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Abstract
Geometrical gain of a luminescent solar concentrator is drastically increased by laying out a luminescent fiber in a luminescent plate with air gap around it and attaching a photovoltaic (PV) cell to the tip of the fiber. The plate converts an incident photon to a first photoluminescence (PL) photon, and the fiber converts it to a second PL photon. Thus, the fiber carries the optical power as a leaf vein transports water and nutrients. The probability of the first PL photon resulting in the second PL photon reaching the PV cell can be measured by exciting a single spot on the plate with a laser beam. In experiment, 2 mm-thick, 50 mm-square and 50 mm-diameter circular devices were assembled with off-the-shelf components. For each case, geometrical gain exceeded 1000 and this probability averaged over the incident area was of the order of 0.01. Connecting multiple small-area devices to a single PV cell with a clear fiber would increase geometrical gain further and alleviate the absorption and scattering of PL photons during waveguiding.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
A luminescent solar concentrator (LSC) was invented in the 1970s to cope with the high cost of photovoltaic (PV) cells at the time [1]. It consists of PV cells attached to the sidewalls of a planar lightguide which contains luminescent materials. They convert incident light to photoluminescent (PL) photons. If emission of PL photons is isotropic, approximately three quarters of them are trapped inside by total internal reflection (TIR) in the lightguide with a refractive index of 1.5. The trapped PL photons become concentrated while they propagate toward the PV cells. Geometrical gain (${G_{geo}}$) is defined as the areal ratio of the incident plane and the PV cells. A larger LSC with high ${G_{geo}}$ could extend the cost advantage further. However, self-absorption poses a problem for this design strategy. In general, the absorption and emission spectra of a luminescent material partially overlap each other. Hence, some of the PL photons are lost while they propagate toward the PV cells. This problem has been recognized since the early days [2,3]. Intensive studies have been devoted for synthesizing an ideal material with a minimum overlap and adequate photostability [4,5]. However, the highest power conversion efficiency evaluated under the standard condition of Air Mass 1.5 Global (AM1.5 G) [6] remains at 7.1%. It was demonstrated with a 50 mm-square device with ${G_{geo}}$= 2.5 in 2008 [7].
In the meantime, the cost of Si-based PV cells continued to drop. Interests in the LSC community have shifted from large-scale power generation to energy-harvesting and sensor applications. For example, building-integrated photovoltaics (BIPVs) such as smart windows [8] aim to exploit aesthetic values of an LSC: it is semitransparent, and it comes in various colors. Other potential applications of LSC technology include projectors [9], gamma-ray astronomy [10], position-sensitive detectors [11], flat-panel displays [12], textiles [13], and more [14]. These proposals take advantages of the feature of large photo-sensitive area of an LSC.
To compete with the falling price of Si-based solar panels, ${G_{geo}}$ needs to increase drastically. In this regard, the two-stage photoconversion scheme reported by Keil in 1969 [15] is noteworthy. In 2014, Flores Daorta et al. extended this concept of “cascade LSC” [16]. Four luminescent rectangular solids surround a square luminescent plate. Small PV cells are attached at the edges of the rectangular solids. Photons incident on the square plate go through two-stage photoconversion. Effective concentration factor of an LSC ($C{F_{eff}}$) is defined as the ratio of its photocurrent to that of a PV cell with an equivalent incident area. Their Monte Carlo simulation shows that $C{F_{eff}}$ of a 6 mm-thick square device increases monotonically with its side length and that it starts to saturate beyond around 50 cm. This is inevitable because more PL photons are lost via self-absorption and matrix absorption/scattering in a larger-scale LSC.
In this paper, a small-scale, leaf-like configuration is proposed for increasing ${G_{geo}}$ while alleviating the photon losses during waveguiding. Its concept, experiments with off-the-shelf components, and some design considerations are described in the following sections.
2. Leaf-inspired LSCs
2.1 Configurations
An example of the configuration proposed here is illustrated in Fig. 1 (a). A luminescent fiber is laid out in the middle of a luminescent plate with air gap around it. The luminescent materials are selected to allow two-stage photoconversion. For example, the plate absorbs blue light and emits green PL photons. Some of them are trapped in the plate. They can enter the fiber and excite the material inside. Then, red PL photons are emitted. A clear fiber connected to the end of the luminescent fiber transports them to a PV cell. The fiber resembles a leaf vein that transports water and nutrients in a leaf.
