Abstract

Applying numerical modeling coupled with experiments, we investigate the properties of wideband resonant reflectors under fully conical light incidence. We show that the wave vectors pertinent to resonant first-order diffraction under fully conical mounting vary less with incident angle than those associated with reflectors in classical mounting. Therefore, as the evanescent diffracted waves drive the leaky modes responsible for the resonance effects, fully-conical mounting imbues reflectors with larger angular tolerance than their classical counterparts. We quantify the angular-spectral performance of representative resonant wideband reflectors in conic and classic mounts by numerical calculations with improved spectra found for fully conic incidence. Moreover, these predictions are verified experimentally for wideband reflectors fashioned in crystalline and amorphous silicon in distinct spectral regions spanning the 1200-1600-nm and 1600-2400-nm spectral bands. These results will be useful in various applications demanding wideband reflectors that are efficient and materially sparse.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
  6. D. Lacour, G. Granet, J.-P. Plumey, and A. Mure-Ravaud, “Polarization independence of a one-dimensional grating in conical mounting,” J. Opt. Soc. Am. A 20(8), 1546–1552 (2003).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  15. M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008).
    [Crossref]
  16. W. W. Ng, C.-S. Hong, and A. Yariv, “Holographic Interference Lithography for Integrated Optics,” IEEE Trans. Electron Dev. 25(10), 1193–1200 (1978).
    [Crossref]

2014 (1)

2013 (1)

D. W. Peters, R. R. Boye, and S. A. Kemme, “Angular sensitivity of guided mode resonant filters in classical and conical mounts,” Proc. SPIE 8633, 86330W (2013).
[Crossref]

2008 (2)

M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008).
[Crossref]

E. Grinvald, T. Katchalski, S. Soria, S. Levit, and A. A. Friesem, “Role of photonic bandgaps in polarization-independent grating waveguide structures,” J. Opt. Soc. Am. A 25(6), 1435–1443 (2008).
[Crossref] [PubMed]

2007 (1)

2005 (1)

2003 (2)

2002 (1)

2001 (2)

D. Lacour, J.-P. Plumey, G. Granet, and A. M. Ravaud, “Resonant waveguide grating: analysis of polarization independent filter,” Opt. Quantum Electron. 33(4), 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(6), 1261–1266 (2001).
[Crossref] [PubMed]

1996 (1)

1995 (1)

1978 (1)

W. W. Ng, C.-S. Hong, and A. Yariv, “Holographic Interference Lithography for Integrated Optics,” IEEE Trans. Electron Dev. 25(10), 1193–1200 (1978).
[Crossref]

Boye, R. R.

D. W. Peters, R. R. Boye, and S. A. Kemme, “Angular sensitivity of guided mode resonant filters in classical and conical mounts,” Proc. SPIE 8633, 86330W (2013).
[Crossref]

Eberhart, R.

R. Eberhart and J. Kennedy, “Particle swarm optimization,” in Proc. IEEE Conference on Neural Networks (IEEE, 1995), pp. 1942–1948.

Fehrembach, A. L.

Fehrembach, A.-L.

Friesem, A. A.

Gaylord, T. K.

Granet, G.

D. Lacour, G. Granet, J.-P. Plumey, and A. Mure-Ravaud, “Polarization independence of a one-dimensional grating in conical mounting,” J. Opt. Soc. Am. A 20(8), 1546–1552 (2003).
[Crossref] [PubMed]

D. Lacour, J.-P. Plumey, G. Granet, and A. M. Ravaud, “Resonant waveguide grating: analysis of polarization independent filter,” Opt. Quantum Electron. 33(4), 451–470 (2001).
[Crossref]

Grann, E. B.

Green, M. A.

M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008).
[Crossref]

Grinvald, E.

Herzig, H.

Hong, C.-S.

W. W. Ng, C.-S. Hong, and A. Yariv, “Holographic Interference Lithography for Integrated Optics,” IEEE Trans. Electron Dev. 25(10), 1193–1200 (1978).
[Crossref]

Iwata, K.

