Abstract

In this paper, we study the excitation of guided resonances (GRs) in photonic-crystal slabs based on point-defected aperiodically-ordered supercells. With specific reference to perforated-slab structures and the Ammann-Beenker octagonal lattice geometry, we carry out full-wave numerical studies of the plane-wave responses and of the underlying modal structures, which illustrate the representative effects induced by the introduction of symmetry-preserving and symmetry-breaking defects. Our results demonstrate that breaking the supercell mirror symmetries via the judicious introduction of point-defects enables for the excitation of otherwise uncoupled GRs, with control on the symmetry properties of their field distributions, thereby constituting an attractive alternative to those GR-engineering approaches based on the asymmetrization of the hole shape. In this framework, aperiodically-ordered supercells seem to be inherently suited, in view of the variety of inequivalent defect sites that they can offer.

© 2009 OSA

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2009 (2)

I. Gallina, A. Ricciardi, M. Pisco, S. Campopiano, G. Castaldi, A. Cusano, A. Cutolo, and V. Galdi, “Parametric study of guided resonances in octagonal photonic quasicrystals,” Microw. Opt. Technol. Lett. 51(11), 2737–2740 (2009).
[CrossRef]

A. Ricciardi, I. Gallina, S. Campopiano, G. Castaldi, M. Pisco, V. Galdi, and A. Cusano, “Guided resonances in photonic quasicrystals,” Opt. Express 17(8), 6335–6346 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6335 .
[PubMed]

2008 (3)

2007 (2)

2006 (1)

2005 (1)

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94(18), 183903 (2005).
[CrossRef] [PubMed]

2004 (2)

K. Nozaki and T. Baba, “Quasiperiodic photonic crystal microcavity lasers,” Appl. Phys. Lett. 84(24), 4875–4877 (2004).
[CrossRef]

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
[CrossRef]

2003 (1)

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68(4), 045115 (2003).
[CrossRef]

2002 (1)

S. H. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

2001 (1)

M. Bayindir, E. Cubukcu, I. Bulu, and E. Ozbay, “Photonic band-gap effect, localization, and waveguiding in the two-dimensional Penrose lattice,” Phys. Rev. B 63(16), 161104 (2001).
[CrossRef]

2000 (1)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16), 10696–10705 (2000).
[CrossRef]

1999 (1)

1995 (1)

K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B 52(11), 7982–7986 (1995).
[CrossRef]

1987 (1)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

1984 (2)

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translation symmetry,” Phys. Rev. Lett. 53(20), 1951–1953 (1984).
[CrossRef]

D. Levine and P. J. Steinhardt, “Quasicrystals: A new class of ordered structures,” Phys. Rev. Lett. 53(26), 2477–2480 (1984).
[CrossRef]

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[CrossRef]

Andreone, A.

E. Di Gennaro, S. Savo, A. Andreone, V. Galdi, G. Castaldi, V. Pierro, and M. R. Masullo, “Mode confinement in photonic quasicrystal point-defect cavities for particle accelerators,” Appl. Phys. Lett. 93(16), 164102 (2008).
[CrossRef]

Astratov, V. N.

Baba, T.

K. Nozaki and T. Baba, “Quasiperiodic photonic crystal microcavity lasers,” Appl. Phys. Lett. 84(24), 4875–4877 (2004).
[CrossRef]

Bayindir, M.

M. Bayindir, E. Cubukcu, I. Bulu, and E. Ozbay, “Photonic band-gap effect, localization, and waveguiding in the two-dimensional Penrose lattice,” Phys. Rev. B 63(16), 161104 (2001).
[CrossRef]

Blech, I.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translation symmetry,” Phys. Rev. Lett. 53(20), 1951–1953 (1984).
[CrossRef]

Bulu, I.

M. Bayindir, E. Cubukcu, I. Bulu, and E. Ozbay, “Photonic band-gap effect, localization, and waveguiding in the two-dimensional Penrose lattice,” Phys. Rev. B 63(16), 161104 (2001).
[CrossRef]

Cahn, J. W.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translation symmetry,” Phys. Rev. Lett. 53(20), 1951–1953 (1984).
[CrossRef]

Campopiano, S.

