Abstract

Polarization independence in a one-dimensional resonant grating waveguide structure involves the simultaneous excitation of two guided modes propagating in different directions. Possible simultaneous excitations occur when the two excited guided modes have either the same polarization, i.e., TE–TE (transverse electric) or TM–TM (transverse magnetic), or different polarizations, i.e., TE–TM. Simultaneous excitations may result in bandgaps and singularities. We confirm and show that in order to achieve polarization independence, it is necessary to find the conditions that minimize the effects of such bandgaps and singularities and experimentally demonstrate tunable polarization independence for simultaneously excited TE–TM-guided modes.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2007 (1)

2006 (2)

N. Ganesh, I. D. Block, and B. T. Cunningham, “Near ultraviolet-wavelength photonic-crystal biosensor with enhanced surface-to-bulk sensitivity ratio,” Appl. Phys. Lett. 89, 316-328 (2006).
[CrossRef]

A.-L. Fehrembach, S. Hernandez, and A. Sentenac, “k gaps for multimode waveguide gratings,” Phys. Rev. B 73, 233405 (2006).
[CrossRef]

2005 (3)

2004 (1)

2003 (2)

2002 (1)

2001 (3)

1998 (1)

F. Lemarchand, A. Sentenac, and H. Giovannini, “Increasing the angular tolerance of resonant grating filters with doubly periodic structures,” Opt. Lett. 15, 1149-1151 (1998).
[CrossRef]

1997 (1)

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

1996 (2)

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

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227-6244 (1996).
[CrossRef]

1995 (1)

1993 (1)

1989 (1)

E. Popov, “Plasmon interactions in metallic gratings: w- and k-minigaps and their connection with poles and zeros,” Surf. Sci. 222, 517-527 (1989).
[CrossRef]

1988 (1)

1987 (2)

D. Heitmann, N. Kroo, C. Schulz, and Z. Szentirmay, “Dispersion anomalies of surface plasmons on corrugated metal-insulator interfaces,” Phys. Rev. B 35, 2660-2666 (1987).
[CrossRef]

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589-1617 (1987).
[CrossRef]

1986 (1)

P. S. J. Russell, “Optics of Floquet-Bloch waves in dielectric gratings,” Appl. Phys. B: Photophys. Laser Chem. 39, 231-246 (1986).
[CrossRef]

Avrutsky, I.

Barnes, W. L.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227-6244 (1996).
[CrossRef]

Block, I. D.

N. Ganesh, I. D. Block, and B. T. Cunningham, “Near ultraviolet-wavelength photonic-crystal biosensor with enhanced surface-to-bulk sensitivity ratio,” Appl. Phys. Lett. 89, 316-328 (2006).
[CrossRef]

Boyko, O.

Celli, V.

Cunningham, B. T.

N. Ganesh, I. D. Block, and B. T. Cunningham, “Near ultraviolet-wavelength photonic-crystal biosensor with enhanced surface-to-bulk sensitivity ratio,” Appl. Phys. Lett. 89, 316-328 (2006).
[CrossRef]

Fehrembach, A.-L.

Friesem, A. A.

Ganesh, N.

N. Ganesh, I. D. Block, and B. T. Cunningham, “Near ultraviolet-wavelength photonic-crystal biosensor with enhanced surface-to-bulk sensitivity ratio,” Appl. Phys. Lett. 89, 316-328 (2006).
[CrossRef]

Gaylord, T. K.

Giovannini, H.

F. Lemarchand, A. Sentenac, and H. Giovannini, “Increasing the angular tolerance of resonant grating filters with doubly periodic structures,” Opt. Lett. 15, 1149-1151 (1998).
[CrossRef]

Granet, G.

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

Grann, E. B.

Heitmann, D.

D. Heitmann, N. Kroo, C. Schulz, and Z. Szentirmay, “Dispersion anomalies of surface plasmons on corrugated metal-insulator interfaces,” Phys. Rev. B 35, 2660-2666 (1987).
[CrossRef]

Hernandez, S.

A.-L. Fehrembach, S. Hernandez, and A. Sentenac, “k gaps for multimode waveguide gratings,” Phys. Rev. B 73, 233405 (2006).
[CrossRef]

Herzig, H. P.

Hierle, R.

Iwata, K.

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals -- Molding the Flow of Light (Princeton U. Press, 1995).

Katchalski, T.

Kikuta, H.

Kitson, S. C.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227-6244 (1996).
[CrossRef]

Kroo, N.

D. Heitmann, N. Kroo, C. Schulz, and Z. Szentirmay, “Dispersion anomalies of surface plasmons on corrugated metal-insulator interfaces,” Phys. Rev. B 35, 2660-2666 (1987).
[CrossRef]

Lacour, D.

