Abstract

The Simultaneous Multiple Surface design method in two dimensions (SMS2D) is applied to the design of aspheric V-groove reflectors. The general design problem is to achieve perfect coupling of two wavefronts after two reflections at the groove, no matter which side of the groove the rays hit first. Two types of configurations are identified, and several symmetric and asymmetric design examples are given. Computer simulations with a commercial simulation package are also shown.

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References

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  1. R. Leutz, L. Fu, and H. Ries, “Carambola reflector for recycling the light,” Appl. Opt. 45, 572–2575 (2005).
  2. Y. Wang, K. Li, and S. Inatsugu, “New retroreflector technology for light-collecting systems,” Opt. Eng. 46(8), 084001 (2007).
    [CrossRef]
  3. Patent pending.
  4. B. van-Brunt, “Mathematical possibility of certain systems in geometrical optics,” J. Opt. Soc. Am. A 11(11), 2905–2914 (1994).
    [CrossRef]
  5. B. van-Brunt, “An existence, uniqueness and analyticity theorem for a class of functional differential equations,” NZ J. Mathematics 22, 101–107 (1993).
  6. R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics, pp. 186–187, (Elsevier, Academic, Press 2004)
  7. R. Winston, “Cavity Enhancement by controlled directional Scattering,” Appl. Opt. 19(2), 195–197 (1980).
    [CrossRef] [PubMed]
  8. W. R. McIntire, “Elimination of the optical Losses Due to Gaps Between Absorbers and Their Reflectors”, Proc. 1980 Ann.Meeeting 3.1:600. AS Int. Solar Energy Society (1980)
  9. H. Ries and J. Muschaweck, “Double-tailored microstructures,” SPIE 3781, 124–128 (1999).
    [CrossRef]

2007 (1)

Y. Wang, K. Li, and S. Inatsugu, “New retroreflector technology for light-collecting systems,” Opt. Eng. 46(8), 084001 (2007).
[CrossRef]

2005 (1)

R. Leutz, L. Fu, and H. Ries, “Carambola reflector for recycling the light,” Appl. Opt. 45, 572–2575 (2005).

1999 (1)

H. Ries and J. Muschaweck, “Double-tailored microstructures,” SPIE 3781, 124–128 (1999).
[CrossRef]

1994 (1)

B. van-Brunt, “Mathematical possibility of certain systems in geometrical optics,” J. Opt. Soc. Am. A 11(11), 2905–2914 (1994).
[CrossRef]

1993 (1)

B. van-Brunt, “An existence, uniqueness and analyticity theorem for a class of functional differential equations,” NZ J. Mathematics 22, 101–107 (1993).

1980 (1)

R. Winston, “Cavity Enhancement by controlled directional Scattering,” Appl. Opt. 19(2), 195–197 (1980).
[CrossRef] [PubMed]

Fu, L.

R. Leutz, L. Fu, and H. Ries, “Carambola reflector for recycling the light,” Appl. Opt. 45, 572–2575 (2005).

Inatsugu, S.

Y. Wang, K. Li, and S. Inatsugu, “New retroreflector technology for light-collecting systems,” Opt. Eng. 46(8), 084001 (2007).
[CrossRef]

Leutz, R.

R. Leutz, L. Fu, and H. Ries, “Carambola reflector for recycling the light,” Appl. Opt. 45, 572–2575 (2005).

Li, K.

Y. Wang, K. Li, and S. Inatsugu, “New retroreflector technology for light-collecting systems,” Opt. Eng. 46(8), 084001 (2007).
[CrossRef]

Muschaweck, J.

H. Ries and J. Muschaweck, “Double-tailored microstructures,” SPIE 3781, 124–128 (1999).
[CrossRef]

Ries, H.

R. Leutz, L. Fu, and H. Ries, “Carambola reflector for recycling the light,” Appl. Opt. 45, 572–2575 (2005).

H. Ries and J. Muschaweck, “Double-tailored microstructures,” SPIE 3781, 124–128 (1999).
[CrossRef]

van-Brunt, B.

