Photonic crystals benefit phosphor performance

The development of efficient phosphors with tailored optical properties has attracted considerable attention from researchers. These efforts have been spurred recently by the emergence of a new and important application: phosphor-capped white LEDs, which have paved the way to solid-state general lighting. Nanophotonic structures—on the scale of the wavelength of light—can affect how light is reflected and transmitted. Engineering phosphors with nanophotonic structures could help improve their performance. However, so far most of the work in the field has been devoted to the material properties of phosphors, rather than the use of engineered photonic structures.

Here we suggest a 1D photonic crystal (PC) as a simple phosphor platform that can enhance fluorescence. A PC is a photonic structure whose refractive index varies periodically. The enhancement is caused by the low group velocity of light in the structure, which prolongs the interaction time of the pump photons with the phosphors. These structures have a photonic band gap (PBG)—a range of wavelengths at which light cannot propagate through the structure—and a photonic band edge (PBE) located just outside the PBG. The group velocity in the PBE is zero, which strengthens the interaction between light and matter.^{1, 2}

The 1D PC structure we modeled is a standard distributed Bragg reflector (DBR), i.e., layers of alternating material types: see Figure 1(a). The refractive indices we set for this model structure are n_L=1.45 (silica) and n_H=1.76 (alumina). The thickness of each layer, d_i, is set at a quarter of the wavelength λ₀, that is, d_i=λ₀/4n_i, where i=L or H for the low and high refractive index materials, respectively, and λ₀ is the central wavelength of the PBG. In our model structure λ₀ is 420nm, and the total number of pairs of alternating layers is 30. We model our structure to have phosphor materials distributed only in the high-refractive-index material, that is, alumina.

The reflectance of light through the structure oscillates with respect to wavelength. When light is incident at the wavelength at which the reflectance exhibits its first minimum (the long wavelength edge of the PBG, λ₁=451.6nm), the electric-field profile oscillates with an amplitude that peaks at the center of the 1D PC structure: see Figure 1(b). The electric field intensity maxima coincide with the high-refractive-index layers where the phosphor materials are distributed. This leads to a novel phosphor structure that may have the potential for efficient pump photon absorption and thus strong fluorescence.

Figure 1. (a) Schematic of a 1D photonic crystal (PC) phosphor structure consisting of N pairs of alternating layers. The circular dots represent fluorescent agents. n_L=1.45and n_H=1.76 are the refractive indices of the alternating layers. d_L, and d_H are the thicknesses of the layers, and λ_p and λ_e are the wavelengths of the pump and emitted light. (b) The electric field intensity (|E|²) profile inside the 1D PC phosphor, consisting of 30 layer pairs, when light of wavelength λ₁(the first photonic band edge on the long wavelength side of the photonic band gap) is incident from the left. arb. unit: Arbitrary units.

Figure 2. Absorbance spectra of the 1D PC phosphor with 30 pairs of layers (red solid line) and of the bulk phosphor with equivalent phosphor thickness (black solid line) (a) when pumped by a monochromatic light source and (b) pumped by a broad-bandwidth (20nm) light source. λ₁, λ₂, and λ₀ are the the first and second photonic band edge and central wavelengths of the photonic band gap, respectively.

We calculated the absorbance of pump photons within the 1D PC structure. Our model allows for the complex refractive index of fluorescent materials to take into account both their dispersive and absorptive nature. Assuming that the fluorescent agents inside the structure have 100% internal quantum efficiency, the fluorescence from the agents is simply proportional to the absorbance of the pump photons. We modeled the reference bulk phosphor as a slab of alumina with a thickness equal to the accumulated thicknesses of the alumina layers in the 1D PC to estimate how the 1D PC structure affects the performance of the phosphor. This ensures that the reference bulk phosphor contains the same amount of fluorescent agents as the 1D PC phosphor, when evaluating the performance of the structure.

Figure 2(a) compares the absorbance of the 1D PC phosphor with that of the bulk phosphor as a function of the pump photon wavelength, λ_p. At λ_p=λ₀ (the center of the PBG), propagation of photons through the PC phosphor is strictly forbidden. This results in poor excitation of the fluorescent agents. In contrast, absorbance of the PC phosphor is significantly enhanced compared with that of the bulk phosphor when λ_p=λ₁ (the first PBE) or λ_p=λ₂ (the second PBE). The absorbance of the PC phosphor at λ_p=λ₁ is approximately seven times larger than that of the bulk phosphor. This clearly demonstrates that structuring the phosphor into a PC and tuning the pump wavelength to the PBE can greatly enhance fluorescence.

To verify the practical merits of the proposed PC phosphor, it is necessary to investigate the case of phosphor excitation using a light source with a finite emission bandwidth. For this purpose, we assume a Gaussian spectral profile with a full width at half-maximum of 20nm. The absorbance of the PC phosphor is still much stronger than that of the bulk phosphor. Figure 2(b) shows the absorbance of the PC phosphor and the bulk phosphor when pumped by the broad-bandwidth light source. Specifically, the absorbance of the PC phosphor is approximately 2.2 times higher at the absorbance peak than that of the bulk phosphor. Further, pump photon absorption is enhanced over a broad spectral range of pump wavelengths. This implies a large tolerance in tuning the peak wavelength of the broad bandwidth pump source, which is extremely important if the PC phosphor is to be considered for use in white LEDs.

In summary, we propose a 1D PC as an efficient phosphor structure that is suitable for white LED applications. Through systematic model calculations, we find that the pump efficiency is improved by tuning the pump photons to the longer wavelength PBE and locating phosphor molecules selectively in the high-refractive-index layers. The improved efficiency results from a low group velocity near PBEs, which allows an enhanced optical excitation of the phosphor molecules. These results are yet to be experimentally demonstrated and confirmed. To this end, we are currently trying to realize the modeled structure using polymer materials.

This work was financially supported by a National Research Foundation grant (2011-0018028) and the World-Class University project (R31-10032), both funded by the Ministry of Education, Science, and Technology of Korea, and in part by Samsung LED Company, Ltd.