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

Lemarchand, F.

A.-L. Fehrembach, A. Talneau, O. Boyko, F. Lemarchand, and A. Sentenac, “Experimental demonstration of a narrowband, angular tolerant, polarization independent, doubly periodic resonant grating filter,” Opt. Lett. 32, 2269-2271 (2007).
[CrossRef] [PubMed]

F. Lemarchand, A. Sentenac, and H. Giovannini, “Increasing the angular tolerance of resonant grating filters with doubly periodic structures,” Opt. Lett. 15, 1149-1151 (1998).
[CrossRef]

Levy-Yurista, G.

Magnusson, R.

Maradudin, A. A.

Marowsky, G.

Martin, G.

Maystre, D.

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals -- Molding the Flow of Light (Princeton U. Press, 1995).

Mizutani, A.

Moharam, M. G.

Morris, M.

Nakagawa, W.

Nakajima, K.

Niederer, G.

Peng, S.

Plumey, J.-P.

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

Pommet, D. A.

Popov, E.

E. Popov, “Plasmon interactions in metallic gratings: w- and k-minigaps and their connection with poles and zeros,” Surf. Sci. 222, 517-527 (1989).
[CrossRef]

Preist, T. W.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227-6244 (1996).
[CrossRef]

Rabady, R.

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]

Russell, P. S. J.

P. S. J. Russell, “Optics of Floquet-Bloch waves in dielectric gratings,” Appl. Phys. B: Photophys. Laser Chem. 39, 231-246 (1986).
[CrossRef]

Sambles, J. R.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227-6244 (1996).
[CrossRef]

Schulz, C.

D. Heitmann, N. Kroo, C. Schulz, and Z. Szentirmay, “Dispersion anomalies of surface plasmons on corrugated metal-insulator interfaces,” Phys. Rev. B 35, 2660-2666 (1987).
[CrossRef]

Sentenac, A.

A.-L. Fehrembach, A. Talneau, O. Boyko, F. Lemarchand, and A. Sentenac, “Experimental demonstration of a narrowband, angular tolerant, polarization independent, doubly periodic resonant grating filter,” Opt. Lett. 32, 2269-2271 (2007).
[CrossRef] [PubMed]

A.-L. Fehrembach, S. Hernandez, and A. Sentenac, “k gaps for multimode waveguide gratings,” Phys. Rev. B 73, 233405 (2006).
[CrossRef]

A.-L. Fehrembach and A. Sentenac, “Unpolarized narrow-band filtering with resonant gratings,” Appl. Phys. Lett. 86, 1105-1108 (2005).
[CrossRef]

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]

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]

F. Lemarchand, A. Sentenac, and H. Giovannini, “Increasing the angular tolerance of resonant grating filters with doubly periodic structures,” Opt. Lett. 15, 1149-1151 (1998).
[CrossRef]

Sharon, A.

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

Soria, S.

Szentirmay, Z.

D. Heitmann, N. Kroo, C. Schulz, and Z. Szentirmay, “Dispersion anomalies of surface plasmons on corrugated metal-insulator interfaces,” Phys. Rev. B 35, 2660-2666 (1987).
[CrossRef]

Talneau, A.

Teitelbaum, E.

Tran, P.

Wang, S. S.

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals -- Molding the Flow of Light (Princeton U. Press, 1995).

Zengerle, R.

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589-1617 (1987).
[CrossRef]

Zyss, J.

Appl. Opt. (1)

Appl. Phys. B: Photophys. Laser Chem. (1)

P. S. J. Russell, “Optics of Floquet-Bloch waves in dielectric gratings,” Appl. Phys. B: Photophys. Laser Chem. 39, 231-246 (1986).
[CrossRef]

Appl. Phys. Lett. (2)

N. Ganesh, I. D. Block, and B. T. Cunningham, “Near ultraviolet-wavelength photonic-crystal biosensor with enhanced surface-to-bulk sensitivity ratio,” Appl. Phys. Lett. 89, 316-328 (2006).
[CrossRef]

A.-L. Fehrembach and A. Sentenac, “Unpolarized narrow-band filtering with resonant gratings,” Appl. Phys. Lett. 86, 1105-1108 (2005).
[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. Mod. Opt. (1)

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589-1617 (1987).
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (6)

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]

Phys. Rev. B (3)

D. Heitmann, N. Kroo, C. Schulz, and Z. Szentirmay, “Dispersion anomalies of surface plasmons on corrugated metal-insulator interfaces,” Phys. Rev. B 35, 2660-2666 (1987).
[CrossRef]

A.-L. Fehrembach, S. Hernandez, and A. Sentenac, “k gaps for multimode waveguide gratings,” Phys. Rev. B 73, 233405 (2006).
[CrossRef]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B 54, 6227-6244 (1996).
[CrossRef]

Surf. Sci. (1)

E. Popov, “Plasmon interactions in metallic gratings: w- and k-minigaps and their connection with poles and zeros,” Surf. Sci. 222, 517-527 (1989).
[CrossRef]

Other (2)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals -- Molding the Flow of Light (Princeton U. Press, 1995).

