OPEN
Light: Science & Applications (2016) 5, e16216; doi:http://dx.doi.org/10.1038/lsa.2016.216
Web End =10.1038/lsa.2016.216
Ofcial journal of the CIOMP 2047-7538/16
http://www.nature.com/lsa
Web End =www.nature.com/lsa
Marina Mariano1, Gregory Kozyreff2, Luis G Gerling3, Pablo Romero-Gomez1, Joaquim Puigdollers3, Jorge Bravo-Abad4 and Jordi Martorell1,5
Extracting the light trapped in a waveguide, or the opposite effect of trapping light in a thin region and guiding it perpendicular to its incident propagation direction, is essential for optimal energetic performance in illumination, display or light harvesting devices. Here we demonstrate that the paradoxical goal of letting as much light in or out while maintaining the wave effectively trapped can be achieved with a periodic array of interpenetrated bers forming a photonic ber plate. Photons entering perpendicular to that plate may be trapped in an intermittent chaotic trajectory, leading to an optically ergodic system. We fabricated such a photonic ber plate and showed that for a solar cell incorporated on one of the plate surfaces, light absorption is greatly enhanced. Conrming this, we found the unexpected result that a more chaotic photon trajectory reduces the production of photon scattering entropy.
Light: Science & Applications (2016) 5, e16216; doi:http://dx.doi.org/10.1038/lsa.2016.216
Web End =10.1038/lsa.2016.216; published online 30 December 2016
Keywords: chaos; ergodicity; ber; light-guiding plate; light harvesting; light trapping
INTRODUCTIONLight trapping and guiding in thin lms combined with efcient light extraction or insertion in the direction orthogonal to the guiding one is essential to obtain energy-efcient light harvesting or emission. In this context, one is faced with two seemingly incompatible constraints namely, to let as much light in or out as possible at any point on the guiding lm surface while maintaining the light effectively trapped across the lm. For several decades, in an attempt to maximize sunlight energy harvesting, researchers of thin lm solar cells have been searching for the optimal system architecture to achieve the most effective light path bending into the cell absorber layer1,2. Many
different approaches have already been explored. Texturing one or both surfaces of the lmin two or three dimensionshas been considered in several forms and instances. In organic cells, hexagonal arrays of nanocolumns3,4 or nanoholes5 have been embossed in the active layer to increase light trapping by scattering.
Other thin lm technologies, such as quantum dot solar cells, have used a light-trapping scheme with a nano-imprinted electrode capable of both diffracting light and collecting the photo-generated carriers6,7,
whereas in amorphous silicon solar cells, a whispering gallery light enhancement in nanospheres8,9 has been used. Texturing the electrodes was also applied to organic cells using a periodic grating10,11 or a
random conguration12. Other approaches to increase the effective light path inside this type of cells have used plasmonic structures13.
The presence of metallic nanoparticles increased the degree of light
ORIGINAL ARTICLE
Intermittent chaos for ergodic light trapping in a photonic ber plate
absorption and exciton dissociation14,15. Different particle shapes have been used to enhance different parts of the spectra, such as nanocubes16 or oligomers17. In light-extracting devices with a similar conguration but a reverse direction of light uxsuch as, for instance, in light-emitting diodes (LEDs)18 or displays19adequate light energy management is another serious issue.
In lms that are much thicker than the wavelength of the light, a random texturing of both lm surfaces will produce a random distribution of light regardless of which direction the beam is coming from20,21. This reduces the probability of escape once the light has been admitted inside the structure. One must take care, however, to introduce just the right amount of surface roughness required for ergodic behavior because even the slightest randomness may pose serious fabrication issues for the harvesting or illumination elements incorporated on them. This is why recent research efforts have aimed at achieving ergodicity within an ordered conguration: a metallic grating structure22, a pyramidal rear reector23,24, a microprism textured surface25, a V-shaped tandem device26, a V-groove surface texturing27 or an array of microlenses28 providing total internal reection at the external device surface have been used to increase the amount of light that passes through the energy conversion layer. However, the goal of ergodic behavior could not be reached or demonstrated.
