Abstract

We report on simulations and measurements of focusing diffractive optical elements, fabricated as two-level binary optics. The diffractive optical elements are designed to separate and focus four specific wavelengths in the infrared. The simulations are based on a local linear grating model, and predict anomalies similar to Wood’s anomalies known from grating diffraction theory. The anomalies are also seen in the measurements, and are excited at the DOE locations predicted by the simulations. The given examples illustrate the usefulness of the model for evaluation of DOE designs. We also present a comparison of the response and spectral uniformity between two different versions of the four-wavelength diffractive optical elements. In the first version, the optical functions for all the four wavelengths are incorporated into the same surface pattern, covering the whole patterned area. In the second version the pattern for each wavelength is kept separate, and cover one fourth of the area, forming a mosaic of the four individual patterns.

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References

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  1. R. F. Wolffenbuttel, “State-of-the-art in integrated optical microspectrometers,” IEEE Trans. Instrum. Meas. 53, 197–202 (2004).
    [CrossRef]
  2. O. Løvhaugen, I.-R. Johansen, K. A. H. Bakke, B. G. Fismen, and S. Nicolas, “Dedicated spectrometers based on diffractive optics: design, modelling and evaluation,” J. Mod. Opt. 51, 2203–2222 (2004).
    [CrossRef]
  3. H. Angelskår, I.-R. Johansen, M. Lacolle, H. Sagberg, and A. S. Sudbø, “Spectral uniformity of two- and four-level diffractive optical elements for spectroscopy,” Opt. Express 17, 10206–10222 (2009).
    [CrossRef] [PubMed]
  4. E. Noponen, J. Turunen, and A. Vasara, “Electromagnetic theory and design of diffractive-lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
    [CrossRef]
  5. Y. Sheng, D. Feng, and S. Larochelle, “Analysis and synthesis of circular diffractive lens with local linear grating model and rigorous coupled-wave theory,” J. Opt. Soc. Am. A 14, 1562–1568 (1997).
    [CrossRef]
  6. A. Herbjørnrød, K. Schjølberg-Henriksen, H. Angelskår, and M. Lacolle, “Resist evaluation for fabrication of diffractive optical elements (DOE) with sub-micron resolution in a MEMS production line,” J. Micromech. Microeng. 19, 125022 (2009).
    [CrossRef]
  7. M. C. Hutley, Diffraction gratings, Techniques of Physics, London: Academic Press, (1982).
  8. GD-Calc.http://software.kjinnovation.com/GD-Calc.html.

2009 (2)

H. Angelskår, I.-R. Johansen, M. Lacolle, H. Sagberg, and A. S. Sudbø, “Spectral uniformity of two- and four-level diffractive optical elements for spectroscopy,” Opt. Express 17, 10206–10222 (2009).
[CrossRef] [PubMed]

A. Herbjørnrød, K. Schjølberg-Henriksen, H. Angelskår, and M. Lacolle, “Resist evaluation for fabrication of diffractive optical elements (DOE) with sub-micron resolution in a MEMS production line,” J. Micromech. Microeng. 19, 125022 (2009).
[CrossRef]

2004 (2)

R. F. Wolffenbuttel, “State-of-the-art in integrated optical microspectrometers,” IEEE Trans. Instrum. Meas. 53, 197–202 (2004).
[CrossRef]

O. Løvhaugen, I.-R. Johansen, K. A. H. Bakke, B. G. Fismen, and S. Nicolas, “Dedicated spectrometers based on diffractive optics: design, modelling and evaluation,” J. Mod. Opt. 51, 2203–2222 (2004).
[CrossRef]

1997 (1)

1993 (1)

Angelskår, H.

A. Herbjørnrød, K. Schjølberg-Henriksen, H. Angelskår, and M. Lacolle, “Resist evaluation for fabrication of diffractive optical elements (DOE) with sub-micron resolution in a MEMS production line,” J. Micromech. Microeng. 19, 125022 (2009).
[CrossRef]

H. Angelskår, I.-R. Johansen, M. Lacolle, H. Sagberg, and A. S. Sudbø, “Spectral uniformity of two- and four-level diffractive optical elements for spectroscopy,” Opt. Express 17, 10206–10222 (2009).
[CrossRef] [PubMed]

Bakke, K. A. H.

O. Løvhaugen, I.-R. Johansen, K. A. H. Bakke, B. G. Fismen, and S. Nicolas, “Dedicated spectrometers based on diffractive optics: design, modelling and evaluation,” J. Mod. Opt. 51, 2203–2222 (2004).
[CrossRef]

Feng, D.

Fismen, B. G.

O. Løvhaugen, I.-R. Johansen, K. A. H. Bakke, B. G. Fismen, and S. Nicolas, “Dedicated spectrometers based on diffractive optics: design, modelling and evaluation,” J. Mod. Opt. 51, 2203–2222 (2004).
[CrossRef]

Herbjørnrød, A.

A. Herbjørnrød, K. Schjølberg-Henriksen, H. Angelskår, and M. Lacolle, “Resist evaluation for fabrication of diffractive optical elements (DOE) with sub-micron resolution in a MEMS production line,” J. Micromech. Microeng. 19, 125022 (2009).
[CrossRef]

Hutley, M. C.

M. C. Hutley, Diffraction gratings, Techniques of Physics, London: Academic Press, (1982).

Johansen, I.-R.

H. Angelskår, I.-R. Johansen, M. Lacolle, H. Sagberg, and A. S. Sudbø, “Spectral uniformity of two- and four-level diffractive optical elements for spectroscopy,” Opt. Express 17, 10206–10222 (2009).
[CrossRef] [PubMed]

O. Løvhaugen, I.-R. Johansen, K. A. H. Bakke, B. G. Fismen, and S. Nicolas, “Dedicated spectrometers based on diffractive optics: design, modelling and evaluation,” J. Mod. Opt. 51, 2203–2222 (2004).
[CrossRef]

Lacolle, M.

