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T. Gallinelli, A. Barbet, F. Druon, F. Balembois, P. Georges, T. Billeton, S.
Chénais, S. Forget
To cite this version:
T. Gallinelli, A. Barbet, F. Druon, F. Balembois, P. Georges, et al.. Enhancing brightness of Lamber- tian light sources with luminescent concentrators: the light extraction issue. Optics Express, Optical Society of America - OSA Publishing, 2019, 27 (8), pp.11830. �10.1364/OE.27.011830�. �hal-02358687�
Enhancing brightness of Lambertian light sources with luminescent concentrators: the light extraction issue
T. GALLINELLI,1 A. BARBET,2 F. DRUON,2 F. BALEMBOIS,2 P. GEORGES,2 T. BILLETON,1 S. CHENAIS,1,* AND S. FORGET1
1Laboratoire de Physique des Lasers, UMR 7538 CNRS, Université Paris 13, Institut Galilée, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France
2Laboratoire Charles Fabry, Institut d’Optique Graduate School, CNRS, Université Paris-Saclay, 91127 Palaiseau Cedex, France
*sebastien.chenais@univ-paris13.fr
Abstract: Luminescent concentrators (LC) enable breaking the limit of geometrical concentration imposed by the brightness theorem. They enable increasing the brightness of Lambertian light sources such as (organic) light-emitting diodes. However, for illumination applications, light emitted in the high-index material needs to be outcoupled to free space, raising important light extraction issues. Supported by an intuitive graphical representation, we propose a simple design for light extraction: a wedged output side facet, breaking the symmetry of the traditional rectangular slab design. Angular emission patterns as well as ray- tracing simulations are reported on Ce:YAG single crystal concentrators cut with different wedge angles, and are compared with devices having flat or roughened exit facets. The wedge output provides a simple and versatile way to simultaneously enhance the extracted power (up to a factor of 2) and the light directivity (radiant intensity increased by up to 2.2.)
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Light-emitting diodes (LEDs) are not only the new reference for general lighting, they have also proved to be reliable and economically-viable alternatives to halogen or arc lamps for more specific, bright illumination sources useful for e.g. automotive [1] or medical applications [2]. LEDs have also recently shown their potential as lower-cost alternatives to lasers or laser diodes for laser pumping [3–5]. More recently, Organic Light-emitting diodes have also emerged as flat, potentially flexible, large-area lighting devices with high potential in lighting, optical communications [6] or medical care [7]. Many of those novel applications triggered by the availability of these sources require the beam to be not only intense but also directional, which enables for example the light beam to be tightly focused. This is challenging with LED chips or OLED panels as their emission is not directional but quasi- Lambertian: their radiance ― also referred to as “brightness”, that is power per unit apparent area and solid angle ― is independent of observation angle. The brightness theorem [8]
indeed states that the irradiance (in W/m2) produced at some remote location by a Lambertian source, will be always lower than the irradiance measured directly onto the exit surface of the emitter (i.e., the source power density). This is important pointing out that this result remains true whatever the nature (imaging or non-imaging) of the optical system between the source and detector, and no matter the number of individual emitters that one could possibly imagine to combine alongside. However, if light is not just refracted or reflected but instead absorbed and reemitted at a lower energy, through a luminescence process, overcoming the brightness theorem becomes possible: this is the key idea behind Luminescent Concentrators (LC). LCs have been proposed in 1976 in the context of photovoltaics to concentrate sunlight with a wide field of view and no need for tracking [9–11]. They consist in a slab of a solid-state fluorescent material surrounded by air (or more generally a lower index material) in which
#357320
Journal © 2019 https://doi.org/10.1364/OE.27.011830
Received 10 Jan 2019; revised 21 Feb 2019; accepted 26 Feb 2019; published 12 Apr 2019
luminescence is guided by Total Internal Reflection (TIR) towards the edges, where the irradiance can reach values higher than the irradiance of incoming radiation by typically one order of magnitude in most practical cases. More recently, LCs have been used in association with LEDs disposed on the top largest surface to produce irradiances that could not be accessible with LEDs alone: this for instance enabled Ti-Sapphire lasers to be pumped for the first time by LEDs [12]. This example shows that the association of planar Lambertian LED light sources with LCs opens a novel route for high-brightness illumination sources that furthermore extends the wavelength capabilities of available LEDs. However, using LED + LC combinations to build bright directional sources requires that the radiation emitted in a high-index material is eventually outcoupled to air, which raises the important issue of light extraction, a long-studied issue in other contexts like device design of LEDs [13], OLEDs [14] or scintillators [15].
