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Design of a lens-to-channel waveguide system as a solar concentrator structure

Yuxiao Liu, Ran Huang, and Christi K. Madsen

Open Access Open Access

Abstract

We present a lens-to-channel waveguide solar concentrator, where the lens array and the channel waveguide act as the primary and the secondary concentrator. Sunlight collected by the lens array is coupled into channel waveguides and exits from one end of the tapered waveguide directly onto photovoltaic cells. A 45°coupler is placed at each lens focal point to couple light into the waveguides. This configuration eliminates any inherent decoupling losses. We provide a detailed math model and simulation results using exemplar system parameters, showing that this structure can achieve 800x concentration at 89.1% optical efficiency under ±0.7° incidence angle.

© 2014 Optical Society of America

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Figures (6)
Fig. 1
Fig. 1 A top schematic view of the lens-waveguide system. Light collected by the lens array is redirected by the couplers placed at each focus. Then it travels inside the waveguide unit and finally exits from the tapered common waveguide directly onto a PV cell. The lens array and the tapered waveguide act as the primary and the secondary concentrators. Since lenses are tilted and the waveguide becomes wider along the z-axis, any decoupling loss is eliminated.

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Fig. 2
Fig. 2 The aberration-free lens focuses incoming light onto its paraxial image plane.

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Fig. 3
Fig. 3 (a) Each coupler is a tilted waveguide/air interface. (b) An illustrative plot of the reflection angles in XZ plane ϕ x 0 = arc tan ( k x 0 / k z 0 ) and YZ plane ϕ y 0 = arc tan ( k y 0 / k z 0 ) . Each ellipse represents a reflection angle range for one particular coupler angle β . It is clear that the 45 ° coupler yields the minimum angles in both planes.

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Fig. 4
Fig. 4 One waveguide unit cell of the concentrator.

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Fig. 5
Fig. 5 (a) An exemplar plot of optical efficiency under different f-numbers and tolerance angles, where α = 1.8 × 10 − 4 c m − 1 , n w = n d = 1.64 , n s = 1.46 and n c = 1 . (b) The performance of the waveguide concentrator. The efficiency remains the same until C 2 ~ 7.9 .

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Fig. 6
Fig. 6 An exemplar plot of the estimated maximum concentration as a function of f-numbers and tolerance angles, where n w = 1.64 .

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Tables (1)

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Table 1 Efficiency Chart for the Optimized Practical Setup

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Equations (10)

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C 1 = M × N × D 2 t × M × N × d C = D 2 2 d × t .
C 2 = W 0 W 0 − 2 l tan σ = 1 1 − 2 l W 0 tan σ ≜ 1 1 − 2 l N tan σ ,
C l = ( D d ) 2 = 1 [ 2 ( f / D ) tan δ M ] 2 ;
θ M = arc tan [ tan δ M + 1 2 ( f / D ) ] .
k → r = k ( sin γ cos Ω , cos θ y 1 − sin 2 γ cos 2 Ω , sin θ y 1 − sin 2 γ cos 2 Ω ) ,
L P ( P , Ω , δ ) = [ ( P − 1 ) + 1 / 2 ] D × cos Θ k z 0 / | k → r | .
L T ( Ω , δ ) = W 0 × cos ( ϕ 0 − σ ) − cos 2 ( ϕ 0 − σ ) − 4 l N tan σ + 4 l N 2 tan 2 σ 2 sin σ × ( k x 0 2 + k z 0 2 ) / | k | 2 ,
C 2max = 1 1−2 l N tanσ = cos θ c sin( ϕ 0M +σ ) ≈ cos θ c sin ϕ 0M ,
C 1 max = 1 2 [ 2 ( f / D ) tan δ M ] 2 ,
C 2 max ≈ cos θ c sin ϕ 0 M ≈ n w cos θ c sin { arc tan [ tan δ M + 1 2 ( f / D ) ] } .
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