Abstract

We propose a simple planar optical differentiator consisting of two grooves on the surface of a slab waveguide. The studied differentiator operates in reflection and enables temporal and spatial differentiation of optical pulses and beams propagating in the waveguide. The differentiation is associated with the excitation of an eigenmode localized at the ridge located between the grooves. The presented numerical simulation results demonstrate high-quality spatial, temporal and the so-called spatiotemporal differentiation. The proposed differentiator may find application in ultrafast analog computing and signal processing systems.

© 2017 Optical Society of America

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References

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  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]
  2. 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]
  3. N. V. Golovastikov, D. A. Bykov, L. L. Doskolovich, and V. A. Soifer, “Analytical description of 3D optical pulse diffraction by a phase-shifted Bragg grating,” Opt. Express 24(17), 18828–18842 (2016).
    [Crossref] [PubMed]
  4. 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]
  5. K. A. Rutkowska, D. Duchesne, M. J. Strain, R. Morandotti, M. Sorel, and J. Azaña, “Ultrafast all-optical temporal differentiators based on CMOS-compatible integrated-waveguide Bragg gratings,” Opt. Express 19(20), 19514–19522 (2011).
    [Crossref] [PubMed]
  6. T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
    [Crossref] [PubMed]
  7. Z. Ruan, “Spatial mode control of surface plasmon polariton excitation with gain medium: from spatial differentiator to integrator,” Opt. Lett. 40(4), 601–604 (2015).
    [Crossref] [PubMed]
  8. 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]
  9. D. A. Bykov, L. L. Doskolovich, N. V. Golovastikov, and V. A. Soifer, “Time-domain differentiation of optical pulses in reflection and in transmission using the same resonant grating,” J. Opt. 15(10), 105703 (2013).
    [Crossref]
  10. N. V. Golovastikov, D. A. Bykov, and L. L. Doskolovich, “Spatiotemporal pulse shaping using resonant diffraction gratings,” Opt. Lett. 40(15), 3492–3495 (2015).
    [Crossref] [PubMed]
  11. 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]
  12. A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Analog computing using reflective plasmonic metasurfaces,” Nano Lett. 15(1), 791–797 (2015).
    [Crossref] [PubMed]
  13. A. Chizari, S. Abdollahramezani, M. V. Jamali, and J. A. Salehi, “Analog optical computing based on a dielectric meta-reflect array,” Opt. Lett. 41(15), 3451–3454 (2016).
    [Crossref] [PubMed]
  14. L. L. Doskolovich, E. A. Bezus, and D. A. Bykov, “Phase-shifted Bragg gratings for Bloch surface waves,” Opt. Express 23(21), 27034–27045 (2015).
    [Crossref] [PubMed]
  15. L. L. Doskolovich, E. A. Bezus, D. A. Bykov, and V. A. Soifer, “Spatial differentiation of Bloch surface wave beams using an on-chip phase-shifted Bragg grating,” J. Opt. 18(11), 115006 (2016).
    [Crossref]
  16. G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3(9), e203 (2014).
    [Crossref]
  17. T. W. Mossberg, “Planar holographic optical processing devices,” Opt. Lett. 26(7), 414–416 (2001).
    [Crossref] [PubMed]
  18. E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta (Lond.) 33(5), 607–619 (1986).
    [Crossref]
  19. J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photonics 1(1), 58–106 (2009).
    [Crossref]
  20. R. Sainidou, J. Renger, T. V. Teperik, M. U. González, R. Quidant, and F. J. García de Abajo, “Extraordinary All-Dielectric Light Enhancement over Large Volumes,” Nano Lett. 10(11), 4450–4455 (2010).
    [Crossref] [PubMed]
  21. F. Zangeneh-Nejad and A. Khavasi, “Spatial integration by a dielectric slab and its planar graphene-based counterpart,” Opt. Lett. 42(10), 1954–1957 (2017).
    [Crossref] [PubMed]
  22. R. D. Kekatpure, A. C. Hryciw, E. S. Barnard, and M. L. Brongersma, “Solving dielectric and plasmonic waveguide dispersion relations on a pocket calculator,” Opt. Express 17(26), 24112–24129 (2009).
    [Crossref] [PubMed]
  23. G. Lifante, Integrated Photonics: Fundamentals (Wiley, 2003).
  24. E. Silberstein, P. Lalanne, J.-P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18(11), 2865–2875 (2001).
    [Crossref] [PubMed]
  25. D. A. Bykov and L. L. Doskolovich, “On the use of the Fourier modal method for calculation of localized eigenmodes of integrated optical resonators,” Comput. Opt. 39(5), 663–673 (2015).
    [Crossref]
  26. N. A. Gippius and S. G. Tikhodeev, “Application of the scattering matrix method for calculating the optical properties of metamaterials,” Phys. - Usp. 52(9), 967–971 (2009).
    [Crossref]

