Abstract

It is generally accepted that diffractive elements designed for multiwavelength operation require deep surface-relief profiles. We show, however, that thin diffractive elements can be designed to operate with more than one wavelength. A novel, to our knowledge, optimization technique is introduced for this purpose. The maximum phase delay is limited to only a few multiples of 2π, and the element can implement different functions for different wavelengths. Examples with fan-out gratings are discussed.

© 1999 Optical Society of America

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References

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    [Crossref] [PubMed]
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1998 (1)

1997 (1)

1996 (1)

1995 (2)

1993 (1)

1991 (1)

D. Faklis, G. M. Morris, “Diffractive lenses in broadband optical system design,” Photonics Spectra 25, 131–134 (1991).

1987 (1)

Allebach, J. P.

Arieli, Y.

Barton, I. M.

Bengtsson, J.

Blair, P.

Eisenberg, N.

Faklis, D.

D. Faklis, G. M. Morris, “Spectral properties of multiorder diffractive lenses,” Appl. Opt. 34, 2462–2468 (1995).
[Crossref] [PubMed]

D. Faklis, G. M. Morris, “Diffractive lenses in broadband optical system design,” Photonics Spectra 25, 131–134 (1991).

D. Faklis, G. M. Morris, “Polychromatic diffractive lenses,” U.S. patent5,589,982 (31December1996).

Farn, M. W.

Lewis, A.

Medeiros, S. S.

Morris, G. M.

D. Faklis, G. M. Morris, “Spectral properties of multiorder diffractive lenses,” Appl. Opt. 34, 2462–2468 (1995).
[Crossref] [PubMed]

D. Faklis, G. M. Morris, “Diffractive lenses in broadband optical system design,” Photonics Spectra 25, 131–134 (1991).

D. Faklis, G. M. Morris, “Polychromatic diffractive lenses,” U.S. patent5,589,982 (31December1996).

Noach, S.

Seldowitz, M. A.

Sommargren, G. E.

Stern, M. B.

Sweeney, D. W.

Taghizadeh, M.

Veldkamp, W. B.

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Figures (5)

Fig. 1
Fig. 1

Optimized solution for a 16-level grating in fused silica designed to generate a 1 × 5 fan-out at λ1 = 0.5320 µm and a 1 × 5 fan-out at λ2 = 0.6328 µm. The performance measures are shown in Table 1. (a) Phase solution with 20 pixels. (b) Efficiency of the diffracted orders.

Fig. 2
Fig. 2

Optimized solution for a 16-level grating in fused silica designed to generate a 1 × 5 fan-out at λ1 = 0.5320 µm and a 1 × 7 fan-out at λ2 = 0.6328 µm. The performance measures are shown in Table 1. (a) Phase solution with 40 pixels. (b) Efficiency of the diffracted orders.

Fig. 3
Fig. 3

Optimized solution for a 16-level grating in fused silica designed to generate a 1 × 4 fan-out at λ1 = 0.5320 µm and a 1 × 21 fan-out at λ2 = 0.6328 µm. The performance measures are shown in Table 1. (a) Phase solution with 50 pixels. (b) Efficiency of the diffracted orders.

Fig. 4
Fig. 4

Solution for a 16-level fused-silica grating designed to generate a 1 × 5 fan-out at λ1 = 0.5355 µm with 20 pixels. (a) The phase and (b) the efficiency of the diffracted orders. The designed efficiency η is 90.46%, and the uniformity error σ is 3.75%.

Fig. 5
Fig. 5

Solution for a 16-level fused-silica grating designed to generate a 1 × 5 fan-out at three wavelengths: λ1 = 0.4416 µm, λ2 = 0.5320 µm, and λ3 = 0.6328 µm. The performance measures are shown in Table 2. (a) Phase solution with 20 pixels. (b) Efficiency of the diffracted orders.

Tables (2)

Tables Icon

Table 1 Performance of Fused-Silica Fan-Out Grating Designs for Dual-Wavelength Operationa

Tables Icon

Table 2 Performance of a 1 × 5 Fan-Out Grating Designed to Operate at Three Distinct Wavelengths in Fused Silicaa

Equations (8)

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cm=1Λ0ΛexpiΦxexp-i2πmx/Λdx=01expiΦxexp-i2πmxdx,
cm=k=1Nexpiϕkexp-iπmxk+xk-1×xk-xk-1sincmxk-xk-1=k=1Nexpiϕkgmxk, xk-1,
cm=cm+expiϕq-expiϕqgxq, xq-1.
cm=cm+gmxq, xq-1-gmxq, xq-1expiϕq+gmxq+1, xq-gmxq+1, xqexpiϕq+1.
γ=λDλnλ-1nλD-1.
ηp=mMp Im,
σp=maxIm-minImmaxIm+minImmMp,
μ=p=1L wpmMpIm-Im02mMp Im,

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