Abstract

Planar optical waveguides made of designable spatially dispersive nanomaterials can offer new capabilities for nanophotonic components. As an example, a thin slab waveguide can be designed to compensate for optical diffraction and provide divergence-free propagation for strongly focused optical beams. Optical signals in such waveguides can be transferred in narrow channels formed by the light itself. We introduce here a theoretical method for characterization and design of nanostructured waveguides taking into account their inherent spatial dispersion and anisotropy. Using the method, we design a diffraction-compensating slab waveguide that contains only a single layer of silver nanorods. The waveguide shows low propagation loss and broadband diffraction compensation, potentially allowing transfer of optical information at a THz rate.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (1)

2016 (4)

2015 (6)

N. Kinsey, M. Ferrera, V. M. Shalaev, and A. Boltasseva, “Examining nanophotonics for integrated hybrid systems: a review of plasmonic interconnects and modulators using traditional and alternative materials,” J. Opt. Soc. Am. B 32(1), 121–142 (2015).
[Crossref]

V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Long-range plasmonic waveguides with hyperbolic cladding,” Opt. Express 23(24), 31109–31119 (2015).
[Crossref] [PubMed]

A. F. Koenderink, A. Alu, and A. Polman, “Nanophotonics: Shrinking light-based technology,” Science 348(6234), 516–521 (2015).
[Crossref] [PubMed]

S. B. Choi, D. J. Park, S. J. Byun, J. Kyoung, and S. W. Hwang, “Near-Zero Index: Optical Magnetic Mirror for Field Enhancement and Subwavelength Imaging Applications,” Adv. Opt. Mater. 3(12), 1719–1725 (2015).
[Crossref]

A. Shevchenko, P. Grahn, V. Kivijärvi, M. Nyman, and M. Kaivola, “Spatially dispersive functional optical metamaterials,” J. Nanophoton. 9(1), 093097 (2015).
[Crossref]

A. Shevchenko, V. Kivijärvi, P. Grahn, M. Kaivola, and K. Lindfors, “Bifacial metasurface with quadrupole optical response,” Phys. Rev. Appl. 4(2), 024019 (2015).
[Crossref]

2014 (1)

A. Shevchenko, P. Grahn, and M. Kaivola, “Internally twisted spatially dispersive optical metamaterials,” J. Nanophoton. 8(1), 083074 (2014).
[Crossref]

2013 (3)

P. Grahn, A. Shevchenko, and M. Kaivola, “Interferometric description of optical metamaterials,” New J. Phys. 15(11), 113044 (2013).
[Crossref]

P. Grahn, A. Shevchenko, and M. Kaivola, “Theoretical description of bifacial optical nanomaterials,” Opt. Express 21(20), 23471–23485 (2013).
[Crossref] [PubMed]

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nature Photon. 7(10), 791–795 (2013).
[Crossref]

2012 (5)

P. Grahn, A. Shevchenko, and M. Kaivola, “Electric dipole-free interaction of visible light with pairs of subwavelength-size silver particles,” Phys. Rev. B 86(3), 035419 (2012).
[Crossref]

P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys. 14(9), 093033 (2012).
[Crossref]

J. Ginn and I. Brener, “Realizing Optical Magnetism from Dielectric Metamaterial,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref] [PubMed]

M. Smit, J. Van Der Tol, and M. Hill, “Moore’s law in photonics,” Laser Photon. Rev. 6(1), 1–13 (2012).
[Crossref]

Y. He, S. He, J. Gao, and X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B. 29(9), 2559–2566 (2012).
[Crossref]

2010 (5)

A. Andryieuski, R. Malureanu, and A. V. Lavrinenko, “Wave propagation retrieval method for chiral metamaterials,” Opt. Express 18(15), 15498–15503 (2010).
[Crossref] [PubMed]

J. Yang, C. Sauvan, T. Paul, C. Rockstuhl, F. Lederer, and P. Lalanne, “Retrieving the effective parameters of metamaterials from the single interface scattering problem,” Appl. Phys. Lett. 97(6), 061102 (2010).
[Crossref]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4(2), 83–91 (2010).
[Crossref]

D. A. B. Miller, “Optical interconnects to electronic chips,” Appl. Opt. 49(25), F59–F70 (2010).
[Crossref] [PubMed]

D. A. B. Miller, “Are optical transistors the logical next step?” Nat. Photon. 4(1), 3–5 (2010).
[Crossref]

2009 (1)

