Fig. 1 (a) A schematic representation of a luminescent solar concentrator (LSC). Solar radiation is absorbed by highly fluorescent dye molecules integrated in a thin, flat-plate waveguide. The dye re-emits photons at a lower energy, which can then be guided to solar cells attached to the edge of the plate by total internal reflection. For a conventional LSC employing isotropically aligned dye molecules, approximately ~75% of the radiation is trapped in the waveguide (here represented by black arrows). A fraction of the absorbed photons is lost from the waveguide if they are re-emitted above the critical angle, or scattered outside of the waveguide (grey arrows). The trapping efficiency is then defined as the fraction of photons emitted from the edge versus photons emitted from the face and edge combined. (b) The emission profile of isotropic dipoles and a linearly aligned, anisotropic dipole. The absorption and emission profile of isotropic dipoles is uniform, while the anisotropic dipole emission is characterized by a sin² θ profile, with little power emitted along the long axis of the dipole molecule. (c) In order to improve the performance of LSCs, we align rod-shaped dichroic dye molecules perpendicular to the waveguide, enhancing the fraction of the total dipole power trapped in the waveguide. A polymerizable liquid crystal host serves as a scaffold. An external diffuser is used to correct for the reduced ability to absorb light incident perpendicular to the waveguide.

Fig. 2 (a) Schematic representation of the dipole orientation within the waveguide of the LSC. The angle between the dipole moment, $\stackrel{\rightharpoonup }{d}$ , and the electric field vector, $\stackrel{\rightharpoonup }{E}$ , of the excitation beam, $\stackrel{\rightharpoonup }{k}$ , is defined as φ. (b) The calculated trapping efficiency as a function of the orientation of a Hertzian dipole with respect to the waveguide for three different refractive indexes of the dye medium. θ = 0° corresponds to a dipole oriented perpendicular to the waveguide, while θ = 90° describes a dipole aligned in the plane of the waveguide. (c) The calculated trapping efficiency as a function of the refractive index of the dye medium, n_S , for vertically aligned dipoles (green line), isotropic dipoles (red line) and in-plane aligned dipoles (blue line). We use the conventional Eq. (2) for the trapping efficiency of isotropic dipoles. (d) The calculated trapping efficiency of an LSC for s and p polarized light based on isotropic dipoles as a function of the angle of the incident light, as measured outside of the waveguide with refractive index of n _S = 1.5 (blue line) and n_S = 1.6 (red line). η_trap is independent of excitation angle for s-polarized light, while η_trap increases 3-5% from normal till 90° incidence for p-polarized light. We also plot η_trap for the case where the dependence of the angular distribution of excited dyes on the angle of the incident light is not taken into account (dotted red and blue lines) (Eq. (2).

Fig. 3 (a) A schematic representation of the side-view of the measurement set up used to determine the trapping efficiency, η_trap , of the LSCs. The isotropic and vertically aligned LSCs are characterized in an integrating sphere to measure the edge and facial emission as a function of excitation wavelength. (b) Schematic representation of the top-view of the set-up used to test the angular dependence of the absorption within isotropic and vertically aligned LSCs. One of the edges of the LSC is placed into an opening of an integrating sphere, which allows the monitoring of the edge emission as a function of the incident angle of the excitation beam. For studies of the effect of an external scattering layer, holographic diffusers are placed in the path of the excitation source at a distance of 1mm from the LSC. (c) The performance of isotropic and homeotropic LSCs at higher optical concentrations is measured by monitoring the efficiency while varying the distance, d, between the excitation spot and the solar cell.

Fig. 4 The measured Optical Quantum Efficiency (OQE) of the facial emission (blue dots), edge emission (green dots) and the total emission (red dots) of (a) the isotropic LSCs, and (b) the vertically aligned LSCs. Both samples absorb 40% of the incoming light. (c) The measured trapping efficiency, η_trap of the isotropically aligned LSCs (red dots) and the vertically aligned, homeotropic, LSCs (green dots). This measured η_trap is the ratio between the edge and the total emission OQEs.

Fig. 5 (a) The power emitted from the edge of an LSC as a function of the incoming angle of the excitation beam for a isotropic LSC and a vertically aligned LSC. The edge power is normalized to the power at normal incidence. The monotonic increase in performance of the vertically aligned LSC is consistent with an increased ability of the vertical dipoles to absorb light at higher angles. The theoretical predictions for the edge emission versus incident angle are plotted as dotted lines. These calculations consider both the change in absorption and the change in trapping efficiency resulting from a change in incidence angle. (b) Effect of an external diffuser on the edge output power of an isotropic (red dots) and homeotropic LSC (green dots). Increasing the diffuser strength improved the performance of the vertically aligned LSC, while the isotropic LSC hardly benefits. This data is not corrected for increased absorption at higher incidence angles.

Fig. 6 (left axis) The external quantum efficiency (EQE) versus geometric gain for vertically aligned LSCs (red dots) and isotropic dipoles (green dots). Both samples absorbed 42% of the incoming radiation. Monte Carlo simulations for uniformly illuminated LSCs (open circles) and simulations of the spot excitation technique (open squares) yield slightly higher results due to the higher trapping efficiency obtained in the Monte Carlo simulations compared to measured trapping efficiencies. (right axis) The measured ratio of the EQE of the vertically aligned LCS is ~16% higher than the isotropic standard for all measured geometric gains, consistent with the higher measured trapping efficiency.