Abstract

An alternative to the well-established Fourier transform infrared (FT-IR) spectrometry, termed discrete frequency infrared (DFIR) spectrometry, has recently been proposed. This approach uses narrowband mid-infrared reflectance filters based on guided-mode resonance (GMR) in waveguide gratings, but filters designed and fabricated have not attained the spectral selectivity (≤ 32 cm−1) commonly employed for measurements of condensed matter using FT-IR spectroscopy. With the incorporation of dispersion and optical absorption of materials, we present here optimal design of double-layer surface-relief silicon nitride-based GMR filters in the mid-IR for various narrow bandwidths below 32 cm−1. Both shift of the filter resonance wavelengths arising from the dispersion effect and reduction of peak reflection efficiency and electric field enhancement due to the absorption effect show that the optical characteristics of materials must be taken into consideration rigorously for accurate design of narrowband GMR filters. By incorporating considerations for background reflections, the optimally designed GMR filters can have bandwidth narrower than the designed filter by the antireflection equivalence method based on the same index modulation magnitude, without sacrificing low sideband reflections near resonance. The reported work will enable use of GMR filters-based instrumentation for common measurements of condensed matter, including tissues and polymer samples.

© 2011 OSA

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T. Sun, J. Wang, J. Ma, Y. Jin, H. He, J. Shao, and Z. Fan, “Ultra-narrow bandwidth resonant reflection grating filters using the second diffracted orders,” Opt. Commun. 282(4), 451–454 (2009).
[CrossRef]

P. C. Mathias, H.-Y. Wu, and B. T. Cunningham, “Employing two distinct photonic crystal resonances for improved fluorescence enhancement,” Appl. Phys. Lett. 95(2), 021111 (2009).
[CrossRef]

2008

L. L. Chan, M. F. Pineda, J. T. Heeres, P. J. Hergenrother, and B. T. Cunningham, “A General Method for Discovering Inhibitors of Protein-DNA Interactions using Photonic Crystal Biosensors,” ACS Chem. Biol. 3(7), 437–448 (2008).
[CrossRef] [PubMed]

P. C. Mathias, N. Ganesh, W. Zhang, and B. T. Cunningham, “Graded Wavelength One-Dimensional Photonic Crystal Reveals Spectral Characteristics of Enhanced Fluorescence,” J. Appl. Phys. 103(9), 094320 (2008).
[CrossRef]

T. Sun, J. Ma, J. Wang, Y. Jin, H. He, J. Shao, and Z. Fan, “Electric field distribution in resonant reflection filters under normal incidence,” J. Opt. A, Pure Appl. Opt. 10(12), 125003 (2008).
[CrossRef]

2007

2006

R. Bhargava, D. C. Fernandez, S. M. Hewitt, and I. W. Levin, “High throughput assessment of cells and tissues: Bayesian classification of spectral metrics from infrared vibrational spectroscopic imaging data,” Biochim. Biophys. Acta 1758(7), 830–845 (2006).
[CrossRef] [PubMed]

2005

D. C. Fernandez, R. Bhargava, S. M. Hewitt, and I. W. Levin, “Infrared spectroscopic imaging for histopathologic recognition,” Nat. Biotechnol. 23(4), 469–474 (2005).
[CrossRef] [PubMed]

G. Bao and K. Huang, “Computational design for guided-mode grating resonances,” J. Opt. Soc. Am. A 22(7), 1408–1413 (2005).
[CrossRef] [PubMed]

2004

2003

2002

B. T. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators B Chem. 81(2-3), 316–328 (2002).
[CrossRef]

B. T. Cunningham, B. Lin, J. Qiu, P. Li, J. Pepper, and B. Hugh, “A plastic colorimetric resonant optical biosensor for multiparallel detection of label-free biochemical interactions,” Sens. Actuators B Chem. 85(3), 219–226 (2002).
[CrossRef]

2001

M. Klanjšek Gunde and M. Maček, “Infrared Optical Constants and Dielectric Response Functions of Silicon Nitride and Oxynitride Films,” Phys. Status Solidi 183, 439–449 (2001).
[CrossRef]

S. Tibuleac and R. Magnusson, “Narrow-linewidth bandpass filters with diffractive thin-film layers,” Opt. Lett. 26(9), 584–586 (2001).
[CrossRef] [PubMed]