Katchalski, T.

Kemme, S. A.

D. W. Peters, R. R. Boye, and S. A. Kemme, “Angular sensitivity of guided mode resonant filters in classical and conical mounts,” Proc. SPIE 8633, 86330W (2013).
[Crossref]

Kennedy, J.

R. Eberhart and J. Kennedy, “Particle swarm optimization,” in Proc. IEEE Conference on Neural Networks (IEEE, 1995), pp. 1942–1948.

Kikuta, H.

Lacour, D.

D. Lacour, G. Granet, J.-P. Plumey, and A. Mure-Ravaud, “Polarization independence of a one-dimensional grating in conical mounting,” J. Opt. Soc. Am. A 20(8), 1546–1552 (2003).
[Crossref] [PubMed]

D. Lacour, J.-P. Plumey, G. Granet, and A. M. Ravaud, “Resonant waveguide grating: analysis of polarization independent filter,” Opt. Quantum Electron. 33(4), 451–470 (2001).
[Crossref]

Levit, S.

Magnusson, R.

Maystre, D.

Mizutani, A.

Moharam, M. G.

Morris, G. M.

Mure-Ravaud, A.

Nakagawa, W.

Nakajima, K.

Ng, W. W.

W. W. Ng, C.-S. Hong, and A. Yariv, “Holographic Interference Lithography for Integrated Optics,” IEEE Trans. Electron Dev. 25(10), 1193–1200 (1978).
[Crossref]

Niederer, G.

Peng, S.

Peters, D. W.

D. W. Peters, R. R. Boye, and S. A. Kemme, “Angular sensitivity of guided mode resonant filters in classical and conical mounts,” Proc. SPIE 8633, 86330W (2013).
[Crossref]

Plumey, J.-P.

D. Lacour, G. Granet, J.-P. Plumey, and A. Mure-Ravaud, “Polarization independence of a one-dimensional grating in conical mounting,” J. Opt. Soc. Am. A 20(8), 1546–1552 (2003).
[Crossref] [PubMed]

D. Lacour, J.-P. Plumey, G. Granet, and A. M. Ravaud, “Resonant waveguide grating: analysis of polarization independent filter,” Opt. Quantum Electron. 33(4), 451–470 (2001).
[Crossref]

Pommet, D. A.

Ravaud, A. M.

D. Lacour, J.-P. Plumey, G. Granet, and A. M. Ravaud, “Resonant waveguide grating: analysis of polarization independent filter,” Opt. Quantum Electron. 33(4), 451–470 (2001).
[Crossref]

Sentenac, A.

Shokooh-Saremi, M.

Soria, S.

Thiele, H.

Yariv, A.

W. W. Ng, C.-S. Hong, and A. Yariv, “Holographic Interference Lithography for Integrated Optics,” IEEE Trans. Electron Dev. 25(10), 1193–1200 (1978).
[Crossref]

IEEE Trans. Electron Dev. (1)

W. W. Ng, C.-S. Hong, and A. Yariv, “Holographic Interference Lithography for Integrated Optics,” IEEE Trans. Electron Dev. 25(10), 1193–1200 (1978).
[Crossref]

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

Opt. Express (1)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

D. Lacour, J.-P. Plumey, G. Granet, and A. M. Ravaud, “Resonant waveguide grating: analysis of polarization independent filter,” Opt. Quantum Electron. 33(4), 451–470 (2001).
[Crossref]

Proc. SPIE (1)

D. W. Peters, R. R. Boye, and S. A. Kemme, “Angular sensitivity of guided mode resonant filters in classical and conical mounts,” Proc. SPIE 8633, 86330W (2013).
[Crossref]

Sol. Energy Mater. Sol. Cells (1)

M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008).
[Crossref]

Other (2)

R. Eberhart and J. Kennedy, “Particle swarm optimization,” in Proc. IEEE Conference on Neural Networks (IEEE, 1995), pp. 1942–1948.