In planar light-emitting devices, classical strategies for light extraction include e.g. surface texturing [16], or surface modification with microlens arrays [17], networks of inverted micropyramids [18] or photonic crystal nanostructures [19]. For LCs based on plastic or crystalline slabs, the realization of such micro or nanostructures is both complicated and costly. The idea to change the geometry of the LC on the macroscopic scale has been investigated by De Boer et al. [20] who proposed to use a Compound Parabolic Concentrator (CPC) attached to the edge: the CPC both increases the emitting area and decreases the emission solid angle (as the étendue is conserved in a passive optical device) but it offers a way out for trapped rays (defined in following section): in the end, the outgoing radiation has a reported brightness that is 4.5 times higher than the brightness of LED illumination, and is more directional.
In this paper we study how more cost-effective and universal techniques can be used to improve the extraction capabilities and beam characteristics of concentrators that are used in the context of illumination. Firstly (section 2), we present a simple graphical representation in k space that enables an easy classification of rays inside a concentrator, offering a convenient tool for making rapid estimates but also understanding what happens in situations where the concentrator loses some of its symmetries. We then present the experimental methods and compare the measurements of concentration factors of a simple rectangular polished slab concentrator with a concentrator in which the output facet is simply frosted (section 3). In section 4, we investigate an original and simple way to improve light extraction from luminescent concentrators, applicable to any material, consisting in cutting the exit facet with a wedge. We studied Ce:YAG single crystals, chosen for their attested very good efficiency as luminescent concentrators under blue LED excitation [21]. The impact of the design on the achievable gain in extracted power, intensity and radiance (brightness) will be finally discussed.
2. Light extraction in luminescent concentrators: representation of internal rays in k space
It is first instructive to gain some insights in the light extraction issue in the “classical”
symmetric rectangular slab design, considered polished on its 6 orthogonal faces, to investigate how this design can be further modified to improve extraction. In this respect, an elegant and insightful picture consists in representing rays only by their direction (in k space).
Usually the problem of extraction is considered in planar light sources (LEDs, OLEDs…), where one dimension is much smaller than the others: in this case, all internal rays that fall within the escape cones (and only 2 cones are considered, with axes normal to the source plane) are directly outcoupled without undergoing any total internal reflection before exiting, while all the others are referred to as “guided rays”, and are subsequently either absorbed, scattered, or coupled to other surface modes. In a 3D macroscopic geometry all 6 faces can contribute to TIR, and escape cones have to be considered on every face of the concentrator.
Escape cones cones of solid
Fig. 1 of int traject the es can ta kz, stil
These con vector inside intersect the outermost pa 2 n² 1− (Fig As far as unambiguous number of TIR do not overlap tangent), that glasses or cr emitters with fraction of lig
and is only 8 dimensions, m not that intuit of self-absorp The spher The trapped Those rays ca
in a rectangul d angle Ωescape =
1. Left: geometry o ternal rays in a re tory of a “trapped scape cap represen ake: its ky compone ll remaining inside
nes can be con the medium n sphere under t art of the sph g. 1, right).
s the caps do ly tell from wh R the ray may
p whenever th is for n highe rystalline mate no reabsorptio ght that can esc
% for YAG (n meaning that th ive and in fact ption effects in re in k space en rays are defin an find endless
lar slab of ind
(
2 1 cosπ θc
= −
of the of the Ce:YA eabsorption-free c d ray” which cann nt the 4 possible k ent is conserved w e the same “escape
sidered as bein normalized to it the form of 6 here emerging o not overlap hich of the 6 f undergo afterw he critical angle er than 2 : th
erials that can on and neglect cape to air from
4
es escape
η =Ω n = 1.84). Thi he same lumin very difficult the physics of nables a very g ned as rays un closed loop tra
ex n of any di
)
θcrit where θcrit
AG slab concentra concentrator. The not escape through k vectors that a ray while the other com e cap” (see text for
ng inside a sph ts value in the
symmetric “c out of an ‘e p, knowing th facets this ray w
wards and the e is below 45°
his condition is n be used as ting Fresnel re m an isotropic m
1 1 1
4 2
scape
π
= −
is fraction is th
ous power flow to observe exp f luminescent c graphical and u ndergoing Tota ajectories in a
imension surro
t is the critical
ator. Right: represe blue circle dots p hout any of the 6 f
y exiting by the fr mponents bounce b r more details).