Fig. 1. Configurations of (a) a leaf LSC proposed here, and (b) multiple devices connected to a PV cell via a clear fiber.
The geometrical gain ${G_{geo}}$ of the configuration in Fig. 1(a) is equal to ${({D/d} )^2}$, where D and d are the diameters of the plate and the fiber, respectively. This is equivalent to that of a cascade LSC in which a second converter is attached to the sidewall of a first converter. In Fig. 1(a), the second converter is placed in the middle of the first converter. Because the average distance that the PL photons propagate in the first luminescent plate is reduced to one half, the photon loss during waveguiding will be alleviated.
Multiple devices can be connected to a single clear fiber via couplers as illustrated in Fig. 1 (b). When N devices are linked, ${G_{geo}}$ increases to $N{\eta _{coupl}}{({D/d} )^2}$, where ${\eta _{coupl}}$ is the efficiency of the coupler. Regarding this efficiency, arc-bend branch structures have been studied for distributing sunlight in a house. Ray tracing simulations show that a proper design ensures ${\eta _{coupl}}$ larger than 90% [17].
2.2 Collection efficiency
In an optical concentrator, the photon flux incident on its front surface is concentrated on a smaller surface. Its effectiveness is characterized by the ratio of the photon fluxes at these surfaces. Concentration factor is defined as $CF = \frac{{{N_{out}}/{A_{out}}}}{{{N_{in}}/{A_{in}}}}$, where ${A_{out}}$ and ${A_{in}}$ are the areas of the two surfaces and ${N_{out}}$ and ${N_{in}}$ are the numbers of the photons arriving at the corresponding surfaces per unit time. Defining optical efficiency ${\eta _{opt}}$ as the ratio ${N_{out}}/{N_{in}}$ and replacing ${A_{in}}/{A_{out}}$ by ${G_{geo}}$, it is rewritten as,
Thus, ${\eta _{opt}}$ defined as the ratio ${N_{out}}/{N_{in}}$ is an important property of an optical concentrator. In an LSC, incident photons are converted to PL photons. The spectrum of PL photons is narrower than that of an incident light in practice. This concentration in wavelength is incorporated in ${\eta _{opt}}$ because integration of the spectral flux at each surface by wavelength gives ${N_{out}}$ and ${N_{in}}$.
The optical efficiency of an LSC is equal to the product of the probabilities involved in harvesting incident photons. Adopting the nomenclatures in Ref. [18], these probabilities are denoted as follows. First, an incident photon is absorbed by the luminescent plate with a probability ${\eta _{abs}}$. Second, the absorbed photon is converted to a PL photon with a probability called quantum yield ${\phi _{PL}}$. Third, some of them are trapped in the plate with a probability ${\eta _{trap}}$. Finally, some of the trapped PL photons survive absorption and scattering in the luminescent plate and they reach its output surface. This probability is denoted as ${\eta _{wg}}$. At the end, ${\eta _{opt}}$ of a conventional LSC is expressed as,
where,The term ${\eta _{abs}}$ is given by the product of the probability of refraction at the boundary with air and the absorptance of the luminescent plate. The former is given by the Fresnel equations. The latter is given by the Lambert-Beer law.
The term ${\eta _{col}}$ is the fraction of the absorbed photons resulting in the PL photons reaching the output surface of an LSC. It is called collection efficiency, internal quantum efficiency, quantum optical efficiency [18], etc. Note that ${\eta _{col}}$ does not depend on the wavelength of an incident photon because the spectrum of PL photons is fixed irrespective of the spectrum of incident photons. However, it depends on the incident position of the excitation photon via the terms ${\eta _{trap}}$ and ${\eta _{wg}}$. Both probabilities become larger when the region near the PV cell is excited. By exciting every single spot on the luminescent plate, one can measure the position dependency of ${\eta _{col}}$. One needs to consider this dependency in case of an LSC under non-uniform illumination. If it is uniform, the value averaged over the whole incident area ($\overline {{\eta _{col}}}$) can be used for calculating ${\eta _{opt}}$ in Eq. (2).
