Abstract

The article demonstrates uncommon manifestation of spatial dispersion in low refractive index contrast 3D periodic dielectric composites with periods of about one tenth of the wavelength. First principles simulations by the well established plane wave method reveal that spatial dispersion leads to appearance of additional optical axes and can compensate anisotropy in certain directions.

© 2017 Optical Society of America

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References

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  1. V. M. Agranovich and V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons (Wiley-Interscience, 1966).
  2. J. H. Burnett, Z. H. Levine, and E. L. Shirley, “Intrinsic birefringence in calcium fluoride and barium fluoride,” Phys. Rev. B 64, 241102 (2001).
    [Crossref]
  3. R. C. Rumpf, “Engineering the dispersion and anisotropy of periodic electromagnetic structures,” Sol. State. Phys. 66, 213–260 (2015).
  4. V. L. Ginzburg, “Electromagnetic waves in isotropic and crystalline media characterized by dielectric permittivity with spatial dispersion,” Sov. Phys. JETP 34(7), 1096–1103 (1958).
  5. H. A. Lorentz, Collected Papers II (Martinus Nijohff, The Hague, 1936), pp. 1–119.
  6. A. Serebriakov, E. Maksimov, F. Bociort, and J. Braat, “The effect of intrinsic birefringence in deep UV-lithography,” Proc. SPIE 5249, 624 (2004).
    [Crossref]
  7. J. H. Burnett, Z. H. Levine, E. L. Shirley, and J. H. Bruning, “Symmetry of spatial-dispersion-induced birefringence and its implications for CaF2 ultraviolet optics,” J. Micro/Nanolith. MEMS MOEMS 1(3), 213–224 (2002).
    [Crossref]
  8. K. Vynck, D. Felbacq, E. Centeno, A. I. Cčbuz, D. Cassagne, and B. Guizal, “All-dielectric rod-type matamaterials at optical frequencies,” Phys. Rev. Lett. 102, 133901 (2009).
    [Crossref]
  9. M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Progr. Phys. 73, 096501 (2010).
    [Crossref]
  10. L. Maigyte, V. Purlis, J. Trull, M. Peckus, C. Cojocaru, D. Gailevičius, M. Malinauskas, and K. Staliunas, “Flat lensing in the visible frequency range by woodpile photonic crystals,” Opt. Lett. 38, 2376–2378 (2013).
    [Crossref] [PubMed]
  11. H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, “Splitting of triply degenerate refractive indices by photonic crystals,” Phys. Rev. B 62(3), 1477–1480 (2000).
    [Crossref]
  12. M. Notomi, “Negative refraction in photonic crystals,” Opt. Quantum. Electron. 34, 133–143 (2002).
    [Crossref]
  13. T. Baba and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum. Electron. 38(7), 909–914 (2002).
    [Crossref]
  14. Y. Loiko, C. Serrat, R. Herrero, and K. Staliunas, “Quantitative analysis of subdiffractive light propagation in photonic crystals,” Opt. Commun. 269, 128–136 (2007).
    [Crossref]
  15. L. Maigyte and K. Staliunas, “Spatial filtering with photonic crystals,” Appl. Phys. Rev. 2, 011102 (2015).
    [Crossref]
  16. M. A. Gorlach and P. A. Belov, “Nonlocality in uniaxially polarizable media,” Phys. Rev. B 92, 085107 (2015).
    [Crossref]
  17. C. Fietz, Y. Urzhumov, and G. Shvets, “Complex k band diagrams of 3D metamaterial/photonic crystals,” Opt. Expr. 19(20), 19027–19041 (2011).
    [Crossref]
  18. A. V. Chebykin, M. A. Gorlach, and P. A. Belov, “Spatial-dispersion-induced birefringence in metamaterials with cubic symmetry,” Phys. Rev. B 92, 045127 (2015).
    [Crossref]
  19. M. A. Gorlach, S. B. Glybovsky, A. A. Hurshkainen, and P.A. Belov, “Giant spatial-dispersion-induced birefringence in metamaterials,” Phys. Rev. B 93, 201115 (2016).
    [Crossref]
  20. K. L. Koshelev and A. A. Bogdanov, “Interplay between anisotropy and spatial dispersion in metamaterial waveguide,” Phys. Rev. B 94, 115439 (2016).
    [Crossref]
  21. M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86(8), 1526–1529 (2001).
    [Crossref] [PubMed]
  22. S. Maruo and J. T. Fourkas, “Recent progress in multiphoton microfabrication,” Laser Photon. Rev. 2(1–2), 100–111 (2008).
    [Crossref]
  23. A. A. Shcherbakov and A. V. Tishchenko, “3D periodic dielectric composite homogenization based on the Generalized Source Method,” J. Opt. 17, 065101 (2015).
    [Crossref]
  24. M. Che, Z-Y. Li, and R.-J. Liu, “Tunable optical anisotropy in three-dimensional photonic crystals,” Phys. Rev. A 76, 023809 (2007).
    [Crossref]
  25. K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65(21), 2646–2649 (1990).
    [Crossref] [PubMed]
  26. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
    [Crossref] [PubMed]
  27. S. G. Johnson and J. D. Joannopoulus, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Expr. 8(3), 173–190 (2001).
    [Crossref]
  28. P. M. Morse and H. Feshbach, Methods of theoretical physics (McGraw-Hill, 1953).
  29. J. F. Nye, Physical Properties of Crystals (Clarendon, 1985).
  30. C. R. Simovski, “On electromagnetic characterization and homogenization of nanostructured metamaterials,” J. Opt. 13, 013001 (2011).
    [Crossref]