2008 (5)

Y. Huang, W. T. Lu, and S. Sridhar, “Nanowire waveguide made from extremely anisotropic metamaterials,” Phys. Rev. A 77(6), 063836 (2008).
[Crossref]

T. Baba, “Slow light in photonic crystals,” Nat. Photon. 2(8), 465–473 (2008).
[Crossref]

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77(19), 195328 (2008).
[Crossref]

D. Kwon, D. H. Werner, A. V. Kildishev, and V. M. Shalaev, “Material parameter retrieval procedure for general bi-isotropic metamaterials and its application to optical chiral negative-index metamaterial design,” Opt. Express 16(16), 11822–11829 (2008).
[Crossref] [PubMed]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, DA. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

2007 (3)

I. I. Smolyaninov, Y. Hung, and C. C. Davis, “Magnifying Superlens in the Visible Frequency Range,” Science 315(5819), 1699–1701 (2007).
[Crossref] [PubMed]

N. Engheta, “Circuits with Light at Nanoscales: Optical Nanocircuits Inspired by Metamaterials,” Science 317(5845), 1698–1702 (2007).
[Crossref] [PubMed]

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D: Appl. Phys. 40(9), 2635 (2007).
[Crossref]

2006 (1)

M. Silveirinha and N. Engheta, “Tunneling of Electromagnetic Energy through Subwavelength Channels and Bends using Epsilon-Near-Zero Materials,” Phys. Rev. Lett. 97(15), 157403 (2006).
[Crossref] [PubMed]

2005 (2)

P. Belov and C. Simovski, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71(19), 193105 (2005).
[Crossref]

D. R. Smith, D. C. Vier, T. H. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005).
[Crossref]

2004 (1)

2002 (1)

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[Crossref]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966 (2000).
[Crossref] [PubMed]

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B. 6(12), 4370 (1972).
[Crossref]

1965 (1)

W. L. Bond, “Measurement of the Refractive Indices of Several Crystals,” J. Appl. Phys. 36(5), 1674–1677 (1965).
[Crossref]

Alu, A.

A. F. Koenderink, A. Alu, and A. Polman, “Nanophotonics: Shrinking light-based technology,” Science 348(6234), 516–521 (2015).
[Crossref] [PubMed]

Anderson, Z.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nature Photon. 7(10), 791–795 (2013).
[Crossref]

Andryieuski, A.

Baba, T.

T. Baba, “Slow light in photonic crystals,” Nat. Photon. 2(8), 465–473 (2008).
[Crossref]

Babicheva, V. E.

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, DA. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

Belov, P.

P. Belov and C. Simovski, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71(19), 193105 (2005).
[Crossref]

Boltasseva, A.

Bond, W. L.

W. L. Bond, “Measurement of the Refractive Indices of Several Crystals,” J. Appl. Phys. 36(5), 1674–1677 (1965).
[Crossref]

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4(2), 83–91 (2010).
[Crossref]

Brener, I.

J. Ginn and I. Brener, “Realizing Optical Magnetism from Dielectric Metamaterial,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref] [PubMed]

Briggs, D. P.

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nature Photon. 7(10), 791–795 (2013).
[Crossref]

Byun, S. J.

S. B. Choi, D. J. Park, S. J. Byun, J. Kyoung, and S. W. Hwang, “Near-Zero Index: Optical Magnetic Mirror for Field Enhancement and Subwavelength Imaging Applications,” Adv. Opt. Mater. 3(12), 1719–1725 (2015).
[Crossref]

Chen, C.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D: Appl. Phys. 40(9), 2635 (2007).
[Crossref]

D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett. 29(1), 50–52 (2004).
[Crossref] [PubMed]

Choi, S. B.

S. B. Choi, D. J. Park, S. J. Byun, J. Kyoung, and S. W. Hwang, “Near-Zero Index: Optical Magnetic Mirror for Field Enhancement and Subwavelength Imaging Applications,” Adv. Opt. Mater. 3(12), 1719–1725 (2015).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B. 6(12), 4370 (1972).
[Crossref]

Davis, C. C.

I. I. Smolyaninov, Y. Hung, and C. C. Davis, “Magnifying Superlens in the Visible Frequency Range,” Science 315(5819), 1699–1701 (2007).
[Crossref] [PubMed]

Engheta, N.

