Abstract

We present simulations and characterization of gold coated diffractive optical elements (DOEs) that have been designed and fabricated in silicon for an industrial application of near-infrared spectroscopy. The DOE design is focusing and reflecting, and two-level and four-level binary designs were studied. Our application requires the spectral response of the DOE to be uniform over the DOE surface. Thus the variation in the spectral response over the surface was measured, and studied in simulations. Measurements as well as simulations show that the uniformity of the spectral response is much better for the four-level design than for the two-level design. Finally, simulations and measurements show that the four-level design meets the requirements of spectral uniformity from the industrial application, whereas the simulations show that the physical properties of diffraction gratings in general make the simpler two-level design unsuitable.

© 2009 Optical Society of America

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References

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    [CrossRef]
  4. 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]
  5. 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]
  6. M. C. Hutley, Diffraction gratings (Academic Press, London, 1982).
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    [CrossRef]
  12. E.D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).
  13. Lumerical FDTD Solutions, http://www.lumerical.com.
  14. T. López-Rios, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, "Surface Shape Resonances in Lamellar Metallic Gratings," Phys. Rev. Lett. 81, 665-668 (1998).
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  15. E. K. Popov, N. Bonod, and S. Enoch, "Comparison of plasmon surface waves on shallow and deep metallic 1D and 2D gratings," Opt. Express 15, 4224-4237 (2007).
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    [CrossRef] [PubMed]

2008 (1)

2007 (1)

2006 (1)

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]

2003 (1)

1998 (1)

T. López-Rios, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, "Surface Shape Resonances in Lamellar Metallic Gratings," Phys. Rev. Lett. 81, 665-668 (1998).
[CrossRef]

1996 (1)

1993 (1)

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]

1986 (1)

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]

Bonod, N.

Emadi, A.

Enoch, S.

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]

García-Vidal, F. J.

T. López-Rios, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, "Surface Shape Resonances in Lamellar Metallic Gratings," Phys. Rev. Lett. 81, 665-668 (1998).
[CrossRef]

Gaylord, T. K.

Grabarnik, S.

Johansen, I.-R.

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]

Li, L.

López-Rios, T.

T. López-Rios, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, "Surface Shape Resonances in Lamellar Metallic Gratings," Phys. Rev. Lett. 81, 665-668 (1998).
[CrossRef]

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]

Mendoza, D.

T. López-Rios, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, "Surface Shape Resonances in Lamellar Metallic Gratings," Phys. Rev. Lett. 81, 665-668 (1998).
[CrossRef]

Moharam, M. G.

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]

Nishihara, H.

Nishio, K.

Noponen, E.

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]

Okano, M.

Okayama, F.

Pannetier, B.

T. López-Rios, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, "Surface Shape Resonances in Lamellar Metallic Gratings," Phys. Rev. Lett. 81, 665-668 (1998).
[CrossRef]

Pietarinen, J.

Popov, E. K.

Sánchez-Dehesa, J.

T. López-Rios, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, "Surface Shape Resonances in Lamellar Metallic Gratings," Phys. Rev. Lett. 81, 665-668 (1998).
[CrossRef]

Sasaki, T.

Satoh, K.

Shiroshita, K.

Sokolova, E.

Turunen, J.

J. Pietarinen, T. Vallius, and J. Turunen, "Wideband four-level transmission gratings with flattened spectral efficiency," Opt. Express 14, 2583-2588 (2006).
[CrossRef] [PubMed]

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]

Ura, S.

Vallius, T.

Vasara, A.

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]

Vdovin, G.

Wolffenbuttel, R. F.

Yotsuya, T.

Appl. Opt. (2)

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. 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)

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

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]

Opt. Express (2)

Phys. Rev. Lett. (1)

T. López-Rios, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, "Surface Shape Resonances in Lamellar Metallic Gratings," Phys. Rev. Lett. 81, 665-668 (1998).
[CrossRef]

Other (6)

M. C. Hutley, Diffraction gratings (Academic Press, London, 1982).

G. J. Swanson, "Binary optics technology: Theoretical limits on the diffraction efficiency of multilevel diffractive optical elements," Tech. Rep. 914 (Massachusetts Institute of Technology, Cambridge, Mass., 1991).

J. W. Goodman, Introduction to Fourier optics, 2nd ed. (McGraw-Hill, 1996).

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

E.D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

Lumerical FDTD Solutions, http://www.lumerical.com.

Supplementary Material (2)

» Media 1: MPG (1855 KB)     
» Media 2: MPG (1827 KB)     

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Figures (16)

Fig. 1.
Fig. 1.

(a) A schematic drawing of the spectrometer system. The tilt angle of the DOE, and the distance between source and detector are exaggerated. (b) The characterization setup consists mainly of a reflective DOE, an input fiber from the source, and a detector. The source position in the figure represents the input fiber end. The input fiber is excited by a halogen lamp emitting white light. The DOE focuses certain wavelength components in the near-infrared on the detector. During characterization, the DOE is partly covered by a movable opaque screen with an aperture which allows us to study the response at different positions on the DOE. In order to switch between operating wavelengths the DOE is rotated around a scan axis, focusing light of one wavelength at a time on the detector at predefined scan angles.

Fig. 2.
Fig. 2.

To the right, the spectral response for two wavelength bands, labeled λ 1 and λ 2, is plotted for two areas of the DOE shown on the left. Typically the diffraction efficiency is not spectrally uniform over the DOE. The figure illustrates a severe case where the resulting response is highly dependent on whether area A or area B is illuminated. The intensity difference between the case where wavelength λ 2 is incident on the detector, compared to λ 1, is larger when area B (bottom) is illuminated than when area A (top) is illuminated. If a sample was present, this could be misinterpreted as absorption of the λ 2 component in a spectroscopic measurement.

