Abstract

An analogue of phase-shifted Bragg grating (PSBG) for Bloch surface waves (BSW) propagating along the interface between a one-dimensional photonic crystal and a homogeneous medium is proposed. The studied structure consists of a set of dielectric ridges located on the photonic crystal surface, the height of which is chosen so that they encode the required distribution of the effective refractive index. Rigorous simulation results of the surface wave diffraction on the proposed structure are compared with the plane wave diffraction on a conventional phase-shifted Bragg grating. The simulation results demonstrate the possibility of using the proposed analogue of PSBG for temporal differentiation of picosecond BSW pulses. The obtained results can find application in the design of the prospective on-chip systems for all-optical analog computing.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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2015 (1)

N. V. Golovastikov, D. A. Bykov, L. L. Doskolovich, and E. A. Bezus, “Spatial optical integrator based on phase-shifted Bragg gratings,” Opt. Commun. 338, 457–460 (2015).
[Crossref]

2014 (8)

D. A. Bykov, L. L. Doskolovich, E. A. Bezus, and V. A. Soifer, “Optical computation of the Laplace operator using phase-shifted Bragg grating,” Opt. Express 22(21), 25084–25092 (2014).
[Crossref] [PubMed]

L. L. Doskolovich, D. A. Bykov, E. A. Bezus, and V. A. Soifer, “Spatial differentiation of optical beams using phase-shifted Bragg grating,” Opt. Lett. 39(5), 1278–1281 (2014).
[Crossref] [PubMed]

N. L. Kazanskiy and P. G. Serafimovich, “Coupled-resonator optical waveguides for temporal integration of optical signals,” Opt. Express 22(11), 14004–14013 (2014).
[Crossref] [PubMed]

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343(6167), 160–163 (2014).
[Crossref] [PubMed]

N. V. Golovastikov, D. A. Bykov, and L. L. Doskolovich, “Resonant diffraction gratings for spatial differentiation of optical beams,” Quantum Electron. 44(10), 984–988 (2014).
[Crossref]

L. Yu, E. Barakat, W. Nakagawa, and H. P. Herzig, “Investigation of ultra-thin waveguide arrays on a Bloch surface wave platform,” J. Opt. Soc. Am. B 31(12), 2996–3000 (2014).
[Crossref]

X. Wu, E. Barakat, L. Yu, L. Sun, J. Wang, Q. Tan, and H. P. Herzig, “Phase-sensitive near field Investigation of Bloch surface wave propagation in curved waveguides,” J. Europ. Opt. Soc. Rapid Publ. 9, 14049 (2014).
[Crossref]

E. A. Bezus, L. L. Doskolovich, D. A. Bykov, and V. A. Soifer, “Phase modulation of Bloch surface waves with the use of a diffraction microrelief at the boundary of a one-dimensional photonic crystal,” JETP Lett. 99(2), 63–66 (2014).
[Crossref]

2013 (1)

2012 (1)

2011 (2)

2010 (5)

S. Randhawa, M. U. González, J. Renger, S. Enoch, and R. Quidant, “Design and properties of dielectric surface plasmon Bragg mirrors,” Opt. Express 18(14), 14496–14510 (2010).
[Crossref] [PubMed]

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,” Phys. Usp. 53(3), 243–256 (2010).
[Crossref]

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Two-dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[Crossref]

E. Descrovi, T. Sfez, M. Quaglio, D. Brunazzo, L. Dominici, F. Michelotti, H. P. Herzig, O. J. F. Martin, and F. Giorgis, “Guided Bloch surface waves on ultrathin polymeric ridges,” Nano Lett. 10(6), 2087–2091 (2010).
[Crossref] [PubMed]

T. Sfez, E. Descrovi, L. Yu, D. Brunazzo, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, O. J. F. Martin, and H. P. Herzig, “Bloch surface waves in ultrathin waveguides: near-field investigation of mode polarization and propagation,” J. Opt. Soc. Am. B 27(8), 1617–1625 (2010).
[Crossref]

2009 (2)

2008 (4)

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008).
[Crossref]

C. Vandenbem, “Electromagnetic surface waves of multilayer stacks: coupling between guided modes and Bloch modes,” Opt. Lett. 33(19), 2260–2262 (2008).
[Crossref] [PubMed]

T. Sfez, E. Descrovi, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Near-field analysis of surface electromagnetic waves in the bandgap region of a polymeric grating written on a one-dimensional photonic crystal,” Appl. Phys. Lett. 93(6), 061108 (2008).
[Crossref]