N. Engheta, “Circuits with Light at Nanoscales: Optical Nanocircuits Inspired by Metamaterials,” Science 317(5845), 1698–1702 (2007).
[Crossref] [PubMed]

M. Silveirinha and N. Engheta, “Tunneling of Electromagnetic Energy through Subwavelength Channels and Bends using Epsilon-Near-Zero Materials,” Phys. Rev. Lett. 97(15), 157403 (2006).
[Crossref] [PubMed]

Feng, Y.

Ferrera, M.

Gao, J.

Y. He, S. He, J. Gao, and X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B. 29(9), 2559–2566 (2012).
[Crossref]

Genov, DA.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, DA. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[Crossref] [PubMed]

Ginn, J.

J. Ginn and I. Brener, “Realizing Optical Magnetism from Dielectric Metamaterial,” Phys. Rev. Lett. 108(9), 097402 (2012).
[Crossref] [PubMed]

Grahn, P.

A. Shevchenko, V. Kivijärvi, P. Grahn, M. Kaivola, and K. Lindfors, “Bifacial metasurface with quadrupole optical response,” Phys. Rev. Appl. 4(2), 024019 (2015).
[Crossref]

A. Shevchenko, P. Grahn, V. Kivijärvi, M. Nyman, and M. Kaivola, “Spatially dispersive functional optical metamaterials,” J. Nanophoton. 9(1), 093097 (2015).
[Crossref]

A. Shevchenko, P. Grahn, and M. Kaivola, “Internally twisted spatially dispersive optical metamaterials,” J. Nanophoton. 8(1), 083074 (2014).
[Crossref]

P. Grahn, A. Shevchenko, and M. Kaivola, “Interferometric description of optical metamaterials,” New J. Phys. 15(11), 113044 (2013).
[Crossref]

P. Grahn, A. Shevchenko, and M. Kaivola, “Theoretical description of bifacial optical nanomaterials,” Opt. Express 21(20), 23471–23485 (2013).
[Crossref] [PubMed]

P. Grahn, A. Shevchenko, and M. Kaivola, “Electric dipole-free interaction of visible light with pairs of subwavelength-size silver particles,” Phys. Rev. B 86(3), 035419 (2012).
[Crossref]

P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys. 14(9), 093033 (2012).
[Crossref]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4(2), 83–91 (2010).
[Crossref]

He, S.

Y. He, S. He, J. Gao, and X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B. 29(9), 2559–2566 (2012).
[Crossref]

He, Y.

Y. He, S. He, J. Gao, and X. Yang, “Nanoscale metamaterial optical waveguides with ultrahigh refractive indices,” J. Opt. Soc. Am. B. 29(9), 2559–2566 (2012).
[Crossref]

Hill, M.

M. Smit, J. Van Der Tol, and M. Hill, “Moore’s law in photonics,” Laser Photon. Rev. 6(1), 1–13 (2012).
[Crossref]

Huang, Y.

Y. Huang, W. T. Lu, and S. Sridhar, “Nanowire waveguide made from extremely anisotropic metamaterials,” Phys. Rev. A 77(6), 063836 (2008).
[Crossref]

Hung, Y.

I. I. Smolyaninov, Y. Hung, and C. C. Davis, “Magnifying Superlens in the Visible Frequency Range,” Science 315(5819), 1699–1701 (2007).
[Crossref] [PubMed]

Hwang, S. W.

S. B. Choi, D. J. Park, S. J. Byun, J. Kyoung, and S. W. Hwang, “Near-Zero Index: Optical Magnetic Mirror for Field Enhancement and Subwavelength Imaging Applications,” Adv. Opt. Mater. 3(12), 1719–1725 (2015).
[Crossref]

Ishii, S.

Jiang, T.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B. 6(12), 4370 (1972).
[Crossref]

Kaivola, M.