2017 (2)

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref] [PubMed]

F. Zangeneh-Nejad and A. Khavasi, “Spatial integration by a dielectric slab and its planar graphene-based counterpart,” Opt. Lett. 42(10), 1954–1957 (2017).
[Crossref] [PubMed]

2016 (3)

2015 (5)

2014 (3)

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]

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3(9), e203 (2014).
[Crossref]

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]

2013 (2)

D. A. Bykov, L. L. Doskolovich, N. V. Golovastikov, and V. A. Soifer, “Time-domain differentiation of optical pulses in reflection and in transmission using the same resonant grating,” J. Opt. 15(10), 105703 (2013).
[Crossref]

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]

2011 (2)

2010 (1)

R. Sainidou, J. Renger, T. V. Teperik, M. U. González, R. Quidant, and F. J. García de Abajo, “Extraordinary All-Dielectric Light Enhancement over Large Volumes,” Nano Lett. 10(11), 4450–4455 (2010).
[Crossref] [PubMed]

2009 (3)

N. A. Gippius and S. G. Tikhodeev, “Application of the scattering matrix method for calculating the optical properties of metamaterials,” Phys. - Usp. 52(9), 967–971 (2009).
[Crossref]

J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photonics 1(1), 58–106 (2009).
[Crossref]

R. D. Kekatpure, A. C. Hryciw, E. S. Barnard, and M. L. Brongersma, “Solving dielectric and plasmonic waveguide dispersion relations on a pocket calculator,” Opt. Express 17(26), 24112–24129 (2009).
[Crossref] [PubMed]

2007 (1)

2001 (2)

1986 (1)

E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta (Lond.) 33(5), 607–619 (1986).
[Crossref]

Abdollahramezani, S.

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.

Babin, S.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3(9), e203 (2014).
[Crossref]

Barnard, E. S.

Bezus, E. A.

Bozhevolnyi, S. I.

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Analog computing using reflective plasmonic metasurfaces,” Nano Lett. 15(1), 791–797 (2015).
[Crossref] [PubMed]

Brongersma, M. L.

Bykov, D. A.

L. L. Doskolovich, E. A. Bezus, D. A. Bykov, and V. A. Soifer, “Spatial differentiation of Bloch surface wave beams using an on-chip phase-shifted Bragg grating,” J. Opt. 18(11), 115006 (2016).
[Crossref]

N. V. Golovastikov, D. A. Bykov, L. L. Doskolovich, and V. A. Soifer, “Analytical description of 3D optical pulse diffraction by a phase-shifted Bragg grating,” Opt. Express 24(17), 18828–18842 (2016).
[Crossref] [PubMed]

L. L. Doskolovich, E. A. Bezus, and D. A. Bykov, “Phase-shifted Bragg gratings for Bloch surface waves,” Opt. Express 23(21), 27034–27045 (2015).
[Crossref] [PubMed]

N. V. Golovastikov, D. A. Bykov, and L. L. Doskolovich, “Spatiotemporal pulse shaping using resonant diffraction gratings,” Opt. Lett. 40(15), 3492–3495 (2015).
[Crossref] [PubMed]

D. A. Bykov and L. L. Doskolovich, “On the use of the Fourier modal method for calculation of localized eigenmodes of integrated optical resonators,” Comput. Opt. 39(5), 663–673 (2015).
[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, N. V. Golovastikov, and V. A. Soifer, “Time-domain differentiation of optical pulses in reflection and in transmission using the same resonant grating,” J. Opt. 15(10), 105703 (2013).
[Crossref]

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]

Cabrini, S.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3(9), e203 (2014).
[Crossref]

Calafiore, G.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3(9), e203 (2014).
[Crossref]

Cao, Q.