B. van-Brunt, “Mathematical possibility of certain systems in geometrical optics,” J. Opt. Soc. Am. A 11(11), 2905–2914 (1994).
[CrossRef]

B. van-Brunt, “An existence, uniqueness and analyticity theorem for a class of functional differential equations,” NZ J. Mathematics 22, 101–107 (1993).

Wang, Y.

Y. Wang, K. Li, and S. Inatsugu, “New retroreflector technology for light-collecting systems,” Opt. Eng. 46(8), 084001 (2007).
[CrossRef]

Winston, R.

R. Winston, “Cavity Enhancement by controlled directional Scattering,” Appl. Opt. 19(2), 195–197 (1980).
[CrossRef] [PubMed]

Appl. Opt. (2)

R. Leutz, L. Fu, and H. Ries, “Carambola reflector for recycling the light,” Appl. Opt. 45, 572–2575 (2005).

R. Winston, “Cavity Enhancement by controlled directional Scattering,” Appl. Opt. 19(2), 195–197 (1980).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

B. van-Brunt, “Mathematical possibility of certain systems in geometrical optics,” J. Opt. Soc. Am. A 11(11), 2905–2914 (1994).
[CrossRef]

NZ J. Mathematics (1)

B. van-Brunt, “An existence, uniqueness and analyticity theorem for a class of functional differential equations,” NZ J. Mathematics 22, 101–107 (1993).

Opt. Eng. (1)

Y. Wang, K. Li, and S. Inatsugu, “New retroreflector technology for light-collecting systems,” Opt. Eng. 46(8), 084001 (2007).
[CrossRef]

SPIE (1)

H. Ries and J. Muschaweck, “Double-tailored microstructures,” SPIE 3781, 124–128 (1999).
[CrossRef]

Other (3)

W. R. McIntire, “Elimination of the optical Losses Due to Gaps Between Absorbers and Their Reflectors”, Proc. 1980 Ann.Meeeting 3.1:600. AS Int. Solar Energy Society (1980)

Patent pending.

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics, pp. 186–187, (Elsevier, Academic, Press 2004)

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Figures (7)

Fig. 1
Fig. 1

Examples of groove reflectors (a) The flat linear 90° reflector is a perfect retroreflector in 2D of plane wavefronts (b) The carambola reflector is a perfect retroreflector for a spherical wavefront.

Fig. 2
Fig. 2

Definition of design problems (a) Type I (b) Type II.

Fig. 3
Fig. 3

Nomenclature to formulate the reflector Type I for two spherical wavefronts.

Fig. 4
Fig. 4

SMS 2D method of reflector design: a) Type I (b) Type II.

Fig. 5
Fig. 5

Ray-trace simulations for a symmetric and an asymmetric Type I reflector for two spherical wavefronts.

Fig. 6
Fig. 6

Ray-trace simulations for a symmetric and an asymmetric Type II reflector, for two spherical wavefronts.

Fig. 7
Fig. 7

Ray-trace simulation of a symmetric V-reflector design for a circular caustic.

Equations (7)

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y ( d 1 ( y ) + d 2 ( y , ε ) ) = 0
ε ( d 2 ( y , ε ) + d 3 ( ε ) ) = 0
y ( d ^ 1 ( y ) + d ^ 2 ( y , φ ) ) = 0
φ ( d ^ 2 ( y , φ ) + d ^ 3 ( φ ) ) = 0
F 1 ( y ) = y ( d 1 ( y ) + d 2 ( y , ε ( y ) ) ) F 2 ( y ) = ε ( d 2 ( y , ε ( y ) ) + d 3 ( ε ( y ) ) ) F 3 ( y ) = y ( d ^ 1 ( y ) + d ^ 2 ( y , φ ( y ) ) ) F 4 ( y ) = φ ( d ^ 2 ( y , φ ( y ) ) + d ^ 3 ( φ ( y ) ) )
F j ( y ) = F j ( h ) + F j ( h ) ( y h ) + ... + F j ( n ) ( h ) n ! ( y h ) n + O ( ( y h ) n + 1 )
F j ( i ) ( h ) = 0

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