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]

S. AbdollahRamezani, K. Arik, A. Khavasi, and Z. Kavehvash, “Analog computing using graphene-based metalines,” Opt. Lett. 40, 5239–5242 (2015).

[Crossref]

M. Minkov and V. Savona, “Automated optimization of photonic crystal slab cavities,” Sci. Rep. 4, 5124 (2015).

[Crossref]

N. V. Golovastikov, D. A. Bykov, L. L. Doskolovich, and V. A. Soifer, “Spatiotemporal optical pulse transformation by a resonant diffraction grating,” J. Exp. Theor. Phys. 121, 785–792 (2015).

[Crossref]

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

[Crossref]

D. R. Solli and B. Jalali, “Analog optical computing,” Nat. Photonics 9, 704–706 (2015).

[Crossref]

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

[Crossref]

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

[Crossref]

W. Zhou, D. Zhao, Y.-C. Shuai, H. Yang, S. Chuwongin, A. Chadha, J.-H. Seo, K. X. Wang, V. Liu, Z. Ma, and S. Fan, “Progress in 2D photonic crystal Fano resonance photonics,” Prog. Quantum Electron. 38, 1–74 (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, 25084–25092 (2014).

[Crossref]

L. C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006).

[Crossref]

M. D. Abràmoff, P. J. Magalhães, and S. J. Ram, “Image processing with ImageJ,” Biophoton. Int. 11, 36–42 (2004).

T. Brosnan and D. W. Sun, “Improving quality inspection of food products by computer vision—a review,” J. Food Eng. 61, 3–16 (2004).

[Crossref]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).

[Crossref]

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).

[Crossref]

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).

[Crossref]

K. S. Nesteruk, I. P. Nikolaev, and A. V. Larichev, “Image differentiation with the aid of a phase knife,” Opt. Spectrosc. 91, 295–299 (2001).

[Crossref]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).

[Crossref]

D. L. Pham, C. Xu, and J. L. Prince, “Current methods in medical image segmentation,” Annu. Rev. Biomed. Eng. 2, 315–337 (2000).

[Crossref]

R. J. Holyer and S. H. Peckinpaugh, “Edge detection applied to satellite imagery of the oceans,” IEEE Trans. Geosci. Remote Sens. 27, 46–56 (1989).

[Crossref]

C. Warde and J. Thackara, “Operating modes of the microchannel spatial light modulator,” Opt. Eng. 22, 695–703 (1983).

[Crossref]

E. R. Reinhardt and W. H. Bloss, “Optical differential operation processor,” Opt. Eng. 17, 69–72 (1978).

[Crossref]

R. Sirohi and V. R. Mohan, “Differentiation by spatial filtering,” Opt. Acta Int. J. Opt. 24, 1105–1113 (1977).

[Crossref]

D. Görlitz and F. Lanzl, “A holographic spatial filter for direction independent differentiation,” Jpn. J. Appl. Phys. 14, 223–228 (1975).

[Crossref]

J. Eu, C. Liu, and A. Lohmann, “Spatial filters for differentiation,” Opt. Commun. 9, 168–171 (1973).

[Crossref]

R. Markham, S. Frey, and G. Hills, “Methods for the enhancement of image detail and accentuation of structure in electron microscopy,” Virology 20, 88–102 (1963).

[Crossref]

A. Youssefi, F. Zangeneh-Nejad, S. Abdollahramezani, and A. Khavasi, “Analog computing by Brewster effect,” Opt. Lett. 41, 3467–3470 (2016).

[Crossref]

S. AbdollahRamezani, K. Arik, A. Khavasi, and Z. Kavehvash, “Analog computing using graphene-based metalines,” Opt. Lett. 40, 5239–5242 (2015).

[Crossref]

M. D. Abràmoff, P. J. Magalhães, and S. J. Ram, “Image processing with ImageJ,” Biophoton. Int. 11, 36–42 (2004).

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).

[Crossref]

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

[Crossref]

L. C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006).

[Crossref]

E. R. Reinhardt and W. H. Bloss, “Optical differential operation processor,” Opt. Eng. 17, 69–72 (1978).

[Crossref]

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

[Crossref]

R. N. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (McGraw-Hill, 1999).

T. Brosnan and D. W. Sun, “Improving quality inspection of food products by computer vision—a review,” J. Food Eng. 61, 3–16 (2004).

[Crossref]

N. V. Golovastikov, D. A. Bykov, L. L. Doskolovich, and V. A. Soifer, “Spatiotemporal optical pulse transformation by a resonant diffraction grating,” J. Exp. Theor. Phys. 121, 785–792 (2015).

