Abstract

Color correction in planar optics configurations can be achieved by resorting to gradient-index rather than uniform-refractive-index substrates. The basic configuration, principle of correction, and calculated and experimental results are presented. The results reveal that, with an appropriate refractive index distribution along the thickness of the substrates, the color can be corrected over a wavelength range up to 155nm depending on incidence angles.

© 2006 Optical Society of America

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References

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1995

1989

R. L. Fisher, Opt. Eng. 28, 616 (1989).

1980

1979

1971

W. Streifer and K. B. Paxton, Appl. Opt. 4, 769 (1971).
[CrossRef]

P. L. Sands, J. Opt. Soc. Am. 61, 777 (1971).
[CrossRef] [PubMed]

Agostinelli, J.

Amitai, Y.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Cho, M. H.

Fisher, R. L.

R. L. Fisher, Opt. Eng. 28, 616 (1989).

Friesem, A. A.

Gabel, C.

Harvey, G.

Iga, K.

Jahns, J.

S. Sinzinger and J. Jahns, Appl. Opt. 36, 4729 (1997).
[CrossRef] [PubMed]

S. Sinzinger and J. Jahns, Microoptics (WILET-VCH, 2003).
[CrossRef]

Kim, P. S.

Kim, Y. S.

Lee, E. H.

Marchand, E. W.

E. W. Marchand, Gradient Index Optics (Academic, 1978).

Oh, C. H.

Park, S.

Paxton, K. B.

W. Streifer and K. B. Paxton, Appl. Opt. 4, 769 (1971).
[CrossRef]

Reinhorn, S.

Sands, P. L.

Shechter, R.

Sinzinger, S.

S. Sinzinger and J. Jahns, Appl. Opt. 36, 4729 (1997).
[CrossRef] [PubMed]

S. Sinzinger and J. Jahns, Microoptics (WILET-VCH, 2003).
[CrossRef]

Song, S. H.

Stone, T.

Streifer, W.

W. Streifer and K. B. Paxton, Appl. Opt. 4, 769 (1971).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

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Figures (4)

Fig. 1
Fig. 1

Basic planar optics configuration with two laterally displaced diffraction gratings arranged on a substrate of uniform refractive index. The incident light, comprising three different wavelengths, λ 1 , λ 2 , and λ 3 , is dispersed and trapped inside the substrate by total internal reflection, and the light of each wavelength propagates along a different path toward the output grating, so each emerges at a different location.

Fig. 2
Fig. 2

Basic planar optics configuration with two laterally displaced diffraction gratings arranged on a GRIN substrate. The incident light is diffracted by the input grating and propagates toward the output grating along a different trajectory for each wavelength, but emerges at one location.

Fig. 3
Fig. 3

Beam trajectories for these different wavelengths. (a) Incidence angle θ inc , max = 4 ° ; (b) incidence angle θ inc , max = 4 ° .

Fig. 4
Fig. 4

Experimental detection of light beams decoupled from the stratified substrate, showing the distance between two successive bounces, z p , for two different wavelengths: (a) λ = 476.5 nm , (b) λ = 568.2 nm . The relative color displacement is 1 mm .

Tables (1)

Tables Icon

Table 1 Bounds and allowable range of wavelengths for θ inc , max = 4 ° , 0 ° , 4 °

Equations (9)

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d d s ( n sub ( r , λ ) d r d s ) = n sub ( r , λ ) ,
n sub 2 ( x , λ ) = n sub 2 ( 0 , λ ) [ 1 ( g λ x ) 2 + 2 3 ( g λ x ) 4 17 45 ( g λ x ) 6 ] ,
x ( z ) = cos ( θ diff ) g λ sin ( g λ z ) .
z p = 1 2 ( 2 π g λ ) .
0 cos ( θ diff ) g λ d .
n sub ( 0 , λ ) sin ( θ diff ) = n sup sin ( θ inc ) + λ Λ x
sin ( θ inc , max ) = λ Λ x n sub ( 0 , λ ) 1 ( g λ d ) 2 .
λ min Λ x sin ( θ inc , max ) + n sub ( 0 , λ min ) 1 ( g λ min d ) 2 = 0 ,
λ max Λ x sin ( θ inc , max ) + n ( 0 , λ max ) = 0 .

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