2016 (2)

M. A. Gorlach, S. B. Glybovsky, A. A. Hurshkainen, and P.A. Belov, “Giant spatial-dispersion-induced birefringence in metamaterials,” Phys. Rev. B 93, 201115 (2016).
[Crossref]

K. L. Koshelev and A. A. Bogdanov, “Interplay between anisotropy and spatial dispersion in metamaterial waveguide,” Phys. Rev. B 94, 115439 (2016).
[Crossref]

2015 (5)

L. Maigyte and K. Staliunas, “Spatial filtering with photonic crystals,” Appl. Phys. Rev. 2, 011102 (2015).
[Crossref]

M. A. Gorlach and P. A. Belov, “Nonlocality in uniaxially polarizable media,” Phys. Rev. B 92, 085107 (2015).
[Crossref]

A. A. Shcherbakov and A. V. Tishchenko, “3D periodic dielectric composite homogenization based on the Generalized Source Method,” J. Opt. 17, 065101 (2015).
[Crossref]

A. V. Chebykin, M. A. Gorlach, and P. A. Belov, “Spatial-dispersion-induced birefringence in metamaterials with cubic symmetry,” Phys. Rev. B 92, 045127 (2015).
[Crossref]

R. C. Rumpf, “Engineering the dispersion and anisotropy of periodic electromagnetic structures,” Sol. State. Phys. 66, 213–260 (2015).

2013 (1)

2011 (2)

C. R. Simovski, “On electromagnetic characterization and homogenization of nanostructured metamaterials,” J. Opt. 13, 013001 (2011).
[Crossref]

C. Fietz, Y. Urzhumov, and G. Shvets, “Complex k band diagrams of 3D metamaterial/photonic crystals,” Opt. Expr. 19(20), 19027–19041 (2011).
[Crossref]

2010 (1)

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Progr. Phys. 73, 096501 (2010).
[Crossref]

2009 (1)

K. Vynck, D. Felbacq, E. Centeno, A. I. Cčbuz, D. Cassagne, and B. Guizal, “All-dielectric rod-type matamaterials at optical frequencies,” Phys. Rev. Lett. 102, 133901 (2009).
[Crossref]