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]

Chizari, A.

Dhuey, S.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3(9), e203 (2014).
[Crossref]

Doskolovich, L. L.

L. L. Doskolovich, E. A. Bezus, D. A. Bykov, and V. A. Soifer, “Spatial differentiation of Bloch surface wave beams using an on-chip phase-shifted Bragg grating,” J. Opt. 18(11), 115006 (2016).
[Crossref]

N. V. Golovastikov, D. A. Bykov, L. L. Doskolovich, and V. A. Soifer, “Analytical description of 3D optical pulse diffraction by a phase-shifted Bragg grating,” Opt. Express 24(17), 18828–18842 (2016).
[Crossref] [PubMed]

N. V. Golovastikov, D. A. Bykov, and L. L. Doskolovich, “Spatiotemporal pulse shaping using resonant diffraction gratings,” Opt. Lett. 40(15), 3492–3495 (2015).
[Crossref] [PubMed]

L. L. Doskolovich, E. A. Bezus, and D. A. Bykov, “Phase-shifted Bragg gratings for Bloch surface waves,” Opt. Express 23(21), 27034–27045 (2015).
[Crossref] [PubMed]

D. A. Bykov and L. L. Doskolovich, “On the use of the Fourier modal method for calculation of localized eigenmodes of integrated optical resonators,” Comput. Opt. 39(5), 663–673 (2015).
[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, N. V. Golovastikov, and V. A. Soifer, “Time-domain differentiation of optical pulses in reflection and in transmission using the same resonant grating,” J. Opt. 15(10), 105703 (2013).
[Crossref]

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]

Duchesne, D.

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]

Fan, S.

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref] [PubMed]

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]

García de Abajo, F. J.

R. Sainidou, J. Renger, T. V. Teperik, M. U. González, R. Quidant, and F. J. García de Abajo, “Extraordinary All-Dielectric Light Enhancement over Large Volumes,” Nano Lett. 10(11), 4450–4455 (2010).
[Crossref] [PubMed]

Gippius, N. A.

N. A. Gippius and S. G. Tikhodeev, “Application of the scattering matrix method for calculating the optical properties of metamaterials,” Phys. - Usp. 52(9), 967–971 (2009).
[Crossref]

Golovastikov, N. V.

Goltsov, A.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3(9), e203 (2014).
[Crossref]

González, M. U.

R. Sainidou, J. Renger, T. V. Teperik, M. U. González, R. Quidant, and F. J. García de Abajo, “Extraordinary All-Dielectric Light Enhancement over Large Volumes,” Nano Lett. 10(11), 4450–4455 (2010).
[Crossref] [PubMed]

Hryciw, A. C.

Hu, J.

J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photonics 1(1), 58–106 (2009).
[Crossref]

Hugonin, J.-P.

Jamali, M. V.

Kazanskiy, N. L.

Kekatpure, R. D.

Khavasi, A.

Khonina, S. N.

Koshelev, A.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3(9), e203 (2014).
[Crossref]

Kulishov, M.

Lalanne, P.

Lou, Y.

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref] [PubMed]

Mashev, L.

E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta (Lond.) 33(5), 607–619 (1986).
[Crossref]

Maystre, D.

E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta (Lond.) 33(5), 607–619 (1986).
[Crossref]

Menyuk, C. R.

J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photonics 1(1), 58–106 (2009).
[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.

Mossberg, T. W.

Nielsen, M. G.

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Analog computing using reflective plasmonic metasurfaces,” Nano Lett. 15(1), 791–797 (2015).
[Crossref] [PubMed]

Peroz, C.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3(9), e203 (2014).
[Crossref]

Popov, E.

E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta (Lond.) 33(5), 607–619 (1986).
[Crossref]

Pors, A.

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Analog computing using reflective plasmonic metasurfaces,” Nano Lett. 15(1), 791–797 (2015).
[Crossref] [PubMed]

Qiu, M.

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref] [PubMed]

Quidant, R.

R. Sainidou, J. Renger, T. V. Teperik, M. U. González, R. Quidant, and F. J. García de Abajo, “Extraordinary All-Dielectric Light Enhancement over Large Volumes,” Nano Lett. 10(11), 4450–4455 (2010).
[Crossref] [PubMed]

Renger, J.

