Abstract

We propose an array of non-imaging micro-concentrators as a mean to recover the loss of sensitivity due to area fill-factor. This is particularly important for those image photo detectors in which complex circuit functions are required and a substantial fraction of the pixel area is consumed, like e.g., 3D camera, SPAD arrays, fluorescence analyzers, etc., but also in CMOS sensors. So far, the low fill-factor was an unacceptable loss of sensitivity precluding from the development of such devices, whereas by using a concentrator array a recovery is possible, up to the inverse square of numerical aperture of the objective lens. By ray tracing, we calculate the concentration factors of several geometries of non-imaging concentrator, i.e., truncated cone, parabolic and compound parabolic, both reflective and refractive. The feasibility of a sizeable recovery of fill-factor (up to 50) is demonstrated.

© 2007 Optical Society of America

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References

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  1. S. Donati, Photodetectors, (Prentice Hall, Upper Saddle River, NJ, 1999), Appendix A2.
  2. W. T. Welford and R. Winston, The Optics of Nonimaging Concentrators, (Academic Press, New York, 1978).
  3. W. T. Welford, J. Minano, and P. Benitez, Nonimaging Optics (Academic Press, New York 2005).
  4. F. Nakamaru, Y. Matsumoto, A. Nakazano: "Novel high efficiency concentrator for optical commu- nications," IEEE Photon. Technol. Lett. 14, (2002), pp. 953-956. (1978).
    [CrossRef]
  5. P. Benitez and J. C. Minano, "Ultrahigh-numerical-aperture imaging concentrator," J. Opt. Soc Am. 14, 1988-1997 (1997).
    [CrossRef]
  6. J. C. Minano, P. Benitez, and J. C. Gonzalez, "RX, a nonimaging concentrator," Appl. Opt. 34, 2226-2235 (1995).
    [CrossRef] [PubMed]
  7. J. O’Gallagher, R. Winston, W. A. Welford, "Axially symmetric nonimaging flux concentrator with maximum theoretical concentration ratio," J. Opt. Soc Am. 4, 66-68 (1987).
    [CrossRef]
  8. C. Niclass, A. Rochas, P.-A. Besse, E. Charbon, "Toward a 3-D camera based on single photon avalanche diode," IEEE J. Sel. Top. Quantum. Electron. 10, 796-802 (2004).
    [CrossRef]
  9. S.-I. Chang, J.-B. Yoon, H. Kim, B.-K. Lee, D. H. Shin, "Microlens array diffuser for a light-emitting diode backlight system," Opt. Lett. 31, 3016-3018 (2006).
    [CrossRef] [PubMed]

2006

2004

C. Niclass, A. Rochas, P.-A. Besse, E. Charbon, "Toward a 3-D camera based on single photon avalanche diode," IEEE J. Sel. Top. Quantum. Electron. 10, 796-802 (2004).
[CrossRef]

1997

P. Benitez and J. C. Minano, "Ultrahigh-numerical-aperture imaging concentrator," J. Opt. Soc Am. 14, 1988-1997 (1997).
[CrossRef]

1995

1987

J. O’Gallagher, R. Winston, W. A. Welford, "Axially symmetric nonimaging flux concentrator with maximum theoretical concentration ratio," J. Opt. Soc Am. 4, 66-68 (1987).
[CrossRef]

Benitez, P.

P. Benitez and J. C. Minano, "Ultrahigh-numerical-aperture imaging concentrator," J. Opt. Soc Am. 14, 1988-1997 (1997).
[CrossRef]

J. C. Minano, P. Benitez, and J. C. Gonzalez, "RX, a nonimaging concentrator," Appl. Opt. 34, 2226-2235 (1995).
[CrossRef] [PubMed]

Besse, P.-A.

C. Niclass, A. Rochas, P.-A. Besse, E. Charbon, "Toward a 3-D camera based on single photon avalanche diode," IEEE J. Sel. Top. Quantum. Electron. 10, 796-802 (2004).
[CrossRef]

Chang, S.-I.

Charbon, E.

C. Niclass, A. Rochas, P.-A. Besse, E. Charbon, "Toward a 3-D camera based on single photon avalanche diode," IEEE J. Sel. Top. Quantum. Electron. 10, 796-802 (2004).
[CrossRef]

Gonzalez, J. C.

Kim, H.

Lee, B.-K.

Minano, J. C.

P. Benitez and J. C. Minano, "Ultrahigh-numerical-aperture imaging concentrator," J. Opt. Soc Am. 14, 1988-1997 (1997).
[CrossRef]

J. C. Minano, P. Benitez, and J. C. Gonzalez, "RX, a nonimaging concentrator," Appl. Opt. 34, 2226-2235 (1995).
[CrossRef] [PubMed]

Niclass, C.

C. Niclass, A. Rochas, P.-A. Besse, E. Charbon, "Toward a 3-D camera based on single photon avalanche diode," IEEE J. Sel. Top. Quantum. Electron. 10, 796-802 (2004).
[CrossRef]

O’Gallagher, J.

J. O’Gallagher, R. Winston, W. A. Welford, "Axially symmetric nonimaging flux concentrator with maximum theoretical concentration ratio," J. Opt. Soc Am. 4, 66-68 (1987).
[CrossRef]

Rochas, A.