E. Descrovi, F. Giorgis, L. Dominici, and F. Michelotti, “Experimental observation of optical bandgaps for surface electromagnetic waves in a periodically corrugated one-dimensional silicon nitride photonic crystal,” Opt. Lett. 33(3), 243–245 (2008).
[Crossref] [PubMed]

2007 (3)

2006 (1)

2005 (2)

N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, “Optical properties of photonic crystal slabs with an asymmetrical unit cell,” Phys. Rev. B 72(4), 045138 (2005).
[Crossref]

S. Jetté-Charbonneau, R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of Bragg gratings based on long-ranging surface plasmon polariton waveguides,” Opt. Express 13(12), 4674–4682 (2005).
[Crossref] [PubMed]

2001 (1)

Alù, A.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343(6167), 160–163 (2014).
[Crossref] [PubMed]

Azaña, J.

Barakat, E.

X. Wu, E. Barakat, L. Yu, L. Sun, J. Wang, Q. Tan, and H. P. Herzig, “Phase-sensitive near field Investigation of Bloch surface wave propagation in curved waveguides,” J. Europ. Opt. Soc. Rapid Publ. 9, 14049 (2014).
[Crossref]

L. Yu, E. Barakat, W. Nakagawa, and H. P. Herzig, “Investigation of ultra-thin waveguide arrays on a Bloch surface wave platform,” J. Opt. Soc. Am. B 31(12), 2996–3000 (2014).
[Crossref]

Berger, N. K.

Berini, P.

Bezus, E. A.

N. V. Golovastikov, D. A. Bykov, L. L. Doskolovich, and E. A. Bezus, “Spatial optical integrator based on phase-shifted Bragg gratings,” Opt. Commun. 338, 457–460 (2015).
[Crossref]

E. A. Bezus, L. L. Doskolovich, D. A. Bykov, and V. A. Soifer, “Phase modulation of Bloch surface waves with the use of a diffraction microrelief at the boundary of a one-dimensional photonic crystal,” JETP Lett. 99(2), 63–66 (2014).
[Crossref]

L. L. Doskolovich, D. A. Bykov, E. A. Bezus, and V. A. Soifer, “Spatial differentiation of optical beams using phase-shifted Bragg grating,” Opt. Lett. 39(5), 1278–1281 (2014).
[Crossref] [PubMed]

D. A. Bykov, L. L. Doskolovich, E. A. Bezus, and V. A. Soifer, “Optical computation of the Laplace operator using phase-shifted Bragg grating,” Opt. Express 22(21), 25084–25092 (2014).
[Crossref] [PubMed]

Boltasseva, A.

Boudreau, S.

Bozhevolnyi, S. I.

Brunazzo, D.

E. Descrovi, T. Sfez, M. Quaglio, D. Brunazzo, L. Dominici, F. Michelotti, H. P. Herzig, O. J. F. Martin, and F. Giorgis, “Guided Bloch surface waves on ultrathin polymeric ridges,” Nano Lett. 10(6), 2087–2091 (2010).
[Crossref] [PubMed]

T. Sfez, E. Descrovi, L. Yu, D. Brunazzo, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, O. J. F. Martin, and H. P. Herzig, “Bloch surface waves in ultrathin waveguides: near-field investigation of mode polarization and propagation,” J. Opt. Soc. Am. B 27(8), 1617–1625 (2010).
[Crossref]

Bykov, D. A.

N. V. Golovastikov, D. A. Bykov, L. L. Doskolovich, and E. A. Bezus, “Spatial optical integrator based on phase-shifted Bragg gratings,” Opt. Commun. 338, 457–460 (2015).
[Crossref]

N. V. Golovastikov, D. A. Bykov, and L. L. Doskolovich, “Resonant diffraction gratings for spatial differentiation of optical beams,” Quantum Electron. 44(10), 984–988 (2014).
[Crossref]

E. A. Bezus, L. L. Doskolovich, D. A. Bykov, and V. A. Soifer, “Phase modulation of Bloch surface waves with the use of a diffraction microrelief at the boundary of a one-dimensional photonic crystal,” JETP Lett. 99(2), 63–66 (2014).
[Crossref]

D. A. Bykov, L. L. Doskolovich, E. A. Bezus, and V. A. Soifer, “Optical computation of the Laplace operator using phase-shifted Bragg grating,” Opt. Express 22(21), 25084–25092 (2014).
[Crossref] [PubMed]

L. L. Doskolovich, D. A. Bykov, E. A. Bezus, and V. A. Soifer, “Spatial differentiation of optical beams using phase-shifted Bragg grating,” Opt. Lett. 39(5), 1278–1281 (2014).
[Crossref] [PubMed]

D. A. Bykov, L. L. Doskolovich, and V. A. Soifer, “Single-resonance diffraction gratings for time-domain pulse transformations: integration of optical signals,” J. Opt. Soc. Am. A 29(8), 1734–1740 (2012).
[Crossref] [PubMed]

D. A. Bykov, L. L. Doskolovich, and V. A. Soifer, “Temporal differentiation of optical signals using resonant gratings,” Opt. Lett. 36(17), 3509–3511 (2011).
[Crossref] [PubMed]

Cao, Q.