2008 (1)

S. Maruo and J. T. Fourkas, “Recent progress in multiphoton microfabrication,” Laser Photon. Rev. 2(1–2), 100–111 (2008).
[Crossref]

2007 (2)

M. Che, Z-Y. Li, and R.-J. Liu, “Tunable optical anisotropy in three-dimensional photonic crystals,” Phys. Rev. A 76, 023809 (2007).
[Crossref]

Y. Loiko, C. Serrat, R. Herrero, and K. Staliunas, “Quantitative analysis of subdiffractive light propagation in photonic crystals,” Opt. Commun. 269, 128–136 (2007).
[Crossref]

2004 (1)

A. Serebriakov, E. Maksimov, F. Bociort, and J. Braat, “The effect of intrinsic birefringence in deep UV-lithography,” Proc. SPIE 5249, 624 (2004).
[Crossref]

2002 (3)

J. H. Burnett, Z. H. Levine, E. L. Shirley, and J. H. Bruning, “Symmetry of spatial-dispersion-induced birefringence and its implications for CaF2 ultraviolet optics,” J. Micro/Nanolith. MEMS MOEMS 1(3), 213–224 (2002).
[Crossref]

M. Notomi, “Negative refraction in photonic crystals,” Opt. Quantum. Electron. 34, 133–143 (2002).
[Crossref]

T. Baba and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum. Electron. 38(7), 909–914 (2002).
[Crossref]

2001 (3)

M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86(8), 1526–1529 (2001).
[Crossref] [PubMed]

J. H. Burnett, Z. H. Levine, and E. L. Shirley, “Intrinsic birefringence in calcium fluoride and barium fluoride,” Phys. Rev. B 64, 241102 (2001).
[Crossref]

S. G. Johnson and J. D. Joannopoulus, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Expr. 8(3), 173–190 (2001).
[Crossref]

2000 (1)

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, “Splitting of triply degenerate refractive indices by photonic crystals,” Phys. Rev. B 62(3), 1477–1480 (2000).
[Crossref]

1990 (2)

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65(21), 2646–2649 (1990).
[Crossref] [PubMed]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[Crossref] [PubMed]

1958 (1)

V. L. Ginzburg, “Electromagnetic waves in isotropic and crystalline media characterized by dielectric permittivity with spatial dispersion,” Sov. Phys. JETP 34(7), 1096–1103 (1958).

Agranovich, V. M.

V. M. Agranovich and V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons (Wiley-Interscience, 1966).

Baba, T.

T. Baba and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum. Electron. 38(7), 909–914 (2002).
[Crossref]

Baumberg, J. J.

M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86(8), 1526–1529 (2001).
[Crossref] [PubMed]

Belov, P. A.

A. V. Chebykin, M. A. Gorlach, and P. A. Belov, “Spatial-dispersion-induced birefringence in metamaterials with cubic symmetry,” Phys. Rev. B 92, 045127 (2015).
[Crossref]

M. A. Gorlach and P. A. Belov, “Nonlocality in uniaxially polarizable media,” Phys. Rev. B 92, 085107 (2015).
[Crossref]

Belov, P.A.

M. A. Gorlach, S. B. Glybovsky, A. A. Hurshkainen, and P.A. Belov, “Giant spatial-dispersion-induced birefringence in metamaterials,” Phys. Rev. B 93, 201115 (2016).
[Crossref]

Bociort, F.

A. Serebriakov, E. Maksimov, F. Bociort, and J. Braat, “The effect of intrinsic birefringence in deep UV-lithography,” Proc. SPIE 5249, 624 (2004).
[Crossref]

Bogdanov, A. A.

K. L. Koshelev and A. A. Bogdanov, “Interplay between anisotropy and spatial dispersion in metamaterial waveguide,” Phys. Rev. B 94, 115439 (2016).
[Crossref]

Braat, J.

