Abstract

The photonic bandgap properties of centered rectangular dimer cylinder structures are reported. The theoretical model is inspired by a crystalline phase found for colloidal self-assembly of asymmetric dimers. The band structures, as a function of degree of lobe fusion and degree of lobe symmetry, are calculated in accordance with the tunable features resulting from seeded emulsion polymerization synthesis. The parameters are varied incrementally from single circular cross section cylinders to lobe-tangent dimer cylinders. Odd, even, and polarization-independent gaps in the guided modes are found for direct and inverted slab structures. A wide range of shape parameter combinations supported relative gap widths up to 19.1% (3–4 odd gap) and 14.6% (1–2 even gap) in direct structures having low to moderate Brillouin zone distortion from the hexagonal. Slab thickness was tuned to overlap even and odd mode gap frequency ranges, generating a 9.9% polarization-independent gap. The results are compared with those from model centered rectangular slabs having dimer particle bases that limit the slab height. Inverted slab structures yielded a large maximum 40.4% 1–2 even mode gap and for up to 25% Brillouin zone distortion still supported significant gaps (>32%).

© 2014 Optical Society of America

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    [CrossRef]

2012

E. K. Riley, E. Y. Fung, and C. M. Watson, “Buckled colloidal crystals with nonspherical bases for two-dimensional slab photonic bandgaps,” J. Appl. Phys. 111, 093504 (2012).
[CrossRef]

E. Y. K. Fung, K. Muangnapoh, and C. M. L. Watson, “Anisotropic photonic crystal building blocks: colloids tuned from mushroom caps to dimers,” J. Mater. Chem. 22, 10507–10513 (2012).
[CrossRef]

2011

H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire, “Design of photonic crystals with multiple and combined bandgaps,” Phys. Rev. E 83, 046703 (2011).
[CrossRef]

X. Ye and L. Qi, “Two-dimensionally patterned nanostructures based on monolayer colloidal crystals: controllable fabrication, assembly, and applications,” Nano Today 6(6), 608–631 (2011).
[CrossRef]

2009

M. D. Weed, H. P. Seigneur, and W. V. Schoenfeld, “Optimization of complete bandgaps for photonic crystal slabs through use of symmetry breaking hole shapes,” Proc. SPIE 7223, 72230Q (2009).
[CrossRef]

S. H. Lee, E. Y. Fung, E. K. Riley, and C. M. Liddell, “Asymmetric colloidal dimers under quasi-2D confinement,” Langmuir 25, 7193–7195 (2009).
[CrossRef]

K. Ohlinger, Y. Lin, and J. S. Qualls, “Maximum and overlapped photonic bandgaps in both transverse electric- and transverse magnetic-polarizations in two-dimensional photonic crystals with low symmetry,” J. Appl. Phys. 106, 063520 (2009).
[CrossRef]

P. Panda, K. P. Yuet, T. A. Hatton, and P. S. Doyle, “Tuning curvature in flow lithography: a new class of concave/convex particles,” Langmuir 25, 5986–5992 (2009).
[CrossRef]

2008

S.-M. Yang, S.-H. Kim, J.-M. Lim, and G.-R. Yi, “Synthesis and assembly of structured colloidal particles,” J. Mater. Chem. 18, 2177–2190 (2008).
[CrossRef]

K. P. Herlihy, J. Nunes, and J. M. DeSimone, “Electrically driven alignment and crystallization of unique anisotropic polymer particles,” Langmuir 24, 8421–8426 (2008).
[CrossRef]

F. Wen, S. David, X. Checoury, M. El Kurdi, and P. Boucaud, “Two-dimensional photonic crystals with large complete photonic bandgaps in both TE- and TM-polarizations,” Opt. Express 16, 12278–12289 (2008).
[CrossRef]

R. Gajić, D. Jovanović, K. Hingerl, R. Meisels, and F. Kuchar, “2D photonic crystals on the Archimedean lattices [tribute to Johannes Kepler (1571–1630)],” Opt. Mater. 30, 1065–1069 (2008).
[CrossRef]

2007

J. A. Champion, Y. K. Katare, and S. Mitragotri, “Particle shape: a new design parameter for micro- and nanoscale drug delivery carriers,” J. Controlled Release 121, 3–9 (2007).
[CrossRef]

I. D. Hosein and C. M. Liddell, “Convectively assembled asymmetric dimer-based colloidal crystals,” Langmuir 23, 10479–10485 (2007).
[CrossRef]

C. W. Neff, T. Yamashita, and C. J. Summers, “Observation of Brillouin zone folding in photonic crystal slab waveguides possessing a superlattice pattern,” Appl. Phys. Lett. 90, 021102 (2007).
[CrossRef]

A. Yethiraj, “Tunable colloids: control of colloidal phase transitions with tunable interactions,” Soft Matter 3, 1099–1115 (2007).
[CrossRef]

2006

2005

S.-I. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, “Experimental demonstration of complete photonic bandgap in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