2000

1998

S. M. Norton, G. M. Morris, and T. Erdogan, “Experimental investigation of resonant-grating filter lineshapes in comparison with theoretical models,” J. Opt. Soc. Am. A 15(2), 464–472 (1998).
[CrossRef]

D. Shin, S. Tibuleac, T. A. Maldonado, and R. Magnusson, “Thin-film optical filters with diffractive elements and waveguides,” Opt. Eng. 37(9), 2634–2646 (1998).
[CrossRef]

1997

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[CrossRef]

A. Sharon, D. Rosenblatt, and A. A. Friesem, “Resonant grating–waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A 14(11), 2985–2993 (1997).
[CrossRef]

1995

1994

1993

1990

M. T. Gale, K. Knop, and R. H. Morf, Proc. Soc. Photo Opt. Instrum. Eng. 1210, 83 (1990).

1989

H. Bertoni, L. Cheo, and T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antenn. Propag. 37(1), 78–83 (1989).
[CrossRef]

1985

L. Mashev and E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55(6), 377–380 (1985).
[CrossRef]

M. Rubin, “Optical properties of soda lime silica glasses,” Sol. Energy Mater. 12(4), 275–288 (1985).
[CrossRef]

Bao, G.

G. Bao and K. Huang, “Computational design for guided-mode grating resonances,” J. Opt. Soc. Am. A 22(7), 1408–1413 (2005).
[CrossRef] [PubMed]

G. Bao and K. Huang, “Optimal design of guided-mode grating resonance filters,” IEEE Photon. Technol. Lett. 16(1), 141–143 (2004).
[CrossRef]

Bertoni, H.

H. Bertoni, L. Cheo, and T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antenn. Propag. 37(1), 78–83 (1989).
[CrossRef]

Bhargava, R.

A. K. Kodali, M. Schulmerich, J. Ip, G. Yen, B. T. Cunningham, and R. Bhargava, “Narrowband midinfrared reflectance filters using guided mode resonance,” Anal. Chem. 82(13), 5697–5706 (2010).
[CrossRef] [PubMed]

R. Bhargava, “Towards a practical Fourier transform infrared chemical imaging protocol for cancer histopathology,” Anal. Bioanal. Chem. 389(4), 1155–1169 (2007).
[CrossRef] [PubMed]

R. Bhargava, D. C. Fernandez, S. M. Hewitt, and I. W. Levin, “High throughput assessment of cells and tissues: Bayesian classification of spectral metrics from infrared vibrational spectroscopic imaging data,” Biochim. Biophys. Acta 1758(7), 830–845 (2006).
[CrossRef] [PubMed]

D. C. Fernandez, R. Bhargava, S. M. Hewitt, and I. W. Levin, “Infrared spectroscopic imaging for histopathologic recognition,” Nat. Biotechnol. 23(4), 469–474 (2005).
[CrossRef] [PubMed]

Boyko, O.

Chan, L. L.

L. L. Chan, M. F. Pineda, J. T. Heeres, P. J. Hergenrother, and B. T. Cunningham, “A General Method for Discovering Inhibitors of Protein-DNA Interactions using Photonic Crystal Biosensors,” ACS Chem. Biol. 3(7), 437–448 (2008).
[CrossRef] [PubMed]

Chaudhery, V.

Cheo, L.

H. Bertoni, L. Cheo, and T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antenn. Propag. 37(1), 78–83 (1989).
[CrossRef]

Cunningham, B. T.

A. K. Kodali, M. Schulmerich, J. Ip, G. Yen, B. T. Cunningham, and R. Bhargava, “Narrowband midinfrared reflectance filters using guided mode resonance,” Anal. Chem. 82(13), 5697–5706 (2010).
[CrossRef] [PubMed]

A. Pokhriyal, M. Lu, V. Chaudhery, C.-S. Huang, S. Schulz, and B. T. Cunningham, “Photonic crystal enhanced fluorescence using a quartz substrate to reduce limits of detection,” Opt. Express 18(24), 24793–24808 (2010).
[CrossRef] [PubMed]

F. Yang, G. Yen, and B. T. Cunningham, “Integrated 2D photonic crystal stack filter fabricated using nanoreplica molding,” Opt. Express 18(11), 11846–11858 (2010).
[CrossRef] [PubMed]