Carballar, A.

Castaldi, G.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343(6167), 160–163 (2014).
[Crossref] [PubMed]

Charbonneau, R.

Chu, S. T.

Descrovi, E.

T. Sfez, E. Descrovi, L. Yu, D. Brunazzo, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, O. J. F. Martin, and H. P. Herzig, “Bloch surface waves in ultrathin waveguides: near-field investigation of mode polarization and propagation,” J. Opt. Soc. Am. B 27(8), 1617–1625 (2010).
[Crossref]

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Two-dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[Crossref]

E. Descrovi, T. Sfez, M. Quaglio, D. Brunazzo, L. Dominici, F. Michelotti, H. P. Herzig, O. J. F. Martin, and F. Giorgis, “Guided Bloch surface waves on ultrathin polymeric ridges,” Nano Lett. 10(6), 2087–2091 (2010).
[Crossref] [PubMed]

T. Sfez, E. Descrovi, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Near-field analysis of surface electromagnetic waves in the bandgap region of a polymeric grating written on a one-dimensional photonic crystal,” Appl. Phys. Lett. 93(6), 061108 (2008).
[Crossref]

E. Descrovi, F. Giorgis, L. Dominici, and F. Michelotti, “Experimental observation of optical bandgaps for surface electromagnetic waves in a periodically corrugated one-dimensional silicon nitride photonic crystal,” Opt. Lett. 33(3), 243–245 (2008).
[Crossref] [PubMed]

Dominici, L.

T. Sfez, E. Descrovi, L. Yu, D. Brunazzo, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, O. J. F. Martin, and H. P. Herzig, “Bloch surface waves in ultrathin waveguides: near-field investigation of mode polarization and propagation,” J. Opt. Soc. Am. B 27(8), 1617–1625 (2010).
[Crossref]

E. Descrovi, T. Sfez, M. Quaglio, D. Brunazzo, L. Dominici, F. Michelotti, H. P. Herzig, O. J. F. Martin, and F. Giorgis, “Guided Bloch surface waves on ultrathin polymeric ridges,” Nano Lett. 10(6), 2087–2091 (2010).
[Crossref] [PubMed]

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Two-dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[Crossref]

T. Sfez, E. Descrovi, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Near-field analysis of surface electromagnetic waves in the bandgap region of a polymeric grating written on a one-dimensional photonic crystal,” Appl. Phys. Lett. 93(6), 061108 (2008).
[Crossref]

E. Descrovi, F. Giorgis, L. Dominici, and F. Michelotti, “Experimental observation of optical bandgaps for surface electromagnetic waves in a periodically corrugated one-dimensional silicon nitride photonic crystal,” Opt. Lett. 33(3), 243–245 (2008).
[Crossref] [PubMed]

Dorofeenko, A. V.

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,” Phys. Usp. 53(3), 243–256 (2010).
[Crossref]

Doskolovich, L. L.

N. V. Golovastikov, D. A. Bykov, L. L. Doskolovich, and E. A. Bezus, “Spatial optical integrator based on phase-shifted Bragg gratings,” Opt. Commun. 338, 457–460 (2015).
[Crossref]

N. V. Golovastikov, D. A. Bykov, and L. L. Doskolovich, “Resonant diffraction gratings for spatial differentiation of optical beams,” Quantum Electron. 44(10), 984–988 (2014).
[Crossref]

E. A. Bezus, L. L. Doskolovich, D. A. Bykov, and V. A. Soifer, “Phase modulation of Bloch surface waves with the use of a diffraction microrelief at the boundary of a one-dimensional photonic crystal,” JETP Lett. 99(2), 63–66 (2014).
[Crossref]

L. L. Doskolovich, D. A. Bykov, E. A. Bezus, and V. A. Soifer, “Spatial differentiation of optical beams using phase-shifted Bragg grating,” Opt. Lett. 39(5), 1278–1281 (2014).
[Crossref] [PubMed]

D. A. Bykov, L. L. Doskolovich, E. A. Bezus, and V. A. Soifer, “Optical computation of the Laplace operator using phase-shifted Bragg grating,” Opt. Express 22(21), 25084–25092 (2014).
[Crossref] [PubMed]

D. A. Bykov, L. L. Doskolovich, and V. A. Soifer, “Single-resonance diffraction gratings for time-domain pulse transformations: integration of optical signals,” J. Opt. Soc. Am. A 29(8), 1734–1740 (2012).
[Crossref] [PubMed]

D. A. Bykov, L. L. Doskolovich, and V. A. Soifer, “Temporal differentiation of optical signals using resonant gratings,” Opt. Lett. 36(17), 3509–3511 (2011).
[Crossref] [PubMed]

Ebbesen, T. W.

