Abstract

Planar waveguides are useful to transport, concentrate and distribute light uniformly over large dimensions. Their capacity to collect and gather light efficiently over a large distance is interesting for many applications, like backlighting and solar concentration. For these reasons, the possibility of making them even more efficient could be of considerable interest for the community. The observation of the ray path inside a graded-index (GRIN) fiber inspired the development of a similar technology inside planar waveguides. In this Letter, we show that it has the potential to dramatically increase the efficiency of planar waveguide-based solar concentrators or backlighting using GRIN planar waveguides.

© 2014 Optical Society of America

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References

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  1. K. W. Beeson, S. M. Zimmerman, P. M. Ferm, “Backlighting apparatus employing an array of microprisms,” U.S. patent5,396,350 (March7, 1995).
  2. W. C. Shieh, G. D. Su, Proc. SPIE 8108, 81080H (2011).
    [CrossRef]
  3. J. H. Karp, E. J. Tremblay, J. E. Ford, Opt. Express 18, 1122 (2010).
    [CrossRef]
  4. S. Bouchard, S. Thibault, Appl. Opt. 51, 6848 (2012).
    [CrossRef]
  5. A. W. Snyder, J. Love, Optical Waveguide Theory (Springer, 1983), Vol. 190, p. 15.
  6. G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, E. Baer, Opt. Express 16, 11540 (2008).
    [CrossRef]
  7. M. Ponting, A. Hiltner, E. Baer, Macromol. Symp. 294, 19 (2010).
    [CrossRef]
  8. B. E. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, 1991), Vol. 22, p. 22.
  9. J. H. Karp, “Planar micro-optic solar concentration,” Ph.D. dissertation (University of California, San Diego, 2010).

2012 (1)

2011 (1)

W. C. Shieh, G. D. Su, Proc. SPIE 8108, 81080H (2011).
[CrossRef]

2010 (2)

J. H. Karp, E. J. Tremblay, J. E. Ford, Opt. Express 18, 1122 (2010).
[CrossRef]

M. Ponting, A. Hiltner, E. Baer, Macromol. Symp. 294, 19 (2010).
[CrossRef]

2008 (1)

Baer, E.

Beadie, G.

Beeson, K. W.

K. W. Beeson, S. M. Zimmerman, P. M. Ferm, “Backlighting apparatus employing an array of microprisms,” U.S. patent5,396,350 (March7, 1995).

Bouchard, S.

Ferm, P. M.

K. W. Beeson, S. M. Zimmerman, P. M. Ferm, “Backlighting apparatus employing an array of microprisms,” U.S. patent5,396,350 (March7, 1995).

Fleet, E.

Ford, J. E.

Hiltner, A.

Jin, Y.

Kamdar, A. R.

Karp, J. H.

J. H. Karp, E. J. Tremblay, J. E. Ford, Opt. Express 18, 1122 (2010).
[CrossRef]

J. H. Karp, “Planar micro-optic solar concentration,” Ph.D. dissertation (University of California, San Diego, 2010).

Kazmierczak, T.

Lane, P. A.

Love, J.

A. W. Snyder, J. Love, Optical Waveguide Theory (Springer, 1983), Vol. 190, p. 15.

Ponting, M.

Rosenberg, A.

Saleh, B. E.

B. E. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, 1991), Vol. 22, p. 22.

Shieh, W. C.

W. C. Shieh, G. D. Su, Proc. SPIE 8108, 81080H (2011).
[CrossRef]

Shirk, J. S.

Snyder, A. W.

A. W. Snyder, J. Love, Optical Waveguide Theory (Springer, 1983), Vol. 190, p. 15.

Su, G. D.

W. C. Shieh, G. D. Su, Proc. SPIE 8108, 81080H (2011).
[CrossRef]

Teich, M. C.

B. E. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, 1991), Vol. 22, p. 22.

Thibault, S.

Tremblay, E. J.

Yang, Y.

Zimmerman, S. M.

K. W. Beeson, S. M. Zimmerman, P. M. Ferm, “Backlighting apparatus employing an array of microprisms,” U.S. patent5,396,350 (March7, 1995).

Appl. Opt. (1)

Macromol. Symp. (1)

M. Ponting, A. Hiltner, E. Baer, Macromol. Symp. 294, 19 (2010).
[CrossRef]

Opt. Express (2)

Proc. SPIE (1)

W. C. Shieh, G. D. Su, Proc. SPIE 8108, 81080H (2011).
[CrossRef]

Other (4)

K. W. Beeson, S. M. Zimmerman, P. M. Ferm, “Backlighting apparatus employing an array of microprisms,” U.S. patent5,396,350 (March7, 1995).

A. W. Snyder, J. Love, Optical Waveguide Theory (Springer, 1983), Vol. 190, p. 15.

B. E. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, 1991), Vol. 22, p. 22.

J. H. Karp, “Planar micro-optic solar concentration,” Ph.D. dissertation (University of California, San Diego, 2010).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Light losses in a homogeneous planar waveguide. (b) Optical system developed in this Letter. This is a graded-index (GRIN) planar waveguide of thickness equal to the maximum height reached by the rays of light ymax and with an array of cylindrical lenses. Each lens has a width D and a focal length f. It produces a spot size d and the angular extent of the rays coupled in the waveguide is θ. The spot is re-imaged at a distance F, which is the period of the GRIN. The angular acceptance of the optical system is φ. Finally, the index at the base of the waveguide (opposed to the lens array) is n0.

Fig. 2.
Fig. 2.

Concentration factor for various F/# of the cylindrical lens for the GRIN and the homogeneous planar solar concentrator. The chosen value for the parameter k is 2. The diameter of the lens D is 2 mm. The thickness of the waveguide ymax is 1 mm. The index at the base of the GRIN waveguide n0 is 1.55.

Fig. 3.
Fig. 3.

Variation of the concentration factor associated with the use of a GRIN waveguide instead of a homogeneous waveguide. The homogeneous waveguide in the ratio is calculated with Clens/k. Only optical systems with F/# that can be used in a compact concentrator with a good concentration factor are presented.

Equations (12)

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Clens=Dd=D2fn0tan(φ)110F/#.
F=MD±kd.
N=Fkd=(MD±kd)kd=MClensk±1.
L=ND=D(MClensk±1).
C=RD(MClensk±1)ymax.
n(y)=n0(1A2y2)1/2.
ymax=n02nymax2A·n0.
C=RD(MClensk±1)n02nymax2n0A.
F/#minn02n02nymax2=12Aymax.
ηdecouple(P,ϕ)=(1kClens)Ptanϕ2ymax,
ηposition(P,ϕ)=R·ηdecoupleexp(αPcosϕ),
ηtotal=P0ϕmaxηposition(P,ϕ)(Lr)2r.

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