Abstract

Blazed transmission gratings have become crucial components in many hybrid optical systems. Shadowing effects are known to occur at their passive blaze facets, which may impair the system’s efficiency performance. For optical designs, it is desirable to have a simple but accurate description of this phenomenon. We show that the efficiency reduction in low diffraction orders is dominated by a linear dependence on the ratio of wavelength to grating period rather than a quadratic dependence as proposed in extended scalar theory. The strength of the electromagnetic shadowing will be determined using rigorous diffraction methods and discussed with respect to imaging optical components. Results are compared to existing ray-optical models.

© 2006 Optical Society of America

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References

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2004 (2)

2003 (1)

R. Brunner, R. Steiner, H.-J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, in Proc. SPIE 5183, 47 (2003).
[CrossRef]

2002 (1)

M. S. L. Lee, Ph. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, J. Opt. A, Pure Appl. Opt. 4, S119 (2002).
[CrossRef]

1999 (2)

1998 (1)

1996 (1)

B. H. Kleemann, A. Mitreiter, and F. Wyrowski, J. Mod. Opt. 43, 1323 (1996).
[CrossRef]

1995 (1)

Astilean, S.

Brunner, R.

R. Brunner, M. Burkhardt, A. Pesch, O. Sandfuchs, M. Ferstl, S. Hohng, and J. O. White, J. Opt. Soc. Am. A 21, 1186 (2004).
[CrossRef]

R. Brunner, R. Steiner, H.-J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, in Proc. SPIE 5183, 47 (2003).
[CrossRef]

Burkhardt, M.

R. Brunner, M. Burkhardt, A. Pesch, O. Sandfuchs, M. Ferstl, S. Hohng, and J. O. White, J. Opt. Soc. Am. A 21, 1186 (2004).
[CrossRef]

R. Brunner, R. Steiner, H.-J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, in Proc. SPIE 5183, 47 (2003).
[CrossRef]

Cambril, E.

M. S. L. Lee, Ph. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, J. Opt. A, Pure Appl. Opt. 4, S119 (2002).
[CrossRef]

Ph. Lalanne, S. Astilean, P. Chavel, E. Cambril, and H. Launois, J. Opt. Soc. Am. A 16, 1143 (1999).
[CrossRef]

Chavel, P.

M. S. L. Lee, Ph. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, J. Opt. A, Pure Appl. Opt. 4, S119 (2002).
[CrossRef]

Ph. Lalanne, S. Astilean, P. Chavel, E. Cambril, and H. Launois, J. Opt. Soc. Am. A 16, 1143 (1999).
[CrossRef]

Chen, Y.

M. S. L. Lee, Ph. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, J. Opt. A, Pure Appl. Opt. 4, S119 (2002).
[CrossRef]

Dobschal, H.-J.

R. Brunner, R. Steiner, H.-J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, in Proc. SPIE 5183, 47 (2003).
[CrossRef]

Ferstl, M.

Gale, M. T.

Golub, M.

Helgert, M.

R. Brunner, R. Steiner, H.-J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, in Proc. SPIE 5183, 47 (2003).
[CrossRef]

Hessler, T.

Hohng, S.

Kleemann, B. H.

B. H. Kleemann, A. Mitreiter, and F. Wyrowski, J. Mod. Opt. 43, 1323 (1996).
[CrossRef]

Kunz, R. E.

Lalanne, Ph.

M. S. L. Lee, Ph. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, J. Opt. A, Pure Appl. Opt. 4, S119 (2002).
[CrossRef]

Ph. Lalanne, S. Astilean, P. Chavel, E. Cambril, and H. Launois, J. Opt. Soc. Am. A 16, 1143 (1999).
[CrossRef]

Launois, H.

Lee, M. S. L.

M. S. L. Lee, Ph. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, J. Opt. A, Pure Appl. Opt. 4, S119 (2002).
[CrossRef]

Levy, U.

U. Levy, E. Marom, and D. Mendlovic, Opt. Commun. 229, 11 (2004).
[CrossRef]

Marom, E.

U. Levy, E. Marom, and D. Mendlovic, Opt. Commun. 229, 11 (2004).
[CrossRef]

Martin, D.

R. Brunner, R. Steiner, H.-J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, in Proc. SPIE 5183, 47 (2003).
[CrossRef]

Mendlovic, D.

U. Levy, E. Marom, and D. Mendlovic, Opt. Commun. 229, 11 (2004).
[CrossRef]

Mitreiter, A.

B. H. Kleemann, A. Mitreiter, and F. Wyrowski, J. Mod. Opt. 43, 1323 (1996).
[CrossRef]

Pesch, A.

Rodier, J. C.

M. S. L. Lee, Ph. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, J. Opt. A, Pure Appl. Opt. 4, S119 (2002).
[CrossRef]

Rossi, M.

Sandfuchs, O.

Sinzinger, S.

Steiner, R.

R. Brunner, R. Steiner, H.-J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, in Proc. SPIE 5183, 47 (2003).
[CrossRef]

Testorf, M.

White, J. O.

Wyrowski, F.

B. H. Kleemann, A. Mitreiter, and F. Wyrowski, J. Mod. Opt. 43, 1323 (1996).
[CrossRef]

Appl. Opt. (2)

J. Mod. Opt. (1)

B. H. Kleemann, A. Mitreiter, and F. Wyrowski, J. Mod. Opt. 43, 1323 (1996).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

M. S. L. Lee, Ph. Lalanne, J. C. Rodier, P. Chavel, E. Cambril, and Y. Chen, J. Opt. A, Pure Appl. Opt. 4, S119 (2002).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (1)

U. Levy, E. Marom, and D. Mendlovic, Opt. Commun. 229, 11 (2004).
[CrossRef]

Proc. SPIE (1)

R. Brunner, R. Steiner, H.-J. Dobschal, D. Martin, M. Burkhardt, and M. Helgert, in Proc. SPIE 5183, 47 (2003).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic of a diffractive blaze structure with period g, height h, and angles α and β. Light incident at angle θ is diffracted into an angle θ m (dashed line, grating normal).

Fig. 2
Fig. 2

Efficiency dependence on the ratio of grating period g to blaze wavelength λ B at normal incidence ( θ = 0 ) for n = 1.49 and unpolarized light. Inset: comparison of RCWA and FEM with IESMP. (b) Efficiency reduction Δ η = η max η for different refractive indices n. Rigorous results for TE, TM polarization, and unpolarized (UP) light, and the ray-optical model (solid lines).

Fig. 3
Fig. 3

(a) Shadowing strength c 1 as a function of the refractive index for the same polarization states as in Fig. 2b. (b) Ratios of the shadowing strength for the unpolarized light of various low diffraction orders m 1 and m 2 .

Tables (1)

Tables Icon

Table 1 Shadowing Parameters from Rigorous Data for θ = 0

Equations (4)

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tan α opt = m λ B g n cos θ m cos θ .
cos β opt sin θ m = 1 n ( sin θ + m λ B g ) .
η = η max [ 1 c m ( n ) ( g λ B ) ν ] ,
c m ( n ) = a [ n ( n 1 ) ] b .

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