In a leaf LSC, the PL photons from the luminescent plate are coupled to the luminescent fiber. Some of them are absorbed. Let us denote these probabilities as ${\eta _{coupl}}$ and ${\eta _{abs2}}$, respectively. The fate of the absorbed photons is similar to that in the first photoconversion process. By adding subscripts to the probabilities in Eq. (3), the collection efficiency of a leaf LSC is expressed as follows.
Note that Eq. (4) does not depend on the wavelength of an incident photon. Thus, one can determine ${\eta _{col}}$ by experiment with monochromatic excitation light as described in Section 3. Once ${\eta _{abs}}$ is measured at each wavelength and $\overline {{\eta _{col}}}$ is determined at a certain excitation wavelength, ${\eta _{opt}}$ can be estimated from Eq. (2) for a leaf LSC under uniform illumination.
3. Experiment
The collection efficiency of a leaf LSC can be determined by the following procedure. First, a laser beam excites a single spot on the luminescent plate to generate green PL photons. The absorptance of the plate ${\eta _{abs}}$ is measured at this excitation wavelength ${\lambda _{ex}}$. The incident optical power ${P_{in}}$ is measured with a power meter. This is converted to the number of the green PL photons generated per unit time, i.e., ${\phi _{PL1}}{\eta _{abs}}{P_{in}}/({hc/{\lambda_{ex}}} )$ where h is the Planck’s constant and c is the speed of light. Second, the optical power exiting the luminescent fiber ${P_{out}}$ is measured with a power meter. Its spectrum is measured with a spectrometer to find its peak wavelength ${\lambda _{peak}}$. Assuming that the emission spectrum of the luminescent fiber is sufficiently narrow, the number of the red PL photons exiting the fiber per unit time is approximated by ${P_{out}}/({hc/{\lambda_{peak}}} )$. Therefore, an approximate value of ${\eta _{col}}$ is given by,
Luminescent plates and luminescent fibers are the main components of the configuration in Fig. 1(a). No clear optical fiber is used in this experiment. Off-the-shelf acrylic plates and fibers are used in this experiment. All surfaces of these components are polished. Because manufacturers regard the information on the luminescent materials as proprietary, we measure their emission and absorption spectra first. Then, a luminescent fiber is assembled with rectangular luminescent plates and its collection efficiency is evaluated. Since ${\phi _{PL1}}$ is unknown, we will assume ${\phi _{PL1}} = 1$ in Eq. (5). This experiment is repeated with a square and a circular device to see how self-absorption manifests itself differently.
3.1 Luminescent plates
First, the absorptance of a 2 mm-thick, 50 mm-square acrylic plate emitting in green (Model 1305 L, Kanase Inc., Japan) was measured with a spectrophotometer (Model UV-3600, Shimadzu Corp., Japan). The result is shown by the solid curve in Fig. 2. Its absorptance is about 0.95 in the wavelength range from 370 nm to 470 nm and is almost zero beyond 530 nm.
Fig. 2. Characteristics of a luminescent plate (Model 1305 L, Kanase Inc., Japan). The solid curve is its absorptance. The inset shows a photograph of the sample and the optical fiber head of a spectrometer for measuring the spectrum of the PL photons exiting the surface of the plate (broken curve). A laser beam is normally incident on a single spot on the plate. The dotted curve is the spectrum of the PL photons measured at the edge surface of the plate after being scaled (see the text for detail).
Second, a laser diode emitting at 405 nm excited a single spot at the center of the plate. As shown in the inset of Fig. 2, an optical fiber guided the PL photons leaking from its top surface obliquely to a spectrometer (Model FLMS 13077, Ocean Optics, USA). The core diameter and the numerical aperture of the optical fiber were 400 µm and 0.22, respectively. The laser light transmitting the plate and the green PL photons leaking forward from entering the plate were absorbed in darkroom. The broken curve in Fig. 2 shows the PL spectrum normalized at its peak intensity.
When the optical fiber head was attached to the center of one of the sidewalls, the spectrometer recorded the PL photons that propagated at least 25 mm inside the plate. The dotted curve in Fig. 2 shows the resultant spectrum after being scaled such that its distribution at longer wavelengths matches that of the broken curve. The peak wavelength shifted from 492 nm to 518 nm due to self-absorption.
In general, the intensity of the PL photons emitted from a uniform luminescent layer depends on the emission angle due to self-absorption inside the luminescent plate [19]. This slight variation in the PL spectrum can be neglected compared to the difference between the broken and dotted curves in Fig. 2.
