Abstract

Resonant-grating lineshapes are compared with results from a previously derived approximate coupled-mode analysis [J. Opt. Soc. Am. A 14, 629 (1997)] and to rigorous coupled-wave analysis. Tunability in resonant position (wavelength and angle) and lineshape is achieved by a novel method involving immersion of a bare resonant-grating structure in various liquids, each with a different refractive index. A comparison is made of different filter features—resonant position, efficiency, and angular width—in the experimental results and the theoretical models. The use of coupled-mode theory allows an intuitive picture to be associated with the observed trends in filter characteristic versus refractive index. This investigation reinforces the idea that the use of coupled-mode theory for resonant-grating analysis can simplify filter design.

© 1998 Optical Society of America

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References

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  1. S. M. Norton, T. Erdogan, G. M. Morris, “Coupled-mode theory of resonant-grating filters,” J. Opt. Soc. Am. A 14, 629–639 (1997).
    [CrossRef]
  2. S. Peng, G. M. Morris, “Resonant scattering from two-dimensional gratings,” J. Opt. Soc. Am. A 13, 993–1005 (1996).
    [CrossRef]
  3. R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
    [CrossRef]
  4. S. S. Wang, R. Magnusson, “Theory and applications of guided-mode filters,” Appl. Opt. 23, 2606–2613 (1993).
    [CrossRef]
  5. M. Nevière, E. Popov, R. Reinisch, “Electromagnetic resonances in linear and nonlinear optics. Phenomenological study of grating behavior through the poles and zeros of the scattering operator,” J. Opt. Soc. Am. A 12, 513–523 (1995).
    [CrossRef]
  6. E. Popov, L. Mashev, D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
    [CrossRef]
  7. M. T. Gale, K. Knop, R. H. Morf, “Zero-order diffractive microstructures for security applications,” Opt. Security Counterfeit. Syst. 1210, 83–89 (1990).
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    [CrossRef]
  9. I. C. Botten, M. S. Craig, M. R. C., J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
    [CrossRef]
  10. S. Peng, G. M. Morris, “Experimental investigation of resonant grating filters based on two-dimensional gratings,” in Diffractive and Holographic Optics Technology III, I. Cindrich, S. H. Lee, Eds., Proc. SPIE2689, 90–94 (1996).
    [CrossRef]
  11. A. Sharon, S. Glasberg, D. Rosenblatt, A. A. Friesem, “Metal-based resonant grating waveguide structures,” J. Opt. Soc. Am. A 14, 588–595 (1997).
    [CrossRef]
  12. A. Sharon, D. Rosenblatt, A. A. Friesem, “Narrow spectral bandwidths with grating waveguide structures,” Appl. Phys. Lett. 69, 4154–4156 (1996).
    [CrossRef]
  13. A. Sharon, D. Rosenblatt, A. A. Friesem, H. G. Weber, H. Engel, R. Steingrueber, “Light modulation with resonant gratings—waveguide structures,” Opt. Lett. 21, 1564–1566 (1996).
    [CrossRef] [PubMed]
  14. 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]
  15. T. Tamir, “Inhomogeneous wave types at planar interfaces. III. Leaky waves,” Optik (Stuttgart) 38, 271–99 (1973).
  16. M. Nevière, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin-film couplers,” Opt. Commun. 9, 48–53 (1973).
    [CrossRef]
  17. W. Streifer, D. R. Scifres, R. D. Burnham, “Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides,” IEEE J. Quantum Electron. QE-12, 422–428 (1976).
    [CrossRef]
  18. J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995).
    [CrossRef]
  19. H. Kogelnik, “Theory of dielectric waveguides,” in Integrated Optics, T. Tamir, ed. (Springer-Verlag, Berlin, 1975), Vol. 7, pp. 13–81.

1997 (2)

1996 (3)

1995 (2)

1994 (1)

1993 (1)

S. S. Wang, R. Magnusson, “Theory and applications of guided-mode filters,” Appl. Opt. 23, 2606–2613 (1993).
[CrossRef]

1992 (1)

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

1990 (1)

M. T. Gale, K. Knop, R. H. Morf, “Zero-order diffractive microstructures for security applications,” Opt. Security Counterfeit. Syst. 1210, 83–89 (1990).

1986 (1)

E. Popov, L. Mashev, D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

1981 (2)

M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
[CrossRef]

I. C. Botten, M. S. Craig, M. R. C., J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

1976 (1)

W. Streifer, D. R. Scifres, R. D. Burnham, “Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides,” IEEE J. Quantum Electron. QE-12, 422–428 (1976).
[CrossRef]

1973 (2)

T. Tamir, “Inhomogeneous wave types at planar interfaces. III. Leaky waves,” Optik (Stuttgart) 38, 271–99 (1973).

M. Nevière, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin-film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

Adams, J. L.

I. C. Botten, M. S. Craig, M. R. C., J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

Andrewartha, J. R.

I. C. Botten, M. S. Craig, M. R. C., J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

Botten, I. C.

I. C. Botten, M. S. Craig, M. R. C., J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

Burnham, R. D.