here of radius e surrounding m caps”, which c extraction cub he direction o will emerge (i position of the
° (the situation s actually met concentrators.
eflections below medium of inde
2
1 1 n
−
heoretically in ws through all perimentally du concentrators [2 useful represent al Internal Ref lossless mediu
ounded by air a l angle (see Fig
entation in k space picture a possible faces. Red dots in ront smallest facet between ± kx and ±
n = k/k0 (mod medium). Esca can be also se be’ whose edg of a ray is en if it does), wha e source. Note n where the six in all practical Considering w the critical a ex n is simply
ndependent on l 6 faces, a resu ue to the large
22].
tation of ‘trapp flection on all um: they exist w
appear as g. 1).
e e n t
±
dulus of k ape cones en as the ges equal nough to atever the
that caps x caps are l plastics, isotropic angle, the given by
(1) the facet ult that is influence ped rays’.
l 6 faces. whenever
the sphere is not totally paved by escape caps, that is when the diagonal of the extraction cube is longer than the sphere diameter — that is, for n> 3 / 2 1.22=
For non-overlapping caps (n> 2 1.41= ), they represent a fraction
2
6 1
1 3 1 2
4
escape trapped
η n
π
= − Ω = − − (2)
for YAG, ηtrapped = 52%.
Each Total Internal Reflection (TIR) changes sign of kx, ky or kz: the trajectory of a
“trapped ray” in k-space is therefore figured by the 8 apices (blue dots in Fig. 1) of a parallelepiped inscribed in the sphere. When considering a ray that belongs to an escape cone (let’s say the cone with ky<0, see red dots in Fig. 1), the kx and kz components can change sign many times when the ray is travelling but ky is conserved. The trajectory is then represented in k-space by a dot bouncing between 4 points with the same ky component, always remaining within the same escape cap, before the ray can eventually exit — the number of reflections undergone by a ray will obviously depend on the position of the luminophore with respect to the exit surface.
In practice, scattering and reabsorption complicates this simple sketch: rays that experience propagation paths that are longer than the reabsorption length will not necessarily escape by the facet defined by the initial ray direction. Trapped rays will acquire a finite lifetime and will not bounce “forever”. In high-quality crystals with large Stokes shift, the reabsorption length can however be quite high. In the Ce:YAG samples used in our study (see next section), the reabsorption length, which is simply estimated here from the inverse of the average absorption coefficient weighted by the fluorescence spectrum, is 3.4 cm, while the typical slab dimensions are in the mm to cm range. As a general rule of thumb, this framework for representing concentrators is useful in cases where the reabsorption length is longer than the typical dimensions of the concentrators.
The concept is here introduced in the simplest case of a symmetric (3 pairs of mutually parallel facets) optically-isotropic medium surrounded by a homogeneous isotropic medium.
It can be especially useful however in more complex situations: for instance, the sphere becomes ellipsoids in anisotropic media; the caps may also have different dimensions if the surrounding medium is not homogeneous, which is the case if the concentrator slab sits on top of a substrate, for example.
In these non-trivial cases, the “trapped ray” area is determined by mapping the zones that are not covered by any cap and by any cap mirror-image: indeed, one has also to remove from the trapped ray region all the rays that will find themselves into an escape cap after one or several reflections. This means that one has to pave the sphere with all the mirror images of the caps through all the symmetry planes (where TIR can occur) to determine what is finally the ‘trapped ray’ (uncovered) region.
From this example, one can see that breaking the symmetry is a simple and efficient strategy to eliminate the existence of trapped rays, and hence improve the fraction of rays that can potentially be outcoupled.
In this paper, we investigated how a simple wedge in one direction, appended to the small exit facet, can significantly improve light extraction.