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008).
[Crossref]

Engheta, N.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343(6167), 160–163 (2014).
[Crossref] [PubMed]

Enoch, S.

Ferrera, M.

Fischer, B.

Galdi, V.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343(6167), 160–163 (2014).
[Crossref] [PubMed]

Genet, C.

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008).
[Crossref]

Giorgis, F.

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Two-dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[Crossref]

E. Descrovi, T. Sfez, M. Quaglio, D. Brunazzo, L. Dominici, F. Michelotti, H. P. Herzig, O. J. F. Martin, and F. Giorgis, “Guided Bloch surface waves on ultrathin polymeric ridges,” Nano Lett. 10(6), 2087–2091 (2010).
[Crossref] [PubMed]

T. Sfez, E. Descrovi, L. Yu, D. Brunazzo, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, O. J. F. Martin, and H. P. Herzig, “Bloch surface waves in ultrathin waveguides: near-field investigation of mode polarization and propagation,” J. Opt. Soc. Am. B 27(8), 1617–1625 (2010).
[Crossref]

E. Descrovi, F. Giorgis, L. Dominici, and F. Michelotti, “Experimental observation of optical bandgaps for surface electromagnetic waves in a periodically corrugated one-dimensional silicon nitride photonic crystal,” Opt. Lett. 33(3), 243–245 (2008).
[Crossref] [PubMed]

T. Sfez, E. Descrovi, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Near-field analysis of surface electromagnetic waves in the bandgap region of a polymeric grating written on a one-dimensional photonic crystal,” Appl. Phys. Lett. 93(6), 061108 (2008).
[Crossref]

Gippius, N. A.

N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, “Optical properties of photonic crystal slabs with an asymmetrical unit cell,” Phys. Rev. B 72(4), 045138 (2005).
[Crossref]

Golovastikov, N. V.

N. V. Golovastikov, D. A. Bykov, L. L. Doskolovich, and E. A. Bezus, “Spatial optical integrator based on phase-shifted Bragg gratings,” Opt. Commun. 338, 457–460 (2015).
[Crossref]

N. V. Golovastikov, D. A. Bykov, and L. L. Doskolovich, “Resonant diffraction gratings for spatial differentiation of optical beams,” Quantum Electron. 44(10), 984–988 (2014).
[Crossref]

González, M. U.

Herzig, H. P.

X. Wu, E. Barakat, L. Yu, L. Sun, J. Wang, Q. Tan, and H. P. Herzig, “Phase-sensitive near field Investigation of Bloch surface wave propagation in curved waveguides,” J. Europ. Opt. Soc. Rapid Publ. 9, 14049 (2014).
[Crossref]

L. Yu, E. Barakat, W. Nakagawa, and H. P. Herzig, “Investigation of ultra-thin waveguide arrays on a Bloch surface wave platform,” J. Opt. Soc. Am. B 31(12), 2996–3000 (2014).
[Crossref]

E. Descrovi, T. Sfez, M. Quaglio, D. Brunazzo, L. Dominici, F. Michelotti, H. P. Herzig, O. J. F. Martin, and F. Giorgis, “Guided Bloch surface waves on ultrathin polymeric ridges,” Nano Lett. 10(6), 2087–2091 (2010).
[Crossref] [PubMed]

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Two-dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[Crossref]

T. Sfez, E. Descrovi, L. Yu, D. Brunazzo, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, O. J. F. Martin, and H. P. Herzig, “Bloch surface waves in ultrathin waveguides: near-field investigation of mode polarization and propagation,” J. Opt. Soc. Am. B 27(8), 1617–1625 (2010).
[Crossref]

T. Sfez, E. Descrovi, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Near-field analysis of surface electromagnetic waves in the bandgap region of a polymeric grating written on a one-dimensional photonic crystal,” Appl. Phys. Lett. 93(6), 061108 (2008).
[Crossref]

Hugonin, J.-P.

Ishihara, T.

N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, “Optical properties of photonic crystal slabs with an asymmetrical unit cell,” Phys. Rev. B 72(4), 045138 (2005).
[Crossref]

Jetté-Charbonneau, S.

