Abstract

A new type of guided-mode resonant grating filter is described. The filter is independent of polarization state for oblique incidence. The filter has a crossed grating structure, and the plane of incidence on the filter contains the symmetric axis of the grating structure. Theoretical considerations and numerical calculations using two-dimensional rigorous coupled-wave analysis show that a rhombic lattice structure is suitable to such filters. In this configuration an incident light wave is diffracted into the waveguide and is divided into two propagation modes whose directions are symmetric with respect to the plane of incidence. In particular, when the propagation directions of the two modes are perpendicular to each other, the fill factor of grating structure can be ∼50%. The filter was designed for an incident angle of 45°. Tolerances of setting errors and fabrication errors for this filter were estimated by numerical calculations.

© 2001 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  6. D. Shin, S. Tibuleac, T. A. Maldonado, R. Magnusson, “Thin-film multilayer optical filters containing diffractive elements and waveguides,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 273–286 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1998 (2)

1996 (2)

1995 (2)

1994 (1)

1992 (1)

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[CrossRef]

1985 (1)

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

Gaylord, T. K.

Grann, E. B.

Liu, Z. S.

Magnusson, R.

Maldonado, T. A.

D. Shin, S. Tibuleac, T. A. Maldonado, R. Magnusson, “Thin-film multilayer optical filters containing diffractive elements and waveguides,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 273–286 (1997).
[CrossRef]

Mashev, L.

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

Moharam, M. G.

Morris, G. M.

Peng, S.

Pommet, D. A.

Popov, E.

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

Shin, D.

R. Magnusson, D. Shin, Z. S. Liu, “Guided-mode resonance Brewster filter,” Opt. Lett. 23, 612–614 (1998).
[CrossRef]

Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, R. Magnusson, “High-efficiency guided-mode resonance filter,” Opt. Lett. 23, 1556–1558 (1998).
[CrossRef]

D. Shin, S. Tibuleac, T. A. Maldonado, R. Magnusson, “Thin-film multilayer optical filters containing diffractive elements and waveguides,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 273–286 (1997).
[CrossRef]

Tibuleac, S.

Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, R. Magnusson, “High-efficiency guided-mode resonance filter,” Opt. Lett. 23, 1556–1558 (1998).
[CrossRef]

D. Shin, S. Tibuleac, T. A. Maldonado, R. Magnusson, “Thin-film multilayer optical filters containing diffractive elements and waveguides,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 273–286 (1997).
[CrossRef]

Wang, S. S.

Young, P. P.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
[CrossRef]

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

Opt. Commun. (1)

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

Opt. Lett. (4)

Other (1)

D. Shin, S. Tibuleac, T. A. Maldonado, R. Magnusson, “Thin-film multilayer optical filters containing diffractive elements and waveguides,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 273–286 (1997).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Geometry of a crossed grating and the plane of incidence. The x axis makes an angle α with the y axis. The z axis is perpendicular to the xy plane.

Fig. 2
Fig. 2

Vector sum of a grating vector K and a tangential component kxy of the wave vector of the incident light. The resonance occurs when the vector sum agrees with the propagation vector in the waveguide layer.

Fig. 3
Fig. 3

Type A nonpolarizing resonant grating filter. The grating structure is rectangular. The plane of incidence is parallel to the x axis. The magnitude of grating vector Kx is 2π/Λx. Diffracted waves in both p and s polarization propagate in the waveguide layer in the x direction.

Fig. 4
Fig. 4

Type B nonpolarizing resonant grating filter. The grating structure is rectangular. The plane of incidence is parallel to x axis. In the waveguide two diffracted waves are generated for the p polarization incidence.

Fig. 5
Fig. 5

Type C nonpolarizing resonant grating filter. The grating structure is rectangular. The grating consists of a rectangular square array; that is, the period and the fill factor in the x direction are the same as those in the y direction. The azimuth angle is 45°. Diffracted waves in both p and s polarization propagate in the waveguide as TE waves in two directions symmetric with respect to the plane of incidence.

Fig. 6
Fig. 6

Our designed nonpolarizing guided-mode resonant grating filter for an incident angle of 10°. (a) Dimensions of the grating structure, (b) calculated spectral reflectance.

Fig. 7
Fig. 7

Type D nonpolarizing resonant grating filter. The grating structure is nonrectangular. The plane of incidence bisects the angle made by the x and y axes. The grating is symmetric with respect to the plane of incidence. The propagation vectors β are perpendicular to each other.

Fig. 8
Fig. 8

Our nonpolarizing guided-mode resonant grating filter designed for an incident angle of 45°. (a) Dimensions of the grating structure, (b) calculated spectral reflectance.

Fig. 9
Fig. 9

Resonant wavelength as a function of angle of incidence.

Fig. 10
Fig. 10

Spectral reflectance of the designed filter when the azimuth angle is 44°.

Fig. 11
Fig. 11

Effects of the error of the grating thickness on resonant wavelengths. (a) Resonant wavelengths of p and s polarization, (b) the difference between them. The horizontal axes indicate grating thickness normalized to the designed thickness 121 nm.

Fig. 12
Fig. 12

Effects of the error of the area fill factor on resonant wavelengths. (a) Resonant wavelengths in p and s polarization, (b) the difference between them. The horizontal axes indicate the area fill factor normalized to the designed value 0.42.

Fig. 13
Fig. 13

Effects of the error of the refractive index of the waveguide on resonant wavelengths. (a) Resonant wavelengths of p and s polarization, (b) the difference between them. The horizontal axes indicate the refractive index normalized to 2.10.

Fig. 14
Fig. 14

Effects of the error of the thickness of the waveguide on resonant wavelengths. (a) Resonant wavelengths of p and s polarization, (b) the difference between them. The horizontal axes indicate thickness normalized to the designed thickness of 160 nm.

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