I. Gallina, A. Ricciardi, M. Pisco, S. Campopiano, G. Castaldi, A. Cusano, A. Cutolo, and V. Galdi, “Parametric study of guided resonances in octagonal photonic quasicrystals,” Microw. Opt. Technol. Lett. 51(11), 2737–2740 (2009).
[CrossRef]

A. Ricciardi, I. Gallina, S. Campopiano, G. Castaldi, M. Pisco, V. Galdi, and A. Cusano, “Guided resonances in photonic quasicrystals,” Opt. Express 17(8), 6335–6346 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6335 .
[PubMed]

Capolino, F.

A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express 14(21), 10021–10027 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-10021 .
[CrossRef] [PubMed]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94(18), 183903 (2005).
[CrossRef] [PubMed]

Castaldi, G.

A. Ricciardi, I. Gallina, S. Campopiano, G. Castaldi, M. Pisco, V. Galdi, and A. Cusano, “Guided resonances in photonic quasicrystals,” Opt. Express 17(8), 6335–6346 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6335 .
[PubMed]

I. Gallina, A. Ricciardi, M. Pisco, S. Campopiano, G. Castaldi, A. Cusano, A. Cutolo, and V. Galdi, “Parametric study of guided resonances in octagonal photonic quasicrystals,” Microw. Opt. Technol. Lett. 51(11), 2737–2740 (2009).
[CrossRef]

E. Di Gennaro, S. Savo, A. Andreone, V. Galdi, G. Castaldi, V. Pierro, and M. R. Masullo, “Mode confinement in photonic quasicrystal point-defect cavities for particle accelerators,” Appl. Phys. Lett. 93(16), 164102 (2008).
[CrossRef]

Colvin, V. L.

Cubukcu, E.

M. Bayindir, E. Cubukcu, I. Bulu, and E. Ozbay, “Photonic band-gap effect, localization, and waveguiding in the two-dimensional Penrose lattice,” Phys. Rev. B 63(16), 161104 (2001).
[CrossRef]

Culshaw, I. S.

Cusano, A.

A. Ricciardi, I. Gallina, S. Campopiano, G. Castaldi, M. Pisco, V. Galdi, and A. Cusano, “Guided resonances in photonic quasicrystals,” Opt. Express 17(8), 6335–6346 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6335 .
[PubMed]

I. Gallina, A. Ricciardi, M. Pisco, S. Campopiano, G. Castaldi, A. Cusano, A. Cutolo, and V. Galdi, “Parametric study of guided resonances in octagonal photonic quasicrystals,” Microw. Opt. Technol. Lett. 51(11), 2737–2740 (2009).
[CrossRef]

Cutolo, A.

I. Gallina, A. Ricciardi, M. Pisco, S. Campopiano, G. Castaldi, A. Cusano, A. Cutolo, and V. Galdi, “Parametric study of guided resonances in octagonal photonic quasicrystals,” Microw. Opt. Technol. Lett. 51(11), 2737–2740 (2009).
[CrossRef]

De la Rue, R. M.

Della Villa, A.

A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express 14(21), 10021–10027 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-10021 .
[CrossRef] [PubMed]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94(18), 183903 (2005).
[CrossRef] [PubMed]

Di Gennaro, E.

E. Di Gennaro, S. Savo, A. Andreone, V. Galdi, G. Castaldi, V. Pierro, and M. R. Masullo, “Mode confinement in photonic quasicrystal point-defect cavities for particle accelerators,” Appl. Phys. Lett. 93(16), 164102 (2008).
[CrossRef]

Digonnet, M.

Enoch, S.

A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express 14(21), 10021–10027 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-10021 .
[CrossRef] [PubMed]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94(18), 183903 (2005).
[CrossRef] [PubMed]

Fan, S.

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
[CrossRef]

Fan, S. H.

S. H. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[CrossRef]

Galdi, V.

A. Ricciardi, I. Gallina, S. Campopiano, G. Castaldi, M. Pisco, V. Galdi, and A. Cusano, “Guided resonances in photonic quasicrystals,” Opt. Express 17(8), 6335–6346 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6335 .
[PubMed]

I. Gallina, A. Ricciardi, M. Pisco, S. Campopiano, G. Castaldi, A. Cusano, A. Cutolo, and V. Galdi, “Parametric study of guided resonances in octagonal photonic quasicrystals,” Microw. Opt. Technol. Lett. 51(11), 2737–2740 (2009).
[CrossRef]

E. Di Gennaro, S. Savo, A. Andreone, V. Galdi, G. Castaldi, V. Pierro, and M. R. Masullo, “Mode confinement in photonic quasicrystal point-defect cavities for particle accelerators,” Appl. Phys. Lett. 93(16), 164102 (2008).
[CrossRef]

A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express 14(21), 10021–10027 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-10021 .
[CrossRef] [PubMed]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94(18), 183903 (2005).
[CrossRef] [PubMed]

Gallina, I.