Kazanskiy, N. L.

Khonina, S. N.

Kulishov, M.

Lahoud, N.

Lalanne, P.

Larochelle, S.

Leosson, K.

Levit, B.

Lisyansky, A. A.

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,” Phys. Usp. 53(3), 243–256 (2010).
[Crossref]

Little, B. E.

Martin, O. J. F.

T. Sfez, E. Descrovi, L. Yu, D. Brunazzo, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, O. J. F. Martin, and H. P. Herzig, “Bloch surface waves in ultrathin waveguides: near-field investigation of mode polarization and propagation,” J. Opt. Soc. Am. B 27(8), 1617–1625 (2010).
[Crossref]

E. Descrovi, T. Sfez, M. Quaglio, D. Brunazzo, L. Dominici, F. Michelotti, H. P. Herzig, O. J. F. Martin, and F. Giorgis, “Guided Bloch surface waves on ultrathin polymeric ridges,” Nano Lett. 10(6), 2087–2091 (2010).
[Crossref] [PubMed]

Mattiussi, G.

Merzlikin, A. M.

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,” Phys. Usp. 53(3), 243–256 (2010).
[Crossref]

Michelotti, F.

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Two-dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[Crossref]

E. Descrovi, T. Sfez, M. Quaglio, D. Brunazzo, L. Dominici, F. Michelotti, H. P. Herzig, O. J. F. Martin, and F. Giorgis, “Guided Bloch surface waves on ultrathin polymeric ridges,” Nano Lett. 10(6), 2087–2091 (2010).
[Crossref] [PubMed]

T. Sfez, E. Descrovi, L. Yu, D. Brunazzo, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, O. J. F. Martin, and H. P. Herzig, “Bloch surface waves in ultrathin waveguides: near-field investigation of mode polarization and propagation,” J. Opt. Soc. Am. B 27(8), 1617–1625 (2010).
[Crossref]

E. Descrovi, F. Giorgis, L. Dominici, and F. Michelotti, “Experimental observation of optical bandgaps for surface electromagnetic waves in a periodically corrugated one-dimensional silicon nitride photonic crystal,” Opt. Lett. 33(3), 243–245 (2008).
[Crossref] [PubMed]

T. Sfez, E. Descrovi, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Near-field analysis of surface electromagnetic waves in the bandgap region of a polymeric grating written on a one-dimensional photonic crystal,” Appl. Phys. Lett. 93(6), 061108 (2008).
[Crossref]

Monticone, F.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343(6167), 160–163 (2014).
[Crossref] [PubMed]

Morandotti, R.

Moss, D. J.

Nakagawa, W.

L. Yu, E. Barakat, W. Nakagawa, and H. P. Herzig, “Investigation of ultra-thin waveguide arrays on a Bloch surface wave platform,” J. Opt. Soc. Am. B 31(12), 2996–3000 (2014).
[Crossref]

T. Sfez, E. Descrovi, L. Yu, D. Brunazzo, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, O. J. F. Martin, and H. P. Herzig, “Bloch surface waves in ultrathin waveguides: near-field investigation of mode polarization and propagation,” J. Opt. Soc. Am. B 27(8), 1617–1625 (2010).
[Crossref]

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Two-dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[Crossref]

T. Sfez, E. Descrovi, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Near-field analysis of surface electromagnetic waves in the bandgap region of a polymeric grating written on a one-dimensional photonic crystal,” Appl. Phys. Lett. 93(6), 061108 (2008).
[Crossref]

Nikolajsen, T.

Park, Y.

Plant, D. V.

Quaglio, M.

T. Sfez, E. Descrovi, L. Yu, D. Brunazzo, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, O. J. F. Martin, and H. P. Herzig, “Bloch surface waves in ultrathin waveguides: near-field investigation of mode polarization and propagation,” J. Opt. Soc. Am. B 27(8), 1617–1625 (2010).
[Crossref]

E. Descrovi, T. Sfez, M. Quaglio, D. Brunazzo, L. Dominici, F. Michelotti, H. P. Herzig, O. J. F. Martin, and F. Giorgis, “Guided Bloch surface waves on ultrathin polymeric ridges,” Nano Lett. 10(6), 2087–2091 (2010).
[Crossref] [PubMed]

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Two-dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[Crossref]

Quidant, R.

Quoc Ngo, N.

Randhawa, S.

Razzari, L.

Renger, J.

Rivas, L. M.

Serafimovich, P. G.

Sfez, T.

