Abstract

Numerical methods for simulating etching and deposition processes were combined with electromagnetic modeling to design guided-mode resonance (GMR) filters with accurately positioned resonances and study how fabrication affects their optical behavior. GMR filters are highly sensitive to structural deformations that arise during fabrication, making accurate placement of their resonances very difficult without active tuning while in operation. Inspired by how thin film resistors are trimmed during fabrication, the numerical tools were used to design a method for adjusting position of GMR resonances at the time of fabrication.

© 2007 Optical Society of America

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References

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  2. Lord Rayleigh, Phil. Mag. 14, 60 (1907).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. R. Magnusson and S. S. Wang, "New principle for optical filters," Appl. Phys. Lett. 61, 1022-1024 (1992).
    [CrossRef]
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    [CrossRef]
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    [PubMed]
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    [CrossRef]
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    [CrossRef]
  15. C. Zuffada, T. Cwik, and C. Ditchman, "Synthesis of novel all-dielectric grating filters using genetic algorithms," presented at Antennas and Propagation Society International Symposium 1997, Montreal, Canada, 1997.
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  27. J. A. Sethian, "Curvature and the Evolution of Fronts," Commun. Math. Phys. 54, 425-499 (1985).
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    [CrossRef]
  29. J. A. Sethian, "An Analysis of Flame Propagation," Ph.D. dissertation, Dept. Mathematics, University of California, Berkeley, CA, 1982.
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  31. R. C. Rumpf, "Design and optimization of nano-optical elements by coupling fabrication to optical behavior," Ph.D. dissertation, University of Central Florida, Orlando, FL, 2006.
  32. M. G. Moharam, E. B. Grann, and D. A. Pommet, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings," J. Opt. Soc. Am. A 12, 1068-1076 (1995).
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2004 (1)

2003 (1)

2002 (2)

2001 (2)

D. Lacour, P. Plumey, G. Granet, and A. M. Ravaud, "Resonant waveguide grating: Analysis of polarization independent filtering," Opt. Quantum Electron. 33, 451-470 (2001).
[CrossRef]

A. Mizutani, H. Kikuta, K. Nakajima, and K. Iwata, "Nonpolarizing guided-mode resonant grating filter for oblique incidence," J. Opt. Soc. Am. A 18, 1261-1266 (2001).
[CrossRef]

2000 (1)

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, T. R. Holzheimer, "Dielectric Frequency-Selective Structures Incorporating Waveguide Gratings," IEEE Trans. Microwave Theory Tech. 48, 553-561 (2000).
[CrossRef]

1999 (1)

S. Kawakami, T. Kawashima, and T. Sato, "Mechanism of shape formation of three-dimensional periodic nanostructures by bias sputtering," Appl. Phys. Lett. 74, 463-465 (1999).
[CrossRef]

1998 (1)

J. A. Cox, R. A. Morgan, R. Wilke, and C. Ford, "Guided-mode grating resonant filter for VCSEL applications," Proc. SPIE 3291, 70-76 (1998).
[CrossRef]

1996 (2)

1995 (2)

1993 (2)

J. E. Roman and K. A. Winick, "Waveguide Grating Filters for Dispersion Compensation and Pulse Compression," IEEE J. Quantum Electron. 29, 975-982 (1993).
[CrossRef]

S. S. Wang and R. Magnusson, "Theory and applications of guided-mode resonance filters," Appl. Opt. 32, 2606-2613 (1993).
[CrossRef] [PubMed]

1992 (2)

R. Magnusson and S. S. Wang, "New principle for optical filters," Appl. Phys. Lett. 61, 1022-1024 (1992).
[CrossRef]

S. Tazawa, S. Matsuo, and K. Saito, "A General Characterization and Simulation Method for Deposition and Etching Technology," IEEE Trans. Semicond. Manuf. 5, 27-33 (1992).
[CrossRef]

1990 (2)

M. T. Gale, K. Knop, and R. Morf, "Zero-order diffractive microstructures for security applications," Proc.SPIE  1210, 83-89 (1990).

S. S. Wang, R. Magnusson, J. S. Bagby, and M. G. Moharam, "Guided-mode resonances in planar dielectric-layer diffraction gratings," J. Opt. Soc. Am. A 7, 1470-1474 (1990).
[CrossRef]

1985 (2)

L. Mashev and E. Popov, "Zero order anomaly of dielectric coated gratings," Opt. Commun. 55, 377-380 (1985).
[CrossRef]

J. A. Sethian, "Curvature and the Evolution of Fronts," Commun. Math. Phys. 54, 425-499 (1985).

1907 (1)

Lord Rayleigh, Phil. Mag. 14, 60 (1907).