To achieve the goal of ergodicity within order, we propose a fundamentally new design based on a light-guiding plate formed by an
1ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona) 08860, Spain; 2Dpartement de Physique, Universit Libre de Bruxelles (ULB), Campus de la Plaine, Bruxelles B-1050, Belgium; 3Departament Enginyeria Electrnica, Universitat Politcnica de Catalunya, Barcelona 08034, Spain;
4Departamento de Fsica Terica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autnoma de Madrid, Madrid 28049, Spain and
5Departament de Fsica, Universitat Politcnica de Catalunya, Terrassa 08222, Spain
Correspondence: G Kozyreff, Email: mailto:[email protected]
Web End [email protected] ; J Martorell, Email: mailto:[email protected]
Web End [email protected] Received 29 December 2015; revised 20 August 2016; accepted 4 September 2016; accepted article preview online 6 September 2016
Intermittent chaos for ergodic light trapping
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a
b c Max
0
Figure 1 Light trapping in a PFP. (a) Schematic drawing of light incidence and trapping in the PFP. Cross section of the electrical eld distribution when a plane wave is incident, (b) on an isolated ber and (c) on an array of intercalated bers. Higher-intensity elds on the caustic coupling to the adjacent bers are clearly visible in c. The numerical calculation was performed assuming an incident plane wave at = 580 nm propagating normally to the axis of the bers, whose diameters were set to 20 m. In c, the period of the array was taken as 14.14 m. In both congurations, the lower half of the bers (n = 1.46)
was assumed to be coated by a dielectric multilayer characterized by the sequence of refractive indexes and thicknesses given in the caption of Figure 4. To better visualize the light trapping in the PFP, the imaginary part of the refractive index was assumed to be zero for all layers. Finally, on the bottom, a perfect electric conductor was introduced as a perfect mirror.
array of interpenetrating bers, shown schematically in Figure 1a. In such a photonic ber plate (PFP), both front and back surfaces are equally textured. We dene the cylinder interpenetration c=d as the ratio between the period of the array and the cylinder diameter. To evaluate the light-harvesting capacity of this PFP, we consider the case in which the back surface is covered by a multilayer nanostructure and a highly metallic reective layer. We analyze the light propagation in this structure by implementing a full-wave vector numerical analysis that assumes a plane wave incident on the ber array normally to the plane dened by the array. As observed in Figure 1b, when the plane wave is incident on an isolated ber, equivalent to a noninterpenetrating ber array, the incoming wave is focused toward the center of the ber and interferes with the reected wave, forming a fairly regular interference pattern with no apparent signs of light trapping. In contrast, when the cross-sections of the bers overlap (c=do1), as observed in Figure 1c, the regular pattern breaks up into a more disordered pattern.
Part of the light intensity distribution of the caustic in one ber connects to a whispering gallery mode (WGM) on the top interface of the adjacent bers. Thus, the opening between bers allows for an effective trapping of the incident light. In addition, polygonal interference patterns with widely varying orientations are observed across the bulk of the ber array. This indicates that light is not just
propagating back and forth between the top and bottom interfaces, as is essentially the case for isolated bers, but rather in all directions, leading to the desired ergodic behavior.
MATERIALS AND METHODSWe implemented an experimental demonstration of light trapping and absorption in arrays of intercalated bers by fabricating a PFP composed of a number of standard optical bers ranging from 10 to 15. To reach the desired degree of interpenetration between adjacent bers, the bers were laid against each other, heated and pulled simultaneously. Details of the procedure followed to obtain the ber array whose cross section is shown in Figure 2a can be found in section SI1 of the Supplementary Information. In contrast to a conguration with a random texturization of the surface, the smooth surface of the periodic ber array allows for the deposition of high-quality layered devices such as a thin lm solar cell (Figure 2b and 2c). Details of the evaporation of a small-molecule organic solar cell when using the ber array as the substrate are given in section SI2 of the Supplementary Information. The architecture of the fabricated solar cell, shown in Figure 2d and 2e, incorporates a junction of a 10 nm Tetraphenyldibenzoperianthene (DBP) layer and a 40 nm C70 layer as donor and acceptor materials, respectively. The conformal and high-quality layer deposition at the central part of any given ber and
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300 m
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Active cell layers
Cell limits
AI ITO
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d e
ITO
AI
ITO (140 nm)
500 nm 500 nm
MoO3/DBP/C70/BCP
MoO3/DBP/C70/BCP (<70 nm)
AI (100 nm)
Figure 2 Fabricated PFP solar cells. (a) SEM cross-section image of a fabricated array containing 11 bers of 70-m diameter. The average interpenetration parameter is c=dB0:95. (b) Schematic drawing of a solar cell deposited on the PFP where the different layers are the transparent conducting electrode ITO (yellow); the hole-transporting layer MoO3, the bilayer junction of DBP/C70 and the electron transporting layer BCP (green); the Al back contact (gray).
