Magneto-optic perturbation theory for near-complete violation of Kirchhoff's law of thermal emission at low magnetic fields

Abstract

Magneto-optic photonic systems can violate Kirchhoff's law of thermal emission by breaking Lorentz reciprocity. We develop a dispersive perturbation theory yielding an analytical expression for magneto-optical resonance frequency shifts in plasmonic semiconductors under applied magnetic fields. This expression shows the shift is governed by the overlap of the mode's optical spin density with the magneto-optical material. We use this expression to design a III-V metasurface that achieves nonreciprocal emissivity contrast of 0.8 at only 0.1 T, and demonstrate that the theory can explain order-of magnitude differences in magnetic field sensitivity between different photonic structures.

Figures (4)

• Figure 1: (a) Schematic of the structure used for theory verification. From top to bottom, the structure consists of a undoped InGaAs grating with d = 5 $\mu$m and grating period $\Lambda$ = 10 $\mu$m that is 0.27 $\mu$m tall, undoped InGaAs substrate that is 4 $\mu$m thick, lightly doped InAs that is 5 $\mu$m thick, and a heavily doped InAs layer that is optically thick enough to act as a perfect reflector. (b) Resulting color plot that shows $\varepsilon_{0.1T}-\varepsilon_{0T}$ for a p-polarized incident wave. An external magnetic field is applied in the z direction within both the InAs layers. The bright yellow band shows the shifted resonance peaks upon application of magnetic field while the darker band are the original locations of the 0 T peaks.The black dots are the perturbation theory predictions at a particular incident angle.
• Figure 2: (a) Emissivity spectra for a range of magnetic fields between 0.15T and -0.15T at 0.05T intervals. The vertical lines are the resonance frequency shifts predicted by the pertubation theory from the 0 T resonance frequency. (b) the change in emissivity where $\Delta \varepsilon = \varepsilon_{0.1T} - \varepsilon_{0T}$ as the applied magnetic field is swept from 0 T to 0.2T. To provide a sense of the high magnetic field sensitivity, the structure in reference [19] is used as a comparison.
• Figure 3: (a) Schematic of a second GMR structure with Germanium on top of a highly doped InAs layer on top of a Au reflector layer. (b) Emissivity spectra at 77 degrees plotted at 0 T and 3T. (c)Comparison of the $\Delta \omega$ frequency shift values as the applied magnetic field strength is increased. The solid lines indicate the perturbation theory prediction for grating structures 1 and 2, while the dots are the frequency shifts calculated directly from FEM simulations.
• Figure 4: (a) Comparisons of the field expression $|Im(E^*_x E_y- E_x E^*_y)|$ between the 1st grating at $72^{\circ}$ and 2nd grating at $77^{\circ}$. (b) Comparisons of the field expression $|Im(E^*_x E_y- E_x E^*_y)|$ within the InAs layer between structure 1 at $72^{\circ}$ and structure 2 at $77^{\circ}$.