Fig. 3.
Fig. 3.

Two periods of the cross-section of a grating with perfectly straight grooves that run perpendicular to the figure. (a): Two-level binary approximation to the sawtooth profile denoted by the dotted line. (b): Four-level binary approximation.

Fig. 4.
Fig. 4.

Sketch of the DOE principle for diffracting the incident light into five focal lines that run in the x direction. Different wavelengths come to a focus at different x positions, indicated with different colors in the figure, and the grooves on the DOE surface hence run predominantly in the y direction. As the DOE is rotated, the focal lines L 1 to L 5 are scanned across the detector, and the desired wavelength bands from the different spectra are detected. In the figure, the wavelength band of L 3 is detected. After the DOE is rotated through an angle α, the wavelength band of L 4 is detected.

Fig. 5.
Fig. 5.

SEM micrograph of a small part of the two-level (a) and four-level (b) DOE surface. The surface is designed to focus five different wavelength components, and thus incorporates five different Fresnel lenses. In (b) the wafer is cut in half, showing a cross-section of the DOE surface profile with the gold coating on top. The bifurcation apparent in (b) is due to the five separate Fresnel lenses incorporated into the surface, giving a complex surface pattern.

Fig. 6.
Fig. 6.

A plot of the height profile of a small part of the DOE area of approximately 40×20 µm. The grooves form a pattern resembling a perturbed linear diffraction grating. A typical period for the grooves on the DOE surface is 2 µm. The surface profile in this figure is representative of the DOE surface, although the typical groove width varies with DOE position.

Fig. 7.
Fig. 7.

(a): Incidence angle on the DOE at 9×9 positions. Each triplet of curves belong to the three wavelengths at 9 y-positions (y 1y 9) for one x-coordinate. The wavelengths are λ 1=1.649 µm, λ 2=1.685 µm, and λ 3=1.736 µm, drawn in solid blue, dashed red, and dotted black, respectively. The triplets corresponding to x 1 and x 9 are denoted at the top of the figure. (b): Modeled grating period on the DOE determined from the grating equation, Eq. (6). Note that the curve triplet corresponding to position x 1 is to the right (longer periods) in this figure, so the subsequent positions x 2x 9 are found from right to left.

Fig. 8.
Fig. 8.

(a): The incidence angle θi and the diffraction angle θd determined for a point on the DOE. The source is denoted by S and the detector by D. (b): The incidence and diffraction angles are used in the simulations for a classically mounted grating with linear grooves.

Fig. 9.
Fig. 9.

Diffraction efficiency for order m=-1 from simulations for the two-level profile, for the three wavelengths λ 1=1.736 µm, λ 2=1.685 µm, and λ 3=1.649 µm in figure (a), (b) and (c), respectively. The diffraction efficiency varies dramatically depending on DOE position.

Fig. 10.
Fig. 10.

Diffraction efficiency from simulations for the four-level profile, for the three wavelengths λ 1=1.733 µm, λ 2=1.685 µm, and λ 3=1.649 µm in figure (a), (b) and (c), respectively.

Fig. 11.
Fig. 11.

The maximal normalized deviation |η-1| in diffraction efficiency across the DOE at each of the 9 x-coordinates for the three wavelengths. (a) Simulations for the two-level profile. (b) Simulations for the four-level profile.

Fig. 12.
Fig. 12.

The diffraction angle of the orders m=1 (a), and m=-2 (b), calculated from the grating equation, Eq. (6), for a grating with period P=2.5 µm and plotted against the incidence angle for the three wavelengths. We see that the limiting incidence angle for diffraction order m=1 is between 18° to 20°.

Fig. 13.
Fig. 13.

E-field intensity for a grating with a two-level (a) and a four-level (b) profile at resonance conditions (for the two-level profile). The period is P=2 µm, incidence angle is 25° and the wavelength is 1.685 µm. Both the incident and reflected fields are plotted.

Fig. 14.
Fig. 14.

The intensity of the electric field upon excitation of the two grating profiles, determined by FDTD simulation. (a) (Media 1) Shows the resonance for the two-level profile, where the incident field excites a standing wave in the grating grooves. This creates a strong, localized field, and results in a dip in the diffraction efficiency for these parameters as discussed above. (b) (Media 2) The corresponding four-level profile does not support the standing wave resonance, so the field is reflected back into the propagating orders.

Fig. 15.
Fig. 15.

(a) Maximal normalized deviation from measurements on a DOE with two-level groove profile. (b) Maximal normalized deviation from measurements on a DOE with four-level groove profile.

Fig. 16.
Fig. 16.

The maximal normalized deviation |η-1| (see Eq. (12)) across the DOE at each of the 9 x-coordinates for the three wavelengths. The data is the mean of three simulations where the groove width was 45%, 50% and 55% of the period, and averaged over 4 positions 0.25 mm from the (xn , ym ) coordinate on the DOE in order to take into account the finite aperture. (a) Simulations for the two-level DOE. (b) Simulations for the four-level DOE.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

f(x,y)=ϕ(x,y)2kavg,
ϕ(x,y)=mod [k(rs+rd),2π] ,
rtot=Atot(x,y)exp(iϕtot(x,y))=n=15Anexp(iϕn(x,y)).
d2=14λavg.
d4=38λavg.
P(sin(θi)+sin(θd,m))=mλ,
xi=iΔx+x0,fori=(1,2,,nx),
yj=jΔy+y0,forj=(1,2,,ny),
γ̅k=ijγijknxny.
Γijk=γijkγ̅k.
Γ̅ij=1nλkΓijk.
ηijk=ΓijkΓ̅ij.

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