Abstract

Dielectric totally internally reflecting concentrators (DTIRCs) which can achieve concentrations close to the thermodynamically allowed limits are introduced. General design methodologies are given explicitly. Geometrical and optical properties of DTIRCs are discussed.

© 1987 Optical Society of America

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References

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  1. W. T. Welford, R. Winston, The Optics of Nonimaging Concentrators, Light and Solar Energy (Academic, New York, 1978), p. 24.
  2. J. O’Gallagher, R. Winston, “Nonimaging Dielectric Elements in Second Stage Concentrators for Photovoltaic System,” in Proceedings, Annual Meeting ASES, Minneapolis (1983), p. 941.
  3. The literature is intensive: see, for example, J. C. Minano, J. M. Ruiz, A. Luque, “Design of Optimal and Ideal 2-D Concentrators with the Collector Immersed in a Dielectric Tube,” Appl. Opt. 22, 3960 (1983); R. Winston, W. T. Welford, “Geometrical Vector Flux and Some New Nonimaging Concentrators,” J. Opt. Soc. Am. 69, 532 (1979).
    [Crossref] [PubMed]
  4. R. Winston, “Principles of Solar Concentrators of a Novel Design,” Sol. Energy 16, 89 (1974).
    [Crossref]
  5. H. Hinterberger, R. Winston, “Efficient Light Coupler for Threshold Cerenkov Counter,” Rev. Sci. Instrum. 37, 1094 (1966).
    [Crossref]
  6. R. Winston, “Dielectric Compound Parabolic Concentrators,” Appl. Opt. 15, 291 (1976).
    [Crossref] [PubMed]
  7. R. L. Cole, A. J. Gorski, R. M. Graven, W. R. McIntire, W. W. Schertz, R. Winston, S. Zwerdling, “Application of Compound Parabolic Concentrators to Solar Photovoltaic Conversion,” Argonne National Laboratory Report ANL-77-42 (1977).
  8. R. Winston, X. Ning, J. O’Gallagher, “Photovoltaic Concentrator with Dielectric Second Stage,” in Proceedings, Annual Meeting ASES, Boulder CO (1986), p. 417.
  9. The linear correlation coefficient r is defined as r={NΣXiYi-ΣXiΣYi}/{NΣXi2-(ΣXi)2]1/2 [NΣYi2-(ΣYi)2]1/2} where N is the number of the (X, Y) pair. The value of r is ranged from 0, where there is no correlation to ±1, when there is complete correlation [see P. R. Bevington, Data Reduction and Error Analysis for the Physica Sciences (McGraw-Hill, New York, 1969), p. 121].

1983 (1)

1976 (1)

1974 (1)

R. Winston, “Principles of Solar Concentrators of a Novel Design,” Sol. Energy 16, 89 (1974).
[Crossref]

1966 (1)

H. Hinterberger, R. Winston, “Efficient Light Coupler for Threshold Cerenkov Counter,” Rev. Sci. Instrum. 37, 1094 (1966).
[Crossref]

Bevington, P. R.

The linear correlation coefficient r is defined as r={NΣXiYi-ΣXiΣYi}/{NΣXi2-(ΣXi)2]1/2 [NΣYi2-(ΣYi)2]1/2} where N is the number of the (X, Y) pair. The value of r is ranged from 0, where there is no correlation to ±1, when there is complete correlation [see P. R. Bevington, Data Reduction and Error Analysis for the Physica Sciences (McGraw-Hill, New York, 1969), p. 121].

Cole, R. L.

R. L. Cole, A. J. Gorski, R. M. Graven, W. R. McIntire, W. W. Schertz, R. Winston, S. Zwerdling, “Application of Compound Parabolic Concentrators to Solar Photovoltaic Conversion,” Argonne National Laboratory Report ANL-77-42 (1977).

Gorski, A. J.

R. L. Cole, A. J. Gorski, R. M. Graven, W. R. McIntire, W. W. Schertz, R. Winston, S. Zwerdling, “Application of Compound Parabolic Concentrators to Solar Photovoltaic Conversion,” Argonne National Laboratory Report ANL-77-42 (1977).

Graven, R. M.

R. L. Cole, A. J. Gorski, R. M. Graven, W. R. McIntire, W. W. Schertz, R. Winston, S. Zwerdling, “Application of Compound Parabolic Concentrators to Solar Photovoltaic Conversion,” Argonne National Laboratory Report ANL-77-42 (1977).

Hinterberger, H.

H. Hinterberger, R. Winston, “Efficient Light Coupler for Threshold Cerenkov Counter,” Rev. Sci. Instrum. 37, 1094 (1966).
[Crossref]

Luque, A.

McIntire, W. R.

