Abstract

Resonant grating reflection filters operating at normal incidence are investigated. At normal incidence these structures are shown to have characteristics different from those of structures operated at oblique incidence. We show how higher-order diffraction within the structure laterally confines the incident energy about the point of incidence and results in a broadened angular selectivity. Multimode structures are shown to exhibit broader angular selectivities and narrower spectral linewidths than those of single-mode structures, achieving angular selectivities hundreds of times broader than what could be obtained at oblique incidence. When compared with that for oblique incidence, the increase in angular selectivity is shown to greatly improve the performance of these filters for spectrally filtering finite incident beams.

© 2001 Optical Society of America

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  1. R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
    [CrossRef]
  2. S. S. Wang, R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19, 919–921 (1994).
    [CrossRef] [PubMed]
  3. S. S. Wang, R. Magnusson, “Multilayer waveguide-grating filters,” Appl. Opt. 34, 2414–2420 (1995).
    [CrossRef] [PubMed]
  4. R. W. Day, S. S. Wang, R. Magnusson, “Filter-response line shapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815–1824 (1996).
    [CrossRef]
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    [CrossRef]
  6. D. K. Jacob, S. C. Dunn, M. G. Moharam, “Design considerations for narrow-band dielectric resonant grating reflection filters of finite length,” J. Opt. Soc. Am. A 17, 1241–1249 (2000).
    [CrossRef]
  7. L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
    [CrossRef]
  8. A. Sharon, D. Rosenblatt, A. A. Friesem, “Resonant grating-waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A 14, 2985–2993 (1997).
    [CrossRef]
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    [CrossRef]
  10. I. D. Avrutskii, G. A. Golubenko, V. A. Sychugov, A. V. Tischenko, “Light reflection from the surface of a corrugated waveguide,” Sov. Tech. Phys. Lett. 11, 401–402 (1985).
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    [CrossRef]
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    [CrossRef]
  13. D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, J. M. Bendickson, “Effects of modulation strength in guided-mode resonant subwavelength gratings at normal incidence,” J. Opt. Soc. Am. A 17, 1221–1230 (2000).
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  14. F. Lemarchand, A. Sentenac, H. Giovannini, “Increasing the angular tolerance of resonant grating filters with doubly periodic structures,” Opt. Lett. 23, 1149–1151 (1998).
    [CrossRef]
  15. D. K. Jacob, “Dielectric resonant grating structures for narrow-band filtering applications,” Ph.D. dissertation (University of Central Florida, Orlando, Fla., 2001).
  16. M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
    [CrossRef]

2000 (2)

1998 (3)

1997 (3)

1996 (1)

R. W. Day, S. S. Wang, R. Magnusson, “Filter-response line shapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815–1824 (1996).
[CrossRef]

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 (2)

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

I. D. Avrutskii, G. A. Golubenko, V. A. Sychugov, A. V. Tischenko, “Light reflection from the surface of a corrugated waveguide,” Sov. Tech. Phys. Lett. 11, 401–402 (1985).

Avrutskii, I. D.

I. D. Avrutskii, G. A. Golubenko, V. A. Sychugov, A. V. Tischenko, “Light reflection from the surface of a corrugated waveguide,” Sov. Tech. Phys. Lett. 11, 401–402 (1985).

Bendickson, J. M.

Brundrett, D. L.

Day, R. W.

R. W. Day, S. S. Wang, R. Magnusson, “Filter-response line shapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815–1824 (1996).
[CrossRef]

Dunn, S. C.

Erdogan, T.

Friesem, A. A.

A. Sharon, D. Rosenblatt, A. A. Friesem, “Resonant grating-waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A 14, 2985–2993 (1997).
[CrossRef]

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

Gaylord, T. K.

Giovannini, H.

Glytsis, E. N.

Golubenko, G. A.

I. D. Avrutskii, G. A. Golubenko, V. A. Sychugov, A. V. Tischenko, “Light reflection from the surface of a corrugated waveguide,” Sov. Tech. Phys. Lett. 11, 401–402 (1985).

Grann, E. B.

Jacob, D. K.

D. K. Jacob, S. C. Dunn, M. G. Moharam, “Design considerations for narrow-band dielectric resonant grating reflection filters of finite length,” J. Opt. Soc. Am. A 17, 1241–1249 (2000).
[CrossRef]

D. K. Jacob, “Dielectric resonant grating structures for narrow-band filtering applications,” Ph.D. dissertation (University of Central Florida, Orlando, Fla., 2001).

Lemarchand, F.

Magnusson, R.

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.

Norton, S. M.

Pommet, D. A.

Popov, E.

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

Rosenblatt, D.

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

A. Sharon, D. Rosenblatt, A. A. Friesem, “Resonant grating-waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A 14, 2985–2993 (1997).
[CrossRef]

Sentenac, A.

Sharon, A.

A. Sharon, D. Rosenblatt, A. A. Friesem, “Resonant grating-waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A 14, 2985–2993 (1997).
[CrossRef]

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

Sychugov, V. A.

I. D. Avrutskii, G. A. Golubenko, V. A. Sychugov, A. V. Tischenko, “Light reflection from the surface of a corrugated waveguide,” Sov. Tech. Phys. Lett. 11, 401–402 (1985).

Tibuleac, S.

Tischenko, A. V.

I. D. Avrutskii, G. A. Golubenko, V. A. Sychugov, A. V. Tischenko, “Light reflection from the surface of a corrugated waveguide,” Sov. Tech. Phys. Lett. 11, 401–402 (1985).

Wang, S. S.