(c) SEM image of a PFP where an organic solar cell was deposited on one side of the plate. The changes in the gray tone are indicative of the different cell layers. SEM cross-section images of the cell layers, (d) at the bottom of a given ber and (e) at the intersection in between two adjacent bers. From the top edge of d and e, one can see the glass ber and the ITO layer (140 nm), followed by a darker zone corresponding to the semiconductor organic junction (~50 nm) and nally a brighter layer corresponding to the back Al contact (100 nm). All such layers, including the buffer layers (not visible in the image) were conformal with the curvature of the bers in both regions d and e. BCP, Bathocuproine; ITO, Indium tin oxide.
at the intersection between two adjacent bers is show in Figure 2d and 2e, respectively. Changes in layer thickness (if any) are at the nanometric scale.
RESULTS AND DISCUSSIONThe nanometric thicknesses of the active layers, which are necessary for optimal exciton separation and charge collection, limit the effective light harvesting by the DBP/C70 junction, whose absorbance is shown in Figure 3a. The level of light trapping in the PFP that can compensate for such a small thickness of the junction can be determined by evaluating the performance of the solar cell relative to the same cell deposited on a at glass substrate. The light-harvesting capacity of the cell evaporated on the PFP substrate was determined by rst measuring the current density versus the applied voltage on the cell. A comparison of the measured photovoltaic parameters (given in Table 1) to the reference cell deposited on a at substrate indicate a
34% increase in short circuit current or, equivalently, in light-harvesting capacity. In addition, it is important to note that as observed in Table 1, deposition of the cell on the PFP does not imply any relevant change in the photovoltaic (PV) parameters more directly linked to the electrical performance of the solar device, such as the ll factor (FF) or the open circuit voltage (VOC). On average, only a 6%
decrease was observed in the FF, whereas for the VOC, even slightly
better values could be obtained for cells on the PFP relative to cells on at substrates. The efciency in converting incident photons to collected charges can be further investigated by measuring the external quantum efciency, shown schematically in Figure 3b. This measurement conrms an increase larger than 30% in light harvesting by the ber array relative to the planar conguration.
To gain further insight into the nature of photon propagation leading to enhanced absorption in the PFP, we consider the trajectory followed by normally incident photons (Figure 4a). Such photons
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follow a ballistic ray trajectory unambiguously determined by Fresnel laws of reection and refraction. Elementary geometrical considerations show that consecutive bounces (labeled by j) within the same ber preserve the angle of internal reection j:
Db bj1 bj 0 1 As noted above, when c=d o1, there is an opening through which photons can pass directly from one ber to the next. When this occurs, j changes abruptly, with high sensitivity to the initial point of incidence for a given photon. This is similar to a mechanical billiard made of a single, truncated cylindrical cell with a periodic boundary, which was proven to be chaotic29. Hence, the photons follow chaotic trajectories, and the system is optically ergodic. To verify this statement, we computed ray trajectories until the light intensity I
was attenuated by a factor of 1015. With the large set of ray segments so generated, we studied the statistics of . Dividing the range of allowed values into steps of 0.01, we determined the cumulative distribution function (CDF) F(). The result, plotted in Figure 2b, is found to be independent of the initial conditions, which clearly establishes ergodicity with respect to the geometrical variables denoting the incidence position and the angle of reection. Another important feature is the discontinuity found in F() at = 0.
From this jump, we infer that a large portion of the ray trajectory (~60% for that particular value of c=d) is regular; that is, the chaos encountered here is intermittent. In other words, most of the ray trajectory is composed of regular segments, separated by brief, abrupt changes. Furthermore, within the regular part, the angle j may be larger in absolute value than the critical angle for total internal reection. When this occurs, light rays are trapped in a WGM of the ber array for several reections without escape losses. Examples of ray trajectories are given in Figure 4a. This simple ballistic approach, with the modication that for each optical incidence on the boundary both reection and refraction are possible, clearly illustrates that ergodic trapping in such a PFP combines the attributes of chaos and whispering gallery. Indeed, changing the initial incident ray and computing a distinct statistical ensemble of ray segments by ray-tracing yields the same CDF, which demonstrates ergodicity. Note that in contrast to the WGMs found in high-Q spheres30 or toroids31,32 used in sensing33 applications, the whispering gallery propagation in the PFP is generally low-Q and interrupted each time the photon trajectory crosses the intersection plane between adjacent bers.
