We propose a novel photonic structure, based on the photonic crystal (PC) effect, which simulations show results in an improved fluorescence efficiency from embedded phosphor. To be specific, the phosphor pumping efficiency can be significantly improved by tuning the pump photon energy to a photonic band-edge (PBE) of the PC phosphor. We have confirmed this theoretically by calculating optical properties of one-dimensional PC phosphor structures using the transfer-matrix method and plane-wave expansion method. For a particular model structure based on a quantum dot phosphor, the fluorescence enhancement factor was estimated to be as high as 6.9 for a monochromatic pump source and 2.2 for a broad bandwidth (20 nm) pump source.
© 2012 OSA
Many light-emitting devices are based on fluorescence, among which the most representative example is phosphor. Phosphor is a widely used and important component in general lighting applications, as demonstrated by the prevalent use of phosphor-capped white light-emitting diodes (LEDs) . Considerable effort has been spent in developing efficient phosphors with optical properties tailored to meet specific application requirements [2–4]. However, most of the developmental work thus far has been devoted to the materials properties of phosphors.
In a photonic crystal (PC) structure the refractive index is periodically modulated . Because the PC structure may possess a photonic band-gap (PBG) region in which light propagation is prohibited, many useful photonic devices have been realized that are much smaller than conventional microphotonic devices, e.g., optical cavities [6,7] and waveguides [8,9]. In this study, we propose to use a one-dimensional (1D) PC as a simple but novel phosphor platform, from which fluorescence can be greatly enhanced compared to that of its bulk counterpart. We employ the transfer-matrix (TM) method and plane-wave expansion (PWE) method to calculate various properties of the PC phosphor such as the electromagnetic field distributions within the PC phosphor and the absorption (and, therefore, the fluorescence) enhancement factor for different pump photon wavelengths.
2. Computational methods
The 1D PC model structure considered here is a standard distributed Bragg reflector (DBR), which consists of layers of two materials with different refractive indices stacked alternately. Figure 1 is a schematic of the 1D PC. The refractive indices we assume for this model structure are nL = 1.45 (for low index materials) and nH = 1.76 (for high index materials), which are the typical refractive indices of silica and alumina, respectively. The thickness of each layer is given by di = λ0/4ni (i = L, H), where λ0, the center wavelength of the PBG, is chosen to be 420 nm. Light-emitting phosphor materials are assumed to be dispersed only in the layers in the structure that have a high refractive index. The rationale for this assumption is explained in Section 3. The total number of pairs of alternating layers is N.
The PWE method is a technique to solve Maxwell’s equations for periodic media. By formulating the equations into an eigenvalue problem, this method allows the exact photonic band structures of an infinite-sized PC to be determined. Figure 2(a) is a diagram of the photonic bands of the model 1D PC calculated using this method. A PBG and photonic band-edges (PBEs) on both sides of the PBG can be clearly identified in Fig. 2(a). We call the first photonic band (which is in the low frequency region) the high index band (HIB) and the second band (in the high frequency region) the low index band (LIB), which correspond to the “dielectric” and “air” bands in .
In contrast to the PWE method, the TM method is a computational technique that is suitable for investigating the optical properties, such as the reflectance, transmittance, and absorbance, of finite-sized 1D PCs . Figure 2(b) displays the reflectance (R) and transmittance (T) spectra of our model 1D PC structures for N = 10 and 30 pairs of layers in the PC, which were calculated using the TM method. As the number of pairs of layers increases, the reflectance and transmittance approach 1 and 0, respectively, within the stop-band of the DBR structure (or the PBG of the 1D PC). This makes the PBEs on both sides of the PBG more discernible. The resultant PBG matches with that calculated by the PWE method and shown in Fig. 2(a). The TM method also provides the electromagnetic field profile across the entire 1D PC, which enables us to anticipate various photonic properties of the PC structure.