A. Shevchenko, M. Nyman, V. Kivijärvi, and M. Kaivola, “Optical wave parameters for spatially dispersive and anisotropic nanomaterials,” Opt. Express 25(8), 8550–8562 (2017).
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V. Kivijärvi, M. Nyman, A. Shevchenko, and M. Kaivola, “Optical-image transfer through a diffraction-compensating metamaterial,” Opt. Express 24(9), 9806–9815 (2016).
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V. Kivijärvi, M. Nyman, A. Shevchenko, and M. Kaivola, “An optical metamaterial with simultaneously suppressed optical diffraction and surface reflection,” J. Opt. 18(3), 035103 (2016).
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A. Shevchenko, V. Kivijärvi, P. Grahn, M. Kaivola, and K. Lindfors, “Bifacial metasurface with quadrupole optical response,” Phys. Rev. Appl. 4(2), 024019 (2015).
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A. Shevchenko, P. Grahn, V. Kivijärvi, M. Nyman, and M. Kaivola, “Spatially dispersive functional optical metamaterials,” J. Nanophoton. 9(1), 093097 (2015).
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A. Shevchenko, P. Grahn, and M. Kaivola, “Internally twisted spatially dispersive optical metamaterials,” J. Nanophoton. 8(1), 083074 (2014).
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P. Grahn, A. Shevchenko, and M. Kaivola, “Interferometric description of optical metamaterials,” New J. Phys. 15(11), 113044 (2013).
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P. Grahn, A. Shevchenko, and M. Kaivola, “Theoretical description of bifacial optical nanomaterials,” Opt. Express 21(20), 23471–23485 (2013).
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P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys. 14(9), 093033 (2012).
[Crossref]

P. Grahn, A. Shevchenko, and M. Kaivola, “Electric dipole-free interaction of visible light with pairs of subwavelength-size silver particles,” Phys. Rev. B 86(3), 035419 (2012).
[Crossref]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
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Kildishev, A. V.

Kinsey, N.

Kivijärvi, V.

A. Shevchenko, M. Nyman, V. Kivijärvi, and M. Kaivola, “Optical wave parameters for spatially dispersive and anisotropic nanomaterials,” Opt. Express 25(8), 8550–8562 (2017).
[Crossref] [PubMed]

V. Kivijärvi, M. Nyman, A. Shevchenko, and M. Kaivola, “Optical-image transfer through a diffraction-compensating metamaterial,” Opt. Express 24(9), 9806–9815 (2016).
[Crossref] [PubMed]

V. Kivijärvi, M. Nyman, A. Shevchenko, and M. Kaivola, “An optical metamaterial with simultaneously suppressed optical diffraction and surface reflection,” J. Opt. 18(3), 035103 (2016).
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A. Shevchenko, P. Grahn, V. Kivijärvi, M. Nyman, and M. Kaivola, “Spatially dispersive functional optical metamaterials,” J. Nanophoton. 9(1), 093097 (2015).
[Crossref]

A. Shevchenko, V. Kivijärvi, P. Grahn, M. Kaivola, and K. Lindfors, “Bifacial metasurface with quadrupole optical response,” Phys. Rev. Appl. 4(2), 024019 (2015).
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A. F. Koenderink, A. Alu, and A. Polman, “Nanophotonics: Shrinking light-based technology,” Science 348(6234), 516–521 (2015).
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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
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D. R. Smith, D. C. Vier, T. H. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005).
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P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nature Photon. 7(10), 791–795 (2013).
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S. B. Choi, D. J. Park, S. J. Byun, J. Kyoung, and S. W. Hwang, “Near-Zero Index: Optical Magnetic Mirror for Field Enhancement and Subwavelength Imaging Applications,” Adv. Opt. Mater. 3(12), 1719–1725 (2015).
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Lederer, F.

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Lindfors, K.

A. Shevchenko, V. Kivijärvi, P. Grahn, M. Kaivola, and K. Lindfors, “Bifacial metasurface with quadrupole optical response,” Phys. Rev. Appl. 4(2), 024019 (2015).
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Y. Huang, W. T. Lu, and S. Sridhar, “Nanowire waveguide made from extremely anisotropic metamaterials,” Phys. Rev. A 77(6), 063836 (2008).
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Markel, V. A.

Markos, P.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
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D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D: Appl. Phys. 40(9), 2635 (2007).
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D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D: Appl. Phys. 40(9), 2635 (2007).
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D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D: Appl. Phys. 40(9), 2635 (2007).
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D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett. 29(1), 50–52 (2004).
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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[Crossref]

Nyman, M.

A. Shevchenko, M. Nyman, V. Kivijärvi, and M. Kaivola, “Optical wave parameters for spatially dispersive and anisotropic nanomaterials,” Opt. Express 25(8), 8550–8562 (2017).
[Crossref] [PubMed]

V. Kivijärvi, M. Nyman, A. Shevchenko, and M. Kaivola, “Optical-image transfer through a diffraction-compensating metamaterial,” Opt. Express 24(9), 9806–9815 (2016).
[Crossref] [PubMed]

V. Kivijärvi, M. Nyman, A. Shevchenko, and M. Kaivola, “An optical metamaterial with simultaneously suppressed optical diffraction and surface reflection,” J. Opt. 18(3), 035103 (2016).
[Crossref]

A. Shevchenko, P. Grahn, V. Kivijärvi, M. Nyman, and M. Kaivola, “Spatially dispersive functional optical metamaterials,” J. Nanophoton. 9(1), 093097 (2015).
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Park, D. J.