S. Boonruang, Two-dimensional Guided Mode Resonant Structures for Spectral Filtering Applications (Ph.D. dissertation, University of Central Florida, 2007).

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Figures (8)

Fig. 1
Fig. 1

Schematic illustration of 1D subwavelength gratings in classic and fully conic mounts. The grating parameters are grating period (Λ), fill factor (F), grating depth (dg), and thickness of the homogeneous sublayer (dh). Here, ng, nh, ns, and n0 denote the refractive indices of the grating, sublayer, substrate and air. TM polarization, emphasized in this paper, has an incident electric field component along the grating vector in each case.

Fig. 2
Fig. 2

Variation of the normalized first-order diffracted wave vector (|Δkdiff,1st|/K) as function of angle of incidence (θinc) and normalized incident wave vector (kinc/K). These are calculated in cases of (a) classical and (b) fully conical mounting respectively where K is the grating vector 2π/Λ.

Fig. 3
Fig. 3

Calculated zeroth-order reflectance (R0) maps of a HCG GMR reflector at (a) classical and (b) fully conical mounting as a function of angle of incidence. The grating parameters are dg = 493 nm, Λ = 786 nm, and F = 0.707. For the ZCG GMR reflector, the R0 maps are also calculated in cases of (c) classical and (d) fully conical mounting. The grating parameters are dg = 470 nm, dh = 255 nm, Λ = 827 nm, and F = 0.643. These HCG and ZCG GMR reflector examples were first published in [14] but with θinc = 0.

Fig. 4
Fig. 4

Plots of the first-order diffracted wave vector (kdiff,1st) as a function of incident angle for a ZCG with Λ = 827 nm and the incident light wavelength λ = 1800 nm under classical (red lines) and fully conical (blue lines) mounting.

Fig. 5
Fig. 5

(a) RCWA simulated TM spectral response of a ZCG reflector with PSO optimized parameters Λ = 560 nm, dg = 330 nm, dh = 190 nm, and F = 0.63 at normal angle of incidence. (b) SEM showing top-view image of a fabricated ZCG reflector. Inset figure shows cross-sectional SEM profile.

Fig. 6
Fig. 6

Calculated R0 maps of a ZCG resonant reflector in (a) classical and (b) fully conical mounting as a function of the angle of incidence. The grating parameters are dg = 330 nm, dh = 190 nm, Λ = 560 nm, and F = 0.63. Experimentally, the measured R0 maps are presented in cases of (c) classical and (d) fully conical mounting.

Fig. 7
Fig. 7

A ZCG wideband reflector for the longer-wave near-IR region (1680–2300 nm). (a) SEM top and cross-sectional views of the a-Si grating on a glass substrate and (b) measured (black line) and calculated (red line) R0 spectra of the corresponding device. The grating parameters are dg = 565 nm, dh = 410 nm, Λ = 858 nm, and F = 0.55.

Fig. 8
Fig. 8

Calculated R0 maps for the ZCG reflector in Fig. 6 under (a) classical and (b) full conical mounting as a function of angle of incidence. Measured R0 maps for a ZCG reflector with the same parameters for (c) classical and (d) fully conical mounting. The angular region is limited to the range of 0°–19° as exclusively zero-order waves propagate in this spectral/angular domain.

Equations (5)

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Classical mounting: k x,m = k inc n 0 sin θ inc mK, k y,m =0,
Fully conical mounting: k x,m = k inc n 0 sin θ inc , k y,m =mK,
| Δ k diff,1st | /K = | | k diff,1st || k diff,1st ( θ inc =0) | | /K
Classical mounting:| Δ k diff,1st |= k inc n 0 sin θ inc ,
Fully conical mounting:| Δ k diff,1st |= ( k inc n 0 sin θ inc ) 2 + K 2 K,

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