In this graphical representation in k space, tilting the output facet by an angle β consists in sliding the escape “cap” of the side edge towards the “pole” (top face escape cone), as represented in Fig. 2. Not only will the rays belonging to this tilted escape cap emerge, but also all those which find themselves in this cap after TIR. As the faces perpendicular to kz are the largest — so that most of TIR events occur on those facets — the new escape cone has to be completed by its mirror image across z axis: tilting the facet therefore increases notably the surface of the sphere that is paved by escape cones. Note that the tilted facet is also still a
possible surfa emerge any m These rays wo to the plane o several exit fa In the end images of the within a thin would be stra
Fig. 2 Rays t on the image exist, here, extrem
3. Experime unpolished We first mea rectangular sl hereafter refe uniformly illu homogenized around 0.3 at along 1 mm a sphere (GL O by the edge, aperture, thus concentrators In the refe was measured In order to through the ex converted in 14.1% given
ace for TIR, e more through th
ould be visuali of the tilted fac acets are possib
d, the loss of e tilted cap an stripe on the ightforwardly
2. A wedged conc that can escape thr e sphere by same e about z axis (bo escape caps and a a thin stripe of tra mity are given by t
ental method exit facets in asured experim ab (St Gobain) erred to as the uminated by a l to yield a con t.% (supplier e at 450 nm. The Optisphere 205) the LC was p s reducing the have a geomet erence sample, d to be η 1 2%= o compare this
xit surface (or a ratio of outc the Stokes shi
especially here he flat side fac ized by represe et. New overla ble.
symmetry cov nd hinders trap edges (see Fi obtained by til
centrator (on the r rough the tilted up polar angle β (on ottom side, hatche all their images ab apped rays remains the image of botto
ds: comparis n symmetric mentally the c ) of 49 × 9 × 1
“reference” sa low-coherence nstant power d estimate) resul
extracted lum ). To ensure th pushed inward effective illum trical concentr
the ratio of ou
% leading to a s value with the equivalently in coupled photon ift between abs
e for rays with cet but instead enting the sym aps appear, rep vers the spher pped ray trajec
ig. 2) Note tha lting the wedge
right) in k space ( p facet belong to th top side, hatched) ed). To determine bout all possible m s for some oblique m cap about the pl
son of light e c rectangular concentration mm (L × l × e ample. The lar e (speckle-free) ensity of 0.48 lting in an exp minescence pow at the sphere e s inside the sp mination area t ration factor G utput power Pre concentration eoretical estim n terms ratio o ns over a num sorption and fl
h a small kz co d from the bott mmetric of the b
presenting direc re almost conti ctories to exist at complete re e with an obliq
(on the left, partia he tilted escape co d), but may also be e whether some “t mirror symmetries e rays. Note: rays e
lane tilted by angl
extraction be r slab concen
factor of a C e) dimensions, rgest area of th ) 450-nm laser mW/cm2. The perimental 97.
wer was measur efficiently colle phere througho
to 42 × 9 mm
= L/e = 42 (se
ref over the inc factor C = G × mates based on
of photons), thi mber of inciden
fluorescence m
omponent that tom side, near bottom cap wit ctions of rays f inuously by su t anymore, ex emoval of trap que angle.
al representation) one slided upwards
elong to its mirror trapped” rays still have to be drawn exiting the bottom le β (not shown).
etween polish ntrators Ce:YAG singl
polished on it he rectangular
diode whose b e Ce3+ doping .5% ± 0.5% ab
red using an in ects all the ligh out a rectangu m2. In the follo ee notations in F cident pump po
× η = 5.04.
“ratio of rays”
is power ratio nt photons and mean waveleng
t will not the apex.
th respect for which uccessive cept here pped rays
. s r l : m
hed and le crystal ts 6 faces,
slab was beam was ratio was bsorption ntegrating ht emitted ular fitted owing, all
Fig. 1) ower P inc
” that exit has to be d reaches th. In the
previous section, we estimated the fraction of photons outcoupled by the side facet to be 8%
of the total number of photons generated inside a perfect lossless concentrator. As all incident photons are not absorbed and as all absorbed photons are not reemitted as fluorescence (i.e.
