A plane wave travels along x1 through the unit cube and hits one object; you set its position, shape, orientation and material. The wavelength is a quarter of the box. Start from the glass ball or the metal plate. Drag the cubes to rotate them; the three plane sliders move the cutting planes. All demos
$$\nabla\times\nabla\times E - k^2\,\varepsilon(x)\,E = 0\ \text{ in } \mathbb{R}^3,\qquad E = E_{\rm inc} + E_s,\quad E_{\rm inc} = e_3\,e^{ikx_1},\quad k = \tfrac{2\pi}{\lambda},\ \lambda = \tfrac14,$$
$$\varepsilon(x) = 1 + \chi_{\Omega}(x)\,\big(\varepsilon_r - 1 + i\,\sigma/\omega\big),\qquad \Omega = \big\{\,|x'_1/a_1|^p + |x'_2/a_2|^p + |x'_3/a_3|^p \le 1\,\big\},$$
with \(x'\) the coordinates relative to the centre \(c\), rotated by the two angles; \(E_s\) satisfies the outgoing radiation condition (absorbing layers around the box), time dependence \(e^{-i\omega t}\). Parameters: \(c, a, p\), the angles, \(\varepsilon_r \in [1, 2.5]\) and \(\sigma/\omega \in [0, 20]\) (large = metal). Grid: \(64^3\) cells.