Spontaneous emission of an optically active molecule near a chiral nanoellipsoid

We have derived and investigated analytical expressions for the spontaneous emission radiative decay rate of an optically active (chiral) molecule placed near a chiral (bi-isotropic) triaxial nanoellipsoid, the size of which is much smaller than the wavelength. Differences in radiative decay rates of optically active molecule enantiomers located near the surface of chiral nanoparticles of spherical, prolate spheroidal, and ellipsoidal shapes have been investigated. It is shown that the change of the nanoparticle's shape from spherical to ellipsoidal results in substantial enhancement of the spontaneous emission radiative decay rate of molecule enantiomers of one type in comparison with the decay rate of the other type of enantiomers.

Figure 1

Electron micrograph of an orf virus (Parapoxvirus) with a distinctive crisscross pattern of the virion's surface. Approximate measurements of the virus are 160 nm in diameter and 260 nm in length. Adapted from [3].

Figure 2

Geometry of the problem of spontaneous emission of an optically active (chiral) molecule (red spiral) placed near a nanoellipsoid made of a chiral (bi-isotropic) material; $\chi =k_0\beta$ is the dimensionless chirality parameter.

Figure 3

Case of a chiral nanosphere. (a) Geometry of calculations. (b) Pseudocolor plot of the $log\left({\gamma }_{\mathrm{rad}}^L/{\gamma }_{\mathrm{rad}}^R\right)$ as a function of ${\varepsilon }^{\prime }$ and ${\mu }^{\prime }$ of a chiral nanosphere. Obtained extrema are ${\gamma }_{\mathrm{rad}}^L/{\gamma }_{\mathrm{rad}}^R\approx 12.8$ and ${\gamma }_{\mathrm{rad}}^R/{\gamma }_{\mathrm{rad}}^L\approx 61.7$. Dashed line shows the solution of Eq. (21), which is the condition for the excitation of chiral-plasmon resonance in a nanosphere (${\tau }_x={\tau }_y={\tau }_z$).

Figure 4

Case of a chiral prolate nanospheroid. (a) Geometry of calculations. (b) Pseudocolor plot of $log\left({\gamma }_{\mathrm{rad}}^L/{\gamma }_{\mathrm{rad}}^R\right)$ as a function of ${\varepsilon }^{\prime }$ and ${\mu }^{\prime }$ of a chiral prolate nanospheroid. Obtained extrema are ${\gamma }_{\mathrm{rad}}^L/{\gamma }_{\mathrm{rad}}^R\approx 22.6$ and ${\gamma }_{\mathrm{rad}}^R/{\gamma }_{\mathrm{rad}}^L\approx 108.7$. Dashed lines show the conditions (21) for the excitation of chiral-plasmon resonance in a prolate nanospheroid (${\tau }_x\ne {\tau }_y={\tau }_z$). Line $x$ shows the solution of Eq. (21). Line $y$ is the solution of the equation, which can be obtained from Eq. (21) by substitution, ${\tau }_x\to {\tau }_y$.

Figure 5

Case of a chiral elongated triaxial nanoellipsoid. (a) Geometry of calculations. (b) Pseudocolor plot of $log\left({\gamma }_{\mathrm{rad}}^L/{\gamma }_{\mathrm{rad}}^R\right)$ as a function as a function of ${\varepsilon }^{\prime }$ and ${\mu }^{\prime }$ of a chiral elongated triaxial nanoellipsoid. Obtained maxima are ${\gamma }_{\mathrm{rad}}^L/{\gamma }_{\mathrm{rad}}^R\approx 17.3$ and ${\gamma }_{\mathrm{rad}}^R/{\gamma }_{\mathrm{rad}}^L\approx 116.8$. Dashed lines show the conditions for the excitation of chiral-plasmon resonance in an elongated triaxial nanoellipsoid (${\tau }_x\ne {\tau }_y$, ${\tau }_x\ne {\tau }_z$, and ${\tau }_y\ne {\tau }_z$). Line $x$ shows the solution of Eq. (21). Lines $y$ and $z$ are solutions of equations, which can be obtained from Eq. (21) by substitutions, ${\tau }_x\to {\tau }_y$ and ${\tau }_x\to {\tau }_z$, respectively.