P. C. Mathias, H.-Y. Wu, and B. T. Cunningham, “Employing two distinct photonic crystal resonances for improved fluorescence enhancement,” Appl. Phys. Lett. 95(2), 021111 (2009).
[CrossRef]

L. L. Chan, M. F. Pineda, J. T. Heeres, P. J. Hergenrother, and B. T. Cunningham, “A General Method for Discovering Inhibitors of Protein-DNA Interactions using Photonic Crystal Biosensors,” ACS Chem. Biol. 3(7), 437–448 (2008).
[CrossRef] [PubMed]

P. C. Mathias, N. Ganesh, W. Zhang, and B. T. Cunningham, “Graded Wavelength One-Dimensional Photonic Crystal Reveals Spectral Characteristics of Enhanced Fluorescence,” J. Appl. Phys. 103(9), 094320 (2008).
[CrossRef]

B. T. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators B Chem. 81(2-3), 316–328 (2002).
[CrossRef]

B. T. Cunningham, B. Lin, J. Qiu, P. Li, J. Pepper, and B. Hugh, “A plastic colorimetric resonant optical biosensor for multiparallel detection of label-free biochemical interactions,” Sens. Actuators B Chem. 85(3), 219–226 (2002).
[CrossRef]

Erdogan, T.

Fan, Z.

T. Sun, J. Wang, J. Ma, Y. Jin, H. He, J. Shao, and Z. Fan, “Ultra-narrow bandwidth resonant reflection grating filters using the second diffracted orders,” Opt. Commun. 282(4), 451–454 (2009).
[CrossRef]

T. Sun, J. Ma, J. Wang, Y. Jin, H. He, J. Shao, and Z. Fan, “Electric field distribution in resonant reflection filters under normal incidence,” J. Opt. A, Pure Appl. Opt. 10(12), 125003 (2008).
[CrossRef]

Fehrembach, A. L.

Fernandez, D. C.

R. Bhargava, D. C. Fernandez, S. M. Hewitt, and I. W. Levin, “High throughput assessment of cells and tissues: Bayesian classification of spectral metrics from infrared vibrational spectroscopic imaging data,” Biochim. Biophys. Acta 1758(7), 830–845 (2006).
[CrossRef] [PubMed]

D. C. Fernandez, R. Bhargava, S. M. Hewitt, and I. W. Levin, “Infrared spectroscopic imaging for histopathologic recognition,” Nat. Biotechnol. 23(4), 469–474 (2005).
[CrossRef] [PubMed]

Friesem, A. A.

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[CrossRef]

A. Sharon, D. Rosenblatt, and A. A. Friesem, “Resonant grating–waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A 14(11), 2985–2993 (1997).
[CrossRef]

Gale, M. T.

M. T. Gale, K. Knop, and R. H. Morf, Proc. Soc. Photo Opt. Instrum. Eng. 1210, 83 (1990).

Ganesh, N.

P. C. Mathias, N. Ganesh, W. Zhang, and B. T. Cunningham, “Graded Wavelength One-Dimensional Photonic Crystal Reveals Spectral Characteristics of Enhanced Fluorescence,” J. Appl. Phys. 103(9), 094320 (2008).
[CrossRef]

Gaylord, T. K.

Grann, E. B.

Guo, H.

He, H.

T. Sun, J. Wang, J. Ma, Y. Jin, H. He, J. Shao, and Z. Fan, “Ultra-narrow bandwidth resonant reflection grating filters using the second diffracted orders,” Opt. Commun. 282(4), 451–454 (2009).
[CrossRef]

T. Sun, J. Ma, J. Wang, Y. Jin, H. He, J. Shao, and Z. Fan, “Electric field distribution in resonant reflection filters under normal incidence,” J. Opt. A, Pure Appl. Opt. 10(12), 125003 (2008).
[CrossRef]

Heeres, J. T.

L. L. Chan, M. F. Pineda, J. T. Heeres, P. J. Hergenrother, and B. T. Cunningham, “A General Method for Discovering Inhibitors of Protein-DNA Interactions using Photonic Crystal Biosensors,” ACS Chem. Biol. 3(7), 437–448 (2008).
[CrossRef] [PubMed]

Hegedus, Z.

Hergenrother, P. J.