W. Streifer, D. R. Scifres, R. D. Burnham, “Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides,” IEEE J. Quantum Electron. QE-12, 422–428 (1976).
[CrossRef]

C., M. R.

I. C. Botten, M. S. Craig, M. R. C., J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

Cadilhac, M.

M. Nevière, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin-film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

Craig, M. S.

I. C. Botten, M. S. Craig, M. R. C., J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

Engel, H.

Erdogan, T.

Friesem, A. A.

Gale, M. T.

M. T. Gale, K. Knop, R. H. Morf, “Zero-order diffractive microstructures for security applications,” Opt. Security Counterfeit. Syst. 1210, 83–89 (1990).

Gaylord, T. K.

Glasberg, S.

Knop, K.

M. T. Gale, K. Knop, R. H. Morf, “Zero-order diffractive microstructures for security applications,” Opt. Security Counterfeit. Syst. 1210, 83–89 (1990).

Kogelnik, H.

H. Kogelnik, “Theory of dielectric waveguides,” in Integrated Optics, T. Tamir, ed. (Springer-Verlag, Berlin, 1975), Vol. 7, pp. 13–81.

Magnusson, R.

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]

S. S. Wang, R. Magnusson, “Theory and applications of guided-mode filters,” Appl. Opt. 23, 2606–2613 (1993).
[CrossRef]

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

Mashev, L.

E. Popov, L. Mashev, D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

Maystre, D.

E. Popov, L. Mashev, D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

Moharam, M. G.

Morf, R. H.

M. T. Gale, K. Knop, R. H. Morf, “Zero-order diffractive microstructures for security applications,” Opt. Security Counterfeit. Syst. 1210, 83–89 (1990).

Morris, G. M.

S. M. Norton, T. Erdogan, G. M. Morris, “Coupled-mode theory of resonant-grating filters,” J. Opt. Soc. Am. A 14, 629–639 (1997).
[CrossRef]

S. Peng, G. M. Morris, “Resonant scattering from two-dimensional gratings,” J. Opt. Soc. Am. A 13, 993–1005 (1996).
[CrossRef]

S. Peng, G. M. Morris, “Experimental investigation of resonant grating filters based on two-dimensional gratings,” in Diffractive and Holographic Optics Technology III, I. Cindrich, S. H. Lee, Eds., Proc. SPIE2689, 90–94 (1996).
[CrossRef]

Nevière, M.

Noponen, E.

J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995).
[CrossRef]

Norton, S. M.

Peng, S.

S. Peng, G. M. Morris, “Resonant scattering from two-dimensional gratings,” J. Opt. Soc. Am. A 13, 993–1005 (1996).
[CrossRef]

S. Peng, G. M. Morris, “Experimental investigation of resonant grating filters based on two-dimensional gratings,” in Diffractive and Holographic Optics Technology III, I. Cindrich, S. H. Lee, Eds., Proc. SPIE2689, 90–94 (1996).
[CrossRef]

Petit, R.

M. Nevière, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin-film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

Popov, E.

Reinisch, R.

Rosenblatt, D.

Saarinen, J.

J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995).
[CrossRef]

Scifres, D. R.

W. Streifer, D. R. Scifres, R. D. Burnham, “Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides,” IEEE J. Quantum Electron. QE-12, 422–428 (1976).
[CrossRef]

Sharon, A.

Steingrueber, R.

Streifer, W.

W. Streifer, D. R. Scifres, R. D. Burnham, “Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides,” IEEE J. Quantum Electron. QE-12, 422–428 (1976).
[CrossRef]

Tamir, T.

T. Tamir, “Inhomogeneous wave types at planar interfaces. III. Leaky waves,” Optik (Stuttgart) 38, 271–99 (1973).

Turunen, J.

J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995).
[CrossRef]

Wang, S. S.

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]

S. S. Wang, R. Magnusson, “Theory and applications of guided-mode filters,” Appl. Opt. 23, 2606–2613 (1993).
[CrossRef]

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

Weber, H. G.

Appl. Opt. (1)

S. S. Wang, R. Magnusson, “Theory and applications of guided-mode filters,” Appl. Opt. 23, 2606–2613 (1993).
[CrossRef]

Appl. Phys. Lett. (2)

A. Sharon, D. Rosenblatt, A. A. Friesem, “Narrow spectral bandwidths with grating waveguide structures,” Appl. Phys. Lett. 69, 4154–4156 (1996).
[CrossRef]

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

IEEE J. Quantum Electron. (1)

W. Streifer, D. R. Scifres, R. D. Burnham, “Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides,” IEEE J. Quantum Electron. QE-12, 422–428 (1976).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Opt. Acta (2)

E. Popov, L. Mashev, D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607–619 (1986).
[CrossRef]

I. C. Botten, M. S. Craig, M. R. C., J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

Opt. Commun. (1)

M. Nevière, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin-film couplers,” Opt. Commun. 9, 48–53 (1973).
[CrossRef]

Opt. Eng. (1)

J. Saarinen, E. Noponen, J. Turunen, “Guided-mode resonance filters of finite aperture,” Opt. Eng. 34, 2560–2566 (1995).
[CrossRef]

Opt. Lett. (2)

Opt. Security Counterfeit. Syst. (1)

M. T. Gale, K. Knop, R. H. Morf, “Zero-order diffractive microstructures for security applications,” Opt. Security Counterfeit. Syst. 1210, 83–89 (1990).