R. Sainidou, J. Renger, T. V. Teperik, M. U. González, R. Quidant, and F. J. García de Abajo, “Extraordinary All-Dielectric Light Enhancement over Large Volumes,” Nano Lett. 10(11), 4450–4455 (2010).
[Crossref] [PubMed]

Ruan, Z.

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref] [PubMed]

Z. Ruan, “Spatial mode control of surface plasmon polariton excitation with gain medium: from spatial differentiator to integrator,” Opt. Lett. 40(4), 601–604 (2015).
[Crossref] [PubMed]

Rutkowska, K. A.

Sainidou, R.

R. Sainidou, J. Renger, T. V. Teperik, M. U. González, R. Quidant, and F. J. García de Abajo, “Extraordinary All-Dielectric Light Enhancement over Large Volumes,” Nano Lett. 10(11), 4450–4455 (2010).
[Crossref] [PubMed]

Salehi, J. A.

Sasorov, P.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3(9), e203 (2014).
[Crossref]

Serafimovich, P. G.

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]

Soifer, V. A.

Sorel, M.

Strain, M. J.

Teperik, T. V.

R. Sainidou, J. Renger, T. V. Teperik, M. U. González, R. Quidant, and F. J. García de Abajo, “Extraordinary All-Dielectric Light Enhancement over Large Volumes,” Nano Lett. 10(11), 4450–4455 (2010).
[Crossref] [PubMed]

Tikhodeev, S. G.

N. A. Gippius and S. G. Tikhodeev, “Application of the scattering matrix method for calculating the optical properties of metamaterials,” Phys. - Usp. 52(9), 967–971 (2009).
[Crossref]

Yankov, V.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3(9), e203 (2014).
[Crossref]

Ye, H.

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref] [PubMed]

Zangeneh-Nejad, F.

Zhou, Y.

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref] [PubMed]

Zhu, T.

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photonics 1(1), 58–106 (2009).
[Crossref]

Comput. Opt. (1)

D. A. Bykov and L. L. Doskolovich, “On the use of the Fourier modal method for calculation of localized eigenmodes of integrated optical resonators,” Comput. Opt. 39(5), 663–673 (2015).
[Crossref]

J. Opt. (2)

L. L. Doskolovich, E. A. Bezus, D. A. Bykov, and V. A. Soifer, “Spatial differentiation of Bloch surface wave beams using an on-chip phase-shifted Bragg grating,” J. Opt. 18(11), 115006 (2016).
[Crossref]

D. A. Bykov, L. L. Doskolovich, N. V. Golovastikov, and V. A. Soifer, “Time-domain differentiation of optical pulses in reflection and in transmission using the same resonant grating,” J. Opt. 15(10), 105703 (2013).
[Crossref]

J. Opt. Soc. Am. A (1)

Light Sci. Appl. (1)

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light Sci. Appl. 3(9), e203 (2014).
[Crossref]

Nano Lett. (2)

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Analog computing using reflective plasmonic metasurfaces,” Nano Lett. 15(1), 791–797 (2015).
[Crossref] [PubMed]

R. Sainidou, J. Renger, T. V. Teperik, M. U. González, R. Quidant, and F. J. García de Abajo, “Extraordinary All-Dielectric Light Enhancement over Large Volumes,” Nano Lett. 10(11), 4450–4455 (2010).
[Crossref] [PubMed]

Nat. Commun. (1)

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref] [PubMed]

Opt. Acta (Lond.) (1)

E. Popov, L. Mashev, and D. Maystre, “Theoretical study of the anomalies of coated dielectric gratings,” Opt. Acta (Lond.) 33(5), 607–619 (1986).
[Crossref]

Opt. Express (5)

Opt. Lett. (8)

Phys. - Usp. (1)

N. A. Gippius and S. G. Tikhodeev, “Application of the scattering matrix method for calculating the optical properties of metamaterials,” Phys. - Usp. 52(9), 967–971 (2009).
[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]

Other (1)

G. Lifante, Integrated Photonics: Fundamentals (Wiley, 2003).

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Figures (7)