I. Gallina, A. Ricciardi, M. Pisco, S. Campopiano, G. Castaldi, A. Cusano, A. Cutolo, and V. Galdi, “Parametric study of guided resonances in octagonal photonic quasicrystals,” Microw. Opt. Technol. Lett. 51(11), 2737–2740 (2009).
[CrossRef]

A. Ricciardi, I. Gallina, S. Campopiano, G. Castaldi, M. Pisco, V. Galdi, and A. Cusano, “Guided resonances in photonic quasicrystals,” Opt. Express 17(8), 6335–6346 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6335 .
[PubMed]

Gratias, D.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translation symmetry,” Phys. Rev. Lett. 53(20), 1951–1953 (1984).
[CrossRef]

Joannopoulos, J. D.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68(4), 045115 (2003).
[CrossRef]

S. H. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68(4), 045115 (2003).
[CrossRef]

Kilic, O.

Kino, G.

Krauss, T. F.

Levine, D.

D. Levine and P. J. Steinhardt, “Quasicrystals: A new class of ordered structures,” Phys. Rev. Lett. 53(26), 2477–2480 (1984).
[CrossRef]

Luo, C.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68(4), 045115 (2003).
[CrossRef]

Masullo, M. R.

E. Di Gennaro, S. Savo, A. Andreone, V. Galdi, G. Castaldi, V. Pierro, and M. R. Masullo, “Mode confinement in photonic quasicrystal point-defect cavities for particle accelerators,” Appl. Phys. Lett. 93(16), 164102 (2008).
[CrossRef]

Mittleman, D. M.

Notomi, M.

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16), 10696–10705 (2000).
[CrossRef]

Nozaki, K.

K. Nozaki and T. Baba, “Quasiperiodic photonic crystal microcavity lasers,” Appl. Phys. Lett. 84(24), 4875–4877 (2004).
[CrossRef]

Ozbay, E.

M. Bayindir, E. Cubukcu, I. Bulu, and E. Ozbay, “Photonic band-gap effect, localization, and waveguiding in the two-dimensional Penrose lattice,” Phys. Rev. B 63(16), 161104 (2001).
[CrossRef]

Pierro, V.

E. Di Gennaro, S. Savo, A. Andreone, V. Galdi, G. Castaldi, V. Pierro, and M. R. Masullo, “Mode confinement in photonic quasicrystal point-defect cavities for particle accelerators,” Appl. Phys. Lett. 93(16), 164102 (2008).
[CrossRef]

A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express 14(21), 10021–10027 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-10021 .
[CrossRef] [PubMed]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94(18), 183903 (2005).
[CrossRef] [PubMed]

Pisco, M.

I. Gallina, A. Ricciardi, M. Pisco, S. Campopiano, G. Castaldi, A. Cusano, A. Cutolo, and V. Galdi, “Parametric study of guided resonances in octagonal photonic quasicrystals,” Microw. Opt. Technol. Lett. 51(11), 2737–2740 (2009).
[CrossRef]

A. Ricciardi, I. Gallina, S. Campopiano, G. Castaldi, M. Pisco, V. Galdi, and A. Cusano, “Guided resonances in photonic quasicrystals,” Opt. Express 17(8), 6335–6346 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6335 .
[PubMed]

Prasad, T.

Ricciardi, A.

A. Ricciardi, I. Gallina, S. Campopiano, G. Castaldi, M. Pisco, V. Galdi, and A. Cusano, “Guided resonances in photonic quasicrystals,” Opt. Express 17(8), 6335–6346 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6335 .
[PubMed]

I. Gallina, A. Ricciardi, M. Pisco, S. Campopiano, G. Castaldi, A. Cusano, A. Cutolo, and V. Galdi, “Parametric study of guided resonances in octagonal photonic quasicrystals,” Microw. Opt. Technol. Lett. 51(11), 2737–2740 (2009).
[CrossRef]

Sakoda, K.

K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B 52(11), 7982–7986 (1995).
[CrossRef]

Savo, S.