L. L. Chan, M. F. Pineda, J. T. Heeres, P. J. Hergenrother, and B. T. Cunningham, “A General Method for Discovering Inhibitors of Protein-DNA Interactions using Photonic Crystal Biosensors,” ACS Chem. Biol. 3(7), 437–448 (2008).
[CrossRef] [PubMed]

Herzig, H. P.

Hewitt, S. M.

R. Bhargava, D. C. Fernandez, S. M. Hewitt, and I. W. Levin, “High throughput assessment of cells and tissues: Bayesian classification of spectral metrics from infrared vibrational spectroscopic imaging data,” Biochim. Biophys. Acta 1758(7), 830–845 (2006).
[CrossRef] [PubMed]

D. C. Fernandez, R. Bhargava, S. M. Hewitt, and I. W. Levin, “Infrared spectroscopic imaging for histopathologic recognition,” Nat. Biotechnol. 23(4), 469–474 (2005).
[CrossRef] [PubMed]

Huang, C.-S.

Huang, K.

G. Bao and K. Huang, “Computational design for guided-mode grating resonances,” J. Opt. Soc. Am. A 22(7), 1408–1413 (2005).
[CrossRef] [PubMed]

G. Bao and K. Huang, “Optimal design of guided-mode grating resonance filters,” IEEE Photon. Technol. Lett. 16(1), 141–143 (2004).
[CrossRef]

Hugh, B.

B. T. Cunningham, B. Lin, J. Qiu, P. Li, J. Pepper, and B. Hugh, “A plastic colorimetric resonant optical biosensor for multiparallel detection of label-free biochemical interactions,” Sens. Actuators B Chem. 85(3), 219–226 (2002).
[CrossRef]

Ip, J.

A. K. Kodali, M. Schulmerich, J. Ip, G. Yen, B. T. Cunningham, and R. Bhargava, “Narrowband midinfrared reflectance filters using guided mode resonance,” Anal. Chem. 82(13), 5697–5706 (2010).
[CrossRef] [PubMed]

Jin, Y.

T. Sun, J. Wang, J. Ma, Y. Jin, H. He, J. Shao, and Z. Fan, “Ultra-narrow bandwidth resonant reflection grating filters using the second diffracted orders,” Opt. Commun. 282(4), 451–454 (2009).
[CrossRef]

T. Sun, J. Ma, J. Wang, Y. Jin, H. He, J. Shao, and Z. Fan, “Electric field distribution in resonant reflection filters under normal incidence,” J. Opt. A, Pure Appl. Opt. 10(12), 125003 (2008).
[CrossRef]

Klanjšek Gunde, M.

M. Klanjšek Gunde and M. Maček, “Infrared Optical Constants and Dielectric Response Functions of Silicon Nitride and Oxynitride Films,” Phys. Status Solidi 183, 439–449 (2001).
[CrossRef]

Knop, K.

M. T. Gale, K. Knop, and R. H. Morf, Proc. Soc. Photo Opt. Instrum. Eng. 1210, 83 (1990).

Kodali, A. K.

A. K. Kodali, M. Schulmerich, J. Ip, G. Yen, B. T. Cunningham, and R. Bhargava, “Narrowband midinfrared reflectance filters using guided mode resonance,” Anal. Chem. 82(13), 5697–5706 (2010).
[CrossRef] [PubMed]

Lai, Z.

Lemarchand, F.

Levin, I. W.

R. Bhargava, D. C. Fernandez, S. M. Hewitt, and I. W. Levin, “High throughput assessment of cells and tissues: Bayesian classification of spectral metrics from infrared vibrational spectroscopic imaging data,” Biochim. Biophys. Acta 1758(7), 830–845 (2006).
[CrossRef] [PubMed]

D. C. Fernandez, R. Bhargava, S. M. Hewitt, and I. W. Levin, “Infrared spectroscopic imaging for histopathologic recognition,” Nat. Biotechnol. 23(4), 469–474 (2005).
[CrossRef] [PubMed]

Li, P.

B. T. Cunningham, B. Lin, J. Qiu, P. Li, J. Pepper, and B. Hugh, “A plastic colorimetric resonant optical biosensor for multiparallel detection of label-free biochemical interactions,” Sens. Actuators B Chem. 85(3), 219–226 (2002).
[CrossRef]

B. T. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators B Chem. 81(2-3), 316–328 (2002).
[CrossRef]

Lin, B.