S. B. Choi, D. J. Park, S. J. Byun, J. Kyoung, and S. W. Hwang, “Near-Zero Index: Optical Magnetic Mirror for Field Enhancement and Subwavelength Imaging Applications,” Adv. Opt. Mater. 3(12), 1719–1725 (2015).
[Crossref]

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J. Yang, C. Sauvan, T. Paul, C. Rockstuhl, F. Lederer, and P. Lalanne, “Retrieving the effective parameters of metamaterials from the single interface scattering problem,” Appl. Phys. Lett. 97(6), 061102 (2010).
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C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77(19), 195328 (2008).
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C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77(19), 195328 (2008).
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A. F. Koenderink, A. Alu, and A. Polman, “Nanophotonics: Shrinking light-based technology,” Science 348(6234), 516–521 (2015).
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D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D: Appl. Phys. 40(9), 2635 (2007).
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D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett. 29(1), 50–52 (2004).
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Rockstuhl, C.

J. Yang, C. Sauvan, T. Paul, C. Rockstuhl, F. Lederer, and P. Lalanne, “Retrieving the effective parameters of metamaterials from the single interface scattering problem,” Appl. Phys. Lett. 97(6), 061102 (2010).
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C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77(19), 195328 (2008).
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J. Yang, C. Sauvan, T. Paul, C. Rockstuhl, F. Lederer, and P. Lalanne, “Retrieving the effective parameters of metamaterials from the single interface scattering problem,” Appl. Phys. Lett. 97(6), 061102 (2010).
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D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D: Appl. Phys. 40(9), 2635 (2007).
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D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett. 29(1), 50–52 (2004).
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D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
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Shalaginov, M. Y.

Sharkawy, A.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D: Appl. Phys. 40(9), 2635 (2007).
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D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett. 29(1), 50–52 (2004).
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A. Shevchenko, M. Nyman, V. Kivijärvi, and M. Kaivola, “Optical wave parameters for spatially dispersive and anisotropic nanomaterials,” Opt. Express 25(8), 8550–8562 (2017).
[Crossref] [PubMed]

V. Kivijärvi, M. Nyman, A. Shevchenko, and M. Kaivola, “Optical-image transfer through a diffraction-compensating metamaterial,” Opt. Express 24(9), 9806–9815 (2016).
[Crossref] [PubMed]

V. Kivijärvi, M. Nyman, A. Shevchenko, and M. Kaivola, “An optical metamaterial with simultaneously suppressed optical diffraction and surface reflection,” J. Opt. 18(3), 035103 (2016).
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A. Shevchenko, V. Kivijärvi, P. Grahn, M. Kaivola, and K. Lindfors, “Bifacial metasurface with quadrupole optical response,” Phys. Rev. Appl. 4(2), 024019 (2015).
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A. Shevchenko, P. Grahn, V. Kivijärvi, M. Nyman, and M. Kaivola, “Spatially dispersive functional optical metamaterials,” J. Nanophoton. 9(1), 093097 (2015).
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A. Shevchenko, P. Grahn, and M. Kaivola, “Internally twisted spatially dispersive optical metamaterials,” J. Nanophoton. 8(1), 083074 (2014).
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P. Grahn, A. Shevchenko, and M. Kaivola, “Interferometric description of optical metamaterials,” New J. Phys. 15(11), 113044 (2013).
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P. Grahn, A. Shevchenko, and M. Kaivola, “Theoretical description of bifacial optical nanomaterials,” Opt. Express 21(20), 23471–23485 (2013).
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P. Grahn, A. Shevchenko, and M. Kaivola, “Electric dipole-free interaction of visible light with pairs of subwavelength-size silver particles,” Phys. Rev. B 86(3), 035419 (2012).
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P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys. 14(9), 093033 (2012).
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Shi, S.