3.2 Luminescent fibers
Emission spectra of a 1.5 mm-diameter acrylic fiber emitting in red (Model FFOR-60, Plastruct, Inc., USA) were measured in a similar manner. Namely, a single spot on the fiber was irradiated by the same laser beam. The solid curves in Fig. 3 are the spectra of the PL photons exiting the tip of the fiber when the distance between the tip and the excited spot along the fiber axis ($x$) was varied from 10 mm to 60 mm in steps of 10 mm. By fitting the intensities of the solid curves at 608 nm with the Lambert-Beer law, the attenuation coefficient of this fiber is calculated to be 0.0941 $\textrm{m}{\textrm{m}^{ - 1}}$ at 608 nm. This is an effective attenuation coefficient of this fiber at this wavelength because the actual propagation distance of the PL photons is longer than the distance along the fiber axis. The emission spectrum with minimum self-absorption peaks at 608 nm as shown next.
Fig. 3. Spectra of the red PL photons measured with a 1.5 mm-diameter luminescent fiber (Model FFOR-60, Plastruct, Inc., USA). The inset shows the setup for this measurement. The dotted curve is the spectrum of the PL photons leaking from the fiber surface after being scaled (see text for detail). The solid curves are the spectra measured at the tip of the luminescent fiber. As the distance between the excited spot and the optical fiber head (denoted as $x$) increases, the photons with shorter wavelengths are lost due to self-absorption.
The spectrum of the PL photons leaking from the fiber surface was also recorded by the setup shown in Fig. 3. A black velvet foil (Acktar Japan, Inc., Model MV-20X20-0) absorbed the transmitting laser light and the PL photons emitted downward. The dotted curve is the resultant spectrum after being scaled such that the distribution at longer wavelengths matches those of the solid curves. Its peak wavelength is 608 nm.
The dotted curve in Fig. 3 matches the emission spectrum of Lumogen F Red 305 well. Hence, it is highly likely that the luminescent material in this fiber is Lumogen F Red 305. This is a standard dye investigated for LSCs in the literatures [20,21]. It is reported that the quantum yield of this material incorporated in polymethyl methacrylate (PMMA) is close to unity [20]. The emission spectrum of a PMMA doped with this dye [21] is reproduced in Fig. 4 (dotted curve). It peaks at 608 nm and has a shoulder at longer wavelengths. So does the measured spectrum shown in Fig. 3 (dotted curve).
Fig. 4. The emission spectrum of Lumogen F Red 305 in Ref. [21] is reproduced (dotted curve). The attenuation coefficient in Ref. [21] is scaled to match the measured value at 608 nm (solid curve). The emission spectrum of the luminescent plate is reproduced from Fig. 2 (broken curve).
The attenuation coefficients in Ref. [21] are scaled such that the datum at 608 nm is equal to 0.0941 $\textrm{m}{\textrm{m}^{ - 1}}$, which is the measured effective attenuation coefficient of this fiber. The result is shown by the solid curve in Fig. 4.
Note that the overlap between the solid curve and the dotted curve in Fig. 4 is relatively large. This fact explains the large redshift in the spectra recorded at the tip of the fiber (solid curves in Fig. 3.)
In Fig. 4, the emission spectrum of the luminescent plate in Fig. 2 is reproduced (broken curve). Although the solid and broken curves overlap, the PL photons with shorter wavelengths are less likely to be absorbed by the luminescent fiber. Accordingly, the absorbance ${\eta _{abs2}}$ in Eq. (4) decreases.
3.3 Collection efficiency
Square and circular samples were assembled with the luminescent components described above. Their photographs taken under room light are shown in Fig. 5(a). The plates appear yellowish because of additive color mixing of the green PL photons and the room light. As shown in the cross section in Fig. 5(b), a 10 mm-wide mirror was used to bridge two luminescent plates with a 1.8 mm-wide gap in between. An optical adhesive tape with refractive index of 1.48 was used to support the two plates. A 1.5 mm-diameter luminescent fiber was placed in the gap. The fiber protruded from the edge of the plates for 20 mm to allow easy handling when coupling a power meter to the edge surface of the fiber at the expense of additional photon loss via self-absorption.
Fig. 5. Configuration of leaf LSCs. (a) Photographs of square and circular samples taken under room light. (b) A schematic drawing of the cross section for the two samples.