R. W. Day, S. S. Wang, R. Magnusson, “Filter-response line shapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815–1824 (1996).
[CrossRef]

S. S. Wang, R. Magnusson, “Multilayer waveguide-grating filters,” Appl. Opt. 34, 2414–2420 (1995).
[CrossRef] [PubMed]

S. S. Wang, R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19, 919–921 (1994).
[CrossRef] [PubMed]

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

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]

IEEE J. Quantum Electron. (1)

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038–2059 (1997).
[CrossRef]

J. Lightwave Technol. (1)

R. W. Day, S. S. Wang, R. Magnusson, “Filter-response line shapes of resonant waveguide gratings,” J. Lightwave Technol. 14, 1815–1824 (1996).
[CrossRef]

J. Opt. Soc. Am. A (6)

Opt. Commun. (1)

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

Opt. Lett. (3)

Sov. Tech. Phys. Lett. (1)

I. D. Avrutskii, G. A. Golubenko, V. A. Sychugov, A. V. Tischenko, “Light reflection from the surface of a corrugated waveguide,” Sov. Tech. Phys. Lett. 11, 401–402 (1985).

Other (1)

D. K. Jacob, “Dielectric resonant grating structures for narrow-band filtering applications,” Ph.D. dissertation (University of Central Florida, Orlando, Fla., 2001).

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Figures (15)

Fig. 1
Fig. 1

Resonant grating reflection filter geometry.

Fig. 2
Fig. 2

Comparison of spectral and angular line shapes obtained by using the interference-waveguide approach with results obtained by using RCWA for obliquely incident resonant grating reflection filters with grating thicknesses dg/λ=0.10 and 1.00.

Fig. 3
Fig. 3

Scattering geometry at normal incidence for spectral and angular dephasing.

Fig. 4
Fig. 4

Angular selectivity for backward-diffracted component strengths of ηB=0.001, 0.10, 0.50, 0.90, and 0.98 for ηd=0.01.

Fig. 5
Fig. 5

Effective grating strength and strength of second-order coefficient versus normalized grating thickness for f=0.7.

Fig. 6
Fig. 6

Comparison of spectral line shapes obtained by using the interference-waveguide approach with results obtained by using RCWA for normally incident resonant grating reflection filters with grating thicknesses dg/λ=0.05, 0.10, 0.20, and 0.25.

Fig. 7
Fig. 7

Same as Fig. 6, but for angular line shapes.

Fig. 8
Fig. 8

Comparison of spectral line shapes obtained by using the interference-waveguide approach with results obtained by using RCWA for normally incident resonant grating reflection filters with grating thicknesses dg/λ=0.70, 0.80, 0.90 and 1.00.

Fig. 9
Fig. 9

Same as Fig. 8, but for angular line shapes.

Fig. 10
Fig. 10

Type 1 and type 2 spectral and angular responses of a resonant grating reflection filter with the following parameters: nc=ns=nL=2.0, nf=nH=2.5, nAR=nfns, dAR=λ/4nAR, dg/λ=0.54, Λ/λ=0.4619, f=0.7, df/λ=0.2733 (type 1), and df/λ=5.0733 (type 2). The diffraction coefficients are ηd=2.04% and ηB=89.50%.

Fig. 11
Fig. 11

Type 1 and type 2 spectral and angular responses of a resonant grating reflection filter with the following parameters: nc=ns=nL=2.0, nf=2.5, nH=3.0, nAR=nfns, dAR=λ/4nAR, dg/λ=0.56, Λ/λ=0.4619, f=0.5, df/λ=0.0737 (type 1), and df/λ=3.6737 (type 2). The diffraction coefficients are ηd=0.58% and ηB=95.32%.

Fig. 12
Fig. 12

Reflected Gaussian beam profile for a resonant grating reflection filter operating at oblique incidence.

Fig. 13
Fig. 13

Normalized reflected power as a function of R.

Fig. 14
Fig. 14

Reflected Gaussian beam profile for a resonant grating reflection filter operating at normal incidence with an angular selectivity ten times greater than that at oblique incidence.

Fig. 15
Fig. 15

Normalized reflected power versus R for a normally incident filter with angular selectivities 10, 25, 50, 75, and 100 times broader than that of an obliquely incident filter.

Tables (3)

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Table 1 Single-Mode Resonant Grating Structure

Tables Icon

Table 2 Multimode Resonant Grating Structure

Tables Icon

Table 3 Narrow-Band Resonant Grating Reflection Filters with Broadened Angular Selectivities

Equations (16)

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ER(ϕ)=ηdexp(iϕ)1-(1-ηd)exp(iϕ),
β0=k0ncsin θinc±2πΛ.
ΔϕFWHM2ηd1-ηd
ΔϕΔλdϕdλλ=λ0Δθdϕdθθ=θ0Δβdϕdββ=β0,
λdϕdλλ=λ0λΛ k0dϕdβ+2dfkf2-β2β=β0,
dϕdθθ=θ0=(k0nccos θ)dϕdββ=β0.
ΔθΔλ/λλΛ1cos θinc.
λdϕdλλ=λ0λΛ k0dϕdβ+2dfkf2-β2+2dgkg2-β2β=β0.
ER(Δϕ)=ηdexp(iΔϕ)1-(1-ηd)exp(iΔϕ),
ER(Δϕ)=-ηd(1-cos Δϕ-ηd)+2ηdηBexp(iφ)ηd2+2(1-ηd)(1-cos Δϕ)-2ηβ(1-cos Δϕ-ηd)exp(iφ).
Einc(kx)=-Einc(x)exp(-ikxx)dx,
 Eref(x)=12π-Einc(kx)ER(kx)exp(ikxx)dkx,
Einc(x)=exp-cos2 θincw2 x2-ik0ncsin θinc x,
Einc(kx)=2πwkexp-kx-k0ncsin θincwk2,
R=Δkx,inc/Δkx,filter,
R=ΔθincΔλ/λΛλcos θinc.

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