From what precedes, it appears important to quantify the degree of coupling into such WGMs from a normally incident plane wave. To this end, we ran a large number of ray simulations, all starting with a normally incident ray and with initial positions uniformly distributed over a spatial period of the PFP. We then computed the average sum of intensities in ray segments such that = 0 and that |i|
4c = arcsin(1/n), where n is the refractive index contrast between the PFP and the air:
C X
a
0.4
DBP
C70
MoO3/DBP/C70/BCP
0.3
Absorbance (a.u.)
0.2
0.1
0
40 35 30 25 20
400 500 600 700
Wavelength (nm)
b
EQE (%)
15 10
50 400
j;bj1bj;jbjj>bc
Ij
500 600 700
Wavelength (nm)
Figure 3 Absorption and charge collection enhancement. (a) Absorbance of a 10-nm layer of DBP (red), a 40-nm layer of C70 (black) and the active plus buffer layers in the cell architecture (green). (b) Measured EQE of a
PFP organic solar cell (green) compared with a planar one (red line) with the same architecture depicted in Figures 2b and 4a. EQE, External quantum efciency.
2
This injection coefcient C depends on the interpenetration parameter c=d. As observed in Figure 4c, the coupling has a broad maximum around c=d = 0.8 and vanishes for small values of c=d and as c=d-1. This conforms to the limit c-0 corresponding to a at PFP, whereas when c-d, the bers that make up the PFP become isolated. This non-monotonic dependence of the PFP light-trapping capacity with c=d was also corroborated by implementing full-wave nite-element method simulations. Specically, to characterize such light connement, we considered an active layer with a very small articial absorption value (Im(n) = 0.001) and set to zero the imaginary part of the refractive index for all other layers. Because the parameter C is dened only in the ray-optic limit, we monitored the coupling instead through the absorption inside the active layers as a function of c=d, for
Table 1 Cell performance (JV measurements)
PV parameters cell type Voc (mV) FF (%) Jsc (mA cm 2) Efciency (%)
PFP 850.9 10.5 52.2 4 4.9 0.4 2.19 0.03
Planar 837.6 9.2 55.9 3 3.7 0.2 1.72 0.15 Percentage change +1.6% 6.5% +34% +27%
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a
Glass
= 580 nm. The resulting curve, shown in Figure 4c, conrms the non-monotonic behavior. The wider width of the absorption curve can be qualitatively explained by the fact that contrary to C, the absorption does not vanish in either the at or the separated cylinder limits for the substrate. In addition, the full-wave vector simulations yield an oscillatory dependence on the overlap parameter. This feature, not captured by the ray optics calculation, results from an interferometric enhancement of the eld inside the cylinders. Indeed, we note that the diameter used in the wave simulations is only 20 m, whereas the ray-optics analysis corresponds to the strict limit /d 0 . The interferometric origin of the modulation is conrmed by the slight shift observed in such a modulation when the absorption is computed at 585 nm instead of 580 nm (cf. Figure 4c).
As shown schematically in Figure 4a, the incident position for a given photon at the top interface of the ber array unambiguously determines the absorption probability for that photon. However, the absorption probability of a photon incident at a nearby position cannot be predicted based on the trajectory of the rst photon (Figure 4a). Here we consider that a change in incidence corresponds to a lateral displacement of the incident photon trajectory. However, similar unpredictability would be found if an angular change in the trajectory were to be applied. Such chaotic character in the photon propagation provides a scattering character in an ordered periodic conguration, which does not undermine the whispering gallery trapping inherent to the circular conguration used. The end result is that photons following chaotic trajectories have higher chances of being absorbed, leading to an unexpected decrease in entropy production for a given photon. Indeed, before a given photon hits the PFP, its state is known with perfect certainty, so the entropy is initially zero. Once that photon enters the ber array, it follows a well-dened ray trajectory within the array with a given number of escape channels (Figure 5a). Denoting the probability for that photon to escape via the ith channel as Pi (i = 1, 2,), we can dene a scattering Gibbs entropy per photon S()as
S y
=kB P0lnP0 X
[afii9826]i
ITO
MoO3
DBP
C70 BCP
AI
b
Cumulative distribution function
Absorption in the active layer (%)
0.2
0
0.5
0.4
0.3
0.2
0.10 0.2 0.4 0.6 0.8 1
1
0.8
0.6
0.4
4 2 0 2 4
[afii9826]
c
0.04
0.03
0.02
C
0.01
0
/d
Figure 4 Chaotic photon trajectories in the PFP. (a) The chaotic character in the photon trajectory is schematically shown by considering slightly different incident positions rapidly leading to completely distinct paths. Here a change in the incidence corresponds to a lateral displacement of the ray without any angle change. Note that inside the fourth ber, ray trajectory 1 follows a regular sequences of reections akin to whispering gallery modes until crossing the gap connecting the fourth with the third bers, at which point it undergoes a sudden change in reection angle 0.