1902 (1)

R. W. Wood, Proc. Roy. Soc. (London) 18, 396 (1902).

Bagby, J. S.

Cox, J. A.

J. A. Cox, R. A. Morgan, R. Wilke, and C. Ford, "Guided-mode grating resonant filter for VCSEL applications," Proc. SPIE 3291, 70-76 (1998).
[CrossRef]

Ding, Y.

Fehrembach, A.

Ford, C.

J. A. Cox, R. A. Morgan, R. Wilke, and C. Ford, "Guided-mode grating resonant filter for VCSEL applications," Proc. SPIE 3291, 70-76 (1998).
[CrossRef]

Gale, M. T.

M. T. Gale, K. Knop, and R. Morf, "Zero-order diffractive microstructures for security applications," Proc.SPIE  1210, 83-89 (1990).

Gaylord, T. K.

Granet, G.

D. Lacour, P. Plumey, G. Granet, and A. M. Ravaud, "Resonant waveguide grating: Analysis of polarization independent filtering," Opt. Quantum Electron. 33, 451-470 (2001).
[CrossRef]

Grann, E. B.

Holzheimer, T. R.

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, T. R. Holzheimer, "Dielectric Frequency-Selective Structures Incorporating Waveguide Gratings," IEEE Trans. Microwave Theory Tech. 48, 553-561 (2000).
[CrossRef]

Iwata, K.

Kawakami, S.

S. Kawakami, T. Kawashima, and T. Sato, "Mechanism of shape formation of three-dimensional periodic nanostructures by bias sputtering," Appl. Phys. Lett. 74, 463-465 (1999).
[CrossRef]

Kawashima, T.

S. Kawakami, T. Kawashima, and T. Sato, "Mechanism of shape formation of three-dimensional periodic nanostructures by bias sputtering," Appl. Phys. Lett. 74, 463-465 (1999).
[CrossRef]

Kikuta, H.

Knop, K.

M. T. Gale, K. Knop, and R. Morf, "Zero-order diffractive microstructures for security applications," Proc.SPIE  1210, 83-89 (1990).

Lacour, D.

D. Lacour, P. Plumey, G. Granet, and A. M. Ravaud, "Resonant waveguide grating: Analysis of polarization independent filtering," Opt. Quantum Electron. 33, 451-470 (2001).
[CrossRef]

Magnusson, R.

Maldonado, T. A.

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, T. R. Holzheimer, "Dielectric Frequency-Selective Structures Incorporating Waveguide Gratings," IEEE Trans. Microwave Theory Tech. 48, 553-561 (2000).
[CrossRef]

Mashev, L.

L. Mashev and E. Popov, "Zero order anomaly of dielectric coated gratings," Opt. Commun. 55, 377-380 (1985).
[CrossRef]

Matsuo, S.

S. Tazawa, S. Matsuo, and K. Saito, "A General Characterization and Simulation Method for Deposition and Etching Technology," IEEE Trans. Semicond. Manuf. 5, 27-33 (1992).
[CrossRef]

Maystre, D.

Mizutani, A.

Moharam, M. G.

Morf, R.

M. T. Gale, K. Knop, and R. Morf, "Zero-order diffractive microstructures for security applications," Proc.SPIE  1210, 83-89 (1990).

Morgan, R. A.

J. A. Cox, R. A. Morgan, R. Wilke, and C. Ford, "Guided-mode grating resonant filter for VCSEL applications," Proc. SPIE 3291, 70-76 (1998).
[CrossRef]

Morris, G. M.

Nakajima, K.

Peng, S.

Peng, S. T.

Plumey, P.

D. Lacour, P. Plumey, G. Granet, and A. M. Ravaud, "Resonant waveguide grating: Analysis of polarization independent filtering," Opt. Quantum Electron. 33, 451-470 (2001).
[CrossRef]

Pommet, D. A.

Popov, E.

L. Mashev and E. Popov, "Zero order anomaly of dielectric coated gratings," Opt. Commun. 55, 377-380 (1985).
[CrossRef]

Ravaud, A. M.

D. Lacour, P. Plumey, G. Granet, and A. M. Ravaud, "Resonant waveguide grating: Analysis of polarization independent filtering," Opt. Quantum Electron. 33, 451-470 (2001).
[CrossRef]

Roman, J. E.