GSolver, Grating Solver Development Company, http://www.gsolver.com.

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Figures (9)

Fig. 1
Fig. 1

Basic GWS configuration with geometrical and optical parameters and incident light orientation denoted by (a) “spherical” angles φ and θ. A specific plane of incidence is defined by the value of φ. (b) “Cartesian” angles θ C along the classical plane of incidence and θ C O N along the full conical plane of incidence.

Fig. 2
Fig. 2

Wave-vector diagrams showing conditions for which TE- and TM-guided modes are simultaneously excited at classical ( λ 1 ) and off-classical ( λ 2 ) incidence.

Fig. 3
Fig. 3

Numerically calculated reflection efficiency as a function of full conical incidence angle θ C O N and the wavelength for TM–TM- and TE–TE-excited guided modes. (a) Circularly polarized incident light, (b) s-polarized incident light, (c) p-polarized incident light. (See color online for details of color-coded reflection efficiency.)

Fig. 4
Fig. 4

Numerically calculated reflection efficiency of right-handed circularly polarized incident light as a function of θ C O N and θ C , for two wavelengths λ 1 = 1.528 μ m and λ 2 = 1.512 μ m , and TE–TM-excited guided modes. Near polarization independence occurs at intersections. (See color online for details of color-coded reflection efficiency.)

Fig. 5
Fig. 5

Numerically calculated angular orientations of the incident light at which the reflection efficiency is 99.99% or more, revealing the angular band structures for four different duty cycles and the corresponding wavelengths. Each segment of the bands is calculated for a different incident light polarization, as labeled. In each figure the star denotes the angular orientation of the incident light at which maximal average reflection efficiency is obtained for two orthogonal polarizations: (a) 50 % grating duty cycle and λ = 1.512 μ m , where a k gap is evident; (b) 41.63% grating duty cycle and λ = 1.508 μ m , where a band crossing is evident; (c) 25% grating duty cycle and λ = 1.503 μ m , where a k y gap corresponding to a frequency bandgap is evident; (d) 47.2% grating duty cycle and λ = 1.5105 μ m , where a k gap is evident.

Fig. 6
Fig. 6

Numerically calculated gray-scale-coded reflection efficiency as a function of the polarization of the incident light [ α , β ] for the same four duty cycles and wavelengths of Fig. 5. The results are for the angular orientation denoted by a star in Fig. 5. The average reflection efficiency and maximal deviations are (a) 91.5 % ± 7.5 % at [ θ C , θ C O N = 1.26 ° , 12.82 ° ] ; (b) 87 % ± 13 % at [ 1.29 ° , 13.15 ° ] ; (c) 57.5 % ± 42.5 % at [ 1.32 ° , 13.01 ° ] ; (d) 93 % ± 1.5 % at [ 1.27 ° , 12.96 ° ] . (See color online for details of color-coded reflection efficiency.)

Fig. 7
Fig. 7

Numerically calculated reflection efficiency as a function of wavelength for four GWSs, each with a different grating duty cycle. The resonances at the higher wavelengths are for TE–TM crossing and classical angular orientations, where s polarization is denoted by the dotted curve and p polarization by squares. The resonances at the lower wavelengths are for TE–TM simultaneous excitations and the conical angular orientations marked by stars in Fig. 5, where the dashed curve denotes maximal polarization and the circles denote minimal polarization obtained from Fig. 6. (a) Grating duty cycle of 50 % , (b) grating duty cycle of 41.63 % , (c) grating duty cycle of 25 % , (d) grating duty cycle of 47.2 % .

Fig. 8
Fig. 8

Experimental arrangement for measuring the reflection efficiency as a function of the incident wavelength, polarization, and angular orientation ( θ C , θ C O N ) .

Fig. 9
Fig. 9

Experimental polarization-independent results. (a) Reflection efficiency as a function of wavelength at classical and off-classical incidence. Solid curve denotes s-polarized incident light, dotted curve p-polarized, and dashed curve 45 ° linearly polarized light. (b) Reflection efficiency as a function of the conical angle θ C O N (for a fixed wavelength). (c) Reflection efficiency as a function of the classical angle θ C (for a fixed wavelength).

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

sin ( θ C ) = sin ( θ ) cos ( φ ) ,
sin ( θ C O N ) = sin ( θ ) sin ( φ ) .
β T E T M 2 = ( k x m K x ) 2 + k y 2 ,

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