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D: Appl. Phys. 40(9), 2635 (2007).
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D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett. 29(1), 50–52 (2004).
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D. R. Smith, D. C. Vier, T. H. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005).
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D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
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P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nature Photon. 7(10), 791–795 (2013).
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J. Yang, C. Sauvan, T. Paul, C. Rockstuhl, F. Lederer, and P. Lalanne, “Retrieving the effective parameters of metamaterials from the single interface scattering problem,” Appl. Phys. Lett. 97(6), 061102 (2010).
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Adv. Opt. Mater. (1)

S. B. Choi, D. J. Park, S. J. Byun, J. Kyoung, and S. W. Hwang, “Near-Zero Index: Optical Magnetic Mirror for Field Enhancement and Subwavelength Imaging Applications,” Adv. Opt. Mater. 3(12), 1719–1725 (2015).
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Appl. Opt. (1)

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J. Opt. (1)

V. Kivijärvi, M. Nyman, A. Shevchenko, and M. Kaivola, “An optical metamaterial with simultaneously suppressed optical diffraction and surface reflection,” J. Opt. 18(3), 035103 (2016).
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J. Opt. Soc. Am. A (1)

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J. Phys. D: Appl. Phys. (1)

D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D: Appl. Phys. 40(9), 2635 (2007).
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M. Smit, J. Van Der Tol, and M. Hill, “Moore’s law in photonics,” Laser Photon. Rev. 6(1), 1–13 (2012).
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D. A. B. Miller, “Are optical transistors the logical next step?” Nat. Photon. 4(1), 3–5 (2010).
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Nature (1)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, DA. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
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Nature Photon. (1)

P. Moitra, Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nature Photon. 7(10), 791–795 (2013).
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New J. Phys. (2)

P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys. 14(9), 093033 (2012).
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P. Grahn, A. Shevchenko, and M. Kaivola, “Interferometric description of optical metamaterials,” New J. Phys. 15(11), 113044 (2013).
[Crossref]

Opt. Express (8)

P. Grahn, A. Shevchenko, and M. Kaivola, “Theoretical description of bifacial optical nanomaterials,” Opt. Express 21(20), 23471–23485 (2013).
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Z. Su, J. Yin, K. Song, Q. Lei, and X. Zhao, “Electrically controllable soft optical cloak based on gold nanorod fluids with epsilon-near-zero characteristic,” Opt. Express 24(6), 6021–6033 (2016).
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T. Jiang, J. Zhao, and Y. Feng, “Stopping light by an air waveguide with anisotropic metamaterial cladding,” Opt. Express 17(1), 170–177 (2009).
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V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Long-range plasmonic waveguides with hyperbolic cladding,” Opt. Express 23(24), 31109–31119 (2015).
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V. Kivijärvi, M. Nyman, A. Shevchenko, and M. Kaivola, “Optical-image transfer through a diffraction-compensating metamaterial,” Opt. Express 24(9), 9806–9815 (2016).
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D. Kwon, D. H. Werner, A. V. Kildishev, and V. M. Shalaev, “Material parameter retrieval procedure for general bi-isotropic metamaterials and its application to optical chiral negative-index metamaterial design,” Opt. Express 16(16), 11822–11829 (2008).
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A. Andryieuski, R. Malureanu, and A. V. Lavrinenko, “Wave propagation retrieval method for chiral metamaterials,” Opt. Express 18(15), 15498–15503 (2010).
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A. Shevchenko, M. Nyman, V. Kivijärvi, and M. Kaivola, “Optical wave parameters for spatially dispersive and anisotropic nanomaterials,” Opt. Express 25(8), 8550–8562 (2017).
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Opt. Lett. (1)

Phys. Rev. A (1)

Y. Huang, W. T. Lu, and S. Sridhar, “Nanowire waveguide made from extremely anisotropic metamaterials,” Phys. Rev. A 77(6), 063836 (2008).
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Phys. Rev. Appl. (1)

A. Shevchenko, V. Kivijärvi, P. Grahn, M. Kaivola, and K. Lindfors, “Bifacial metasurface with quadrupole optical response,” Phys. Rev. Appl. 4(2), 024019 (2015).
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Phys. Rev. B (4)

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77(19), 195328 (2008).
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P. Belov and C. Simovski, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71(19), 193105 (2005).
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D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
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P. Grahn, A. Shevchenko, and M. Kaivola, “Electric dipole-free interaction of visible light with pairs of subwavelength-size silver particles,” Phys. Rev. B 86(3), 035419 (2012).
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Phys. Rev. B. (1)

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B. 6(12), 4370 (1972).
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Phys. Rev. E (1)

