Abstract

The field of view and gain of optical concentrators used within free space optical communications systems are constrained by conservation of etendue. In this Letter, consideration of the processes in a fluorescent concentrator leads to a simple design strategy for these concentrators for this application. Significantly, because fluorescent concentrators do not conserve etendue, this can lead to concentrators with wider fields of view and higher gains. A model of a fluorescent concentrator containing a quantum dot material suggests that it could have a gain 50 times higher than an etendue conserving concentrator with the same field of view.

© 2014 Optical Society of America

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References

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2013 (2)

2012 (2)

2009 (1)

J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, Sol. Energy Mater. Sol. Cells 93, 176 (2009).
[CrossRef]

2006 (1)

M.-K. So, C. Xu, A. M. Loening, S. S. Gambhir, and J. Rao, Nat. Biotechnol. 24, 339 (2006).
[CrossRef]

1997 (1)

J. M. Kahn and J. R. Barry, Proc IEEE 85, 265 (1997).
[CrossRef]

1979 (1)

1976 (1)

Azhar, A. H.

A. H. Azhar, T.-A. Tran, and D. C. O’Brien, IEEE Photon. Technol. Lett. 25, 171 (2013).
[CrossRef]

Barry, J. R.

J. M. Kahn and J. R. Barry, Proc IEEE 85, 265 (1997).
[CrossRef]

Batchelder, J. S.

Bösch, A.

J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, Sol. Energy Mater. Sol. Cells 93, 176 (2009).
[CrossRef]

Bouchet, O.

Cole, T.

Dai Prè, M.

Dimroth, F.

J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, Sol. Energy Mater. Sol. Cells 93, 176 (2009).
[CrossRef]

El Tabach, M.

Faulkner, G.

Gambhir, S. S.

M.-K. So, C. Xu, A. M. Loening, S. S. Gambhir, and J. Rao, Nat. Biotechnol. 24, 339 (2006).
[CrossRef]

Glunz, S. W.

J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, Sol. Energy Mater. Sol. Cells 93, 176 (2009).
[CrossRef]

Goldschmidt, J. C.

J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, Sol. Energy Mater. Sol. Cells 93, 176 (2009).
[CrossRef]

Grobe, L.

Gueutier, E.

Gun’ko, Y. K.

F. Purcell-Milton and Y. K. Gun’ko, J. Mater. Chem. 22, 16687 (2012).
[CrossRef]

Helmers, H.

J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, Sol. Energy Mater. Sol. Cells 93, 176 (2009).
[CrossRef]

Hoa, L.-M.

Jianhui, L.

Kahn, J. M.

J. M. Kahn and J. R. Barry, Proc IEEE 85, 265 (1997).
[CrossRef]

Kaye, G. W. C.

G. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants and Some Mathematical Functions, 14th ed. (Longman, 1973) p. 96.

Laby, T. H.

G. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants and Some Mathematical Functions, 14th ed. (Longman, 1973) p. 96.

Loening, A. M.

M.-K. So, C. Xu, A. M. Loening, S. S. Gambhir, and J. Rao, Nat. Biotechnol. 24, 339 (2006).
[CrossRef]

Martucci, A.

McClenaghan, N. D.

Musgraves, J. D.

Novak, J.

Novak, S.

O’Brien, D.

O’Brien, D. C.

A. H. Azhar, T.-A. Tran, and D. C. O’Brien, IEEE Photon. Technol. Lett. 25, 171 (2013).
[CrossRef]

Peters, M.

J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, Sol. Energy Mater. Sol. Cells 93, 176 (2009).
[CrossRef]

Porcon, P.

Purcell-Milton, F.

F. Purcell-Milton and Y. K. Gun’ko, J. Mater. Chem. 22, 16687 (2012).
[CrossRef]

Rao, J.

M.-K. So, C. Xu, A. M. Loening, S. S. Gambhir, and J. Rao, Nat. Biotechnol. 24, 339 (2006).
[CrossRef]

Richardson, K.