3. Electric field intensity profiles and phosphor design
We first examined electromagnetic field profiles within the 1D PC structure at various pump photon wavelengths, utilizing the TM method. We found that the peaks in the electric field amplitude tend to correspond to the position of PC layers with a high refractive index if the pump wavelength is tuned to be within the HIB. In contrast, when the pump wavelength is tuned to be within the LIB the electric field amplitude coincides better with the positions of the PC layers with the low refractive index. This is the reason for the names “HIB” and “LIB”. Consequently, if a 1D PC structure is to be adopted for phosphor applications, it is only necessary to embed fluorescent agents in the either high or low refractive index layers when the pump photon wavelength belongs to the HIB or LIB, respectively. Note that a large overlap between the electric field and dipole oscillators results in a high optical transition probability and, therefore, strong photon emission . If the pump photon wavelength is within the LIB, the wavelength of emitted photons, which is typically longer than the pump photon wavelength, may fall in the PBG of the PC structure. This may result in poor photon escape even if enhanced phosphor excitation occurs. For this reason, we consider the case where the pump wavelength lies within either the PBG or the HIB, and not the LIB.
Figure 3(a) shows the reflectance spectrum of our model 1D PC structure containing N = 30 pairs of layers. λ1 and λ3 are the wavelengths of the first and the second reflectance minima in the HIB region, while λ2 is the wavelength of the first reflectance maximum between λ1 and λ3. For the particular 1D PC structure considered here, the representative pump wavelengths are λ0 = 420 nm, λ1 = 451.6 nm, λ2 = 455.5 nm, and λ3 = 461.9 nm.
Shown in Fig. 3(b) are the electric field intensity profiles inside the 1D PC structure when light is incident from the left at the specific wavelengths of λ0, λ1, λ2, and λ3. It can be seen from Fig. 3(b) that the incident photons that have the same wavelength as the PBG center (i.e., λp = λ0) are completely reflected by the PC structure, while the electric field intensity inside the structure rapidly decays along the propagation axis. Incident photons with a wavelength matching the wavelength of the first reflectance maximum (λp = λ2) show a similar tendency, although an extra lobe of low intensity appears within the PC after the initial decay. In contrast, the incident photons with wavelengths of the zero of reflectance (i.e., λp = λ1 or λ3) exhibit features similar to resonant tunneling; this is often identified by the formation of a standing wave with large field amplitudes across the PC structure. The intensity envelope for λ1 is single-lobed while that for λ3 is double-lobed. It is also worth noting that, for λp = λ1 or λ3, the electric field intensity maxima coincide with the high refractive index layers, as those two wavelengths belong to the HIB. As a consequence, photons of wavelength λ1 or λ3 are expected to interact strongly with the high refractive index material in the 1D PC, if any optically active agent exists there. This may lead to a novel phosphor structure, which may have the potential for efficient pump photon absorption and thus strong fluorescence. In fact, there have been reports on enhanced optical phenomena due to slow light at PBEs [13–15].
4. Fluorescence enhancement factors
We now turn our attention to the performance characteristics of the 1D PC structure as a phosphor. Because a phosphor contains fluorescent, and therefore absorbing, agents its refractive index should be expressed by a complex number, e.g., n - iκ. Hence, reflectance and transmittance should be recalculated using this complex refractive index. It should be noted that in the present case only the refractive index of the high refractive index layer needs to be expressed as a complex number because we assume that fluorescent agents are dispersed only in the layers of high refractive index. Absorbance (A) is then deduced from reflectance and transmittance using the simple energy conservation law, i.e., A = 1 – R – T. In order to estimate the fluorescence intensity, we assume that the internal quantum efficiency of the fluorescent agents inside the phosphor is unity. The fluorescence from the fluorescent agents is then simply proportional to the absorbance of the pump photons. This assumption should be reasonable as long as fluorescent agents are scarce enough within the phosphor structure (so that absorption does not alter much the band structure properties of the 1D PC) and at the same time the pump intensity is kept low (so that fluorescent agents remain unsaturated). We choose CdSe/ZnS core-shell quantum dots (QDs) as the fluorescent agents in our model calculations, which have been drawing attention as a new nanophotonic material with a strong light-emitting ability . The molar absorption coefficient (or molar absorptivity) of the QDs is taken from previous studies to be ε = 105 cm−1M−1 , while the QD molar concentration is assumed to be 10−4 M.
