Magnetophotonic intensity effects in hybrid metal-dielectric structures

The magneto-optical properties of a hybrid metal-dielectric structure consisting of a one-dimensional gold grating on top of a magnetic waveguide layer are studied experimentally and theoretically. It is demonstrated that a magnetic field applied in the longitudinal configuration (in the plane of the magnetic film and perpendicular to the slits in the gold grating) to the metal-dielectric structure modifies the field distribution of the optical modes and thus changes the mode excitation conditions. In the optical far field, this manifests in the alteration of the optical transmittance or reflectance when the structure becomes magnetized. This magneto-optical effect is shown to represent a novel class of effects related to the magnetic-field-induced modification of the Bloch modes of the periodic hybrid structure. That is why we define this effect as “longitudinal magnetophotonic intensity effect” (LMPIE). The LMPIE has two contributions, odd and even in magnetization. While the even LMPIE is maximal for the light polarized perpendicular to the grating slits (TM) and minimal for the orthogonal polarization (TE), the odd LMPIE takes maximum values at some intermediate polarization and vanishes for pure TM and TE polarizations. Two principal modes of the magnetic layer—TM and TE—acquire in the longitudinal magnetic field additional field components and thus turn into quasi-TM and quasi-TE modes, respectively. The largest LMPIE is observed for excitation of the antisymmetrical quasi-TE mode by TM-polarized light. The value of the LMPIE measured for the plasmonic structure with a magnetic film of Bi${}_2$Dy${}_1$Fe${}_4$Ga${}_1$O${}_{12}$ composition is about 1% for the even effect and 2% for the odd one. However, the plasmonic structure with a magnetic film with a higher concentration of bismuth (Bi${}_{2.97}$Er${}_{0.03}$Fe${}_4$Al${}_{0.5}$Ga${}_{0.5}$O${}_{12}$) gives significantly larger LMPIE: even LMPIE reaches 24% and odd LMPIE is 9%. Enhancement of the magneto-optical figure of merit (defined as the ratio of the specific Faraday angle of a magnetic film to its absorption coefficient) of the magnetic films potentially causes the even LMPIE to exceed 100% as is predicted by calculations. Thus, the nanostructured material described here may be considered as an ultrafast magnetophotonic light valve.

Figure 1

Calculated even and odd longitudinal magneto-optical intensity effects in reflection versus angle of incident light polarization ψ ($\psi =0^{\circ }$ and $\psi =\pm {90}^{\circ }$ correspond to $p$ and $s$ polarization, respectively) for incidence angles $\theta =0^{\circ }$ and $\theta ={10}^{\circ }$. Light wavelength is 700 nm. The inset shows light incidence configuration. The magnetic film of thickness 1 μm was assumed to be on top of a silica substrate ($\varepsilon =2.25$). The optical parameters of the magnetic film are chosen to be the following: ${\varepsilon }_0=5.34+0.012i$, $g=(2.3+0.2i)\times {10}^{-3}$, and $b=3\times {10}^{-5}$, corresponding to a bismuth-substituted iron garnet film at the near-infrared spectral range. Calculations were made using the rigorous coupled-waves analysis (see Sec. 3).

Figure 2

(a) Schematic of the MPC and configuration of light incidence. (b) Quasi-TE and quasi-TM modes of the MPC. The long brown arrows represent principal components of the electromagnetic field, and the short blue arrows represent components induced by magnetization.

Figure 3

Calculated modes of the experimentally studied MPC-A in the nonmagnetized state. (a) Dispersion of the TM (black curves) and TE modes (green curves) calculated by the S-matrix method. Inset shows a region at around the Γ point where degeneration of the TM and TE modes takes place. Filled and open circles indicate symmetric and antisymmetric modes, respectively. Numbers (1)–(3) refer to the mode orders (see the text). (b) Color plots showing electromagnetic field distributions of different symmetric TM modes at the Γ point. The real parts of $E_z$ and $H_y$ field components are shown. All values are normalized to the unity.

