etched gratings as non-resonant (or broad band detectors), particularly with an additional illumination with white light. As it is shown in Figures 7 and 8, the width of a plasmonic response can be equal to about 1 T which allows to detect radiation with frequency range of about 0.25 THz. A broadening of the line under illumination is observed in all samples. According to theoretical considerations presented in [PERSON] [37], the width \(w\) of the resonance is a sum of two contributions: \(w=\gamma+\Gamma\), where \(\gamma\) is a scattering decay while \(\Gamma\) is a radiative decay. However, as it is shown in [PERSON] [37], in the case of a 2 DEG with a high electron mobility, \(\Gamma/\gamma\sim\sigma_{0}\) and \(\Gamma>>\gamma\) ; \(\sigma_{0}\) is a static conductivity at \(B=0\). The last relation means that in fact \(w\approx\Gamma\) due to a large value of \(\sigma_{0}\). Thus, one can conclude that broadening of the line is related to an increase of \(\Gamma\) which is consistent with the fact that conductivity of CdTe/CdMgTe QWs increases under illumination. The results show that grating metamaterials presented in this work can be useful as magnetic field tuneable (quasi-) resonant detectors of THz radiation. Looking on transmission spectra presented above we find that a typical width of the resonant line is equal to about \(\Delta B\approx 0.4\) T which corresponds to uncertainity of frequency equal to \(\Delta f\approx 0.12\) THz (the relation between \(\Delta B\) and \(\Delta f\) is determined from \(\omega_{\sigma}=eB/m^{*}\)). However, in the case of etched grating on a single quantum well (Figure 8), \(\Delta B\approx 0.18\) T which leads to \(\Delta f\approx 0.05\) THz and \(\Delta f/f\approx 0.02\). Let us also note that this detector shows a resonant line which is due to plasmonic excitations. Thus, it is a detector with a strong plasmonic response. Generally, this offers a broader possibility to tune the resonance (by geometry of the sample, influence of white light), in comparison with a detector based on the CR which response frequency is firmly fixed by the electron effective mass. In conclusion, we carried out low-temperature magnetotransmission measurements on semiconductor metamaterials based on CdTe/CdMgTe modulation doped structures which formed one or two quantum wells with a 2 DEG. The samples were equipped with Au or etched gratings. We showed that metamaterials studied showed a response to monochromatic THz radiation resulted from excitation of plasmons in two-dimensional quantum wells. By studying samples with etched gratings of different geometrical parameters we showed an influence of the etching process on depopulation of quantum wells. Also, we showed a strong response of plasmonic resonances to illumination of metamaterials with white light. A broad spectrum of response exhibited by samples with different parameters of grating allows us to propose such metamaterials as possible THz detectors and filters (both resonant and quasi-resonant) working at high magnetic fields, tuneable by magnetic field and white light. Conceptualization and methodology, D.Y. and J.L. ; investigation D.Y., M.S., K.K., R.B., R.R., G.K., T.W. and J.W., writing--original draft preparation, review and editing, supervision, J.L. All authors have read and agreed to the published version of the manuscript. This research was partially supported by Polish National Science Centre UMO-2015/17/B/ST7/03630 and UMO-2017/27/N/ST7/01771 grants and the Foundation for Polish Science through a TEAM/2016-3/25 and the IRA Programme co-financed by EU within SG OP (grants No. MAB/2017/1 and MAB/2018/19). The authors declare no conflict of interest.