H. Angelskår, I.-R. Johansen, M. Lacolle, H. Sagberg, and A. S. Sudbø, “Spectral uniformity of two- and four-level diffractive optical elements for spectroscopy,” Opt. Express 17, 10206–10222 (2009).
[CrossRef] [PubMed]

A. Herbjørnrød, K. Schjølberg-Henriksen, H. Angelskår, and M. Lacolle, “Resist evaluation for fabrication of diffractive optical elements (DOE) with sub-micron resolution in a MEMS production line,” J. Micromech. Microeng. 19, 125022 (2009).
[CrossRef]

Larochelle, S.

Løvhaugen, O.

O. Løvhaugen, I.-R. Johansen, K. A. H. Bakke, B. G. Fismen, and S. Nicolas, “Dedicated spectrometers based on diffractive optics: design, modelling and evaluation,” J. Mod. Opt. 51, 2203–2222 (2004).
[CrossRef]

Nicolas, S.

O. Løvhaugen, I.-R. Johansen, K. A. H. Bakke, B. G. Fismen, and S. Nicolas, “Dedicated spectrometers based on diffractive optics: design, modelling and evaluation,” J. Mod. Opt. 51, 2203–2222 (2004).
[CrossRef]

Noponen, E.

Sagberg, H.

Schjølberg-Henriksen, K.

A. Herbjørnrød, K. Schjølberg-Henriksen, H. Angelskår, and M. Lacolle, “Resist evaluation for fabrication of diffractive optical elements (DOE) with sub-micron resolution in a MEMS production line,” J. Micromech. Microeng. 19, 125022 (2009).
[CrossRef]

Sheng, Y.

Sudbø, A. S.

Turunen, J.

Vasara, A.

Wolffenbuttel, R. F.

R. F. Wolffenbuttel, “State-of-the-art in integrated optical microspectrometers,” IEEE Trans. Instrum. Meas. 53, 197–202 (2004).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

R. F. Wolffenbuttel, “State-of-the-art in integrated optical microspectrometers,” IEEE Trans. Instrum. Meas. 53, 197–202 (2004).
[CrossRef]

J. Micromech. Microeng. (1)

A. Herbjørnrød, K. Schjølberg-Henriksen, H. Angelskår, and M. Lacolle, “Resist evaluation for fabrication of diffractive optical elements (DOE) with sub-micron resolution in a MEMS production line,” J. Micromech. Microeng. 19, 125022 (2009).
[CrossRef]

J. Mod. Opt. (1)

O. Løvhaugen, I.-R. Johansen, K. A. H. Bakke, B. G. Fismen, and S. Nicolas, “Dedicated spectrometers based on diffractive optics: design, modelling and evaluation,” J. Mod. Opt. 51, 2203–2222 (2004).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Express (1)

Other (2)

M. C. Hutley, Diffraction gratings, Techniques of Physics, London: Academic Press, (1982).

GD-Calc.http://software.kjinnovation.com/GD-Calc.html.

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Figures (6)

Fig. 1.
Fig. 1.

After light is transmitted through a sample, the DOE is used to focus the light into four focal lines (L1–L4). Each focal line contains a spectrum in the near infrared. When the DOE is rotated the spectra are scanned across the detector. Four wavelength bands centered on the design wavelengths are sequentially detected.

Fig. 2.
Fig. 2.

a) The gold coated silicon DOE with 6×6 patterned squares. The circles above the DOE indicate the position of the source S and detector D projected into the DOE plane. b) An SEM image showing a cross-section of the two-level mélange DOE for four wavelengths. The groove width in the cross section in this image is approximately 875 nm. The bifurcation, or split ridge, is due to the “mixing” of patterns for four wavelengths.

Fig. 3.
Fig. 3.

Comparison of the DOE response in a) simulations and b) measurements. Data points for a given x-coordinate are connected with a line. In total there are six clusters of data points, each consisting of four sets of connected points corresponding to the four wavelengths, as given by the color coding. There is one such cluster for measurements done at each of the six x-positions on the DOE. For example, the points around 31° in a) correspond to x = 6 and y = 1…6 for the four wavelengths. The diffraction efficiency and intensity is plotted against the mean of the diffraction and incidence angles for each given position. a) Diffraction efficiency from simulations. The diffraction efficiency is normalized to the average efficiency for each wavelength, and averaged over simulation results for 7×7 different points within the aperture for each aperture position. b) Detector intensity normalized to the average intensity for each wavelength.

Fig. 4.
Fig. 4.

Diffraction efficiency as in Fig. 3(a), but corrected with a normalized distance factor 1/r 2 where r is the normalized distance from the source to a given DOE position. The correction factor is introduced in order to take into account the fact that the illumination is varying across the DOE.

Fig. 5.
Fig. 5.

Comparison of the normalized DOE response in measurements. a) shows normalized intensity for the mélange DOE, and b) shows normalized intensity for the mosaic DOE. Data points for a given x-coordinate are connected with a line. In total there are six clusters of points, corresponding to six x-positions. Each cluster consists of four sets of connected points corresponding to the four wavelengths, as given by the color coding.

Fig. 6.
Fig. 6.

Normalized DOE response showing the spectral uniformity from simulations. We see that the resonance anomaly around 25° degrees is stronger than in the measurements on the mélange DOE in Fig. 5(a), but similar in strength with that of the mosaic DOE 5(b).

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