pump absorption efficiency and fluorescence Quantum yield are below unity), we can expect a theoretical ratio of outcoupled photons over incident photons slightly lower than 8%: in fact, the quantum yield is as high as 97% in Ce:YAG and absorption is 97.5%, which does not make so much difference. However, the experimental value is almost twice higher than the expectation from these simple considerations. This can be attributed for some part to reabsorption, which reduces the number of trapped rays and redirects them in all extraction cones. It is also due for another part to scattering on defects on the surfaces and to diffraction around sharp corners and edges. It is possible to evaluate the relative importance of reabsorption and diffraction/scattering effects, by resorting to ray-tracing simulations, which can include the effect of reabsorption but do not go beyond ray propagation considered within the limits of geometrical optics. We used Light Tools software to model a perfectly polished LC with a refractive index n = 1.84, having passive losses corresponding to a measured 97%
transmission over 100 mm of propagation in Ce:YAG. Reabsorption was taken into account by considering the medium as homogeneously doped with an isotropic emitter whose absorption and emission spectra were those experimentally measured, while the luminophore concentration was calculated from the experimental absorption at 450 nm. The simulation yields a photonic extraction efficiency of 11.3% (9.6% in power ratio), meaning that starting from the rough estimate of 8% based only on geometrical considerations, reabsorption accounts for an additional 3.3%. The remaining difference of 2.8% between the experimental 14.1% efficiency and the simulated value of 11.3% is accounted by all phenomena that are not taken into account by ray tracing simulations, i.e. scattering and diffraction. Adding some further scattering seems to be a straightforward and simple idea to increase the light extraction, an idea that we explored in order to compare it with the wedge structure presented in the next section. The symmetric polished slab of 49 × 9 × 1 mm dimensions was left polished on 5 sides and frosted on one of the smallest facets of dimension 9 × 1 mm. The exit facet was roughened using abrasive grinding over a brass tool in order to obtain a RMS roughness of 430 nm, measured using Atomic Force Microscopy. An increase in the extracted power of up to 50% was observed, corresponding to a concentration factor of 8. The intensity indicatrix was measured in one angular dimension with a simplified version of the experiment described by Parel et al. [23] that is shown in Fig. 3a.
Fig. 3 power centra profile sterad i) with law ap
Intensity p grinded one h frosted sampl concentrator, explanation o 4. Light extr We then inve paths that are significant pe In order to the reference 20°, 40°, and Figs. 4 and 5)
3. a) experimental r-meter (fiber cor al point of the edg
es (the radius in dian in this given d
h polished emissio ppears in dotted lin
profiles (see F have an angle le is however in which som f these ripples raction in we stigated the inf e stable upon s rcentage of tra o experimental Ce:YAG cryst
60° around a ).
l set up for radian re diameter: 1 mm ge emitting area o
the polar diagram direction) of a Ce:Y on facet ; ii) with nes on i) and ii).
Fig. 3b) reveal -dependent int
much closer f me smooth rip
is detailed in t edged lumine
fluence of a we successive TIR apped rays prop ly investigate t tal and fabrica rotation axis d
nt intensity indica m) rotates at a fix f the Ce:YAG lum m is set proporti YAG luminescent frosted output sur
that both the tensity that is from an ideal
pples can be the Appendix
escent conce edge on the ex R processes (se pagating in a hi the role of wed ated different s defined as the
atrix measurement xed distance of 7 minescent concent onal to the inten concentrator excit urface. Theoretical
‘polished’ ref close to Lam Lambertian so observed. Th
x.
entrators xit facet, a way
ee Fig. 2) and igh index med dging in a real samples with th
longest edge
t. A fiber-coupled 0 mm around the trator. b) Intensity nsity in Watts per ted at λ = 450 nm:
Lambert’s cosine
ference sample mbert’s cosine
ource than the he origin and
y to eliminate c are responsibl dium surrounde device, we sta hree wedge an of the exit sur
d e y r : e
e and the law. The polished physical
closed ray le for the ed by air.
arted from ngles β of rface (see
Fig. 4 (linke extrac base emitte the co on the
The extrac tilted surface extent from contribution compromising simulations (u surface.
The measu angle results between simu simulation ten account. As d polishing defe also be seen th fact that as far trapped rays using simulat sideways. Fro associated to is, 1.3 times m
4. Power extractio ed crosses) for we cted through the ti of the slab insert ed by the portion o oncentrator was in e top surface to ens
cted measured (denoted as P the side facet from the sol g the TIR pro using LightTo ured and simul in a net high ulated and exp
nds to undere discussed in se ects, especially hat close to β = r as β ≠ 0 there in a perfectly tion to evaluate
om Fig. 4, on a maximum ex more than the
on efficiency η m edged concentrato ilted output surfac ted into the integ of small side facet ntroduced in the in sure that all light c
total power P Pup), but also ts (noted Presi
le wedged to operties of the
ols software) t lated extracted her total extrac perimental data estimate the ex ction 3, this ca y along the line
= 0, the depend e is mathematic lossless medi e the fractions ne can clearly
xtraction effici ratio obtained
measured (black d ors with different ce and Pdown is the grating sphere. Pre
ts inserted into the ntegrating sphere u coming from the w
Ptot not only co from the botto
idue) so thatPto p side is ex
whole device to assign the r powers are rep cted power Pto
a for Ptot with xtraction, altho an be attributed es, which reduc dence with ang
cally no more um. Excellent s of Ptot that a
see an optim iency Pup/Pinc = d from the refe
dots) and simulate wedge angles β.