A. Serebriakov, E. Maksimov, F. Bociort, and J. Braat, “The effect of intrinsic birefringence in deep UV-lithography,” Proc. SPIE 5249, 624 (2004).
[Crossref]

Bruning, J. H.

J. H. Burnett, Z. H. Levine, E. L. Shirley, and J. H. Bruning, “Symmetry of spatial-dispersion-induced birefringence and its implications for CaF2 ultraviolet optics,” J. Micro/Nanolith. MEMS MOEMS 1(3), 213–224 (2002).
[Crossref]

Burnett, J. H.

J. H. Burnett, Z. H. Levine, E. L. Shirley, and J. H. Bruning, “Symmetry of spatial-dispersion-induced birefringence and its implications for CaF2 ultraviolet optics,” J. Micro/Nanolith. MEMS MOEMS 1(3), 213–224 (2002).
[Crossref]

J. H. Burnett, Z. H. Levine, and E. L. Shirley, “Intrinsic birefringence in calcium fluoride and barium fluoride,” Phys. Rev. B 64, 241102 (2001).
[Crossref]

Cassagne, D.

K. Vynck, D. Felbacq, E. Centeno, A. I. Cčbuz, D. Cassagne, and B. Guizal, “All-dielectric rod-type matamaterials at optical frequencies,” Phys. Rev. Lett. 102, 133901 (2009).
[Crossref]

Ccbuz, A. I.

K. Vynck, D. Felbacq, E. Centeno, A. I. Cčbuz, D. Cassagne, and B. Guizal, “All-dielectric rod-type matamaterials at optical frequencies,” Phys. Rev. Lett. 102, 133901 (2009).
[Crossref]

Centeno, E.

K. Vynck, D. Felbacq, E. Centeno, A. I. Cčbuz, D. Cassagne, and B. Guizal, “All-dielectric rod-type matamaterials at optical frequencies,” Phys. Rev. Lett. 102, 133901 (2009).
[Crossref]

Chan, C. T.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[Crossref] [PubMed]

Charlton, M. B.

M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86(8), 1526–1529 (2001).
[Crossref] [PubMed]

Che, M.

M. Che, Z-Y. Li, and R.-J. Liu, “Tunable optical anisotropy in three-dimensional photonic crystals,” Phys. Rev. A 76, 023809 (2007).
[Crossref]

Chebykin, A. V.

A. V. Chebykin, M. A. Gorlach, and P. A. Belov, “Spatial-dispersion-induced birefringence in metamaterials with cubic symmetry,” Phys. Rev. B 92, 045127 (2015).
[Crossref]

Cojocaru, C.

Felbacq, D.

K. Vynck, D. Felbacq, E. Centeno, A. I. Cčbuz, D. Cassagne, and B. Guizal, “All-dielectric rod-type matamaterials at optical frequencies,” Phys. Rev. Lett. 102, 133901 (2009).
[Crossref]

Feshbach, H.

P. M. Morse and H. Feshbach, Methods of theoretical physics (McGraw-Hill, 1953).

Fietz, C.

C. Fietz, Y. Urzhumov, and G. Shvets, “Complex k band diagrams of 3D metamaterial/photonic crystals,” Opt. Expr. 19(20), 19027–19041 (2011).
[Crossref]

Fourkas, J. T.

S. Maruo and J. T. Fourkas, “Recent progress in multiphoton microfabrication,” Laser Photon. Rev. 2(1–2), 100–111 (2008).
[Crossref]

Gailevicius, D.

Ginzburg, V. L.

V. L. Ginzburg, “Electromagnetic waves in isotropic and crystalline media characterized by dielectric permittivity with spatial dispersion,” Sov. Phys. JETP 34(7), 1096–1103 (1958).

V. M. Agranovich and V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons (Wiley-Interscience, 1966).

Glybovsky, S. B.