In the following text, we compare the 1D PC phosphor with a bulk phosphor. We form the reference bulk phosphor by removing all the layers with a low refractive index from the corresponding 1D PC phosphor, thus ensuring that the reference bulk phosphor contains the same amount of fluorescent agents as the 1D PC phosphor. The difference between the two samples is that one has a periodicity in the refractive index profile, while the other does not. Therefore, we may attribute any change in fluorescence to this structural difference. Finally, the overall enhancement factor in fluorescence can be expressed by the absorbance ratio between the PC phosphor and its bulk counterpart as we have already assumed that fluorescence is proportional to the absorbance of pump photons; it is therefore implicit that the fluorescence enhancement factor corresponds to the enhanced luminescence in the total solid angle of 4π steradians.
Figure 4(a) compares the absorbance of the 1D PC phosphor with that of the bulk phosphor as a function of the pump photon wavelength, λp. The absorbance spectrum of the PC phosphor resembles the transmittance spectrum of the corresponding 1D PC shown in Fig. 2(b). At λp = λ0 = 420 nm (the center of the PBG), pump photons are subject to total reflection except for those penetrating a finite distance into the phosphor, because propagation of photons through the PC phosphor is strictly forbidden. This results in poor excitation of fluorescent agents, i.e., QDs. Thus the condition λp = λ0 (more generally, pumping the PC phosphor at any wavelength within the PBG) is unsuitable. On the contrary, absorbance of the PC phosphor is significantly enhanced compared to that of the bulk phosphor when λp = λ1 = 451.6 nm (the PBE) or λp = λ3 = 461.9 nm (the second PBE), as expected from our earlier discussion. In particular, the absorbance of the PC phosphor at λp = λ1 is approximately 7 times larger than that of the bulk phosphor. Figure 4(b) displays how the fluorescence enhancement factor at λp = λ1 (i.e., where the enhancement is maximum) changes as a function of the number of pairs of layers, N. The enhancement factor increases monotonically as N increases, from 2.6 for N = 10 to 6.9 for N = 30.This clearly demonstrates that a greatly enhanced fluorescence is attainable by structuring phosphor into a PC and tuning the PBE (preferrably in the HIB) of the PC to the pump wavelength. It should be noted that λ1 undergoes a blueshift as N increases. This is a well-known property of DBRs. Therefore, for each N in Fig. 4(b), the enhancement factor has been determined for a shifted spectral position of λ1.
So far, we have investigated the case where the pump photons used for phosphor excitation are monochromatic. However, phosphor excitation is typically achieved using a light source with a broad emission bandwidth. For example, standard white LEDs that are commercially available consist of a blue LED with a yellow phosphor cap. The blue LED contributes a blue hue to the overall color and at the same time serves as the excitation source for the yellow phosphor . In order to demonstrate the practical merits of the proposed PC phosphor, it is therefore necessary to investigate the case of phosphor excitation using a light source with a finite emission bandwidth. For this purpose, a gaussian spectral profile with a full-width at half-maximum (FWHM) bandwidth of 20 nm is assumed.
Shown in Fig. 5(a) are the absorbance of the PC phosphor and the bulk phosphor, when pumped by the broad bandwidth light source, as a function of the “peak” wavelength of the gaussian spectral profile. Two major differences between this spectra and that of the previous case using monochromatic light pumping, which is shown in Fig. 4(a), should be noted. The first difference is that the maximum absorbance is substantially reduced, which results in a reduction in the absorption enhancement factor from 6.9 to 2.2. The absorbance peak, however, is broader, which results in a large useful bandwidth for the pump source. The second difference is that the wavelength for maximum absorbance does not coincide with λ1 and it is redshifted by approximately 5 nm compared to the wavelength from the monochromatic pumping case. While the absorbance reduction is simply due to the fact that a broad bandwidth light source contains photons at wavelengths other than the optimized one (λ = λ1), the shift in the absorbance peak wavelength can also be explained. Those photons emitted from the broad bandwidth light source with wavelengths shorter than λ1 fall in the PBG. Thus, their propagation through the PC phosphor is forbidden and only the fluorescent agents within a short distance from the surface can be excited, which results in a poor excitation efficiency. Consequently, the absorbance peak of pump photons with a gaussian spectral profile is effectively shifted to a wavelength that is longer than λ1. Nevertheless, the absorbance of the PC phosphor is still much stronger than that of the bulk phosphor. Specifically, the absorbance of the PC phosphor is approximately 2.2 times higher at the absorbance peak of λ = 457 nm (instead of λ1 = 451.6 nm) than the absorbance of the bulk phosphor. Further, the enhancement in pump photon absorption is preserved over a very broad spectral range of pump wavelengths (Δλ ~50 nm). This implies a large tolerance in wavelength tuning between the peak wavelength of the broad bandwidth pump source and the PBE of the PC phosphor, which is extremely important if the PC phosphor is to be considered for use in white LEDs.