T. Sfez, E. Descrovi, L. Yu, D. Brunazzo, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, O. J. F. Martin, and H. P. Herzig, “Bloch surface waves in ultrathin waveguides: near-field investigation of mode polarization and propagation,” J. Opt. Soc. Am. B 27(8), 1617–1625 (2010).
[Crossref]

E. Descrovi, T. Sfez, M. Quaglio, D. Brunazzo, L. Dominici, F. Michelotti, H. P. Herzig, O. J. F. Martin, and F. Giorgis, “Guided Bloch surface waves on ultrathin polymeric ridges,” Nano Lett. 10(6), 2087–2091 (2010).
[Crossref] [PubMed]

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Two-dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[Crossref]

T. Sfez, E. Descrovi, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Near-field analysis of surface electromagnetic waves in the bandgap region of a polymeric grating written on a one-dimensional photonic crystal,” Appl. Phys. Lett. 93(6), 061108 (2008).
[Crossref]

Silberstein, E.

Silva, A.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343(6167), 160–163 (2014).
[Crossref] [PubMed]

Slavík, R.

Soifer, V. A.

Sun, L.

X. Wu, E. Barakat, L. Yu, L. Sun, J. Wang, Q. Tan, and H. P. Herzig, “Phase-sensitive near field Investigation of Bloch surface wave propagation in curved waveguides,” J. Europ. Opt. Soc. Rapid Publ. 9, 14049 (2014).
[Crossref]

Tan, Q.

X. Wu, E. Barakat, L. Yu, L. Sun, J. Wang, Q. Tan, and H. P. Herzig, “Phase-sensitive near field Investigation of Bloch surface wave propagation in curved waveguides,” J. Europ. Opt. Soc. Rapid Publ. 9, 14049 (2014).
[Crossref]

Tikhodeev, S. G.

N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, “Optical properties of photonic crystal slabs with an asymmetrical unit cell,” Phys. Rev. B 72(4), 045138 (2005).
[Crossref]

Vandenbem, C.

Vinogradov, A. P.

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,” Phys. Usp. 53(3), 243–256 (2010).
[Crossref]

Wang, J.

X. Wu, E. Barakat, L. Yu, L. Sun, J. Wang, Q. Tan, and H. P. Herzig, “Phase-sensitive near field Investigation of Bloch surface wave propagation in curved waveguides,” J. Europ. Opt. Soc. Rapid Publ. 9, 14049 (2014).
[Crossref]

Wu, X.

X. Wu, E. Barakat, L. Yu, L. Sun, J. Wang, Q. Tan, and H. P. Herzig, “Phase-sensitive near field Investigation of Bloch surface wave propagation in curved waveguides,” J. Europ. Opt. Soc. Rapid Publ. 9, 14049 (2014).
[Crossref]

Yu, L.

X. Wu, E. Barakat, L. Yu, L. Sun, J. Wang, Q. Tan, and H. P. Herzig, “Phase-sensitive near field Investigation of Bloch surface wave propagation in curved waveguides,” J. Europ. Opt. Soc. Rapid Publ. 9, 14049 (2014).
[Crossref]

L. Yu, E. Barakat, W. Nakagawa, and H. P. Herzig, “Investigation of ultra-thin waveguide arrays on a Bloch surface wave platform,” J. Opt. Soc. Am. B 31(12), 2996–3000 (2014).
[Crossref]

T. Sfez, E. Descrovi, L. Yu, D. Brunazzo, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, O. J. F. Martin, and H. P. Herzig, “Bloch surface waves in ultrathin waveguides: near-field investigation of mode polarization and propagation,” J. Opt. Soc. Am. B 27(8), 1617–1625 (2010).
[Crossref]

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Two-dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[Crossref]

Appl. Phys. Lett. (2)

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Two-dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[Crossref]

T. Sfez, E. Descrovi, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, and H. P. Herzig, “Near-field analysis of surface electromagnetic waves in the bandgap region of a polymeric grating written on a one-dimensional photonic crystal,” Appl. Phys. Lett. 93(6), 061108 (2008).
[Crossref]

J. Europ. Opt. Soc. Rapid Publ. (1)

X. Wu, E. Barakat, L. Yu, L. Sun, J. Wang, Q. Tan, and H. P. Herzig, “Phase-sensitive near field Investigation of Bloch surface wave propagation in curved waveguides,” J. Europ. Opt. Soc. Rapid Publ. 9, 14049 (2014).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

JETP Lett. (1)

E. A. Bezus, L. L. Doskolovich, D. A. Bykov, and V. A. Soifer, “Phase modulation of Bloch surface waves with the use of a diffraction microrelief at the boundary of a one-dimensional photonic crystal,” JETP Lett. 99(2), 63–66 (2014).
[Crossref]