A laser diode emitting at 405 nm was used to excite a single 1 mm-diameter spot on the plate. The sample was placed on the black velvet foil to absorb the PL photons emitted downward as well as the unabsorbed laser light. There was air gap between the plate and the foil to allow TIR in the plate. A power meter (Model PD300-SH, Ophir Optronics, Israel) recorded ${P_{out}}$, the power of the PL photons exiting the fiber tip. The protruded fiber region and most of the sensitive area of the power meter head (10 mm × 10 mm) was covered by the black foil to exclude stray light. The incident optical power ${P_{in}}$ was measured with the same power meter. The absorptance ${\eta _{abs}}$ at 405 nm was 0.958 for these 2.0 mm-thick plates (see Fig. 2). Collection efficiency ${\eta _{col}}$ was calculated from Eq. (5). This process was repeated for up to 25 spots on the plates shown in the insets of Fig. 6. In each graph, the locations of excitation spots are indicated together with the definition of the coordinate system.
Fig. 6. Collection efficiency evaluated for (a) a square sample and (b) a circular sample. Each inset shows a schematic drawing of the sample and the locations of the excited spots.
For the square sample, ${\eta _{col}}$ decreases as the excitation spot moves away from the fiber as shown in Fig. 6(a). This is caused by self-absorption of the green PL photons in the plate. It also decreases monotonically with the distance along the fiber. This is attributed to self-absorption of the red PL photons in the fiber.
For the circular sample, ${\eta _{col}}$ is larger when the excitation spot is near the perimeter as shown in Fig. 6(b) (see open circles). This can be attributed to the increased reflectance at the edge surface of the perimeter as explained below. The photographs in Fig. 7 shows the PL photons leaking from the sample. Note that the bright regions in these color images appear whitish because these pixel values are saturated. This is caused by the auto-gain control feature of a digital camera used here.
Fig. 7. Photographs of the circular sample when its single spot is excited by a laser beam. The x coordinate of the excited spot was fixed at 25 mm. The y coordinate of the excited spot was set to (a) 10 mm, (b) 15 mm, and (c) 20 mm.
When the excitation spot is at $({x,y} )= ({25\textrm{mm},10\textrm{mm}} )$, the region on the fiber close to this point becomes bright as shown in Fig. 7(a). This is where many green PL photons arrive after propagating inside the plate. When the y coordinate is set to 15 mm and 20 mm, two more bright regions appear on the fiber as shown in Fig. 7(b) and (c). These additional regions are where many green PL photons arrive after being reflected by the edge surface. As the excitation spot is moved toward the perimeter, the incident angle on the sidewall at the perimeter approaches the critical angle for TIR. The reflectance increases sharply, and more green PL photons are directed toward the fiber. The two bright regions on the fiber move closer to the perimeter in Fig. 7(c) as the y coordinate of the excitation spot is 20 mm.
In addition, there are some notable features in Fig. 7. First, the lower half of the sample is dark while its perimeter is bright. Some green PL photons enter the lower plate, propagate inside by repeating TIR, and exit at the sidewall. Namely, some green PL photons miss the fiber. This is because the plates are 2.0 mm thick while the fiber diameter is 1.5 mm. Second, a concentric pattern appears around the excitation spot. The mechanism behind is believed to be re-emission of the green PL photons following self-absorption. This phenomenon has been modeled and verified by experiment for the case of a transparent plate with a thin luminescent layer [22]. The intensity of re-emission is several orders of magnitude lower than that of the initial PL photons. Note again that some pixel values are saturated in these photographs. Third, gradual intensity variation of the red PL photons is observed in the protruded region of the luminescent fiber. This is also caused by re-emission after self-absorption events. Finally, the tip of the fiber is bright, indicating that the edge surface is not polished well enough to prevent scattering.
3.4 Effect of edge reflection
As apparent from Fig. 7, green PL photons leaked from the sidewall at the perimeter of the luminescent plate. The edge surface of each assembly excluding its protruded fiber region was covered by a reflective film and the measurement was repeated. As shown in Fig. 8(a), collection efficiency of the square sample increased twofold. As for the circular sample, it also increased substantially when the spots away from the perimeter were excited as shown in Fig. 8(b). In case of the square sample, average collection efficiency $\overline {{\eta _{col}}}$ increased to 0.0076 from 0.0039 by attaching the reflective film to the perimeter sidewall. That of the circular sample increased to 0.0085 from 0.0055.
