Abstract

In this paper, we show that bandstop and bandpass filters with versatile spectral attributes can be implemented with modulated films possessing asymmetric grating profiles. The profile asymmetry breaks the resonant leaky mode degeneracy at normal incidence thereby permitting precise spectral spacing of interacting leaky modes with interesting implications in optical filter design. Several example filters, containing only a single grating layer, are designed with this methodology to demonstrate the concept.

© 2004 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. Z. S. Liu and R. Magnusson, �??Concept of multiorder multimode resonant optical filters,�?? IEEE Photonics Tech. Lett. 14, 1091-1093 (2002).
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Appl. Opt.

Appl. Phys.

P. Vincent and M. Neviere, �??Corrugated dielectric waveguides: A numerical study of the second-order stop bands,�?? Appl. Phys. 20, 345-351 (1979).
[CrossRef]

IEEE J. Quantum Electron.

R. F. Kazarinov and C. H. Henry, �??Second-order distributed feedback lasers with mode selection provided by first-order radiation loss,�?? IEEE J. Quantum Electron QE-21, 144-150 (1985).
[CrossRef]

D. Rosenblatt, A. Sharon, and A. A. Friesem, �??Resonant grating waveguide structures,�?? IEEE J. Quantum Electron. 33, 2038-2059 (1997).
[CrossRef]

IEEE Photonics Tech. Lett.

Z. S. Liu and R. Magnusson, �??Concept of multiorder multimode resonant optical filters,�?? IEEE Photonics Tech. Lett. 14, 1091-1093 (2002).
[CrossRef]

IEEE Trans. Microwave Theory and Tech.

S. T. Peng, T. Tamir, and H. L. Bertoni, �??Theory of periodic dielectric waveguides,�?? IEEE Trans. Microwave Theory and Tech. MTT-23, 123-133 (1975).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Proc. IEEE

T. K. Gaylord and M. G. Moharam, �??Analysis and applications of optical diffraction by gratings,�?? Proc. IEEE 73, 894-937 (1985).
[CrossRef]

Proc. SPIE

R. Magnusson, Y. Ding, K. J. Lee, D. Shin, P. S. Priambodo, P. P. Young, and T. A. Maldonado, �??Photonic devices enabled by waveguide-mode resonance effects in periodically modulated films,�?? Proc. SPIE 5225, 20-34 (2003).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Brillouin diagram showing second stopband detail for a single-layer waveguide grating. Both gratings have cover index nc=1, substrate index ns=1.48, average grating index navg=2, high grating index nh=2.05, period Λ=0.3μm, thickness d=0.14μm. (a) Grating with symmetric profile (Type I) and fill factor F=0.33; (b) Grating with asymmetric profile (Type II). F1=0.2, F2=0.13, and M=0.5. In the figure, k0=2π/λ where λ is the wavelength in free space, K=2π/Λ, and βR is the real part of the propagation constant of the leaky mode. Note that these dispersion curves are associated with the TE0 mode and have been transferred to the first Brillouin zone. The dashed curves show the resonance spectrum at normal incidence (not to scale).

Fig. 2.
Fig. 2.

Estimated resonance locations based on the eigenfunction of the equivalent homogeneous waveguide. Material parameters are indicated on the figure.

Fig. 3.
Fig. 3.

Spectra of a narrowband reflection filter. The parameters are: F1=0.397, F2=0.051, M=0.5, d=0.67μm, Λ=1μm, nc=1, nh=3.48, ns=1.48, and navg=2.445. ηR is the reflectance, ηT is the transmittance.

Fig. 4
Fig. 4

Field profiles of the excitation wave S0 and leaky modes S±1 pertaining to the resonant filter in Example 1.

Fig. 5.
Fig. 5.

Spectra of a wideband reflection structure. The parameters are: F1=0.35, F2=0.1, M=0.52, d=0.45μ, Λ=1μ, nc=1, nh=3.48, ns=1.48, and navg=2.45.

Fig. 6.
Fig. 6.

Spectra of a transmission structure. The parameters are: F1=0.5, F2=0.05, M=0.55, d=0.39μm, Λ=1μm, nc=1, nh=3.48, ns=1.48, and navg=2.667.

Equations (1)

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n l = n avg 2 F n h 2 ( 1 F )

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