R. L. Cole, A. J. Gorski, R. M. Graven, W. R. McIntire, W. W. Schertz, R. Winston, S. Zwerdling, “Application of Compound Parabolic Concentrators to Solar Photovoltaic Conversion,” Argonne National Laboratory Report ANL-77-42 (1977).

Minano, J. C.

Ning, X.

R. Winston, X. Ning, J. O’Gallagher, “Photovoltaic Concentrator with Dielectric Second Stage,” in Proceedings, Annual Meeting ASES, Boulder CO (1986), p. 417.

O’Gallagher, J.

R. Winston, X. Ning, J. O’Gallagher, “Photovoltaic Concentrator with Dielectric Second Stage,” in Proceedings, Annual Meeting ASES, Boulder CO (1986), p. 417.

J. O’Gallagher, R. Winston, “Nonimaging Dielectric Elements in Second Stage Concentrators for Photovoltaic System,” in Proceedings, Annual Meeting ASES, Minneapolis (1983), p. 941.

Ruiz, J. M.

Schertz, W. W.

R. L. Cole, A. J. Gorski, R. M. Graven, W. R. McIntire, W. W. Schertz, R. Winston, S. Zwerdling, “Application of Compound Parabolic Concentrators to Solar Photovoltaic Conversion,” Argonne National Laboratory Report ANL-77-42 (1977).

Welford, W. T.

W. T. Welford, R. Winston, The Optics of Nonimaging Concentrators, Light and Solar Energy (Academic, New York, 1978), p. 24.

Winston, R.

R. Winston, “Dielectric Compound Parabolic Concentrators,” Appl. Opt. 15, 291 (1976).
[Crossref] [PubMed]

R. Winston, “Principles of Solar Concentrators of a Novel Design,” Sol. Energy 16, 89 (1974).
[Crossref]

H. Hinterberger, R. Winston, “Efficient Light Coupler for Threshold Cerenkov Counter,” Rev. Sci. Instrum. 37, 1094 (1966).
[Crossref]

R. Winston, X. Ning, J. O’Gallagher, “Photovoltaic Concentrator with Dielectric Second Stage,” in Proceedings, Annual Meeting ASES, Boulder CO (1986), p. 417.

R. L. Cole, A. J. Gorski, R. M. Graven, W. R. McIntire, W. W. Schertz, R. Winston, S. Zwerdling, “Application of Compound Parabolic Concentrators to Solar Photovoltaic Conversion,” Argonne National Laboratory Report ANL-77-42 (1977).

W. T. Welford, R. Winston, The Optics of Nonimaging Concentrators, Light and Solar Energy (Academic, New York, 1978), p. 24.

J. O’Gallagher, R. Winston, “Nonimaging Dielectric Elements in Second Stage Concentrators for Photovoltaic System,” in Proceedings, Annual Meeting ASES, Minneapolis (1983), p. 941.

Zwerdling, S.

R. L. Cole, A. J. Gorski, R. M. Graven, W. R. McIntire, W. W. Schertz, R. Winston, S. Zwerdling, “Application of Compound Parabolic Concentrators to Solar Photovoltaic Conversion,” Argonne National Laboratory Report ANL-77-42 (1977).

Appl. Opt. (2)

Rev. Sci. Instrum. (1)

H. Hinterberger, R. Winston, “Efficient Light Coupler for Threshold Cerenkov Counter,” Rev. Sci. Instrum. 37, 1094 (1966).
[Crossref]

Sol. Energy (1)

R. Winston, “Principles of Solar Concentrators of a Novel Design,” Sol. Energy 16, 89 (1974).
[Crossref]

Other (5)

W. T. Welford, R. Winston, The Optics of Nonimaging Concentrators, Light and Solar Energy (Academic, New York, 1978), p. 24.

J. O’Gallagher, R. Winston, “Nonimaging Dielectric Elements in Second Stage Concentrators for Photovoltaic System,” in Proceedings, Annual Meeting ASES, Minneapolis (1983), p. 941.

R. L. Cole, A. J. Gorski, R. M. Graven, W. R. McIntire, W. W. Schertz, R. Winston, S. Zwerdling, “Application of Compound Parabolic Concentrators to Solar Photovoltaic Conversion,” Argonne National Laboratory Report ANL-77-42 (1977).

R. Winston, X. Ning, J. O’Gallagher, “Photovoltaic Concentrator with Dielectric Second Stage,” in Proceedings, Annual Meeting ASES, Boulder CO (1986), p. 417.

The linear correlation coefficient r is defined as r={NΣXiYi-ΣXiΣYi}/{NΣXi2-(ΣXi)2]1/2 [NΣYi2-(ΣYi)2]1/2} where N is the number of the (X, Y) pair. The value of r is ranged from 0, where there is no correlation to ±1, when there is complete correlation [see P. R. Bevington, Data Reduction and Error Analysis for the Physica Sciences (McGraw-Hill, New York, 1969), p. 121].