Fig. 8. Collection efficiency evaluated for the samples with reflective films covering its edge surface. (a) a square sample and (b) a circular sample.
3.5 Effect of luminescent material
The experiment was repeated with a 2.0 mm-thick square luminescent plate emitting in orange (Model 9889 L, Kanase Inc., Japan). The solid curve in Fig. 9(a) is its absorptance ${\eta _{abs}}$. The emission spectrum of the PL photons leaking from the surface is shown by the broken curve. It has two peaks. The peak at shorter wavelengths completely disappears in the spectrum of the PL photons exiting the plate from its edge (dotted curve). This is due to self-absorption as evident from the overlap between the solid and dotted curves. The peak at 405 nm is the scattered excitation light, indicating possible granular nature of the luminescent material in this plate. The non-zero absorptance beyond 550 nm is probably due to matrix absorption and/or scattering.
Fig. 9. Characteristics of a 2.0 mm-thick luminescent plate emitting in orange (Model 9889 L, Kanase Inc.) and the collection efficiency evaluated with an assembly using these plates: (a) absorptance and emission spectrum of the luminescent plate and (b) the collection efficiency measured without the edge mirror.
As shown in Fig. 9(b), the collection efficiency measured with this plate decreases with the coordinate x as in the case of Fig. 6(a). The dependency on the coordinate y, on the other hand, is markedly enhanced in Fig. 9(b). This is due to severer self-absorption in this plate. In case of $y$= 2 mm, for example, the PL photons with shorter wavelengths can reach the fiber, leading to higher collection efficiency.
4. Discussions
4.1 Collection efficiency
Below is an order of magnitude discussion for the measured collection efficiency. For the case of isotropic emission, the trapping probability of PL photons in a planar waveguide is approximately given by $\cos {\theta _c}$ where ${\theta _c}$ is the critical angle for TIR [1]. In this experiment, assuming an isotropic emitter in a polymethyl methacrylate (PMMA) plate (refractive index 1.49) surrounded by air, ${\eta _{trap1}} = 0.74$. Assuming a PMMA core surrounded by air cladding for a luminescent fiber, ${\eta _{trap2}} = 0.55$ [23]. The probability of surviving absorption and scattering in the plate is roughly estimated by the ratio of the areas under the dotted and broken curves in Fig. 2, i.e., ${\eta _{wg1}} \sim 0.49$. As for the fiber, ${\eta _{wg2}} \sim 0.35$ from the curve at $x =$30 mm in Fig. 3. Plugging these in Eq. (4), ${\eta _{col}}$ is roughly equal to $0.07 \times {\eta _{coupl}}\;{\phi _{PL2}}{\eta _{abs2}}$. From the measured value of $\overline {{\eta _{col}}} \sim 0.01$, the product ${\eta _{coupl}}\;{\phi _{PL2}}{\eta _{abs2}}$ in Eq. (4) is 0.14 for the devices in this experiment.
As apparent in Fig. 2 and Fig. 3, self-absorption is the major source of PL photon loss in the luminescent components assembled in this experiment. Decreasing the lateral dimension of a luminescent plate alleviates this photon loss. In addition, the trapping efficiency becomes larger because more PL photons generated in the region near the fiber can reach the PV cell. Finally, the coupling efficiency ${\eta _{coupl}}$ in this experiment can be improved by properly designing the geometrical conditions such as the diameter of the fiber and the reflecting film around it.
4.2 Concentration factor
Unlike a concentrator based on lenses and mirrors, an LSC can harvest diffuse light. Kerrouche et al. studied optical efficiency of LSCs under oblique illumination for BIPV applications [24]. Note that they define optical efficiency of an LSC as the ratio of the optical power at its front and edge surfaces. Others define it as the ratio of the photon counts [15,18]. We have adopted the latter as described in Section 2.2.