Nano Lett. (1)

E. Descrovi, T. Sfez, M. Quaglio, D. Brunazzo, L. Dominici, F. Michelotti, H. P. Herzig, O. J. F. Martin, and F. Giorgis, “Guided Bloch surface waves on ultrathin polymeric ridges,” Nano Lett. 10(6), 2087–2091 (2010).
[Crossref] [PubMed]

Opt. Commun. (1)

N. V. Golovastikov, D. A. Bykov, L. L. Doskolovich, and E. A. Bezus, “Spatial optical integrator based on phase-shifted Bragg gratings,” Opt. Commun. 338, 457–460 (2015).
[Crossref]

Opt. Express (7)

D. A. Bykov, L. L. Doskolovich, E. A. Bezus, and V. A. Soifer, “Optical computation of the Laplace operator using phase-shifted Bragg grating,” Opt. Express 22(21), 25084–25092 (2014).
[Crossref] [PubMed]

N. K. Berger, B. Levit, B. Fischer, M. Kulishov, D. V. Plant, and J. Azaña, “Temporal differentiation of optical signals using a phase-shifted fiber Bragg grating,” Opt. Express 15(2), 371–381 (2007).
[Crossref] [PubMed]

M. Kulishov and J. Azaña, “Design of high-order all-optical temporal differentiators based on multiple-phase-shifted fiber Bragg gratings,” Opt. Express 15(10), 6152–6166 (2007).
[Crossref] [PubMed]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “All-optical 1st and 2nd order integration on a chip,” Opt. Express 19(23), 23153–23161 (2011).
[Crossref] [PubMed]

N. L. Kazanskiy and P. G. Serafimovich, “Coupled-resonator optical waveguides for temporal integration of optical signals,” Opt. Express 22(11), 14004–14013 (2014).
[Crossref] [PubMed]

S. Randhawa, M. U. González, J. Renger, S. Enoch, and R. Quidant, “Design and properties of dielectric surface plasmon Bragg mirrors,” Opt. Express 18(14), 14496–14510 (2010).
[Crossref] [PubMed]

S. Jetté-Charbonneau, R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of Bragg gratings based on long-ranging surface plasmon polariton waveguides,” Opt. Express 13(12), 4674–4682 (2005).
[Crossref] [PubMed]

Opt. Lett. (8)

C. Vandenbem, “Electromagnetic surface waves of multilayer stacks: coupling between guided modes and Bloch modes,” Opt. Lett. 33(19), 2260–2262 (2008).
[Crossref] [PubMed]

E. Descrovi, F. Giorgis, L. Dominici, and F. Michelotti, “Experimental observation of optical bandgaps for surface electromagnetic waves in a periodically corrugated one-dimensional silicon nitride photonic crystal,” Opt. Lett. 33(3), 243–245 (2008).
[Crossref] [PubMed]

N. L. Kazanskiy, P. G. Serafimovich, and S. N. Khonina, “Use of photonic crystal cavities for temporal differentiation of optical signals,” Opt. Lett. 38(7), 1149–1151 (2013).
[Crossref] [PubMed]

N. Quoc Ngo, “Design of an optical temporal integrator based on a phase-shifted fiber Bragg grating in transmission,” Opt. Lett. 32(20), 3020–3022 (2007).
[Crossref] [PubMed]

L. L. Doskolovich, D. A. Bykov, E. A. Bezus, and V. A. Soifer, “Spatial differentiation of optical beams using phase-shifted Bragg grating,” Opt. Lett. 39(5), 1278–1281 (2014).
[Crossref] [PubMed]

D. A. Bykov, L. L. Doskolovich, and V. A. Soifer, “Temporal differentiation of optical signals using resonant gratings,” Opt. Lett. 36(17), 3509–3511 (2011).
[Crossref] [PubMed]

R. Slavík, Y. Park, M. Kulishov, and J. Azaña, “Terahertz-bandwidth high-order temporal differentiators based on phase-shifted long-period fiber gratings,” Opt. Lett. 34(20), 3116–3118 (2009).
[Crossref] [PubMed]

L. M. Rivas, S. Boudreau, Y. Park, R. Slavík, S. Larochelle, A. Carballar, and J. Azaña, “Experimental demonstration of ultrafast all-fiber high-order photonic temporal differentiators,” Opt. Lett. 34(12), 1792–1794 (2009).
[Crossref] [PubMed]

Phys. Rev. B (1)

N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, “Optical properties of photonic crystal slabs with an asymmetrical unit cell,” Phys. Rev. B 72(4), 045138 (2005).
[Crossref]

Phys. Today (1)

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008).
[Crossref]

Phys. Usp. (1)

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,” Phys. Usp. 53(3), 243–256 (2010).
[Crossref]

Quantum Electron. (1)

N. V. Golovastikov, D. A. Bykov, and L. L. Doskolovich, “Resonant diffraction gratings for spatial differentiation of optical beams,” Quantum Electron. 44(10), 984–988 (2014).
[Crossref]

Science (1)

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343(6167), 160–163 (2014).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

(a) Geometry of the structure. (b) Effective refractive indices of BSW of two adjacent orders vs. h c (ТЕ-polarization).