D. R. Smith, D. C. Vier, T. H. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005).
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M. Silveirinha and N. Engheta, “Tunneling of Electromagnetic Energy through Subwavelength Channels and Bends using Epsilon-Near-Zero Materials,” Phys. Rev. Lett. 97(15), 157403 (2006).
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J. Ginn and I. Brener, “Realizing Optical Magnetism from Dielectric Metamaterial,” Phys. Rev. Lett. 108(9), 097402 (2012).
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I. I. Smolyaninov, Y. Hung, and C. C. Davis, “Magnifying Superlens in the Visible Frequency Range,” Science 315(5819), 1699–1701 (2007).
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Figures (6)

Fig. 1
Fig. 1 A side view of a nanomaterial waveguide, which is treated as a Fabry-Perot resonator. Mode profiles in the three joint waveguide segments (1, 2, and 3) are shown schematically by black solid lines in (a). The nanomaterial waveguide (segment 2) acts as a Fabry-Perot resonator with end facet reflection and transmission coefficients ρij and τij as shown in a top view (b). Light is incident from segment 1. The blue dashed lines indicate the wave propagation. The reflection and transmission coefficients of the nanomaterial waveguide are calculated from the electric field distributions at distances dr and dt, from the nanomaterial entrance and exit facets, respectively.
Fig. 2
Fig. 2 The designed nanomaterial slab waveguide. The waveguide consists of an array of silver nanorods separated by transverse and longitudinal periods of Λx = 80 nm and Λz = 180 nm, respectively. The nanorods are 30 nm thick in the x and y directions and 130 nm long. They are embedded in a 120 nm thick layer of ZnO on a SiO2 substrate.
Fig. 3
Fig. 3 The mode index spectra for the designed nanomaterial slab waveguide. The real part nr of the mode index for the propagation angles φ = 0 (the blue line) and φ = 15° (the red line) is shown in (a). The black line shows ndc (15°) = nr(0)/cos 15°. The crossing point of the black and red lines yields a diffraction-compensation wavelength of 1310 nm. The imaginary part ni for the angles φ = 0 (the blue line) and φ = 15° (the red line) is shown in (b).
Fig. 4
Fig. 4 A polar plot of the mode index for the designed nanomaterial waveguide (a) and a sinusoidal fit to the electric field profile at x = 0 and y = 180 nm (b). The blue line in (a) shows the real part of the mode index nr as a function of the mode propagation angle φ (with respect to the z axis) at λ = 1310 nm. The white circles show the values of nr obtained as λ / ( λ ˜ z cos φ ), where λ ˜ z is the periodicity of the field in the waveguide along z, obtained by fitting the field with a decaying sinusoid. The red line in (a) represents the imaginary part ni multiplied by a factor of 10. The sinusoidal fitting curve is shown by the green line in (b). The black line shows the profile of the field component Ex at a propagation angle of 15°.
Fig. 5
Fig. 5 Propagation of Gaussian beams in (a) an isotropic slab waveguide with n = nr(0) and (b) the designed nanomaterial waveguide. The colorbars in (a) and (b) show the intensity normalized to its maximum at the beam waist. The beam in (a) has a wavelength of 1310 nm. The white dashed lines represent the beam 1/e2 radius. The beam intensity profiles on a xz plane in the middle of the nanomaterial layer are shown in (b). Nanorods are visible as dark rectangles. The beams have an initial waist radius of 300 nm and wavelengths of 1280 nm, 1310 nm, and 1370 nm.
Fig. 6
Fig. 6 Wave propagation in a slab waveguide. The refractive indices of the waveguide core, substrate, and cladding are n1, nsubs, and nclad, respectively. Each waveguide mode can be represented by a sum of two plane waves that undergo multiple internal reflections from the waveguide boundaries. The dashed black and grey lines trace the propagation of these waves. The quantities ϕ1 and ϕ2 are the phase shifts upon the reflection at the two boundaries.