[Crossref]

N. V. Golovastikov, D. A. Bykov, and L. L. Doskolovich, “Resonant diffraction gratings for spatial differentiation of optical beams,” Quantum Electron. 44, 984–988 (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, 25084–25092 (2014).

[Crossref]

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

[Crossref]

W. Zhou, D. Zhao, Y.-C. Shuai, H. Yang, S. Chuwongin, A. Chadha, J.-H. Seo, K. X. Wang, V. Liu, Z. Ma, and S. Fan, “Progress in 2D photonic crystal Fano resonance photonics,” Prog. Quantum Electron. 38, 1–74 (2014).

[Crossref]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).

[Crossref]

W. Zhou, D. Zhao, Y.-C. Shuai, H. Yang, S. Chuwongin, A. Chadha, J.-H. Seo, K. X. Wang, V. Liu, Z. Ma, and S. Fan, “Progress in 2D photonic crystal Fano resonance photonics,” Prog. Quantum Electron. 38, 1–74 (2014).

[Crossref]

N. Dalal and B. Triggs, “Histograms of oriented gradients for human detection,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2005), pp. 886–893.

N. V. Golovastikov, D. A. Bykov, L. L. Doskolovich, and V. A. Soifer, “Spatiotemporal optical pulse transformation by a resonant diffraction grating,” J. Exp. Theor. Phys. 121, 785–792 (2015).

[Crossref]

N. V. Golovastikov, D. A. Bykov, and L. L. Doskolovich, “Resonant diffraction gratings for spatial differentiation of optical beams,” Quantum Electron. 44, 984–988 (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, 25084–25092 (2014).

[Crossref]

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

[Crossref]

J. Eu, C. Liu, and A. Lohmann, “Spatial filters for differentiation,” Opt. Commun. 9, 168–171 (1973).

[Crossref]

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]

W. Zhou, D. Zhao, Y.-C. Shuai, H. Yang, S. Chuwongin, A. Chadha, J.-H. Seo, K. X. Wang, V. Liu, Z. Ma, and S. Fan, “Progress in 2D photonic crystal Fano resonance photonics,” Prog. Quantum Electron. 38, 1–74 (2014).

[Crossref]

K. X. Wang, Z. Yu, S. Sandhu, and S. Fan, “Fundamental bounds on decay rates in asymmetric single-mode optical resonators,” Opt. Lett. 38, 100–102 (2013).

[Crossref]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).

[Crossref]

R. Markham, S. Frey, and G. Hills, “Methods for the enhancement of image detail and accentuation of structure in electron microscopy,” Virology 20, 88–102 (1963).

[Crossref]

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

[Crossref]

L. C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006).

[Crossref]

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).

[Crossref]

N. V. Golovastikov, D. A. Bykov, L. L. Doskolovich, and V. A. Soifer, “Spatiotemporal optical pulse transformation by a resonant diffraction grating,” J. Exp. Theor. Phys. 121, 785–792 (2015).

[Crossref]

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

[Crossref]

R. Gonzales and R. Woods, Digital Image Processing, 3rd ed. (Prentice Hall, 2008).

D. Görlitz and F. Lanzl, “A holographic spatial filter for direction independent differentiation,” Jpn. J. Appl. Phys. 14, 223–228 (1975).

[Crossref]

R. Markham, S. Frey, and G. Hills, “Methods for the enhancement of image detail and accentuation of structure in electron microscopy,” Virology 20, 88–102 (1963).

[Crossref]

R. J. Holyer and S. H. Peckinpaugh, “Edge detection applied to satellite imagery of the oceans,” IEEE Trans. Geosci. Remote Sens. 27, 46–56 (1989).

[Crossref]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).

[Crossref]

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).

[Crossref]

D. R. Solli and B. Jalali, “Analog optical computing,” Nat. Photonics 9, 704–706 (2015).

[Crossref]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).

[Crossref]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).

[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).

[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

A. Rosenfeld and A. C. Kak, Digital Picture Processing (Academic, 1982).

A. Youssefi, F. Zangeneh-Nejad, S. Abdollahramezani, and A. Khavasi, “Analog computing by Brewster effect,” Opt. Lett. 41, 3467–3470 (2016).

[Crossref]

S. AbdollahRamezani, K. Arik, A. Khavasi, and Z. Kavehvash, “Analog computing using graphene-based metalines,” Opt. Lett. 40, 5239–5242 (2015).