e power emitted th
esidue represents th e sphere. Inset: Ex up to 1 mm behin wedge is efficiently
onsists in the p om base end (
tot up down
P =P +P xperimentally
e: we therefore relative contrib ported in Fig. 4
ot. Very good h a slight devi ough reabsorp
d to scattering ces the fraction gle β is steeper:
endless closed t agreement at are extracted up mum angle for
= 16% through erence non-wed
ed by ray tracing Pup is the power hrough the bottom he remaining light xperimental setup nd the wedge limit
y collected.
power emitted (Pdown), and to
residue
+P . Isol very difficult e relied on ra bution of each 4. Increasing th
agreement is iation for β = tion is here ta g on sharp edge n of trapped ra : this correspon d paths correspo t higher angles
pwards, downw r Pup close to h the tilted sur dged polished
g r m t : t
from the o a lesser ating the t without ay tracing h emitting he wedge
obtained 0 where aken into es and on ays. It can nds to the onding to s justifies wards, or β = 50°
rface, that slab (β =
0). The whole For wedge an with an incide 33°, redirectin angles.
In order t intensity prof obtained usin with simulate quasi-Lamber good matchin slightly smoo above (diffra interesting to bottom emissi cone is narrow
Fig. 5 simula wedge
The highe angle γmax = 5 the reference a “Lambertia normal incide also concentra applications. I
e extracted pow ngles > 50°, ra
ent angle that i ng them to the to be able to file angular m ng the setup de ed intensity pro
rtian profiles p ng can be see other in experim action and po
note that the l ion in terms of wing as wedge
5. Intensity profile ations (right). The e rotation axis.
er intensity is o 52°: it is 2.2 ti
sample (as the an approximati ence). Wedgin ates the radiati If we define Δγ
wer reaches 25 ays coming fro is in average h bottom base, w
characterize measurements o
escribed previo ofiles. The inte previously repo en between sim
mental profiles lishing defect light emitted th f total power, b angle is increa
s measured for eac ese profile section
obtained for th imes higher tha e non-wedged L ion” was used
g the LC not ion in angle sp γFWHM as the an
5% for large an om the concent higher than the
which explains the brightness on the various ously (see Fig.
ensity is strong orted (Fig. 3), mulated and e s for allegedly ts having been hrough the top but also shows ased.
ch wedge angle (le ns correspond to o
he wedged sam an the average LC shows ripp d by taking th only enhances ace, which can ngular width a
ngles, twice as trator volume e TIR limit ang s the relative in s of the wedg s wedged con . 3 left) are sh gly angle-depe especially for experimental v y the same reas n ignored in surface is bot
angle concent
eft) and calculated one angular coord
mple with β = e intensity mea ples around γ = he average val s intensity in p n be a useful fe at half maximu
s much as the r will hit the to gle θlim = Arcsi ncrease of Pdown ge LCs, we p ncentrators. Th hown in Fig. 5 endent and far large wedge a values: the pat
sons already m the simulatio th predominant tration, i.e. the
d using ray tracing dinate γ about the
60° and an ob asured around
= 0° as discusse lue of intensit particular direc eature for some um, it shrinks fr
reference.
p surface in (1/n) =
n at large performed he results 5 together from the angles. A tterns are mentioned
on). It is t over the
emission
g e
bservation γ = 0° in ed earlier, ty around ctions but e lighting from 100°
for the reference down to 52° for the LC with β = 60°. Table 1 summarizes the gain in terms of total extracted power and maximum intensity with respect to the reference unwedged concentrator.
Table 1. Summary of photometric properties of wedged concentrators compared to the reference polished symmetric slab.γmax is the value of γ corresponding to the
maximum intensity.