B. T. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators B Chem. 81(2-3), 316–328 (2002).
[CrossRef]

B. T. Cunningham, B. Lin, J. Qiu, P. Li, J. Pepper, and B. Hugh, “A plastic colorimetric resonant optical biosensor for multiparallel detection of label-free biochemical interactions,” Sens. Actuators B Chem. 85(3), 219–226 (2002).
[CrossRef]

Liu, W.

Liu, Y.

Lu, M.

Ma, J.

T. Sun, J. Wang, J. Ma, Y. Jin, H. He, J. Shao, and Z. Fan, “Ultra-narrow bandwidth resonant reflection grating filters using the second diffracted orders,” Opt. Commun. 282(4), 451–454 (2009).
[CrossRef]

T. Sun, J. Ma, J. Wang, Y. Jin, H. He, J. Shao, and Z. Fan, “Electric field distribution in resonant reflection filters under normal incidence,” J. Opt. A, Pure Appl. Opt. 10(12), 125003 (2008).
[CrossRef]

Macek, M.

M. Klanjšek Gunde and M. Maček, “Infrared Optical Constants and Dielectric Response Functions of Silicon Nitride and Oxynitride Films,” Phys. Status Solidi 183, 439–449 (2001).
[CrossRef]

Magnusson, R.

Maldonado, T. A.

D. Shin, S. Tibuleac, T. A. Maldonado, and R. Magnusson, “Thin-film optical filters with diffractive elements and waveguides,” Opt. Eng. 37(9), 2634–2646 (1998).
[CrossRef]

Mashev, L.

L. Mashev and E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55(6), 377–380 (1985).
[CrossRef]

Mathias, P. C.

P. C. Mathias, H.-Y. Wu, and B. T. Cunningham, “Employing two distinct photonic crystal resonances for improved fluorescence enhancement,” Appl. Phys. Lett. 95(2), 021111 (2009).
[CrossRef]

P. C. Mathias, N. Ganesh, W. Zhang, and B. T. Cunningham, “Graded Wavelength One-Dimensional Photonic Crystal Reveals Spectral Characteristics of Enhanced Fluorescence,” J. Appl. Phys. 103(9), 094320 (2008).
[CrossRef]

Moharam, M. G.

Morf, R. H.

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Figures (9)

Fig. 1
Fig. 1

GMR filter design comprised on a soda lime glass substrate, a Si3N4 waveguide/grating layer, and an air superstrate. The device is illuminated from the superstrate side at normal incidence with a plane wave polarized parallel to the grating lines for excitation of TE modes, and with a plane wave polarized perpendicular to the grating lines for TM modes.

Fig. 2
Fig. 2

Effect on guided-mode resonances of dispersion and absorption properties of Si3N4 and soda lime, when a TE-polarized wave is normally incident on GMR filters with grating period Λ = 2.5 μm, duty cycle f = 0.5, and Si3N4 total thickness dgr + dwg = 0.6 μm. (a) Reflectance spectra of three filters with different grating depths without considering the dispersion characteristics of both Si3N4 and soda lime. The refractive indices chosen are nSiN = 2.02 and nSL = 1.47. (b) Reflectance spectra considering the dispersion characteristics of both Si3N4 [31] and soda lime glass [32]. (c) The dispersion relation for a simplified dielectric waveguide, where the refractive indices used are the same as those in (a). The phase matching condition requires β = (2π)/Λ, where the grating period Λ = 2.5 μm. (d) Explanation of the observed red shift of guided mode resonances by comparing dispersion curves for the TE0 mode using nSiN = 2.01 and nSL = 1.46 near 2550 cm−1 with that in (c). (e-f) Distribution of the electric field amplitude (|E|) in a unit cell of the filter with grating depth dgr = 50 nm for illumination at (e) υ = 2549 cm−1 without considering the dispersion characteristics of both Si3N4 and soda lime and at (f) υ = 2559 cm−1 considering the dispersion properties of both Si3N4 and soda lime. (g-h) Comparison of electric field amplitude profiles shown in (e) and (f) at x = 1.25 μm (left) and near the center of the waveguide layer at z = 200 nm (right).

