Abstract

The peaks in the reflectivity spectrum of waveguide gratings observed when the incident beam couples to a mode of the structure are promising features for many applications. However their weak angular tolerance and their strong polarization sensitivity, especially under oblique incidence, limit their interest in practice. These problems can be overcome by forming slow degenerate modes outside the usual high symmetry points of the Brillouin zone with a complex periodic pattern [ Fehrembach, Appl. Phys. Lett. 86, 121105 (2005) ]. We show experimentally that spectrally sharp, λΔλ4000, polarization-independent, angularly tolerant optical resonances can be obtained by exciting these modes under oblique incidence.

© 2009 Optical Society of America

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References

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  1. E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta 33, 607-619 (1986).
    [CrossRef]
  2. D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038-2059 (1997).
    [CrossRef]
  3. F. Lemarchand, A. Sentenac, and H. Giovannini, “Increasing the angular tolerance of resonant grating filters with doubly periodic structures,” Opt. Lett. 23, 1149-1151 (1998).
    [CrossRef]
  4. A.-L. Fehrembach, D. Maystre, and A. Sentenac, “Phenomenological theory of filtering by resonant dielectric gratings,” J. Opt. Soc. Am. A 19, 1136-1144 (2002).
    [CrossRef]
  5. S. Peng and M. G. Morris, “Experimental demonstration of resonant anomalies in diffraction from two-dimensional gratings,” Opt. Lett. 21, 549-551 (1996).
    [CrossRef] [PubMed]
  6. A.-L. Fehrembach, A. Talneau, O. Boyko, F. Lemarchand, and A. Sentenac, “Experimental demonstration of a narrow-band, angular tolerant, polarization independent, doubly periodic resonant grating filter,” Opt. Lett. 32, 2269-2271 (2007).
    [CrossRef] [PubMed]
  7. A. Mizutani, H. Kikuta, K. Nakajima, and K. Iwata, “Nonpolarizing guided-mode resonant grating filter for oblique incidence,” J. Opt. Soc. Am. A 18, 1261-1266 (2001).
    [CrossRef]
  8. D. Lacour, J.-P. Plumey, G. Granet, and A. M. Ravaud, “Resonant waveguide grating: analysis of polarization independent filtering,” Opt. Quantum Electron. 33, 451-470 (2001).
    [CrossRef]
  9. A.-L. Fehrembach and A. Sentenac, “Study of waveguide grating eigenmodes for unpolarized filtering applications,” J. Opt. Soc. Am. A 20, 481-488 (2003).
    [CrossRef]
  10. A.-L. Fehrembach and A. Sentenac, “Unpolarized narrow-band filtering with resonant gratings,” Appl. Phys. Lett. 86, 121105-3 (2005).
    [CrossRef]
  11. G. Niederer, H. P. Herzig, J. Shamir, H. Thiele, M. Schnieper, and C. Zschokke, “Tunable oblique incidence resonant grating filter for telecommunications,” Appl. Opt. 43, 1683-1694 (2004).
    [CrossRef] [PubMed]
  12. A. Sharon, D. Rosenblatt, and A. A. Friesem, “Narrow spectral bandwidths with grating waveguide filters,” Appl. Phys. Lett. 69, 4154-4156 (1996).
    [CrossRef]
  13. G. Niederer, W. Nakagawa, and H. P. Herzig, “Design and characterization of a tunable polarization-independent resonant grating filter,” Opt. Express 13, 2196-2200 (2005).
    [CrossRef] [PubMed]
  14. T. Clausnitzer, A. Tishchenko, E.-B. Kley, H.-J. Fuchs, D. Schelle, O. Parriaux, and U. Kroll, “Narrowband, polarization-independent free-space wave notch filter,” J. Opt. Soc. Am. A 22, 2799-2803 (2005).
    [CrossRef]
  15. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758-2767 (1997).
    [CrossRef]
  16. The angular tolerance of the resonance is estimated by calculating the FWHM of the reflectivity peak with respect to the incidence angle when the grating is illuminated by a plane wave.
  17. S. Boonruang, A. Greenwell, and M. G. Moharam, “Broadening the angular tolerance in two-dimensional grating resonance structures at oblique incidence,” Appl. Opt. 46, 7982-7992 (2007).
    [CrossRef] [PubMed]