E. Di Gennaro, S. Savo, A. Andreone, V. Galdi, G. Castaldi, V. Pierro, and M. R. Masullo, “Mode confinement in photonic quasicrystal point-defect cavities for particle accelerators,” Appl. Phys. Lett. 93(16), 164102 (2008).
[CrossRef]

Shechtman, D.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translation symmetry,” Phys. Rev. Lett. 53(20), 1951–1953 (1984).
[CrossRef]

Skolnick, M. S.

Solgaard, O.

Steinhardt, P. J.

D. Levine and P. J. Steinhardt, “Quasicrystals: A new class of ordered structures,” Phys. Rev. Lett. 53(26), 2477–2480 (1984).
[CrossRef]

Steurer, W.

W. Steurer and D. Sutter-Widmer, “Photonic and phononic quasicrystals,” J. Phys. D Appl. Phys. 40(13), R229–R247 (2007).
[CrossRef]

Stevenson, R. M.

Suh, W.

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
[CrossRef]

Sutter-Widmer, D.

W. Steurer and D. Sutter-Widmer, “Photonic and phononic quasicrystals,” J. Phys. D Appl. Phys. 40(13), R229–R247 (2007).
[CrossRef]

Tayeb, G.

A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express 14(21), 10021–10027 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-10021 .
[CrossRef] [PubMed]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. 94(18), 183903 (2005).
[CrossRef] [PubMed]

Wang, Z.

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
[CrossRef]

Whittaker, D. M.

Yablonovitch, E.

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Figures (12)

Fig. 1
Fig. 1

Problem geometry. (a) 3-D view of the defect-free aperiodically-ordered supercell based on the Ammann-Beenker octagonal tiling, in the associated Cartesian reference system. (b)-(e) 2-D views (x-y plane) of the representative point-defected configurations considered.

Fig. 2
Fig. 2

Transmittance response (for normal plane-wave incidence, with y-polarized electric field) pertaining to the defect-free supercell in Fig. 1(a), with r=0.25a and h=0.75a.

Fig. 12
Fig. 12

Modal solutions (labeled as e1, e2, e3, and e4, respectively) corresponding to the plane-wave-excited fields in Fig. 11.

Fig. 3
Fig. 3

Parameter configuration as in Fig. 2. (a), (b) Electric field maps (x- and y-component, respectively) at the resonant frequency ν=0.1454 , and z=0. (c), (d) Corresponding modal solution (labeled as a2 in Table 1).

Fig. 4
Fig. 4

As in Fig. 2, but pertaining to the point-defected supercell in Fig. 1(b).

Fig. 5
Fig. 5

As in Fig. 3, but pertaining to the point-defected supercell in Fig. 1(b). The resonant frequency is ν=0.1421 , and the modal solution is labeled as b2 in Table 1.

Fig. 6
Fig. 6

As in Fig. 2, but pertaining to the point-defected supercell in Fig. 1(c).

Fig. 7
Fig. 7

As in Fig. 3, but pertaining to the point-defected supercell in Fig. 1(c). The resonant frequency is ν=0.1411 , and the modal solution is labeled as c1 in Table 1.

Fig. 8
Fig. 8

As in Fig. 2, but pertaining to the point-defected supercell in Fig. 1(d).

Fig. 9
Fig. 9

Electric field maps (at z=0) corresponding to the two resonances in Fig. 8. (a), (b) ν=0.1435 (x- and y-component, respectively); (c), (d) ν=0.1453 (x- and y-component, respectively). (e)-(h) Corresponding modal solutions (labeled as d2 and d3, respectively in Table 1).

Fig. 10
Fig. 10

As in Fig. 2, but pertaining to the point-defected supercell in Fig. 1(e).

Fig. 11
Fig. 11

Electric field maps (at z=0) corresponding to the four resonant frequencies in Fig. 10. (a), (b) ν=0.1429 (x- and y- component, respectively). (c), (d) ν=0.1432 (x- and y- component, respectively). (e), (f) ν=0.1453 (x- and y- component, respectively). (g), (h) ν=0.1457 (x- and y- component, respectively).

Tables (1)

Tables Icon

Table 1 Summary of results from the modal analysis and the study of the transmittance responses. The basic properties (normalized eigen-frequencies and relevant symmetries) of the leaky modes supported by the structures are summarized (with reference to the electric-field y-component, directly relevant for the coupling), and are matched with the resonances observed in the transmittance responses.

Equations (1)

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νp,q=(paL)2+(qaL)2,p,q=0,±1,±2,,

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