Fig. 3
Fig. 3

Effect on reflectance spectra of higher-order modes. Reflectance spectra of two filters when a TE-polarized wave is normally incident. Grating period Λ = 2.2 mm, grating depth dgr = 0.3 μm, waveguide layer thickness dwg = 0.5 μm (black), and dwg = 1.5 μm (red). (b-d) Electric field amplitude distribution of (b) the TE0 mode at a resonance wavenumber (υ = 2811 cm−1) for structure of dwg = 0.5 μm, (c) the TE0 mode at a resonance wavenumber (υ = 2475 cm−1) and (d) the TE1 mode at a resonance wavenumber (υ = 3001 cm−1) for structure of dwg = 1.5 μm.

Fig. 4
Fig. 4

Schematic of the design optimization procedure for reflection narrowband GMR filters.

Fig. 5
Fig. 5

(a) Calculated reflectance spectra of a GMR filter with Λ = 2.5 μm, dwg = 0.3 μm, and dgr = 0.3 μm. The peak wavenumber value (PWV) and the filter bandwidth (full width at half-maximum, or FWHM) are determined by Lorentzian curve fitting. (b) Illustration of the in-band integration (IIB) and the out-of-band integration (IOB).

Fig. 6
Fig. 6

PWV, FWHM, and Rpeak of GMR filters with different grating depths (dgr), waveguide layer thicknesses (dwg), and grating periods (Λ): (a) 2.1 μm, (b) 2.2 μm, (c) 2.3 μm, (d) 2.4 μm, (e) 2.5 μm, and (f) 2.6 μm, when a TE-polarized wave is normally incident. The color bar code for PWV, FWHM, and Rpeak are given below each row.

Fig. 7
Fig. 7

PWV, FWHM, and Rpeak of GMR filters with different grating depths (dgr), waveguide layer thicknesses (dwg), and grating periods (Λ): (a) 2.1 μm, (b) 2.2 μm, (c) 2.3 μm, (d) 2.4 μm, (e) 2.5 μm, and (f) 2.6 μm, for TM-polarized normally incident illumination. The color bar code for PWV, FWHM, and Rpeak are given below each row.

Fig. 8
Fig. 8

Design of narrowband GMR filters with PWV of 2600 cm−1 for various bandwidths: (a) 32 cm−1, (b) 24 cm−1, (c) 16 cm−1, and (d) 8 cm−1, when a TE or TM-polarized light is normally incident. The grating periods and the layer thicknesses are denoted as a set of numbers.

Fig. 9
Fig. 9

(a) Comparison of GMR filter designs for TE PWV of 2600 cm−1 using AR thin-film equivalence concept (blue) and using our optimal design method for 24 cm−1 bandwidth and the same fitted PWV (red), when TE-polarized light is normally incident. The FWHM bandwidth of the AR designed filter is 86 cm−1. Inset: PWV vs. the grating period for GMR filters with AR thin-film equivalent thicknesses at the specified wavenumber of 2600 cm−1. The layer thicknesses are dwg = 0.478 μm (quarter-wave) and dgr = 0.606 μm (quarter-wave). The grating period is tuned to match the targeted PWV of 2600 cm−1, resulting in the grating period Λ = 2.42 μm for the AR designed filter. (b) E-field enhancement distribution for TE polarization in the GMR structure using AR approximation design at a resonance wavenumber of 2600 cm−1 (left) and in the structure using optimal design method for 24 cm−1 bandwidth at a resonance wavenumber of 2599 cm−1 (right).

Tables (1)

Tables Icon

Table 1 Summary of Designed GMR Reflectance Filters with a PWV of 2600 cm−1 for Various Bandwidths

Equations (5)

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k 0 n c sinθ ±p( 2π Λ )=β
k 0 d n SiN 2 n SL 2 = tan 1 n SL 2 n Air 2 n SiN 2 n SL 2 +π ( TE 1 )
k 0 d n SiN 2 n SL 2 = tan 1 n SiN 2 n SL 2 n Air 2 n Air 2 n SiN 2 n SL 2 +π ( TM 1 )
max{ n c , n s }| n c sinθ p νΛ |max{ n gr , n wg }
R(ν)= R 0 +( R peak R 0 ) Δν 2/π Δν/(2π) (ν ν 0 ) 2 + (Δν/2) 2

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