β = 0° β = 0°, frosted edge facet
β = 20°
β = 40°
β = 60°
Gain in extracted power: Ptot(β)/Ptot(β = 0): from all faces (measured) Pup(β)/Pup(β = 0): from top face only (simulated)
1 1.5 1.5
1.37
1.75 1.86
1.96 1.78
Maximum gain in Intensity:
g (γmax) = I (γmax) / Iref (γ~0°) experimentally measured g (γmax) simulated
1 1.5 1.2 1.1
1.64 1.8
2.2 2.2 Brightness Concentration factor at γmax (see text
for definition) computed from exp. data
5.3 8 6.5 7.1 5.9
In Table 1 is also reported the ‘Brightness concentration factor’, calculated as follows.
The standard ‘concentration factor’ C defined as a ratio of irradiances at the output and input area is not an adequate metric when radiation is directional and detected after free-space propagation. It should be replaced by a brightness (or radiance) ratio of output and input radiation fields, or CB = Bout/Bin. In general, this brightness enhancement factor will depend on the direction of observation, except of course in the case of an angle-independent brightness, that is for a Lambertian source. When both input and output fields are Lambertian, the brightness concentration factor simply equals the classical concentration factor C. It is the case for our reference sample, so that Bout, ref = Cref x Bin, ref. The incident brightness for a typical Lambertian source such as LEDs (we write PLED the power of this source) is Bin, ref = BLED = PLED / (π.S) where S is the illuminated surface of the concentrator. For wedged concentrators, CB will be a more complex function of observation angle:
( ) out( ) ( ) coscos
[ ]
B ref
LED
C B C g
B
γ β
γ = = × γ × β γ
− (3)
where Cref is the usual concentration factor for the unaltered symmetric slab, g(γ) the gain in intensity at observation angle γ compared to the reference rectangular slab at normal incidence, and the last term a tilting term that takes into account the modification of apparent area. Table 1 reveals that highest brightness is obtained for β = 40° as a compromise between gain in intensity and increase of apparent area. It however remains slightly lower than the brightness achievable with the frosted device of maximal RMS roughness. Hence, depending on the parameter that one wishes to optimize (total extracted power, intensity in a specific direction or brightness), the optimal design will not be the same.
It has also to be noticed that a simple wedge in one direction obviously sharpens the beam in only one direction while keeping the emission pattern in the perpendicular direction coarsely Lambertian. It is illustrated by the simulation of the 3D emission pattern for the 60°- wedged LC reported in Fig. 6.
It is interesting to note that the apparently complex 3D intensity profile is indeed straightforward to interpret when looking back at the angular 3D representation. As soon as the wedge angle is higher than the critical angle, escape cones overlap. Rays that belong to the intersection of two different cones will statistically preferentially exit through the largest surface. Here, the small tilted edge facet and the large top surface respective escape cones have a strong overlap (for α > −3° using notations of Fig. 6 as β = 60° > θcrit = 33°) whose
shape is easily bottom of the flat facet opp reflections on the visual rep at least quali resorting to so
Fig. 6 Conce the no region larges
For furthe accessible at multiple wed Luminescent 5. Conclusio LCs are versa from Lamber can be seen a symmetric sla into account t output facet, compared to t in a way that ranges betwe extracted pow of extracted p while keeping For the d have presente in angle spac enables makin classical sym
y recognizable e profile corresp posed to the w n the opposite f presentation of itatively most ometimes very
6. 3D ray diagram entrator with a we ormal of the tilted n on top is due to st top surface.
er optimization low cost, we dges can be c
Concentrator.
on
atile photonic rtian Light sou s novel tools in ab geometry w the light extrac a solution lead the polished re t is shown to en 40° (optim wer). In compar
power compar g the source La esign of Lumi ed a simple fram ce that mixes t
ng rapid estima mmetric slab
e in Fig. 6 (rig ponds to the in wedge. It betray face and comin rays provided
of the physic time-consumi
of light emitted th edge angle of 60°.
d surface, α des
o the overlap of th
n of wedged co edges in obliqu considered to
components th urces like array n the Light sou ith orthogonal ction issue. We
ding at the sam ference) and to be very depen mized brightnes
rison, roughen red to the refe ambertian.
inescent Conc mework based the usual optic ates and also c design used
ght). A smaller ntersection wit
ys the presenc ng back. With by the represe cs of the ligh ng numerical r
hrough the top tilt . The central direc scribes rotation ab he escape cone of
oncentrators w ue directions optimize the
hat can be used ys of LEDs or urce design too
polished facet investigated th me time to mor
o a more direct ndent on the w ss) to more tha ning the exit fa erence, but yie centrators base on an intuitive cal indicatrix w conceptualizing
in Luminesce
circular-shape th the image of ce of rays und this simple ex entation in k sp ht emission of ray-tracing sim
ted surface (only) ction (α ϕ= =0
bout wedge axis.