M. A. Gorlach, S. B. Glybovsky, A. A. Hurshkainen, and P.A. Belov, “Giant spatial-dispersion-induced birefringence in metamaterials,” Phys. Rev. B 93, 201115 (2016).
[Crossref]

Gorlach, M. A.

M. A. Gorlach, S. B. Glybovsky, A. A. Hurshkainen, and P.A. Belov, “Giant spatial-dispersion-induced birefringence in metamaterials,” Phys. Rev. B 93, 201115 (2016).
[Crossref]

A. V. Chebykin, M. A. Gorlach, and P. A. Belov, “Spatial-dispersion-induced birefringence in metamaterials with cubic symmetry,” Phys. Rev. B 92, 045127 (2015).
[Crossref]

M. A. Gorlach and P. A. Belov, “Nonlocality in uniaxially polarizable media,” Phys. Rev. B 92, 085107 (2015).
[Crossref]

Guizal, B.

K. Vynck, D. Felbacq, E. Centeno, A. I. Cčbuz, D. Cassagne, and B. Guizal, “All-dielectric rod-type matamaterials at optical frequencies,” Phys. Rev. Lett. 102, 133901 (2009).
[Crossref]

Harris, A.

M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86(8), 1526–1529 (2001).
[Crossref] [PubMed]

Herrero, R.

Y. Loiko, C. Serrat, R. Herrero, and K. Staliunas, “Quantitative analysis of subdiffractive light propagation in photonic crystals,” Opt. Commun. 269, 128–136 (2007).
[Crossref]

Ho, K. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[Crossref] [PubMed]

Hurshkainen, A. A.

M. A. Gorlach, S. B. Glybovsky, A. A. Hurshkainen, and P.A. Belov, “Giant spatial-dispersion-induced birefringence in metamaterials,” Phys. Rev. B 93, 201115 (2016).
[Crossref]

Joannopoulus, J. D.

S. G. Johnson and J. D. Joannopoulus, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Expr. 8(3), 173–190 (2001).
[Crossref]

Johnson, S. G.

S. G. Johnson and J. D. Joannopoulus, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Expr. 8(3), 173–190 (2001).
[Crossref]

Kawakami, S.

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, “Splitting of triply degenerate refractive indices by photonic crystals,” Phys. Rev. B 62(3), 1477–1480 (2000).
[Crossref]

Kawashima, T.

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, “Splitting of triply degenerate refractive indices by photonic crystals,” Phys. Rev. B 62(3), 1477–1480 (2000).
[Crossref]

Kosaka, H.

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, “Splitting of triply degenerate refractive indices by photonic crystals,” Phys. Rev. B 62(3), 1477–1480 (2000).
[Crossref]

Koshelev, K. L.

K. L. Koshelev and A. A. Bogdanov, “Interplay between anisotropy and spatial dispersion in metamaterial waveguide,” Phys. Rev. B 94, 115439 (2016).
[Crossref]

Leung, K. M.

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65(21), 2646–2649 (1990).
[Crossref] [PubMed]

Levine, Z. H.

J. H. Burnett, Z. H. Levine, E. L. Shirley, and J. H. Bruning, “Symmetry of spatial-dispersion-induced birefringence and its implications for CaF2 ultraviolet optics,” J. Micro/Nanolith. MEMS MOEMS 1(3), 213–224 (2002).
[Crossref]

J. H. Burnett, Z. H. Levine, and E. L. Shirley, “Intrinsic birefringence in calcium fluoride and barium fluoride,” Phys. Rev. B 64, 241102 (2001).
[Crossref]

Li, Z-Y.

M. Che, Z-Y. Li, and R.-J. Liu, “Tunable optical anisotropy in three-dimensional photonic crystals,” Phys. Rev. A 76, 023809 (2007).
[Crossref]

Liu, R.-J.

