Photomagnonic nanocavities for strong light–spin-wave interaction

The interaction of visible and near-infrared light with spin waves in appropriately designed dual nanocavities, for both photons and magnons, is investigated by means of rigorous calculations, correct to arbitrary order in the magneto-optical coupling parameter. It is shown that the concurrent localization of the interacting photon and magnon fields in the same region of space for a long period of time enhances their mutual interaction, provided that specific selection rules are fulfilled. Our results provide evidence for the occurrence of strong effects, beyond the linear response approximation, which lead to enhanced modulation of light by spin waves through multimagnon absorption and emission processes by a photon.

Figure 1

Schematic view of a symmetric photomagnonic cavity, formed by a trilayer ${\mathrm{TiO}}_2$/Bi:YIG/${\mathrm{TiO}}_2$ sandwiched between two ${\mathrm{SiO}}_2/{\mathrm{TiO}}_2$ multilayer Bragg mirrors. Each Bragg mirror consists of 14 periods, with lattice constant $a$, of alternating ${\mathrm{SiO}}_2$ and ${\mathrm{TiO}}_2$ layers, of thickness $0.6a$ and $0.4a$, respectively. The total thickness of the trilayer is fixed at $1.5a$ and the middle Bi:YIG film, $0.7a$ thick, is magnetically saturated perpendicular to the interfaces.

Figure 2

(a) Optical transmittance of the structure of Fig. 1, in the absence of magnonic excitation, in a narrow spectral range within the lowest Bragg gap where defect modes appear, for $s$- and $p$-polarized light incident at an angle corresponding to $q_{\parallel }a=1.2$. (b)–(e) Relative (with the respect to the incident field) amplitude profiles of the electric field components $i=x$ (dotted line), $i=y$ (dashed line), $i=z$ (solid line) at the corresponding resonances pointed with arrows in (a). The shaded areas mark the region of the magnetic film.

Figure 3

Oscillatory behavior of the optical resonance (b) [see Fig. 2], induced by a second-order $\left(n=2\right)$ perpendicular standing spin wave of relative amplitude $\eta =0.1$, about its eigenfrequency ${\omega }_0$ $\left({\omega }_{0}a/c=1.88271\right)$ in the absence of magnonic excitation, as manifested in a sequence of snapshots of the corresponding transmittance within a period of the spin wave.

Figure 4

Time variation of the modulus [(a),(b)] and phase [(c),(d)] of the complex transmission and reflection coefficients, respectively, for $p$-polarized light incident with $q_{\parallel }a=1.2$ on the structure of Fig. 1 at the given eigenfrequency ${\omega }_{0}a/c=1.88271$ of resonance (b) of Fig. 2, induced by a second-order $\left(n=2\right)$ perpendicular standing spin wave of relative amplitude $\eta =0.1$. Solid and dotted lines refer to $p$-to-$p$ and $p$-to-$s$ polarization scattering processes, respectively. (e), (f) Relative intensities of the inelastically (with respect to the elastically) transmitted and reflected light beams.

Figure 5

(a) Relative (with respect to the incident field) amplitude profiles of the electric field components $i=x$ (dotted line), $i=y$ (dashed line), $i=z$ (solid line) at the eigenfrequency of the lowest optical resonance ${\omega }_{0}a/c=1.88305$ of an asymmetric version of the structure of Fig. 1 where the thickness of the ${\mathrm{TiO}}_2$ layer on the left (right) side of the Bi:YIG film is $0.2a\left(0.6a\right)$, illuminated by $p$-polarized light incident at an angle corresponding to $q_{\parallel }a=1.2$, in the absence of magnonic excitation. Oscillatory behavior of this optical resonance, induced by a uniform precession mode of angular frequency ${\mathrm{\Omega }}_0$ (b) and a first-order $\left(n=1\right)$ perpendicular standing spin wave (c), both of relative amplitude $\eta =0.1$, as manifested in a sequence of snapshots of the corresponding transmittance within a period of the spin wave. (d), (e) Corresponding relative intensities of the inelastically (with respect to the elastically) transmitted light beams.