2007 (2)

2005 (3)

2004 (1)

2003 (1)

2002 (1)

2001 (2)

A. Mizutani, H. Kikuta, K. Nakajima, and K. Iwata, “Nonpolarizing guided-mode resonant grating filter for oblique incidence,” J. Opt. Soc. Am. A 18, 1261-1266 (2001).
[CrossRef]

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

1998 (1)

1997 (2)

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

L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758-2767 (1997).
[CrossRef]

1996 (2)

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

S. Peng and M. G. Morris, “Experimental demonstration of resonant anomalies in diffraction from two-dimensional gratings,” Opt. Lett. 21, 549-551 (1996).
[CrossRef] [PubMed]

1986 (1)

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

Boonruang, S.

Boyko, O.

Clausnitzer, T.

Fehrembach, A.-L.

Friesem, A. A.

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

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

Fuchs, H.-J.

Giovannini, H.

Granet, G.

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

Greenwell, A.

Herzig, H. P.

Iwata, K.

Kikuta, H.

Kley, E.-B.

Kroll, U.

Lacour, D.

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

Lemarchand, F.

Li, L.

Mashev, L.

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

Maystre, D.

A.-L. Fehrembach, D. Maystre, and A. Sentenac, “Phenomenological theory of filtering by resonant dielectric gratings,” J. Opt. Soc. Am. A 19, 1136-1144 (2002).
[CrossRef]

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

Mizutani, A.

Moharam, M. G.

Morris, M. G.

Nakagawa, W.

Nakajima, K.

Niederer, G.

Parriaux, O.

Peng, S.

Plumey, J.-P.

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

Popov, E.

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

Ravaud, A. M.

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

Rosenblatt, D.

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

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

Schelle, D.

Schnieper, M.

Sentenac, A.

Shamir, J.

Sharon, A.

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

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

Talneau, A.

Thiele, H.

Tishchenko, A.

Zschokke, C.

Appl. Opt. (2)

Appl. Phys. Lett. (2)

A.-L. Fehrembach and A. Sentenac, “Unpolarized narrow-band filtering with resonant gratings,” Appl. Phys. Lett. 86, 121105-3 (2005).
[CrossRef]

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

IEEE J. Quantum Electron. (1)

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

J. Opt. Soc. Am. A (5)

Opt. Acta (1)

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

Opt. Express (1)

Opt. Lett. (3)

Opt. Quantum Electron. (1)

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

Other (1)

The angular tolerance of the resonance is estimated by calculating the FWHM of the reflectivity peak with respect to the incidence angle when the grating is illuminated by a plane wave.

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Figures (4)

Fig. 1
Fig. 1

Graphical representation of coupling condition for four guided waves. (a) At normal incidence. (b) At oblique incidence.

Fig. 2
Fig. 2

Description of the manufactured component designed with the Fourier modal method [15]. (a) Top view of component: periodic pattern (period d = 890 nm ) of four air holes A, B, C (diameters d A = 257 nm , d B = 347 nm , d C = 170 nm ). (b) Four-layer stack of Ta 2 O 5 and Si O 2 on a glass substrate [refractive indices n ( air ) = 1 , n ( Ta 2 O 5 ) = 2.093 , n ( Si O 2 ) = 1.47 , and n ( glass ) = 1.443 , and layer thickness from top to bottom of 220, 109, 63, and 126 nm ; first is engraved].

Fig. 3
Fig. 3

(a) Calculated and (b) measured resonance positions with respect to the angle of incidence ( θ ) and wavelength ( λ ) for both polarizations s ̂ (squares) and p ̂ (crosses). Inset: Scanning electron microscopy image of the component.

Fig. 4
Fig. 4

(a) Calculated resonance at θ = 5.765 ° of incidence (point A) and at θ = 5.465 ° (point B). (b) Measured resonance at θ = 5.8 ° (point A ) and at θ = 5.5 ° (point B ).

Equations (2)

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k inc + m K x + n K y k m ,
{ k inc + K x = k inc + K y k m 1 k inc + K x = k inc + K y k m 2 } .

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