[Crossref]

D. Görlitz and F. Lanzl, “A holographic spatial filter for direction independent differentiation,” Jpn. J. Appl. Phys. 14, 223–228 (1975).

[Crossref]

K. S. Nesteruk, I. P. Nikolaev, and A. V. Larichev, “Image differentiation with the aid of a phase knife,” Opt. Spectrosc. 91, 295–299 (2001).

[Crossref]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).

[Crossref]

J. Eu, C. Liu, and A. Lohmann, “Spatial filters for differentiation,” Opt. Commun. 9, 168–171 (1973).

[Crossref]

W. Zhou, D. Zhao, Y.-C. Shuai, H. Yang, S. Chuwongin, A. Chadha, J.-H. Seo, K. X. Wang, V. Liu, Z. Ma, and S. Fan, “Progress in 2D photonic crystal Fano resonance photonics,” Prog. Quantum Electron. 38, 1–74 (2014).

[Crossref]

J. Eu, C. Liu, and A. Lohmann, “Spatial filters for differentiation,” Opt. Commun. 9, 168–171 (1973).

[Crossref]

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]

W. Zhou, D. Zhao, Y.-C. Shuai, H. Yang, S. Chuwongin, A. Chadha, J.-H. Seo, K. X. Wang, V. Liu, Z. Ma, and S. Fan, “Progress in 2D photonic crystal Fano resonance photonics,” Prog. Quantum Electron. 38, 1–74 (2014).

[Crossref]

M. D. Abràmoff, P. J. Magalhães, and S. J. Ram, “Image processing with ImageJ,” Biophoton. Int. 11, 36–42 (2004).

R. Markham, S. Frey, and G. Hills, “Methods for the enhancement of image detail and accentuation of structure in electron microscopy,” Virology 20, 88–102 (1963).

[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

M. Minkov and V. Savona, “Automated optimization of photonic crystal slab cavities,” Sci. Rep. 4, 5124 (2015).

[Crossref]

R. Sirohi and V. R. Mohan, “Differentiation by spatial filtering,” Opt. Acta Int. J. Opt. 24, 1105–1113 (1977).

[Crossref]

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

[Crossref]

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).

[Crossref]

K. S. Nesteruk, I. P. Nikolaev, and A. V. Larichev, “Image differentiation with the aid of a phase knife,” Opt. Spectrosc. 91, 295–299 (2001).

[Crossref]

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

[Crossref]

K. S. Nesteruk, I. P. Nikolaev, and A. V. Larichev, “Image differentiation with the aid of a phase knife,” Opt. Spectrosc. 91, 295–299 (2001).

[Crossref]

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).

[Crossref]

R. J. Holyer and S. H. Peckinpaugh, “Edge detection applied to satellite imagery of the oceans,” IEEE Trans. Geosci. Remote Sens. 27, 46–56 (1989).

[Crossref]

D. L. Pham, C. Xu, and J. L. Prince, “Current methods in medical image segmentation,” Annu. Rev. Biomed. Eng. 2, 315–337 (2000).

[Crossref]

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

[Crossref]

D. L. Pham, C. Xu, and J. L. Prince, “Current methods in medical image segmentation,” Annu. Rev. Biomed. Eng. 2, 315–337 (2000).

[Crossref]

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]

M. D. Abràmoff, P. J. Magalhães, and S. J. Ram, “Image processing with ImageJ,” Biophoton. Int. 11, 36–42 (2004).

E. R. Reinhardt and W. H. Bloss, “Optical differential operation processor,” Opt. Eng. 17, 69–72 (1978).

[Crossref]

A. Rosenfeld and A. C. Kak, Digital Picture Processing (Academic, 1982).

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]

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).

[Crossref]

K. Sakoda, Optical Properties of Photonic Crystals, Vol. 80 of Springer Series in Optical Sciences (Springer, 2005).

M. Minkov and V. Savona, “Automated optimization of photonic crystal slab cavities,” Sci. Rep. 4, 5124 (2015).

[Crossref]

W. Zhou, D. Zhao, Y.-C. Shuai, H. Yang, S. Chuwongin, A. Chadha, J.-H. Seo, K. X. Wang, V. Liu, Z. Ma, and S. Fan, “Progress in 2D photonic crystal Fano resonance photonics,” Prog. Quantum Electron. 38, 1–74 (2014).