The spectrum of the incident light can be quite different from a standard one such as AM1.5 G. Hence, it is worthwhile to show how an LSC performs under different incident spectra. The concentration factor $CF$ of an LSC is expressed for an arbitrary incident spectrum ${S_{in}}(\lambda )$ below. Because the term ${\eta _{col}}$ in Eq. (2) does not depend on the wavelength $\lambda$ of the incident photons, only the term ${\eta _{abs}}$ is modified. It is given by the product of the probability of refraction at the air-plate boundary and the weighted average of the absorptance of the plate. Let $\mu (\lambda )$, d and R be the attenuation coefficient, thickness, and reflectance, respectively. Then, $CF$ of an LSC under uniform illumination is given by,
Effective concentration factor ($C{F_{eff}}$) is defined as the ratio of photocurrent of an LSC to that of its PV cell alone. By incorporating the quantum efficiency of a PV cell ${\eta _{PV}}(\lambda )$, Eq. (6) is modified as follows.
For numerical examples, let us assume the characteristics in Fig. 10. The two emission spectra were measured with a white LED and a halogen lamp. The quantum efficiency was measured with a polycrystalline Si PV cell. For the samples described in Section 3, ${G_{geo}} \sim 1400$ and ${\eta _{col}} \sim 0.01$ for normal incidence. Table 1 lists $CF$ and $C{F_{eff}}$ calculated for these spectra. Note that these values are for a 2 mm-thick leaf LSC with a 5 cm-square incident surface. By connecting N devices as illustrated in Fig. 1(b), $N$-fold increase is expected.
Table 1. Concentration factors of a single leaf LSC calculated with the spectra in Fig. 10
Flores Daorta et al. measured $C{F_{eff}}$ of a 6 mm-thick 11 cm-square cascade LSC under AM1.5 G. It was 0.67 [16]. In case of a 2 mm-thick, 5 cm-square leaf LSC, the corresponding value is 1.2 (see Table 1). This might be attributed to reduced self-absorption loss in the leaf LSC. Significant increase in $C{F_{eff}}$ is expected for the configuration in Fig. 1(b).
4.3 Energy-harvesting by volume
Geometrical gain of the configuration in Fig. 1(b) is proportional to the number of devices connected to a single PV cell via a clear fiber. Let us consider the implementation illustrated in Fig. 11. Just like leaves in a tree, luminescent plates may overlap each other. The upper plates in Fig. 11 absorb blue light in an incident spectrum ${S_{in}}$ and emit green PL photons ${S_{PL1}}$. The lower devices harvest a part of the light transmitted by the upper devices (${T_1}{S_{in}}$). In addition, they harvest a part of the green PL photons leaking from the upper devices.
Fig. 11. Concept of integrating leaf LSCs to form a tree-like structure. The footprint for installing a solar panel is utilized efficiently.
The tree-like implementation departs from the conventional concept of a solar panel in a sense that sunlight is harvested by the volume filled with multiple devices. Hence, a given footprint can be utilized efficiently. Luminescent materials should be selected to absorb incident light as much as possible.
In a BIPV system, a traditional panel configuration might be preferred. Square devices such as one in Fig. 5(a) can be connected by a clear fiber. Such an implementation might look like a tiled LSC. It differs in a sense that the converted energy is transferred optically to a single PV cell, resulting in a larger geometrical gain.
5. Conclusions
A leaf-like LSC is proposed for increasing geometrical gain of an LSC drastically while alleviating the PL photon loss during waveguiding. It is constructed by laying out a luminescent fiber in a luminescent plate and attaching a PV cell to the tip of the fiber. By selecting doping materials appropriately, two-stage photoconversion takes place. Its collection efficiency is defined as the probability of a first PL photon generated in the plate resulting in a second PL photon reaching the PV cell. In the experiment with off-the-shelf components, 2 mm-thick luminescent plates emitting in green and a 1.5 mm-diameter fiber emitting in red were characterized first. They were assembled to form 50 mm square and 50 mm-diameter samples with geometrical gain exceeding 1000. Collection efficiency was evaluated by exciting a single spot on each device with a laser beam. When averaged over the incident area, both samples exhibited collection efficiency of the order of 0.01. The mechanisms limiting this efficiency are self-absorption, trapping, and optical coupling between the plates and the fiber. Decreasing the lateral dimension of the plate will alleviate self-absorption. Multiple leaf-like modules can be connected to a PV cell through a clear fiber to increase the geometrical gain further. A tree-like implementation will allow one to harvest sunlight by volume, utilizing the footprint for installing a solar panel efficiently.
Acknowledgments
We thank Kenta Hoga, Kohei Okada and other members in our laboratory for their assistance in the experiment.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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