(b) CDF of the change in over a long series of computed ray segments, all produced by the same incident ray. The jump at = 0 indicates that most of the ray trajectory is regular, and the observed chaos is of the intermittent type. The CDF depends on a single geometrical parameter, the ratio c=d between the array period and the ber diameter (here: 0.92). (c)
Full-wave simulation of absorption in the active layer at 580 nm (solid red squares) and at 585 nm (empty red squares). The lines are a guide for the eye. WGM injection parameter, measuring the efciency of the coupling between a normally incoming plane wave and WGM inside the PFP (blue solid line). Values of c=d larger than 1 correspond to disjoined cylinders. In b and c, ray-optics computations were performed at 580 nm. The indexes of the different layers in the structure used from the top ITO to the bottom: all layers in the order shown on the right hand side of a are 1.83 + 0.007i,2.05 + 0.0i, 2.06 + 0.57i, 2.19 + 0.40i, 1.71 + 0.003i and 1.01 + 7.03i. The layer thicknesses used were, from ITO to Al, 140, 8, 10, 40, 8 and 100 nm, respectively. To correctly visualize light trapping in the PFP when using the full-wave simulation, we set all dielectric refractive indexes to be purely real, except for the absorbing layers, in which the imaginary part was set to 0.001.
jPjlnPj 3 where P0 is the overall probability of absorption through the bottom interface, kB is Boltzmanns constant, and is the incidence coordinate shown in the inset of Figure 5b. Note that the above expression only represents the entropy production in the system associated with light trapping. Other processes that result from the absorption of photons, such as re-emission of light or heat dissipation, also generate entropy3436 but are not discussed here. Using a ray tracing code, the above expression of the entropy can easily be calculated. Alternative denitions of entropy such as KolmogorovSinay entropy, used to characterize other chaotic optical processes37, have a less immediate implementation here. Indeed, the dimension of the phase space increases each time a ray is refracted at the silicaair interface. Figure 5b displays the calculated scattering entropy as a function of . In the vicinity of = /2, the entropy is nearly constant; it is nearly equal to the value associated with a at geometry. However, there is a sharp transition at o1.1 rad and 42.03 rad, where the entropy production undergoes an abrupt drop and becomes a non-smooth function of . This marks the transition at which the rays enter the gap between adjacent cylinders immediately after the rst reection at the bottom interface. The rapid changes in S() are evidence of the chaotic sensitivity to initial conditions. Besides, the drop in S() indicates that despite the chaotic nature of photon propagation in the ber array, there is less uncertainty regarding the nal state of the photons compared with the at conguration. Indeed, they are trapped for
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a
1
P2
P1
P3
P3 P4
2
b
1
0.8
0.6
0.4
S([afii9835]) /k B
[afii9835]
P2 P1
0.2
0 1 1.5 2
[afii9835]
Figure 5 Scattering entropy. (a) Two different photon trajectories corresponding to photons entering the ber array in different angular locations. Photons may either be absorbed at the bottom multilayer or escape the array in a new direction when hitting the top interface with a nonzero probability Pi. (b) Entropy generated per photon as a function of the incident position . Photons that fall on the array in the vicinity of the ber intercalation (around = 1 and = 2 above) reside for a longer time inside the array. As a result, they have a larger probability to be absorbed, so the uncertainty of their nal state is reduced, and the production of entropy lowered. Inset: schematic drawing showing the angle indicating the ray incident position.
relatively long times into whispering gallery trajectories and therefore have greater probability to be collected at the bottom interface. Hence, the region of low value of S() indicates efcient trapping.