C. Niclass, A. Rochas, P.-A. Besse, E. Charbon, "Toward a 3-D camera based on single photon avalanche diode," IEEE J. Sel. Top. Quantum. Electron. 10, 796-802 (2004).
[CrossRef]

Shin, D. H.

Welford, W. A.

J. O’Gallagher, R. Winston, W. A. Welford, "Axially symmetric nonimaging flux concentrator with maximum theoretical concentration ratio," J. Opt. Soc Am. 4, 66-68 (1987).
[CrossRef]

Winston, R.

J. O’Gallagher, R. Winston, W. A. Welford, "Axially symmetric nonimaging flux concentrator with maximum theoretical concentration ratio," J. Opt. Soc Am. 4, 66-68 (1987).
[CrossRef]

Yoon, J.-B.

Appl. Opt.

IEEE J. Sel. Top. Quantum. Electron.

C. Niclass, A. Rochas, P.-A. Besse, E. Charbon, "Toward a 3-D camera based on single photon avalanche diode," IEEE J. Sel. Top. Quantum. Electron. 10, 796-802 (2004).
[CrossRef]

J. Opt. Soc Am.

P. Benitez and J. C. Minano, "Ultrahigh-numerical-aperture imaging concentrator," J. Opt. Soc Am. 14, 1988-1997 (1997).
[CrossRef]

J. O’Gallagher, R. Winston, W. A. Welford, "Axially symmetric nonimaging flux concentrator with maximum theoretical concentration ratio," J. Opt. Soc Am. 4, 66-68 (1987).
[CrossRef]

Opt. Lett.

Other

S. Donati, Photodetectors, (Prentice Hall, Upper Saddle River, NJ, 1999), Appendix A2.

W. T. Welford and R. Winston, The Optics of Nonimaging Concentrators, (Academic Press, New York, 1978).

W. T. Welford, J. Minano, and P. Benitez, Nonimaging Optics (Academic Press, New York 2005).

F. Nakamaru, Y. Matsumoto, A. Nakazano: "Novel high efficiency concentrator for optical commu- nications," IEEE Photon. Technol. Lett. 14, (2002), pp. 953-956. (1978).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Light from the objective lens reaches the entrance aperture (of area Ai) under a solid angle Ωi and the concentrator collects it in a smaller aperture of area Ao within the solid angle Ωo.

Fig. 2.
Fig. 2.

Dependence of the concentration factor C as a function of numerical aperture NAi 2 of the objective lens. Horizontal asymptote is set by the area ratio, whereas the roll off as NAi -2 is due to solid angles ratio. Filling the concentrator with index of refraction n0 moves the break point by a factor n2 0 to the right. The curve is representative of a real concentrator.

Fig. 3.
Fig. 3.

Geometries of non-imaging concentrators: TCC (truncated-cone concentrator), PPC (plain paraboloid concentrator) and CPC (compound parabolic concentrator)

Fig. 4.
Fig. 4.

Spatial and angular coordinates to be considered in the calculation of efficiency and concentration factor.

Fig. 5.
Fig. 5.

Effective concentration C of the TCC versus the NAi of input rays, filling a cone of rays up to NAi, with length L as a parameter. Output diameter is 10 µm. Gap is g=0. Values of effective concentrations are, at small input angles, C=65, 50, 40, 25, 21, 16, 11, about 2–3 times less than the input/output area ratio of 200, 160, 120, 81, 61, 41, 20, and close to the sin-2αwall values of 68, 55, 45, 25, 20, 15 and 10 (see Fig. 3 for αwall).

Fig. 6.
Fig. 6.

Effective concentration of the PPC versus the NAi of input rays, with length L as a parameter. Output diameter is 10 µm. Gap is g=0. To ease the comparison, input/output diameters are the same as for the TCC of Fig. 5. Input diameters are: 142, 127, 110, 90, 78, 64, 46 µm. Values of concentration are consistently larger than those of the TCC and approach the geometrical area ratio at small NA, despite the fast roll off at high C.

Fig. 7.
Fig. 7.

Effective concentration of CPC versus numerical aperture and with length as a parameter. Concentrations corresponding to L are 200. 165, 120, 80, 60, 40, 20. The output diameter is 10 µm. Output gap to detector (from top left- to bottom right) is 0, 1, 2 and 4 µm.

Fig. 8.
Fig. 8.

Performance of TCC, PPC and CPC. reflective (no prefix) and refractive (r- prefix). Effective concentration is plotted vs input ray NAi, and for a g=1-µm air gap for reflective types. The concentrator length L is 150 µm for TCC and PPC, and 350 µm for the CPC. All have a geometrical area ratio concentration of 60.

Fig. 9.
Fig. 9.

Relative irradiance leaking out of a pixel of diameter D=10 µm as a function of distance, for a reflective PPC of C=21. Parameter is gap g (5 and 10 µm).

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

P o = E o A o
C = E o E i
P o = C E i A o
C A i A o
n i 2 A i Ω i = n o 2 A o Ω o
C n o 2 Ω o Ω i
C ( n o N A o N A i ) 2
N A iA 2 = n o 2 N A o 2 C A

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