M. Che, Z-Y. Li, and R.-J. Liu, “Tunable optical anisotropy in three-dimensional photonic crystals,” Phys. Rev. A 76, 023809 (2007).
[Crossref]

Liu, Y. F.

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65(21), 2646–2649 (1990).
[Crossref] [PubMed]

Loiko, Y.

Y. Loiko, C. Serrat, R. Herrero, and K. Staliunas, “Quantitative analysis of subdiffractive light propagation in photonic crystals,” Opt. Commun. 269, 128–136 (2007).
[Crossref]

Lorentz, H. A.

H. A. Lorentz, Collected Papers II (Martinus Nijohff, The Hague, 1936), pp. 1–119.

Maigyte, L.

Maksimov, E.

A. Serebriakov, E. Maksimov, F. Bociort, and J. Braat, “The effect of intrinsic birefringence in deep UV-lithography,” Proc. SPIE 5249, 624 (2004).
[Crossref]

Malinauskas, M.

Maruo, S.

S. Maruo and J. T. Fourkas, “Recent progress in multiphoton microfabrication,” Laser Photon. Rev. 2(1–2), 100–111 (2008).
[Crossref]

Morse, P. M.

P. M. Morse and H. Feshbach, Methods of theoretical physics (McGraw-Hill, 1953).

Nakamura, M.

T. Baba and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum. Electron. 38(7), 909–914 (2002).
[Crossref]

Netti, M. C.

M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86(8), 1526–1529 (2001).
[Crossref] [PubMed]

Notomi, M.

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Progr. Phys. 73, 096501 (2010).
[Crossref]

M. Notomi, “Negative refraction in photonic crystals,” Opt. Quantum. Electron. 34, 133–143 (2002).
[Crossref]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon, 1985).

Parker, G. J.

M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86(8), 1526–1529 (2001).
[Crossref] [PubMed]

Peckus, M.

Purlis, V.

Rumpf, R. C.

R. C. Rumpf, “Engineering the dispersion and anisotropy of periodic electromagnetic structures,” Sol. State. Phys. 66, 213–260 (2015).

Sato, T.

H. Kosaka, A. Tomita, T. Kawashima, T. Sato, and S. Kawakami, “Splitting of triply degenerate refractive indices by photonic crystals,” Phys. Rev. B 62(3), 1477–1480 (2000).
[Crossref]

Serebriakov, A.

A. Serebriakov, E. Maksimov, F. Bociort, and J. Braat, “The effect of intrinsic birefringence in deep UV-lithography,” Proc. SPIE 5249, 624 (2004).
[Crossref]

Serrat, C.

Y. Loiko, C. Serrat, R. Herrero, and K. Staliunas, “Quantitative analysis of subdiffractive light propagation in photonic crystals,” Opt. Commun. 269, 128–136 (2007).
[Crossref]

Shcherbakov, A. A.

A. A. Shcherbakov and A. V. Tishchenko, “3D periodic dielectric composite homogenization based on the Generalized Source Method,” J. Opt. 17, 065101 (2015).
[Crossref]

Shirley, E. L.

J. H. Burnett, Z. H. Levine, E. L. Shirley, and J. H. Bruning, “Symmetry of spatial-dispersion-induced birefringence and its implications for CaF2 ultraviolet optics,” J. Micro/Nanolith. MEMS MOEMS 1(3), 213–224 (2002).
[Crossref]

J. H. Burnett, Z. H. Levine, and E. L. Shirley, “Intrinsic birefringence in calcium fluoride and barium fluoride,” Phys. Rev. B 64, 241102 (2001).
[Crossref]

Shvets, G.

C. Fietz, Y. Urzhumov, and G. Shvets, “Complex k band diagrams of 3D metamaterial/photonic crystals,” Opt. Expr. 19(20), 19027–19041 (2011).
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Supplementary Material (2)

NameDescription
» Visualization 1: MP4 (856 KB)      Distortion of isofrequency surface with period-to-wavelength ratio increase for tetragonal lattice composite being effectively uniaxial medium at infinitely small period.
» Visualization 2: MP4 (858 KB)      Distortion of isofrequency surface with period-to-wavelength ratio increase for orthorhombic lattice composite being effectively biaxial medium at infinitely small period.