[Crossref]

W. Zhou, D. Zhao, Y.-C. Shuai, H. Yang, S. Chuwongin, A. Chadha, J.-H. Seo, K. X. Wang, V. Liu, Z. Ma, and S. Fan, “Progress in 2D photonic crystal Fano resonance photonics,” Prog. Quantum Electron. 38, 1–74 (2014).

[Crossref]

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

[Crossref]

R. Sirohi and V. R. Mohan, “Differentiation by spatial filtering,” Opt. Acta Int. J. Opt. 24, 1105–1113 (1977).

[Crossref]

N. V. Golovastikov, D. A. Bykov, L. L. Doskolovich, and V. A. Soifer, “Spatiotemporal optical pulse transformation by a resonant diffraction grating,” J. Exp. Theor. Phys. 121, 785–792 (2015).

[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, 25084–25092 (2014).

[Crossref]

D. R. Solli and B. Jalali, “Analog optical computing,” Nat. Photonics 9, 704–706 (2015).

[Crossref]

T. Brosnan and D. W. Sun, “Improving quality inspection of food products by computer vision—a review,” J. Food Eng. 61, 3–16 (2004).

[Crossref]

C. Warde and J. Thackara, “Operating modes of the microchannel spatial light modulator,” Opt. Eng. 22, 695–703 (1983).

[Crossref]

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).

[Crossref]

N. Dalal and B. Triggs, “Histograms of oriented gradients for human detection,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2005), pp. 886–893.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).

[Crossref]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).

[Crossref]

W. Zhou, D. Zhao, Y.-C. Shuai, H. Yang, S. Chuwongin, A. Chadha, J.-H. Seo, K. X. Wang, V. Liu, Z. Ma, and S. Fan, “Progress in 2D photonic crystal Fano resonance photonics,” Prog. Quantum Electron. 38, 1–74 (2014).

[Crossref]

K. X. Wang, Z. Yu, S. Sandhu, and S. Fan, “Fundamental bounds on decay rates in asymmetric single-mode optical resonators,” Opt. Lett. 38, 100–102 (2013).

[Crossref]

C. Warde and J. Thackara, “Operating modes of the microchannel spatial light modulator,” Opt. Eng. 22, 695–703 (1983).

[Crossref]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).

[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

R. Gonzales and R. Woods, Digital Image Processing, 3rd ed. (Prentice Hall, 2008).

D. L. Pham, C. Xu, and J. L. Prince, “Current methods in medical image segmentation,” Annu. Rev. Biomed. Eng. 2, 315–337 (2000).

[Crossref]

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).

[Crossref]

W. Zhou, D. Zhao, Y.-C. Shuai, H. Yang, S. Chuwongin, A. Chadha, J.-H. Seo, K. X. Wang, V. Liu, Z. Ma, and S. Fan, “Progress in 2D photonic crystal Fano resonance photonics,” Prog. Quantum Electron. 38, 1–74 (2014).

[Crossref]

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]

W. Zhou, D. Zhao, Y.-C. Shuai, H. Yang, S. Chuwongin, A. Chadha, J.-H. Seo, K. X. Wang, V. Liu, Z. Ma, and S. Fan, “Progress in 2D photonic crystal Fano resonance photonics,” Prog. Quantum Electron. 38, 1–74 (2014).

[Crossref]

W. Zhou, D. Zhao, Y.-C. Shuai, H. Yang, S. Chuwongin, A. Chadha, J.-H. Seo, K. X. Wang, V. Liu, Z. Ma, and S. Fan, “Progress in 2D photonic crystal Fano resonance photonics,” Prog. Quantum Electron. 38, 1–74 (2014).

[Crossref]

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]

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]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).

[Crossref]

D. L. Pham, C. Xu, and J. L. Prince, “Current methods in medical image segmentation,” Annu. Rev. Biomed. Eng. 2, 315–337 (2000).

[Crossref]

H. Kasprzak, “Differentiation of a noninteger order and its optical implementation,” Appl. Opt. 21, 3287–3291 (1982).

[Crossref]

J. A. Davis, W. V. Brandt, D. M. Cottrell, and R. M. Bunch, “Spatial image differentiation using programmable binary optical elements,” Appl. Opt. 30, 4610–4614 (1991).

[Crossref]

J. Lancis, T. Szoplik, E. Tajahuerce, V. Climent, and M. Fernández-Alonso, “Fractional derivative Fourier plane filter for phase-change visualization,” Appl. Opt. 36, 7461–7464 (1997).