Optik (Stuttgart) (1)

T. Tamir, “Inhomogeneous wave types at planar interfaces. III. Leaky waves,” Optik (Stuttgart) 38, 271–99 (1973).

Other (2)

H. Kogelnik, “Theory of dielectric waveguides,” in Integrated Optics, T. Tamir, ed. (Springer-Verlag, Berlin, 1975), Vol. 7, pp. 13–81.

S. Peng, G. M. Morris, “Experimental investigation of resonant grating filters based on two-dimensional gratings,” in Diffractive and Holographic Optics Technology III, I. Cindrich, S. H. Lee, Eds., Proc. SPIE2689, 90–94 (1996).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Illustration of resonant-grating structure used in both experiment and theoretical analysis. Note that the liquid fills both the cover region and part of the grating region. The duty cycle defined in this paper is given by a/Λ.

Fig. 2
Fig. 2

Example of a TE resonance reflection peak. Resonances are characterized by a narrow (in angle or wavelength) reflection peak, which when designed to support only zeroth-order diffraction, can theoretically reach 100%. For this example the following structural parameters were used: nliq=1.45, nsub=1.453, nHI=2.01, d=0.1416 µm, λ = 0.78033 µm, Λ=0.38 µm, D.C. = 0.4 (see Fig. 1).

Fig. 3
Fig. 3

SEM of the fabricated resonant-grating structure. The bumpy surface is most likely due to polymerization resulting from the chemistry of Si3N4 etching with CHF3 gas.

Fig. 4
Fig. 4

Illustration of resonance scanning setup. The system is a computer-controlled angular scanning system that plots the ratio of the incident to the reflected power. The power is normalized to the incident power from mirror M. Other components are labeled as follows: T.D.L., tunable diode laser; B.E., beam expander; C, chopper, D1 and D2, silicon detectors; S sample; and P, polarizer.

Fig. 5
Fig. 5

Plots of resonance reflection peaks for different liquids. The peak farthest to the right represents the lowest refractive-index liquid, and successive peaks to the left represent liquids with incrementing refractive index. Note: For clarity, not all refractive indexes in Table 1 are represented in this plot. As described in the text, the data are filtered with a Fourier algorithm, and Fresnel effects are taken into account. The bottom axis is the angle of the light in the liquid layer relative to the normal (x direction) of the structure.

Fig. 6
Fig. 6

Plot of peak resonance efficiency versus different liquid refractive indices. The plus signs indicate experimental data, and the dashed curve indicates loss due to random scatter according to Eq. (8). The empirical loss parameters α and α0 that best fit the data were 0.001 and 0.8, respectively. The error bars represent deviations found in typical angular scans. Other mechanisms such as absorption, incident beam size, and first-order diffraction contribute to the loss at high refractive indices.

Fig. 7
Fig. 7

Plot indicating the resonances proximity to first-order cutoff. If the angle corresponding to first-order cutoff [see Eq. (10)] approaches the angle of the resonance reflection peak, then energy at the sides of the peak will be shed into the first order. This has the effect of reducing the linewidth and efficiency of the resonance peak. Notice that this effect is highly suspect at measured higher refractive-index values.

Fig. 8
Fig. 8

Plot of resonance peak position in angle versus liquid refractive index, comparing experimental data, RCWA, and the angular position determined from the ideal waveguide dispersion relation combined with the coupling equation, Eq. (1). Even considering the high index variation between liquid and Si3N4, the ideal waveguide approximation gives an excellent fit to both experiment and RCWA.

Fig. 9
Fig. 9

Plot of angular resonance width (FWHM) versus liquid refractive index. The experimental data fit well the values obtained from the coupled-mode calculations and angular FWHM values from profiling the resonances by using RCWA. The coupled-mode approach takes far less computation time than RCWA. The error bars represent variations due to filtering and sources of error in the measurements.

Fig. 10
Fig. 10

Plot of confinement factor versus liquid refractive index for TE polarization. The confinement factor was calculated by using standard ideal waveguide methodology (see Ref. 19). Note that for our structure, increasing confinement of the bound-mode field corresponds to increasing resonance width.

Tables (1)

Tables Icon

Table 1 Refractive-Index Values for Liquids Used in Cover–Grating Regiona

Equations (11)

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βr=kz+mK,
β=βr+iγ.
R=|r|2=|ca|2kz-2πΛG-β02+γ2,
Δθ=180π λ2πcos(θpeak)Δkz=180π λγπcos(θpeak),
θpeak=sin-1(Nr-λ/ΛG),
R=|cw|2(ΛGλpeak/2π)2[λ-ΛG(sin θ+Nr)]2+ΛG2Ni2,
Δλ=λpeakΛGπγλpeak.
R=α0S2(S+α)2,
SΔζ±1k02d2K2,
Re(β)k0nsub,liq=k0nliq sin(θin)-2π/Λ,
κ=0dΔEyυEyρdx,

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