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Figures (8)

Fig. 1
Fig. 1

Side view of a DTIRC. The extreme rays hitting the portion P1,P2 converge into P 3 . Rays hitting the portion P2, P3 can exit at whatever angle barely satisfies TIR (the maximum concentration method) or in parallel (the phase-conserving method).

Fig. 2
Fig. 2

Typical optical path consists of four parts: l1, l2, l3, and l4. For rays converging at the bottom left-hand corner, the portion l4 is zero.

Fig. 3
Fig. 3

When the front surface curvature is small, the portion P1,P2 is just a hyperbola, and the portion P2,P3 is just an arc of an equiangular spiral.

Fig. 4
Fig. 4

Concentrations as functions of one acceptance angle for both DTIRC and CPC. With the same acceptance angle, DTIRC has a higher concentration.

Fig. 5
Fig. 5

Idealness of the DTIRC decreases with the acceptance angle, while the idealness of CPC is one.

Fig. 6
Fig. 6

Family of DTIRCs with a different front surface arc angle. Because of curved front surfaces, DTIRCs can be made smaller.

Fig. 7
Fig. 7

DTIRC height and the total height decrease with the front surface arc angle.

Fig. 8
Fig. 8

Comparisons of computer simulated angular acceptance curves with data for a DTIRC with a design acceptance angle of 21.64°.

Tables (3)

Tables Icon

Table I Comparison of Concentrations (Index = 1.5, Arc Angle = 30°, Exit Aperture = 1 cm)

Tables Icon

Table II Concentrations vs Arc Angle (Index = 1.5, Acceptance Angle = 22°, Exit = 1 cm)

Tables Icon

Table III Arc Angle vs Linear Correlation Coefficient (Index of Refraction = 1.47, Acceptance Angle = 22°)

Equations (24)

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C max = n 1 2 / n 2 2 sin 2 θ a ,
θ c = sin ( n 1 / n 2 ) ,
n d s = l 1 + n ( l 2 + l 3 + l 4 ) = const .
F ( θ ) = I b ( θ ) / I c / C g ,
R = d 1 / ( 2 sin φ ) .
θ = sin - 1 [ sin ( θ + θ a ) / n ] - θ .
l 1 = 2 R sin 2 [ ( θ + θ a ) / 2 ] .
H = ½ ( d 1 + d 0 ) cot ( Θ ) ,
C = 2 R sin 2 [ ( θ a + φ ) / 2 ] + n ( d 1 + d 0 ) / [ 2 sin ( Θ ) ] .
Optical path length :             C = l 1 + n [ l 2 + ( l 3 x 2 + l 3 y 2 ) 1 / 2 ] ;
Height :             l 2 cos ( θ ) + l 3 y - R [ cos ( θ ) - cos ( φ ) ] = H ;
Length :             R sin ( θ ) + l 2 sin ( θ ) - l 3 x = - d 0 / 2.
l 2 = { [ ( c - l 1 ) / n ] 2 - [ R sin ( θ ) + d 0 / 2 ] 2 - H 2 } / { ( c - l 1 ) / n + [ R sin ( θ ) + d 0 / 2 ] sin θ - H cos θ } .
θ 0 = π - Θ - 2 θ c ,
Optical path length :             C = l 1 + n ( l 2 + l 3 + l 4 ) ;
Height :             l 2 cos ( θ ) + l 3 cos ( θ 0 ) = H ;
Length :             R sin ( θ ) + l 2 sin ( θ ) - l 3 sin ( θ 0 ) = - d 0 / 2 + l 4 / sin ( θ 0 ) .
l 2 = { ( C - l 1 ) / 2 - H / cos ( θ 0 ) - [ R sin ( θ ) - H / cos ( θ 0 ) + d 0 / 2 ] sin ( θ 0 ) } / [ 1 - cos ( θ ) / cos ( θ 0 ) + sin ( θ ) sin ( θ 0 ) + cos ( θ ) sin ( θ 0 ) tan ( θ 0 ) ] ,
l 3 = [ H - l 2 cos ( θ ) ] / cos ( θ 0 ) ,
l 4 = [ R sin ( θ ) + l 2 sin ( θ ) - l 3 sin ( θ 0 ) + d 0 / 2 ] sin ( θ 0 ) .
x = R sin ( θ ) + l 2 sin ( θ ) ;
y = H - l 2 cos ( θ ) + R [ cos ( θ ) - cos ( φ ) ] .
X j + 1 = [ H + R sin ( θ ) - Y i + X i tan ( θ c + θ ) - R sin ( θ ) cot ( θ ) ] / [ tan ( θ c + θ ) - cot ( θ ) ] ;
Y i + 1 = ( X i + 1 - X i ) tan ( θ c + θ ) + Y i .

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