Nonreciprocal optical properties in resonant hybrid photonic crystals

The present work is devoted to the theoretical study of the nonreciprocal optical properties in hybrid (isotropic and anisotropic) periodic multilayers for photon energy values chosen close to the electronic energy gaps of semiconductors (excitons). The optical properties of these resonant nonmagnetic photonic crystals, where linear and quadratic spatial dispersion effects are both present, will be studied in the framework of exciton-polariton self-consistent solutions of the Maxwell and Schrödinger equations in the effective-mass approximation. The main interesting optical properties, namely, giant transmission, absorption suppression, and optical unidirectional propagation, will be computed by implementing a two-layer “minimum model.”

Figure 1

One-dimensional hybrid (isotropic-anisotropic) multilayer. Brown layers are the quantum wells, yellow layers are the barriers of the quantum wells, and sky blue layers are the uniaxial layers.

Figure 2

Photon dispersion curves at normal incidence in the range of exciton-polariton energies. The $x$-polarized eigenvalues are represented by mauve dots, and the $y$-polarized ones are shown by blue dots. The $x$ and $y$ polarizations are used to indicate the majority contribution of the $x$ or $y$ component to the electric field intensity. (a) $\mathrm{\Delta }\alpha =0^{\circ }$ (no absolute gap is present). (b) $\mathrm{\Delta }\alpha ={10}^{\circ }$ (two absolute gaps are present).

Figure 3

Optical response at normal incidence. $\mathrm{\Delta }\alpha ={90}^{\circ }$. Reflectivity: dashed red line; transmission: dotted blue line; and absorbance: solid green line. (a) Forward incident waves are TM polarized, while backward ones are TE polarized. (b) Forward incident waves are TE polarized, while backward ones are TM polarized.

Figure 4

(a) Absorbance intensity computed as a function of the energy for normal incident TM (crosses) and TE (open circles) polarizations. $N=32$. (b) FWHM of the absorbance peak, computed for the TM (crosses) and TE (open circles) polarizations as a function of the quantum well number.

Figure 5

The $x$-polarized eigenvalues are represented by mauve dots, and the $y$-polarized ones are shown by blue dots. The $x$ and $y$ polarizations are used to indicate the majority contribution of the $x$ and $y$ components to the electric field intensity, respectively. (a) Normal incidence dispersion curves of a reciprocal asymmetric elementary cell in the energy range of the first absolute gap. (b) Dispersion curves in an enlarged energy scale and close to the unperturbed exciton energy.

Figure 6

Forward normal optical response of the reciprocal multilayer of Fig. 5. Reflectivity: dashed red line; transmission: dotted blue line; and absorbance: solid green line. (a) TM polarization. (b) TE polarization.

Figure 7

Exciton-polariton dispersion curves of hybrid resonant photonic crystals with axial spectral asymmetry and dielectric functions: ${\varepsilon }_{\parallel }=12.24$ and ${\varepsilon }_{\perp }=8.24$. The exciton transition energy is $E_{\mathrm{ex}}\left(0\right)=1.525$ eV.

Figure 8

Exciton-polariton dispersion curves of hybrid resonant photonic crystals. $E_{\mathrm{ex}}\left(0\right)=1.735$ eV, ${\varepsilon }_{\parallel }=18.24,{\varepsilon }_{\perp }=2.24,\theta ={20}^{\circ }$. (a) Axial spectral asymmetry: ${\alpha }_L={45}^{\circ },{\alpha }_R={30}^{\circ },k_{\parallel }\ne 0,{\varepsilon }_{xz}\ne 0$. (b) Axial spectral symmetry: ${\alpha }_L={45}^{\circ },{\alpha }_R=0^{\circ },k_{\parallel }\ne 0,{\varepsilon }_{xz}=0$.

Figure 9

Dispersion curves of Fig. 8 in enlarged energy scales: (a) close to the energy of the second absolute energy gap and (b) close to the exciton energy $[E_{\mathrm{ex}}\left(0\right)=3.5175$ eV] in resonance with the stationary inflection point.

Figure 10

Forward optical response for an $S$-polarized non-normal incident wave on a hybrid cluster of $N=32+2$ quantum wells for the bulk parameter values in Fig. 9. Reflectivity: dashed red line; transmission: dotted blue line; and absorbance: solid green line.