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Anisotropic light emissions in luminescent solar concentrators–isotropic systems

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Abstract

In this paper we develop a model to describe the emission profile from randomly oriented dichroic dye molecules in a luminescent solar concentrator (LSC) waveguide as a function of incoming light direction. The resulting emission is non-isotropic, in contradiction to what is used in almost all previous simulations on the performance of LSCs, and helps explain the large surface losses measured in these devices. To achieve more precise LSC performance simulations we suggest that the dichroic nature of the dyes must be included in the future modeling efforts.

©2013 Optical Society of America

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Figures (5)

Fig. 1
Fig. 1 a) Schematic definition of the dipole, the incoming light and the emitted light for both the absorption (left) event and the emission (right) event. In the left Fig. the black arrow represents the dipole moment for absorption defined by a zenith (θ) and an azimuthal (φ) angle with respect to the axis system. In the right image the emitted photon ( k ) is also defined by a zenith (α) and an azimuthal (β) angle with respect to the axis system. The large grey arrow in both pictures represents the direction of the incoming light which is circularly polarzied (curved black arrow). b) polarization of the emitted light as function of two linear polarizations orthogonal to k .
Fig. 2
Fig. 2 Emission profile from isotropic dye ensembles illuminated from the top, both the side view (left) and the top view (right). The axis of these emission profile have aribitrary units. The units are the same on both axes and the emission originates from the center of the profile.
Fig. 3
Fig. 3 Emission profile from isotropic dye ensembles illuminated at a 50 degree angle to the surface normal, both the side view (left) and the top view (right). The axis of these emission profile have aribitrary units. The units are the same on both axes and the emission originates from the center of the profile.
Fig. 4
Fig. 4 The initial fraction of photons emitted by isotropic dichroic dye ensembles trapped in a polycarbonate (squares) or a PMMA (triangles) waveguide when illuminated with sunlight at different incident angles with respect to the waveguide normal.
Fig. 5
Fig. 5 Calculated surface loss from LSCs as function of the average number of photon reabsorption/re-emission events for PC (grey) and PMMA (black) waveguides containing isotropic emitters (solid lines) or dichroic dyes (dotted lines). The lines of isotropic emitters in PMMA (solid black) and dichroic emitters in PC (dotted grey) are almost coincident.

Tables (1)

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Table 1 Theoretical fractional surface loss from LSCs with an isotropic emitter as a function of number of reabsorption/re-emission events.

Equations (14)

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I( α,β ) ( e i μ ) 2 ( e f ν ) 2 Ω
I( α,β ) ( e i μ ) 2 ( e f μ ) 2 Ω .
μ =( sinθcosφ sinθsinφ cosθ ), e i = 1 2 ( 1 i 0 )
k =( sinαcosβ sinαsinβ cosα )
e f,1 =( cosαcosβ cosαsinβ sinα ) e f,2 =( sinβ cosβ 0 )
e f =( cosγcosαcosβsinγsinβ cosγcosαsinβ+sinγcosβ cosγsinα )
I( α,β ) 0 2π ( e i μ ) 2 ( e f μ ) 2 Ω dγ
I( α,β )= 0 2π dγ 0 2π dφ 0 π dθsinθf( Ω )( ( e i μ ) 2 ( e f μ ) 2 )
I( α,β )( 3+ cos 2 α )
α c = sin 1 ( 1 n )
η trap =cos( α c )= ( 1 1 n 2 ) 1 2
η sl = i=0 x ¯ η PL i+1 ( η trap i ( 1 η trap ) )
η trap,0 = 0 2π dβ α c π α c dαI( α,β )sinα 0 2π dβ 0 π dαI( α,β )sinα
η sl = η PL ( 1 η trap,0 )+ η PL 2 ( η trap,0 ( 1 η trap,1 ) )+ η PL 3 ( η trap,0 η trap,1 ( 1 η trap,2 ) )+...
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