f the tilted surfac
while keeping a (to totally rem e directionality
d to enhance t r OLEDs. Lum olbox, but this ts to be revisite he influence of re power extra tional emission wedge angle.
an 60° (optimi acet allows only elds the maxim ed on low-reab e 3-dimensiona with the conc g different dev ent solar conc
ed partial erosi f the escape co dergoing partia xample, we can
pace can help f concentrator mulations.
of a Luminescent
0) corresponds to The circular dark e with that of the
all modificatio move trapped y of emission
the brightness minescent conc s requires the tr ed in order to f f a simple wed action (up to fa n (intensity up Optimum wed ized intensity y a gain in 1.5 mum gain in b bsorption mate al representatio ept of escape viations append centrators. We
ion at the one of the al Fresnel n see that capturing rs, before
t o k e
ons easily rays), or n from a
available centrators raditional fully take dge on the actor of 2 to x 2.2), dge angle and total 5 in terms brightness erials, we on of rays
cones. It ded to the edging a
concentrator serve as a sou sources.
Appendix The ripples o on the “histor incidence betr event can esc reproduced w distribution of It can be before escapi (here for sim with 1 (blue) coming from initial fluorop both faces (F experienced 0 inhomogeneo by the ripples ripples will be the concentra luminescence where the exc degree). To e 450 nm diode excite the LC reduced — he We observed as expected an
Fig. 7 numb comin having b) ext
appears as a s urce of inspira
bserved on Fig ry” of a ray tra rays the fact th cape the LC with ray tracin
f luminescence understood ea ng the LC. In mplification in t
or two (orange the image poin phore (dotted l Fig. 7(b)), we o
0, 1, 2 or 3 TI us repartition o s observed in F e washed out a ator. It is not th sources follo citation light en xperimentally es by a Xe dis C at 400 nm fo
ence leading to in this case (F nd as also obse
7. (See text) a) S ers of TIR before ng from the image
g bounced twice b tension of this repr
solution that is ation for more
g. 3 for the ref ajectory: for in hat only rays d with an angle ng simulation e along the thic asily by drawi Fig. 7(a)), we the middle of e) TIR on the nts (relatively t line). If we ex observe in the IR overlap wh of the energy in Fig. 3. The pos and not seen if he case when a ow an expone
nters the LC (th check this, we charge lamp fo or example, a w o homogenizati Fig. 8) the disa erved with the
imple representati escaping the LC. I e of the source by before exiting can b resentation to mult
s easily transf sophisticated
ference polishe nstance, the m directly emitte e near zero de
s (see Fig. 5 ckness e (1mm ing the path o e show the ray
the LC) and e LC large sides to the bottom f xpand this repr e far field that
ile for other d n any plane pa sition of maxim f the density of
absorption is s ntial decaying his also explai e reduced the a
ollowed by a m wavelength wh ion of the lumi appearance of t frosted sample
ion of the path o In blue, rays suffe y the LC large fa be represented as c tiple TIR on both l
ferrable to any designs of LC
ed concentrato minimum intens ed by chromop egree. This ef 5) and result m) due a strong of rays sufferi ys coming fro escape withou s. Those rays c face of the LC resentation to t for some dire directions they arallel to the ou ma depends on f luminescence strong: because g distribution ins the large di absorption of t monochromato here the Cerium inescence dens the ripples for e.
of some rays expe ering only TIR can ace (point labelled coming from the p large LC faces.
y material and C-based high-b
or informs in s sity observed a phores without
ffect can be v from the non absorption at 4 ing one or sev m a single flu ut any reflectio can also be des C in this examp multiple refle ections the ray
don’t. The re utput facet, ma n source locatio e is homogeneo e of Beer-Lam starting at the issymmetry aro the LC by repl or. It is then po
m absorption i sity along the t the reference
eriencing different n be represented as d “1”), while rays point “2” (orange)
d that can brightness
some way at normal t any TIR very well n-uniform
450 nm.
veral TIR uorophore on (grey), scribed as ple) of the ctions on ys having sult is an aterialized on, hence ous inside mbert law, e surface ound zero lacing the ossible to is largely thickness.
polished,
t s s .
