Fluorescence enhancement and nonreciprocal transmission of light waves by nanomaterial interfaces

In an optically absorbing or amplifying linear medium, the energy flow density of interfering optical waves is in general periodically modulated in space. This makes the wave transmission through a material boundary, as described by the Fresnel transmission coefficients, nonreciprocal and apparently violating the energy conservation law. The modulation has been previously described in connection to ordinary homogeneous nonmagnetic materials. In this work, we extend the description to nanomaterials with designed structural units that can be magnetic at optical frequencies. We find that in such a “metamaterial” the modulation in energy flow can be used to enhance optical far-field emission in spite of the fact that the material is highly absorbing. We also demonstrate a nanomaterial design that absorbs light, but simultaneously eliminates the power flow modulation and returns the reciprocity, which is impossible to achieve with a nonmagnetic material. We anticipate that these unusual optical effects can be used to increase the efficiency of nanostructured light emitters and absorbers, such as light-emitting diodes and solar cells.

Figure 1

A plane wave is incident from medium 1 onto an interface between media 1 and 2, and is split into reflected and transmitted waves. TE- and TM-polarized waves are shown in (a) and (b), respectively.

Figure 2

Metal-dielectric stack metamaterial. (a) Structure. (b) Spectrum of $n$ for normal-incidence waves. (c) Spectrum of $\eta$. (d) Spectra of $\epsilon$ and $\mu$ in blue and red lines, respectively. In all spectra, solid and dashed lines correspond to the real and imaginary parts of the quantities, respectively.

Figure 3

Spectra of radiation from inside the metamaterial. In (a), the spectra show the intensity of radiation at $z=0$ created by a plane-wave source at $z=-{\mathrm{\Lambda }}_z$ inside the metal-dielectric stack metamaterial, normalized to the intensity of radiation in infinite glass. The dipole is either inside an infinite metamaterial [case (1), blue line] or at a distance of ${\mathrm{\Lambda }}_z$ from the material interface with an ambient medium [case (2), red line]. The Poynting vector outside the material in case (2) is composed of two contributions, which are shown in (b). The terms proportional to $\text{Re}\left\{\eta \right\}$ and $\text{Im}\left\{\eta \right\}$ are shown with the blue and red curves, respectively. The effective plane-wave transmittances of the metamaterial-glass interface are shown in (c), $T_{12}$ with a blue and $T_{21}$ with a red line.

Figure 4

Microscopic field distributions of light radiated from inside the metamaterial. The plane-wave radiation source is positioned at $z=-{\mathrm{\Lambda }}_z$ (a) in an infinite metamaterial and (b) near the metamaterial-glass interface. The source emits at ${\lambda }_0=$ 538.5 nm. The gray areas show the position of the metal layers of the metamaterial. The blue curve shows the microscopic Poynting vector obtained by a full numerical simulation, while the red curve shows the Poynting vector as predicted by the wave parameter description. The values of the Poynting vectors at $z=0$ are denoted by $S_{\infty }\left(0\right)$ and $S_{\text{out}}\left(0\right)$. (c) The microscopic electric-field amplitude corresponding to the case in (b).

Figure 5

Spectra of radiation from two systems shown in the insets: (1) source in the middle of a two-layer metamaterial slab on top of a silver mirror, and (2) the same source in glass, at a distance of ca. $\lambda /4$ from the mirror.

Figure 6

A three-dimensional view of one layer of a disk-dimer metamaterial; the lattice is extended also in the $z$ direction (not shown).

Figure 7

Spectra of (a) refractive index and (b) impedance of the disk-dimer metamaterial for waves propagating along the $z$ axis. In each plot, the blue line shows the real and the red line the imaginary part of the quantity. The spectra of the plane-wave transmittances $T_{12}$ and $T_{21}$ and reflectance $R$ of the metamaterial-glass interface are shown in (c) with red, blue, and green curves, respectively. Full numerical simulation results are shown at two chosen wavelengths for both $T_{12}$ (red circles) and $T_{21}$ (blue crosses). The pictures of (d) are the distributions of electric-field amplitude in logarithmic scale at the chosen wavelengths and propagation directions.