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Figures (5)

Fig. 1
Fig. 1 Considered scaffold structure (a); and isofrequency surface (b) for Λ/λ = 0.1 possessing seven optical axes marked with red lines.
Fig. 2
Fig. 2 (a) Dependence of maximum effective refractive index difference of two modes propagating in 〈110〉 direction from Λ/λ ratio in doubly logarithmic scale. Four curves correspond to different refractive indices of a dielectric material constituting the scaffold structure shown in Fig. 1(a) with Λ1 = Λ2 = Λ3. (b) Dependence of coefficients p1,2 from (Λ/λ)2 in Eq. (4).
Fig. 3
Fig. 3 (a) Isofrequency surface of effectively uniaxial crystal for small period value Λ1/λ = 0.025. (b) Distortion of the uniaxial crystal isofrequency surface and position of 8 additional optical axes for period to wavelength ratio Λ1/λ = 0.2 (see Visualization 1 for sequential period change). Considered scaffold structure shown in Fig. 1(a) has tetragonal lattice with period relations Λ2 = Λ1, Λ3 = 1.1Λ1. Axis scales are the same as in Fig. 1(b).
Fig. 4
Fig. 4 Dependence of parameters, which define spatial dispersion terms in Eqs. (5, 6), from (Λ/λ)2 for (a) tetragonal lattice and (b) orthorhombic lattice.
Fig. 5
Fig. 5 (a) Isofrequency surface of effectively biaxial crystal for small period value Λ1/λ = 0.025. (b) Distortion of the biaxial crystal isofrequency surface and position of 8 additional optical axes for period to wavelength ratio Λ1/λ = 0.2 (see Visualization 2 for sequential period change). Considered scaffold structure shown in Fig. 1(a) has orthorhombic lattice with period relations Λ2 = 0.9Λ1, Λ3 = 1.1Λ1. Axis scales are the same as in Fig. 1(b).

Equations (6)

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ε α β ( q ) = ε α β ( 0 ) + ζ α β γ δ q γ q δ + ,
E α ( r ) = E α i n c ( r ) + i ω μ 0 V ( δ α β + 1 k b 2 x α x β ) exp ( i k b | r r | ) 4 π | r r | J β ( r ) d V ,
E α m k b 2 δ α β k α m k β m k m 2 k b 2 ( Δ ε ε b ) m m E β m = E α m i n c .
ε α β = ε ( 0 ) δ α β + n 2 ( s ^ ) { [ p 2 + ( p 1 p 2 ) s ^ α 2 ] δ α β + p 3 s ^ α s ^ β }
ε = ( ε 11 ( 0 ) 0 0 0 ε 11 ( 0 ) 0 0 0 ε 33 ( 0 ) ) + n 2 ( s ^ ) ( p 1 s 1 2 + p 4 s 2 2 + p 5 s 3 2 p 2 s 1 s 2 0 p 2 s 1 s 2 p 4 s 1 2 + p 1 s 2 2 + p 5 s 3 2 0 0 0 p 6 ( s 1 2 + s 2 2 ) + p 3 s 3 2 )
ε = ( ε 11 ( 0 ) 0 0 0 ε 22 ( 0 ) 0 0 0 ε 33 ( 0 ) ) + n 2 ( s ^ ) ( p 1 s 1 2 + p 2 s 2 2 + p 3 s 3 2 0 p 4 s 1 s 3 0 p 5 s 1 2 + p 6 s 2 2 + p 7 s 3 2 p 8 s 2 s 3 p 4 s 1 s 3 p 8 s 2 s 3 p 9 s 1 2 + p 10 s 2 2 + p 11 s 3 2 )

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