Scarpantonio, L.

So, M.-K.

M.-K. So, C. Xu, A. M. Loening, S. S. Gambhir, and J. Rao, Nat. Biotechnol. 24, 339 (2006).
[CrossRef]

Tran, T.-A.

A. H. Azhar, T.-A. Tran, and D. C. O’Brien, IEEE Photon. Technol. Lett. 25, 171 (2013).
[CrossRef]

Turnbull, R.

Willeke, G.

J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, Sol. Energy Mater. Sol. Cells 93, 176 (2009).
[CrossRef]

Winston, R.

Wolf, M.

Xu, C.

M.-K. So, C. Xu, A. M. Loening, S. S. Gambhir, and J. Rao, Nat. Biotechnol. 24, 339 (2006).
[CrossRef]

Zewail, A. H.

Appl. Opt. (2)

IEEE Photon. Technol. Lett. (1)

A. H. Azhar, T.-A. Tran, and D. C. O’Brien, IEEE Photon. Technol. Lett. 25, 171 (2013).
[CrossRef]

J. Lightwave Technol. (1)

J. Mater. Chem. (1)

F. Purcell-Milton and Y. K. Gun’ko, J. Mater. Chem. 22, 16687 (2012).
[CrossRef]

Nat. Biotechnol. (1)

M.-K. So, C. Xu, A. M. Loening, S. S. Gambhir, and J. Rao, Nat. Biotechnol. 24, 339 (2006).
[CrossRef]

Opt. Mater. Express (1)

Proc IEEE (1)

J. M. Kahn and J. R. Barry, Proc IEEE 85, 265 (1997).
[CrossRef]

Sol. Energy Mater. Sol. Cells (1)

J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S. W. Glunz, and G. Willeke, Sol. Energy Mater. Sol. Cells 93, 176 (2009).
[CrossRef]

Other (1)

G. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants and Some Mathematical Functions, 14th ed. (Longman, 1973) p. 96.

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Figures (6)

Fig. 1.
Fig. 1.

Schematic diagram showing cross-section through a slab concentrator with a detector at one end. Also shown are representative incident and transmitted rays of light.

Fig. 2.
Fig. 2.

Product of the transmission coefficient and the probability of absorption for three different optical densities. The solid line is when Oit=10, the dashed line is when Oit=1, and the dotted line is when Oit=0.1.

Fig. 3.
Fig. 3.

Fraction of light emitted within the slab concentrator that arrives at a detector placed along one edge of the slab as a function of OeL. The crosses are the calculated points and the solid line has a slope of 1. This is the region in which the EPCF of the concentrator will become independent of length.

Fig. 4.
Fig. 4.

Relative absorption (solid line) and emission spectra (dashed line) of Qdot705 (data downloaded from http://www.fluorophores.tugraz.at/).

Fig. 5.
Fig. 5.

Contours of concentrator EPFC for a 10 μm thick concentrator at different lengths and optical densities at the incident wavelength for Qdot705 with substrate absorption coefficients of 2m1.

Fig. 6.
Fig. 6.

Contours of the EPCF for a 10 μm thick concentrator at different lengths and optical densities at the incident wavelength for Qdot705 with a substrate absorption coefficient of 2m1 and with a mirror added behind the concentrator.

Equations (7)

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G=n2sin2φ,
EPCF=T×Fi×Qy×Fr×L/t,
TFi(θi)=T(θi)(1exp(Oit/cos(θt))),
Fr(Oe,L)=1πL0L0π/2θcπ/2(exp[Oe(2Ly)/sinθsinϕ])sinθdydϕdθ+1πL0L0π/2θcπ/2(exp[Oey/sinθsinφ])sinθdydφdθ.
Fi=(1exp(Oit)).
EPCF0.12QyOi/Oe.
Fr¯=P(λ)Fr(Oe(λ),L)dλ.

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