Fig. 2
Fig. 2

(a) Geometry of a PSBG for plane electromagnetic waves. (b) the refractive index profile of the considered PSBG. (c) Analogue of PSBG for BSW. The length scales in (c) correspond to the considered example, except the ridge height increased by 3 times for clarity.

Fig. 3
Fig. 3

Absolute values (left vertical axis) and phases (right vertical axis) of the PSBG complex reflection coefficient vs. angular frequency. Solid lines show the values for a BSW grating at N per = 4 (red curves) and N per = 5 (green curves). Dashed lines show the corresponding values for a conventional PSBG for plane electromagnetic waves.

Fig. 4
Fig. 4

The field distribution | E y ( x , z ) | generated upon BSW diffraction at a PSBG ( N per = 4 ) (a) and at a Bragg grating without defect having 9 periods (b). Grating ridge height is shown tripled (51 nm instead of 17 nm) for visual purposes.

Fig. 5
Fig. 5

(а) Normalized spectrum of the incident BSW pulse (dotted black curve); amplitude and phase of the PSBG transfer function at N per = 4 (solid red curves). (b) Envelope of the incident BSW pulse (solid black curve, right vertical axis), absolute value of the envelope of the reflected pulse (solid blue curve, left vertical axis), and absolute value of the analytically computed derivative of the Gaussian function (dashed green curve, left vertical axis). The exact derivative is normalized so that its amplitude is equal to the amplitude of the reflected pulse.

Fig. 6
Fig. 6

Envelope of the incident BSW pulse (solid black curve, right vertical axis), absolute value of the envelope of the reflected BSW pulse (solid blue curve, left vertical axis) at N per = 5 , and absolute value of the analytically computed derivative of the Gaussian function (dashed green curve, left vertical axis).

Tables (1)

Tables Icon

Table 1 Pearson correlation coefficient r between exact and optically computed derivatives and maximal amplitude of the reflected pulse P max for incident pulses with different durations T .

Equations (11)

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

E y , 1 ( x , z ) = exp ( i k x , 0 x ) { C 1 + exp [ i k z , 1 ( z + h 1 ) ] + C 1 exp ( i k z , 1 z ) } , h 1 z < 0 , E y , 2 ( x , z ) = exp ( i k x , 0 x ) { C 2 + exp [ i k z , 2 ( z + d ) ] + C 2 exp [ i k z , 2 ( z + h 1 ) ] } , d z < h 1 ,
cos ( k ˜ d ) = cos ( k z , 1 h 1 ) cos ( k z , 2 h 2 ) k z , 1 2 + k z , 2 2 2 k z , 1 k z , 2 sin ( k z , 1 h 1 ) sin ( k z , 2 h 2 ) .
E y , d ( x , z ) = exp ( i k x , 0 x ) exp [ i k z , d ( z h c ) ] ,
exp ( 2 i k z , 1 h c ) = exp ( i k z , 1 h 1 ) С k z , d + k z , 1 k z , d k z , 1 ,
n ˜ 1 l 1 = n ˜ 2 l 2 = λ B / 4 ,
H ( ω ) = R ( ω + ω 0 ) ,
B ( x , z , t ; ω ) = P ( z , ω ) exp [ i ω c n eff ( ω ) x ] exp ( i ω t ) ,
u inc ( x , z , t ) = exp [ i ω 0 c n eff ( ω 0 ) x i ω 0 t ] P inc ( x , z , t ) = G ( ω ω 0 ) B ( x , z , t ; ω ) d ω ,
P inc ( 0 , 0 , t ) = G ( ω ) exp ( i ω t ) d ω .
u refl ( x , z , t ) = exp [ i ω 0 c n eff ( ω 0 ) x i ω 0 t ] P refl ( x , z , t ) = G ( ω ω 0 ) B ( x , z , t ; ω ) R ( ω ) d ω ,
P refl ( 0 , 0 , t ) = G ( ω ) R ( ω + ω 0 ) exp ( i ω t ) d ω .

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