The intermittent chaotic propagation described above provides a good qualitative explanation for the enhanced absorption by the active materials from the solar cell deposited on the backside of the PFP shown in Figure 3b. However, in the experimental implementation, there are several additional subtleties that increase the difculty of reaching an accurate quantitative prediction of the measured increase in light-harvesting capacity. For instance, in the bilayer junction used, the exciton generation distribution in the direction perpendicular to the layered architecture is greatly affected by the wavelength of the incident photon. In other words, blue-shifted photons may generate a larger quantity of excitons in the C70 layer, whereas red-shifted photons are more likely to be absorbed by the DBP layer. The high vacuum evaporation procedure used for the deposition of the active layers over a non-at substrate, such as the ber array, may result in nanometric variations in the thicknesses of such layers. Indeed, in the central part of the ber, the layers may be slightly thicker than in the neighborhood of the ber intersection. The nal orientation of DBP molecules may be signicantly different on the PFP substrate leading to a birefringence, which may signicantly alter the DBP layer refractive index. In addition, as observed in Figure 3a, the degree of ber interpenetration increases as one moves away from the center of
the array. All such effects should be incorporated in a model aiming at a quantitative description of the external quantum efciency.
CONCLUSIONSIn this work, we propose a fundamentally novel light propagation regime that enables the effective trapping of light incident orthogonally to the plane dened by a novel trapping plate design. We show that the incident light trajectory can be effectively bended and remain intermittently trapped in interrupted guided trajectories within the plate. This paradoxical combination of light perpendicularly incident to the PFP plane and of trapping within that same guide is the result of intermittent chaotic light propagation in an array of parallel inter-penetrated optical bers. A similar behavior can only be achieved by introducing a randomization of the surface, which would lead to strong limitations in the implementation of well-structured devices. In the ber array conguration we propose, we have incorporated a solar cell and experimentally demonstrated that the light-harvesting capacity of the cell can be increased by more than 30%. To a large extent, the increased absorption capacity of the PFP results from photons following chaotic trajectories, which have higher chances of being absorbed. This leads to the unexpected result that the presence of chaos implies a lower increase in the scattering entropy. In addition, we have demonstrated that the fabrication of well-ordered devices can be conducted without detrimental effects on the parameters that determine the electrical performance of such a device. Finally, the interest in the novel light-guiding mechanism we propose well exceeds photovoltaics and may contribute to many relevant applications in future illumination systems, displays or wearable devices. For instance, our approach may have a signicant impact on portable display devices incorporating edge-lit LED guiding plates for LCD illumination where o5% of the emitted light reaches the users eye. In such systems, the guidance across the plate must compete with very homogenous light extraction. The effective 90 light bending and trapping of the PFP may markedly improve such poor light management, resulting in a drastic reduction in the power consumption of such illumination or display systems.
CONFLICT OF INTERESTThe authors declare no conict of interest.
AUTHOR CONTRIBUTIONSMM fabricated the PFP; MM, LGG, PR-G and JP fabricated and measured the
solar cells. MM, with the assistance of PR-G, deposited the ITO electrode on
the PFP. JB-A developed the full-wave theory and performed the corresponding
numerical simulations. GK developed the theory and performed ray tracing
numerical simulations. GK and JM wrote the manuscript with the assistance of
all other authors. JM conceived the concept of PFP and planned and
coordinated all the work.
ACKNOWLEDGEMENTSMM, PR-G and JM acknowledge nancial support from the Spanish
MINECO (Severo Ochoa Program, grant no. SEV-2015-0522), the
MINECO and the Fondo Europeo de Desarrollo Regional FEDER (grant
no. MAT2014-52985-R), the Fundacio Privada Cellex, and from the EC
FP7 Program (ICT-2011.35) under grant no. NMP3-SL-2013-604506. GK is
a Research Associate of the Fonds de la Recherche ScientiqueFNRS
(Belgium). GK thanks Thomas Gilbert for useful comments. JB-A
acknowledges nancial support from the Spanish MINECO/FEDER
(grant no. MAT2015-66128-R). LGG and JP acknowledge nancial support
from the Spanish MINECO (grant no. ENE2014-56237-C4) and Mexicos
grant program CONACyT.
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Light: Science & Applications
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Copyright Nature Publishing Group Dec 2016
Abstract
Extracting the light trapped in a waveguide, or the opposite effect of trapping light in a thin region and guiding it perpendicular to its incident propagation direction, is essential for optimal energetic performance in illumination, display or light harvesting devices. Here we demonstrate that the paradoxical goal of letting as much light in or out while maintaining the wave effectively trapped can be achieved with a periodic array of interpenetrated bers forming a photonic ber plate. Photons entering perpendicular to that plate may be trapped in an intermittent chaotic trajectory, leading to an optically ergodic system. We fabricated such a photonic ber plate and showed that for a solar cell incorporated on one of the plate surfaces, light absorption is greatly enhanced. Conrming this, we found the unexpected result that a more chaotic photon trajectory reduces the production of photon scattering entropy.
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