Equations (39)

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r = ρ 12 + τ 12 τ 21 ρ 23 1 ρ 21 ρ 23 exp ( 2 i β z W ) exp ( 2 i β z W ) ,
t = τ 12 τ 23 1 ρ 21 ρ 23 exp ( 2 i β z W ) exp ( i β z W ) .
ρ i j = η i 1 η j 1 η i 1 + η j 1 ,
τ i j = 2 η i 1 η i 1 + η j 1 ,
tan ( k 0 n 1 2 n in 2 D ) = n 1 2 n in 2 n in 2 n subs 2 + n in 2 n clad 2 n 1 2 n in 2 n in 2 n subs 2 n in 2 n clad 2
E i ( x , y , z ) = u ^ i b ( y ) exp ( i [ β x x + β in , z ( z + W / 2 ) ] ) ,
E r ( x , y , z ) = v ^ r b ( y ) exp ( i [ β x x β in , z ( z + W / 2 ) ] ) ,
E t ( x , y , z ) = u ^ t b ( y ) exp ( i [ β x x + β in , z ( z W / 2 ) ] ) ,
r = E r ( z = W / 2 ) E i ( z = W / 2 ) = r i ,
t = E t ( z = W / 2 ) E i ( z = W / 2 ) = t i .
E T ( x , y , z ) = E i ( x , y , z ) + E r ( x , y , z ) , z W / 2 ,
E T ( x , y , z ) = E t ( x , y , z ) , z W / 2 ,
r = b ( y ) v ^ E T ( 0 , y , W / 2 d r ) d y i b 2 ( y ) d y exp ( i β in , z d r ) v ^ u ^ exp ( 2 i β in , z d r )
t = b ( y ) u ^ E T ( 0 , y , W / 2 + d t ) d y i b 2 ( y ) d y exp ( i β in , z d t ) .
E ( x , y , z ) = E ^ ( y , β x ) exp ( i ( β x x + β z z ) ) d β x ,
E ( x , z ) = E ^ ( β x ) exp ( i ( β x x + β z z ) ) d β x .
n r ( φ ) = n r ( 0 ) cos φ .
2 k 0 n 1 D sin θ + ϕ 1 + ϕ 2 = 2 π m ,
n in = n 1 cos θ .
tan ϕ 1 2 = ( n 1 2 n clad 2 ) σ [ 1 sin 2 θ ( 1 n clad 2 n 1 2 ) 1 ] 1 / 2 ,
tan ϕ 2 2 = ( n 1 2 n subs 2 ) σ [ 1 sin 2 θ ( 1 n subs 2 n 1 2 ) 1 ] 1 / 2 ,
tan ( k 0 n 1 2 n in 2 D ) = n 1 2 n 1 2 n in 2 n in 2 n subs 2 / n subs 2 + n in 2 n clad 2 / n clad 2 n 1 2 n in 2 n 1 4 n in 2 n subs 2 n in 2 n clad 2 ( n subs 2 n clad 2 ) .
E ( x , y , z ) = E 0 ( y ) exp ( i ( β x x + β z z ) ) .
J ( x , y , z ) = K 0 ( y ) δ ( z ) exp ( i ( β x x ) ,
A ( x , y , z ) = A 0 ( y ) exp ( i β x x ) exp ( i β z | z | ) ,
2 A + k 2 ( y ) A = μ 0 J ,
A i ( x , y , z ) = K i ( y ) μ 0 2 i β z exp ( i ( β x x + β z | z | ) ) ,
E ( x , y , z ) = i ω [ A ( x , y , z ) + k 2 A ( x , y , z ) ] .
U x = ( 1 β x 2 k 2 ) K x ( y ) + i β x k 2 y K y ( y ) ,
U y = i β x k 2 y K x ( y ) + ( 1 + 1 k 2 y 2 ) K y ( y ) ,
U z = β x β z k 2 K x ( y ) + i β z k 2 y K y ( y ) ,
U i = 2 β z μ 0 ω E i ( y ) .
K x = U x β x β z U z ,
K y = U y + i β z y U z .
J x = 2 β z μ 0 ω [ E x ( y ) β x β z E z ( y ) ] δ ( z ) exp ( i β x x ) ,
J y = 2 β z μ 0 ω [ E y ( y ) y E z ( y ) i β z ] δ ( z ) exp ( i β x x ) .
r b ( y ) v ^ = E T ( x , y , z ) i exp ( i [ β x x β in , z ( z + W / 2 ) ] ) u ^ b ( y ) exp ( i 2 β in , z ( z + W / 2 ) ) .
r b ( y ) = v ^ E T ( x , y , z ) i exp ( i [ β x x β in , z ( z + W / 2 ) ] ) v ^ u ^ b ( y ) exp ( i 2 β in , z ( z + W / 2 ) ) .
r = b ( y ) v ^ E T ( 0 , y , W / 2 d r ) d y i b 2 ( y ) d y exp ( i β in , z d r ) v ^ u ^ exp ( i 2 β in , z d r )

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