Figure 4

Measured spectra of transmission through the demagnetized MPC-A $T_0$ (upper brown curves) as well as odd (thin blue curves) and even (thick red curves) LMPIE at three different polarization angles: (a) ψ = 0°, (b) ψ = 90°, and (c) ψ = 36°. Incidence angle was about 0.3°. The LMPIE was measured at an external magnetic field of 160 mT. Arrows indicate the spectral positions of the TE and TM resonances taken from their calculated dispersion in Fig. 3. In the notation of TM and TE modes, the upper index shows the mode symmetry, while the bottom one indicates the mode order.

Figure 5

Color plots of the electromagnetic field distribution in the near field of the MPC-A. $E_y$ field inside the (a) nonmagnetized and (b) magnetized structure in the case of TM-polarized normally incident light at λ = 705 nm. The field is normalized by $H_y$ of the incident light. (c) $E_y$ and (d) $H_y$ of the quasi-TE mode in the magnetized structure. $H_y$ field inside the (e) nonmagnetized and (f) magnetized structure in the case of TM-polarized normally incident light at λ = 705 nm.

Figure 6

The even LMPIE calculated for an MPC with the magnetic film of composition Bi${}_2$Dy${}_1$Fe${}_4$Ga${}_1$O${}_{12}$ and a gold grating with the following parameters: $d$ = 360 nm, grating thickness is $h_{gr}$ = 63 nm, slit width is $r$ = 270 nm. (a) The incident wave is TM polarized, (b) the incident wave is TE polarized. Vertical lines indicate the spectral positions of the TM modes (black lines) and TE modes (green lines), which are symmetric (dashed lines) and antisymmetric (dash-dotted lines). The light is normally incident. The optical and magneto-optical parameters of the MPC are the same as for the experimental sample.

Figure 7

Experimentally measured for the MPC-A odd (blue symbols) and even (red symbols) LMPIE versus the polarization angle ψ at λ = 703 nm (filled circles) and λ = 705 nm (open squares). Incidence angle is 0.3°. External magnetic field is 160 mT. Solid and dashed lines are meant as guides to the eyes.

Figure 8

Experimentally measured angle dispersion for the even LMPIE. (a) Color plot for ${\delta }_{\mathrm{even}}$ versus incidence angle and illumination light frequency. Blue lines connect points of equal $k$. Black lines with dots indicate calculated dispersion of the quasi-TE modes. Spectral dependence of ${\delta }_{\mathrm{even}}$ for (b) normal and (c) oblique incidence (θ = 3º). Incident light is TM polarized. External magnetic field is 240 mT.

Figure 9

Experimentally measured magnetic field dependence of the even LMPIE in the MPC-A. The even LMPIE is represented here by $|{\delta }_1|+|{\delta }_2|$ (circular symbols), where ${\delta }_1$ and ${\delta }_2$ are the positive and negative peaks of the even LMPIE at λ = 703 and 705 nm, respectively [see Fig. 4]. Solid line is a parabolic fit. Incident light is TM polarized and normally incident.

Figure 10

Measured spectra of (a) odd and (b) even LMPIE for the MPC-B. (a) The polarization angle is ψ = 36°, and the incidence angle of light incidence is θ = 1°; (b) ψ = 0°, and light is normally incident. $B$ = 160 mT.

Figure 11

Calculated maximum achievable value of the even LMPIE in transmission (solid blue curves) and in reflection (dashed red curves) versus the thickness of the magnetic layer $h_m$. All other geometrical parameters of the MPC were varied to get the largest possible value of ${\delta }_{\mathrm{even}}$ at the wavelengths range of 650–900 nm with the condition that $T\left(0\right)>10\%$. MPCs with magnetic films of three different compositions are considered: (a) Bi${}_2$Dy${}_1$Fe${}_4$Ga${}_1$O${}_{12}$, (b) Bi${}_{2.97}$Er${}_{0.03}$Fe${}_4$Al${}_{0.5}$Ga${}_{0.5}$O${}_{12}$, and (c) Bi${}_3$Fe${}_5$O${}_{12}$ (see Sec. 3). The light hits the sample under normal incidence and is TM polarized. It is assumed that an external magnetic field saturates magnetization of the magnetic film.