Nonreciprocity in millimeter wave devices using a magnetic grating metamaterial

The control and manipulation of many of light's fundamental properties, such as reflectivity, has become a topic of increasing interest since the advent of engineered electromagnetic structures—now known as metamaterials. Many of these metamaterial structures are based on the properties of dielectric materials. Magnetic materials, on the other hand, have long been known to interact with electromagnetic waves in unusual ways; in particular, their nonreciprocal properties have enabled rapid advances in millimeter wave technology. Here, we show how a structured magnetic grating can be employed to engineer electromagnetic response at frequencies upwards of hundreds of gigahertz. In particular, we investigate how nonreciprocal reflection can be induced and controlled in this spectral region through the composition of the magnetic grating. Moreover, we find that both surface and guided polaritons contribute to high-frequency nonreciprocity; the nature of these is also investigated. Control of electromagnetic radiation at high frequencies is a current challenge of communications technology where our magnetic gradient might be employed in devices including signal processing filters and unidirectional isolators.

Figure 1

(a) Geometry of a nanostructured magnetic film of thickness $d$ where the individual stripes have width $d_1$ and spaced by $d_2$. The geometry of the incident electromagnetic wave is also shown; a TE-polarized incident beam whose E field is directed along $z$ and perpendicular to the structuring direction. (b) Illustration of the Kretschmann ATR geometry with the magnetic grating, static applied field ${\mathbf{H}}_0$, and the coordinate axes. The incident wave (also TE-polarized) is at an angle $\theta$ with respect to the surface normal inside a dielectric prism.

Figure 2

(a) ATR spectra maps showing the reflectance as a function of incident angle and frequency. The overlayer has a dielectric constant of ${\varepsilon }_p=2.968$ and the substrate's is ${\varepsilon }_s=1.33$. The middle layer takes the effective dielectric constant of the metallic grating ${\varepsilon }_{\mathrm{eff}}$, albeit being nonmagnetic [so that $\overleftrightarrow{\mu }\left(\omega \right)=1$]. Here, $f_m=0.61$, and $d=0.1$ cm. Note that all three dielectric constants are purely real, and in (b) we show the effect of damping by making the dielectric constant of the substrate ${\varepsilon }_3=1.33+0.5i$.

Figure 3

ATR spectra map for the same dielectric parameters as 3(b) except now the magnetic permeability is also included [according to Eq. (5)]. We note the distinct nonreciprocity in the reflectivity for $\left|\theta \right|>{50}^{\circ }$ at frequencies ranging from about 30–80 GHz. Using the horizontal black line, as a guide, at 150 GHz we can see there is also substantial nonreciprocity even at that frequency.

Figure 4

ATR spectra maps for different values of the filling factor, $f_1$. The color bar on the right gives the reflectance values, which in the maps are plotted as a function of both the incident angle and the frequency. The specific parameters for these plots are ${\mu }_0{H}_0=0.4\mathrm{T}$, $d=0.1\mathrm{cm}$, $\alpha =0.02$. The dielectric parameters for all layers are those of Fig. 2.

Figure 5

Geometry used for the calculation of the dispersion relation for bound polaritons.

Figure 6

(a) Dispersion relations for bound polariton states in the three-layer geometry when the effective medium is not magnetic. The color map presents the ${log}_{10}\left(\right|\mathcal{M}\left|\right)$ as a function of Re($k_{\parallel }$) and ω as discussed in the text. (b)–(d) Profiles of guided waves at different frequencies.

Figure 7

(a) Dispersion relations for bound polariton states in the three-layer geometry with the magnetic metallic material. The color map presents the ${log}_{10}\left(\right|\mathcal{M}\left|\right)$ as a function of Re($k_{\parallel }$) and $\omega$ as discussed in the text. (b)–(e) polariton profiles which are different.