Fig. 1
Fig. 1 Geometry of a conventional (non-integrated) three-layer resonant structure (a) and of the proposed two-groove planar differentiator (c), and the corresponding refractive (effective refractive) index profile (b). The effective refractive index profile in (b) and the dimensions in (c) correspond to one of the examples considered below.
Fig. 2
Fig. 2 Reflection spectrum of the planar structure R p l ( k x , ω ) at h c l = λ 0 / 8 = 79 nm (а) and its horizontal (b) and inclined (c) cross-sections corresponding to the spatial TF at ω 0 = 2.99 10 15 s 1 ( λ 0 = 630 nm ) and the temporal TF at k x , 0 , 1 = 0 .02211 nm 1 ( θ 0 , 1 = 53.56 ° ) , respectively. The cross-sections are marked with white dotted lines in (a). Dotted ellipse in (a) and vertical lines in (b) and (c) show the 1/e2 level of the spectra of the input optical signals considered in the examples below.
Fig. 3
Fig. 3 Reflection spectrum of the planar structure R p l ( k x , ω ) at h c l = λ 0 / 4 = 158 nm (а) and its horizontal (b) and inclined (c) cross-sections corresponding to the spatial TF at ω 0 = 2.99 10 15 s 1 ( λ 0 = 630 nm ) and the temporal TF at k x , 0 , 2 = 0 .02243 nm 1 ( θ 0 , 2 = 54.69 ° ) , respectively. The cross-sections are shown with white dotted lines in (a). Dotted vertical lines in (b) and (c) show the 1/e2 level of the spectra of the input optical signals considered in the examples below.
Fig. 4
Fig. 4 Field ( | H y | 2 ) distributions of the eigenmodes of the planar structure: h c l = λ 0 / 8 = 78.75 nm , θ 0 = θ 0 , 1 , ω p , 1 = 3.020 10 15 4.77 10 14 i s 1 (a); h c l = λ 0 / 4 = 157.5 nm , θ 0 = θ 0 , 2 , ω p , 2 = 2.992 10 15 1.57 10 14 i s 1 (b).
Fig. 5
Fig. 5 Absolute value of the profile of the reflected beam (solid black curve) and of the exact derivative of the incident beam profile (dashed red curve) (left vertical axis), and the profile of the incident beam (dotted black curve, right vertical axis) at h c l = λ 0 / 8 (a) and h c l = λ 0 / 4 (b).
Fig. 6
Fig. 6 Absolute values of the envelope of the reflected pulse (solid black curve) and of the exact derivative of the incident pulse (dashed red curve) (left vertical axis), and the envelope of the incident pulse (dotted black curve, right vertical axis) at h c l = λ 0 / 8 (a) and h c l = λ 0 / 4 (b).
Fig. 7
Fig. 7 (a) Absolute value of the spatiotemporal envelope of the reflected optical signal. (b) Cross-section of the absolute value of the spatiotemporal envelope along the dashed line shown in (a) (solid black curve) and the absolute value of the analytically computed directional derivative of the incident signal (dashed red curve). Dotted black curve shows the cross-section of the spatiotemporal profile of the incident signal.

Equations (9)

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u inc ( x inc , z inc ) = exp ( i k 0 n sup z inc ) P inc ( x inc ) = exp ( i k 0 n sup z inc ) G ( k x , inc ) exp ( i k x , inc x inc ) d k x , inc ,
k x = k 0 n sup sin ( θ + θ 0 ) k x , inc cos θ 0 + k x , 0 ,
P refl ( x refl ) = G ( k x , inc ) R ( k x ) exp ( i k x , inc x refl ) d k x , inc .
H s ( k x , inc ) = R ( k x , inc cos θ 0 + k x , 0 ) .
H t ( ω inc ) = R ( ω inc + ω 0 ) ,
H s t ( k x , inc , ω inc ) = R ( k x , inc cos θ 0 + ω inc + ω 0 c n sup sin θ 0 , ω inc + ω 0 ) .
H s ( k x , inc ) α k x , inc , H t ( ω inc ) β ω inc , H st ( k x , inc , ω inc ) = α k x , inc + β ω inc ,
P refl ( x refl , t ) = i ( α E i n c ( x refl , t ) x refl β E i n c ( x refl , t ) t ) = 2 i exp ( x refl 2 / σ x 2 t 2 / σ t 2 ) ( α x refl / σ x 2 β t / σ t 2 ) ,
β α n sup c t g θ 0 + 1 cos θ 0 1 Re [ ω p / k x ] ,

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