J. E. Roman and K. A. Winick, "Waveguide Grating Filters for Dispersion Compensation and Pulse Compression," IEEE J. Quantum Electron. 29, 975-982 (1993).
[CrossRef]

Saito, K.

S. Tazawa, S. Matsuo, and K. Saito, "A General Characterization and Simulation Method for Deposition and Etching Technology," IEEE Trans. Semicond. Manuf. 5, 27-33 (1992).
[CrossRef]

Sato, T.

S. Kawakami, T. Kawashima, and T. Sato, "Mechanism of shape formation of three-dimensional periodic nanostructures by bias sputtering," Appl. Phys. Lett. 74, 463-465 (1999).
[CrossRef]

Sentenac, A.

Sethian, J. A.

J. A. Sethian, "Curvature and the Evolution of Fronts," Commun. Math. Phys. 54, 425-499 (1985).

Tazawa, S.

S. Tazawa, S. Matsuo, and K. Saito, "A General Characterization and Simulation Method for Deposition and Etching Technology," IEEE Trans. Semicond. Manuf. 5, 27-33 (1992).
[CrossRef]

Tibuleac, S.

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, T. R. Holzheimer, "Dielectric Frequency-Selective Structures Incorporating Waveguide Gratings," IEEE Trans. Microwave Theory Tech. 48, 553-561 (2000).
[CrossRef]

Turunen, J.

Vahimaa, P.

Vallius, T.

Wang, S. S.

Wilke, R.

J. A. Cox, R. A. Morgan, R. Wilke, and C. Ford, "Guided-mode grating resonant filter for VCSEL applications," Proc. SPIE 3291, 70-76 (1998).
[CrossRef]

Winick, K. A.

J. E. Roman and K. A. Winick, "Waveguide Grating Filters for Dispersion Compensation and Pulse Compression," IEEE J. Quantum Electron. 29, 975-982 (1993).
[CrossRef]

Wood, R. W.

R. W. Wood, Proc. Roy. Soc. (London) 18, 396 (1902).

Young, P. P.

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, T. R. Holzheimer, "Dielectric Frequency-Selective Structures Incorporating Waveguide Gratings," IEEE Trans. Microwave Theory Tech. 48, 553-561 (2000).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

S. Kawakami, T. Kawashima, and T. Sato, "Mechanism of shape formation of three-dimensional periodic nanostructures by bias sputtering," Appl. Phys. Lett. 74, 463-465 (1999).
[CrossRef]

R. Magnusson and S. S. Wang, "New principle for optical filters," Appl. Phys. Lett. 61, 1022-1024 (1992).
[CrossRef]

Commun. Math. Phys. (1)

J. A. Sethian, "Curvature and the Evolution of Fronts," Commun. Math. Phys. 54, 425-499 (1985).

IEEE J. Quantum Electron. (1)

J. E. Roman and K. A. Winick, "Waveguide Grating Filters for Dispersion Compensation and Pulse Compression," IEEE J. Quantum Electron. 29, 975-982 (1993).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, T. R. Holzheimer, "Dielectric Frequency-Selective Structures Incorporating Waveguide Gratings," IEEE Trans. Microwave Theory Tech. 48, 553-561 (2000).
[CrossRef]

IEEE Trans. Semicond. Manuf. (1)

S. Tazawa, S. Matsuo, and K. Saito, "A General Characterization and Simulation Method for Deposition and Etching Technology," IEEE Trans. Semicond. Manuf. 5, 27-33 (1992).
[CrossRef]

J. Opt. Soc. Am. A (7)

Opt. Commun. (1)

L. Mashev and E. Popov, "Zero order anomaly of dielectric coated gratings," Opt. Commun. 55, 377-380 (1985).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

D. Lacour, P. Plumey, G. Granet, and A. M. Ravaud, "Resonant waveguide grating: Analysis of polarization independent filtering," Opt. Quantum Electron. 33, 451-470 (2001).
[CrossRef]

Phil. Mag. (1)

Lord Rayleigh, Phil. Mag. 14, 60 (1907).

Proc. Roy. Soc. (London) (1)

R. W. Wood, Proc. Roy. Soc. (London) 18, 396 (1902).

Proc. SPIE (1)

J. A. Cox, R. A. Morgan, R. Wilke, and C. Ford, "Guided-mode grating resonant filter for VCSEL applications," Proc. SPIE 3291, 70-76 (1998).
[CrossRef]

SPIE (1)

M. T. Gale, K. Knop, and R. Morf, "Zero-order diffractive microstructures for security applications," Proc.SPIE  1210, 83-89 (1990).

