Nematic reorientation effects on resonant modes, wavelength mismatch, and slow-light phenomena in one-dimensional magnetophotonic crystals with a dual anisotropic defect

The present study is devoted to the investigation of spectral properties of an alternated sequence of magnetic and dielectric layers containing a dual defect based on magnetic and nematic layers. Combining the Hydrodynamic Continuum Theory for nematic liquid crystals and Berreman's formalism, we determine how the nematic ordering affects the light localization, polarization rotation, and slow-light phenomena observed in the magnetophotonic system. In particular, we analyze the effects associated with a field-induced reorientation of the director in a nematic defect with strong planar boundary conditions. Our results reveal that field-induced reorientation of the nematic ordering can be used as an efficient mechanism to tune and control the spectral properties of magnetophotonic structure, anomalies in group velocity, and the wavelength mismatch between resonant mode and maximum polarization. The effects of nematic layer thickness are also analyzed.

Figure 1

Schematic representation of a multilayered structure consisting of an alternated sequence of $\mathrm{SiO}{}_2$ dielectric (white) and Bi:YIG magnetic (red) layers, containing two central defects: one magnetic and the other nematic (purple). The unperturbed nematic director $\widehat{\mathbf{n}}$ is parallel to the $x$ axis. Here the thicknesses of both dielectric (${\ell }_s$) and magnetic (${\ell }_m$) layers are equal to 180 nm.

Figure 2

Director orientation profile along a nematic layer with thickness $d_n$. The profiles correspond to the solutions of Eqs. (3) and (4) for distinct values of the applied external voltage: $V/V_{th}=1.5$ (black solid line), $V/V_{th}=3.0$ (red dashed line), and $V/V_{th}=6.0$ (blue dotted line). Due to the strong planar anchoring ($\alpha (z=0)=\alpha (z=d_n)=0$), one can note that the maximum value of the director tilt angle occurs at the center of the nematic defect, with ${\alpha }_m\to \pi /2$ for $V\gg V_{th}$.

Figure 3

Density plot of the transmission spectra of the dual defect magnetophotonic structure as a function of the nematic defect thickness, $d_n$. Here we consider a nematic defect presenting a director aligned along the $x$ axis ($V/V_{th}=0$), with a birefringence $\mathrm{\Delta }n=0.16$. The thickness of the magnetic defect was maintained constant, with $d_m=2{\ell }_m$ and ${\ell }_m={\ell }_s=180$ nm. Notice that the insertion of nematic defect modifies the light localization condition of the magnetophotonic structure for $d_n>{\ell }_m/2$, with the emergence of two distinct resonant modes inside the band gap.

Figure 4

(a) Polarization rotation angle of the transmitted wave by a 1D magnetophotonic structure containing a dual defect. We used the same parameters as Fig. 3, with $d_m=360$ nm. A pronounced enhancement of maximum polarization angle takes place as the thickness of the nematic defect is increased. (b) Wavelength mismatch between resonant modes in transmittance spectrum (black solid line) and polarization rotation angle (red dashed line), with $d_m=360$ nm and $d_n=480\text{nm}$. The gray region marks the band gap width.

Figure 5

(a) Density plot of the transmission spectra of the dual defect magnetophotonic structure as a function of the applied voltage in the nematic layer, with $d_n=480$ nm. We used the same parameters as Fig. 3. For $V>V_{th}$, we observe that the director reorientation modifies the Bragg conditions of resonant modes, being characterized by a wavelength shift and transmittance change of modes. (b) Transmittance of resonant modes as function of the applied voltage in the nematic defect, with $d_n=480$ nm. Notice that the applied voltage can be used to switch the mode with highest transmittance.

Figure 6

Polarization rotation angle as function of the applied voltage in the nematic defect. The same parameters as Fig. 3 were used, with $d_n=480$ nm and $\mathrm{\Delta }n=0.16$. We observe a pronounced reduction of the polarization rotation angle associated with the first resonant mode, which is accompanied by a small increase of the polarization rotation angle associated with second resonant mode.

Figure 7

(a) Ellipticity of the transmitted light by a 1D magnetophotonic structure containing a dual defect, considering different applied voltages on the nematic layer: $V/V_{th}=0$ (black solid line), $V/V_{th}=2$ (red dashed line), $V/V_{th}=8$ (blue dotted line). We used the same parameters as Fig. 3, with $d_m=360$ nm and $d_n=480$ nm. The gray region marks the band gap width. Notice that the nematic reorientation reduces the peak and valley amplitudes of the ellipticity close to the wavelength where the maximum polarization rotation occurs, ${\lambda }_R=690$ nm. (b) Voltage dependence of the ellipticity peak-valley difference, $\mathrm{\Delta }{\xi }_{P-V}={\xi }_P-{\xi }_V$. The inset shows the reduction of ${\xi }_P$ (black solid line) and ${\xi }_V$ (red dashed line) as the applied voltage is raised above the Freedericksz threshold.

Figure 8

Group velocity spectra (in units of $c$) of magnetophotonic crystal with a dual defect, considering different applied voltages on the nematic layer: $V/V_{th}=0$ (black solid line), $V/V_{th}=2$ (red dashed line), and $V/V_{th}=8$ (blue dashed-dotted line). The gray region marks the band gap width. Notice that an anomaly on the group velocity takes place due to the mismatch between wavelength positions of resonant modes and maximum polarization rotations.