Figure 5(b) is the fluorescence enhancement factor when pumped by the broad bandwidth light source, shown as a function of the number of pairs of layers in the PC. For each value of N, the enhancement factor is estimated at the peak absorbance wavelength. Unlike the case of a monochromatic pump source, the absorption enhancement factor varies little with the number of pairs of layers in the phosphor, due to the broadness of the absorbance spectrum. In other words, the characteristics of the PC phosphor are not sensitive to the number of pairs of layers when a broad bandwidth pump source is used for phosphor excitation. We have shown the simulation results only for the layer pair numbers greater than 10, because the band structure and therefore the PBE identification becomes obscure progressively as the pair number gets smaller. In addition, the absorbance peak shifts significantly for small N so that deduced enhancement factor loses its relevance. According to Fig. 5(b), 10 pairs of layers would be as efficient as 20 or even 30 pairs of layers in terms of the phosphor excitation efficiency, which apparently has a big impact on real applications, such as shorter processing time and higher fabrication yield at the end.
The PC phosphor properties investigated so far are only valid provided the absorption by fluorescent agents remains low; thus, the changes in the corresponding photonic band structure of the 1D PC phosphor are negligible. In reality, however, one may have to substantially increase the concentration of fluorescent agents to meet the efficacy requirement. Figure 6(a) shows the reflectance spectrum of the 1D PC structure of 30 pairs of layers, when the concentration of the QDs embedded in the high index layers is 10−2 M. Although the number of pairs of layers is large, the simulated reflectance spectrum indicates that the band structure of the 1D PC phosphor is degraded by heavy absorption. Specifically, the PBE in the HIB (on the longer wavelength side) is no longer as clear as before. Shown in Fig. 6(b) is the resultant fluorescence enhancement factor as a function of QD concentration (or, equivalently, as a function of the absorption coefficient), which is calculated assuming that the LED-like broad bandwidth pump source (20 nm in FWHM) is employed. The enhancement factor drops to approximately 1.5 when the absorption coefficient is increased to 1,000 cm−1. Beyond this value, however, the fluorescence enhancement factor rapidly approaches unity, implying that the 1D PC phosphor does not provide enhanced fluorescence compared to the conventional bulk phosphor in the condition of extremely high QD concentrations (or, absorption coefficients).
We have proposed a 1D PC as a novel structure to enhance the fluorescence output from phosphors, which should have a high impact on white LED applications. We anticipate that the phosphor pump efficiency of the 1D PC can be greatly improved compared to that of a conventional bulk phosphor when the pump photon wavelength is properly tuned with respect to the PBG of the 1D PC. Through systematic and thorough model calculations, we conclude that a PBE (preferably in the HIB) is the best spectral position to which the pump photon wavelength should be tuned. This position is optimum owing to the low group velocity near the PBEs, and therefore results in the enhanced interaction of pump photons with fluorescent agents within phosphor. Using a specific PC phosphor model structure, we estimated a pump photon absorption enhancement factor of up to 6.9 when a monochromatic pump source is employed. The enhancement factor remains greater than 2 when a pump source with a broad bandwidth is used, and the benefit of a relaxed tolerance in wavelength tuning is gained. We also found that the 1D PC phosphor provides an enhanced fluorescence efficiency compared to a bulk phosphor until its absorption coefficient reaches 1,000 cm−1.
This study was financially supported by Samsung LED Co., Ltd., and supported in part by a National Research Foundation grant (2011-0018028) and the World Class University project (R31-10032), both funded by the Ministry of Education, Science & Technology of Korea.
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