[Crossref]

M. D. Abràmoff, P. J. Magalhães, and S. J. Ram, “Image processing with ImageJ,” Biophoton. Int. 11, 36–42 (2004).

R. J. Holyer and S. H. Peckinpaugh, “Edge detection applied to satellite imagery of the oceans,” IEEE Trans. Geosci. Remote Sens. 27, 46–56 (1989).

[Crossref]

N. V. Golovastikov, D. A. Bykov, L. L. Doskolovich, and V. A. Soifer, “Spatiotemporal optical pulse transformation by a resonant diffraction grating,” J. Exp. Theor. Phys. 121, 785–792 (2015).

[Crossref]

T. Brosnan and D. W. Sun, “Improving quality inspection of food products by computer vision—a review,” J. Food Eng. 61, 3–16 (2004).

[Crossref]

D. Görlitz and F. Lanzl, “A holographic spatial filter for direction independent differentiation,” Jpn. J. Appl. Phys. 14, 223–228 (1975).

[Crossref]

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

[Crossref]

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]

D. R. Solli and B. Jalali, “Analog optical computing,” Nat. Photonics 9, 704–706 (2015).

[Crossref]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature 407, 983–986 (2000).

[Crossref]

R. Sirohi and V. R. Mohan, “Differentiation by spatial filtering,” Opt. Acta Int. J. Opt. 24, 1105–1113 (1977).

[Crossref]

J. Eu, C. Liu, and A. Lohmann, “Spatial filters for differentiation,” Opt. Commun. 9, 168–171 (1973).

[Crossref]

E. R. Reinhardt and W. H. Bloss, “Optical differential operation processor,” Opt. Eng. 17, 69–72 (1978).

[Crossref]

C. Warde and J. Thackara, “Operating modes of the microchannel spatial light modulator,” Opt. Eng. 22, 695–703 (1983).

[Crossref]

K. X. Wang, Z. Yu, S. Sandhu, and S. Fan, “Fundamental bounds on decay rates in asymmetric single-mode optical resonators,” Opt. Lett. 38, 100–102 (2013).

[Crossref]

C.-S. Guo, Q.-Y. Yue, G.-X. Wei, L.-L. Lu, and S.-J. Yue, “Laplacian differential reconstruction of in-line holograms recorded at two different distances,” Opt. Lett. 33, 1945–1947 (2008).

[Crossref]

J. P. Ryle, D. Li, and J. T. Sheridan, “Dual wavelength digital holographic Laplacian reconstruction,” Opt. Lett. 35, 3018–3020 (2010).

[Crossref]

A. Youssefi, F. Zangeneh-Nejad, S. Abdollahramezani, and A. Khavasi, “Analog computing by Brewster effect,” Opt. Lett. 41, 3467–3470 (2016).

[Crossref]

S. AbdollahRamezani, K. Arik, A. Khavasi, and Z. Kavehvash, “Analog computing using graphene-based metalines,” Opt. Lett. 40, 5239–5242 (2015).

[Crossref]

K. S. Nesteruk, I. P. Nikolaev, and A. V. Larichev, “Image differentiation with the aid of a phase knife,” Opt. Spectrosc. 91, 295–299 (2001).

[Crossref]

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).

[Crossref]

L. C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006).

[Crossref]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).

[Crossref]

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).

[Crossref]

W. Zhou, D. Zhao, Y.-C. Shuai, H. Yang, S. Chuwongin, A. Chadha, J.-H. Seo, K. X. Wang, V. Liu, Z. Ma, and S. Fan, “Progress in 2D photonic crystal Fano resonance photonics,” Prog. Quantum Electron. 38, 1–74 (2014).

[Crossref]

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

[Crossref]

M. Minkov and V. Savona, “Automated optimization of photonic crystal slab cavities,” Sci. Rep. 4, 5124 (2015).

[Crossref]

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

[Crossref]

R. Markham, S. Frey, and G. Hills, “Methods for the enhancement of image detail and accentuation of structure in electron microscopy,” Virology 20, 88–102 (1963).

[Crossref]

R. Gonzales and R. Woods, Digital Image Processing, 3rd ed. (Prentice Hall, 2008).

N. Dalal and B. Triggs, “Histograms of oriented gradients for human detection,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2005), pp. 886–893.

A. Rosenfeld and A. C. Kak, Digital Picture Processing (Academic, 1982).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

K. Sakoda, Optical Properties of Photonic Crystals, Vol. 80 of Springer Series in Optical Sciences (Springer, 2005).

R. N. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (McGraw-Hill, 1999).