Other (10)

S. M. Norton, "Resonant grating structures: theory, design, and applications," PhD dissertation, Rochester, New York, University of Rochester, 1997.

A. Hessel and A. Oliner, "Wood’s anomalies and leaky waves," presented at 1962 Symposium on Electromagnetic Theory and Antennas, Copenhagan, Denmark, 1962.

G. Niederer, M. Salt, H. P. Herzig, T. Overstolz, W. Noell, and N. F. Rooij, "Resonant grating filter for a MEMS based add-drop device at oblique incidence," IEEE/LEOS International Conference on Optical MEMS, 99-100 (2002).
[CrossRef]

H. P. Herzig, Micro-optics: Elements, systems and applications, (Taylor & Francis, Philadelphia, PA, 1998).

R. E. Collin, Field Theory of Guided Waves, Second ed., (IEE Press, New York, NY, 1991).

K. Okamoto, Fundamentals of Optical Waveguides, (Academic Press, New York, NY, 2000).

J. A. Sethian, "An Analysis of Flame Propagation," Ph.D. dissertation, Dept. Mathematics, University of California, Berkeley, CA, 1982.

J. A. Sethian, Level Set Methods and Fast Marching Methods: Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science (Cambridge University Press, New York, NY, 1999).

R. C. Rumpf, "Design and optimization of nano-optical elements by coupling fabrication to optical behavior," Ph.D. dissertation, University of Central Florida, Orlando, FL, 2006.

C. Zuffada, T. Cwik, and C. Ditchman, "Synthesis of novel all-dielectric grating filters using genetic algorithms," presented at Antennas and Propagation Society International Symposium 1997, Montreal, Canada, 1997.

Supplementary Material (2)

» Media 1: AVI (539 KB)     
» Media 2: AVI (524 KB)     

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Figures (11)

Fig. 1.
Fig. 1.

Regions of resonance for a guided-mode resonance filter.

Fig. 3.
Fig. 3.

Block diagram of string method.

Fig. 4.
Fig. 4.

Three main mechanisms for modeling sputter deposition and etching.

Fig. 5.
Fig. 5.

Concept and geometry of rigorous coupled-wave analysis.

Fig. 6.
Fig. 6.

GMR tuning concept.

Fig. 7.
Fig. 7.

Reflectance of “perfect” GMR filter.

Fig. 8.
Fig. 8.

Tuning response of “perfect” GMR filter.

Fig. 9.
Fig. 9.

Tune by deposition process: An initial grating is formed onto a substrate. As material is deposited onto the grating surface, thickness of the GMR core increases pushing resonance to a longer wavelength.

Fig. 10.
Fig. 10.

(545 kb) Movie showing how reflection spectrum evolves during additive tuning process. [Media 1]

Fig. 11.
Fig. 11.

Tune by etching process: An initial core layer is deposited onto a bare substrate. A grating is formed into the core using a transfer etch process and mask is removed. Subsequent etching reduces thickness of the GMR core pushing resonance to a shorter wavelength.

Fig. 12.
Fig. 12.

(389 kb) Movie showing how reflection spectrum evolves during subtractive tuning process. [Media 2]

Equations (16)

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

n g sin θ m = n 1 sin θ inc m λ 0 Λ
max [ n 1 , n 2 ] β m k 0 n g
β m k 0 = n g sin θ m
max [ n 1 , n 2 ] n 1 sin θ inc m λ 0 Λ n g
X = [ x 1 x 2 x N ]
R = [ r 1 r 2 r N ]
X ( t + Δ t ) = X ( t ) + Δ t · R ( t )
r dep ( x i ) = d 90° + 90° V T x i ϕ cos n ( ϕ ) cos ( ϕ θ ) 90° + 90° cos n + 1 ( ϕ )
r etch ( x i ) = b cos θ + c sin 2 θ cos θ
r redep ( x i ) = e 2 90° + 90° V S x i ϕ cos ( ϕ θ )
r ( x i ) = [ r dep ( x i ) + r etch ( x i ) + r redep ( x i ) ] n ̂ ( x i )
E i ( z ) = Σ m Σ n S i m , n exp [ j ( k x m , n x + k y m , n y ) ]
ε i x y = Σ m Σ n a i m , n exp [ j ( G x m , n x + G y m , n y ) ]
a i m , n = 1 A A ε i x y exp [ j ( G x m , n x + G y m , n y ) ] dA
k m , n = k inc G m , n
G m , n = m K 1 + n K 2

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