J. P. Rolland, B. W. Maynor, L. E. Euliss, A. E. Exner, G. M. Denison, and J. M. DeSimone, “Direct fabrication and harvesting of monodisperse, shape-specific nanobiomaterials,” J. Am. Chem. Soc. 127, 10096–10100 (2005).
[CrossRef]

A. Mohraz and M. J. Solomon, “Direct visualization of colloidal rod assembly by confocal microscopy,” Langmuir 21, 5298–5306 (2005).
[CrossRef]

2004

G.-R. Yi, V. N. Manoharan, E. Michel, M. T. Elsesser, S.-M. Yang, and D. J. Pine, “Colloidal clusters of silica or polymer microspheres,” Adv. Mater. 16, 1204–1208 (2004).
[CrossRef]

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, “Guiding 1.5  μm light in photonic crystals based on dielectric rods,” Appl. Phys. Lett. 85, 6110–6112 (2004).
[CrossRef]

2003

L. F. Marsal, T. Trifonov, A. Rodríguez, J. Pallares, and R. Alcubilla, “Larger absolute photonic bandgap in two-dimensional air-silicon structures,” Physica E 16, 580–585 (2003).
[CrossRef]

2002

M. Hase, M. Egashira, N. Shinya, H. Miyazaki, K. M. Kojima, and S.-I. Uchida, “Optical transmission spectra of two-dimensional quasi-periodic photonic crystals based on Penrose-tiling and octagonal tiling systems,” J. Alloys Compd. 342, 455–459 (2002).
[CrossRef]

C. G. Bostan and R. M. de Ridder, “Design of photonic crystal slab structures with absolute gaps in guided modes,” J. Optoelectron. Adv. Mater. 4, 921–928 (2002).

2001

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

T. Gong and D. W. M. Marr, “Electrically switchable colloidal ordering in confined geometries,” Langmuir 17, 2301–2304 (2001).
[CrossRef]

Y. Xia, B. Gates, and Z.-Y. Li, “Self-assembly approaches to three-dimensional photonic crystals,” Adv. Mater. 13, 409–413 (2001).
[CrossRef]

R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, “Effects of shapes and orientations of scatterers and lattice symmetries on the photonic bandgap in two-dimensional photonic crystals,” J. Appl. Phys. 90, 4307–4313 (2001).
[CrossRef]

Y. Yin and Y. Xia, “Self-assembly of monodispersed spherical colloids into complex aggregates with well-defined sizes, shapes, and structures,” Adv. Mater. 13, 267–271 (2001).
[CrossRef]

1999

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

1998

Z.-Y. Li, J. Wang, and B.-Y. Gu, “Creation of partial bandgaps in anisotropic photonic-bandgap structures,” Phys. Rev. B 58, 3721–3729 (1998).
[CrossRef]

Alcubilla, R.

L. F. Marsal, T. Trifonov, A. Rodríguez, J. Pallares, and R. Alcubilla, “Larger absolute photonic bandgap in two-dimensional air-silicon structures,” Physica E 16, 580–585 (2003).
[CrossRef]

Asano, T.

S.-I. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, “Experimental demonstration of complete photonic bandgap in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

Assefa, S.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, “Guiding 1.5  μm light in photonic crystals based on dielectric rods,” Appl. Phys. Lett. 85, 6110–6112 (2004).
[CrossRef]

Bienstman, P.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, “Guiding 1.5  μm light in photonic crystals based on dielectric rods,” Appl. Phys. Lett. 85, 6110–6112 (2004).
[CrossRef]

Bostan, C. G.

C. G. Bostan and R. M. de Ridder, “Design of photonic crystal slab structures with absolute gaps in guided modes,” J. Optoelectron. Adv. Mater. 4, 921–928 (2002).

Boucaud, P.

Champion, J. A.

J. A. Champion, Y. K. Katare, and S. Mitragotri, “Particle shape: a new design parameter for micro- and nanoscale drug delivery carriers,” J. Controlled Release 121, 3–9 (2007).
[CrossRef]

Checoury, X.

David, S.

de Ridder, R. M.

C. G. Bostan and R. M. de Ridder, “Design of photonic crystal slab structures with absolute gaps in guided modes,” J. Optoelectron. Adv. Mater. 4, 921–928 (2002).

Denison, G. M.

J. P. Rolland, B. W. Maynor, L. E. Euliss, A. E. Exner, G. M. Denison, and J. M. DeSimone, “Direct fabrication and harvesting of monodisperse, shape-specific nanobiomaterials,” J. Am. Chem. Soc. 127, 10096–10100 (2005).
[CrossRef]

DeSimone, J. M.

K. P. Herlihy, J. Nunes, and J. M. DeSimone, “Electrically driven alignment and crystallization of unique anisotropic polymer particles,” Langmuir 24, 8421–8426 (2008).
[CrossRef]

J. P. Rolland, B. W. Maynor, L. E. Euliss, A. E. Exner, G. M. Denison, and J. M. DeSimone, “Direct fabrication and harvesting of monodisperse, shape-specific nanobiomaterials,” J. Am. Chem. Soc. 127, 10096–10100 (2005).
[CrossRef]

Doyle, P. S.

P. Panda, K. P. Yuet, T. A. Hatton, and P. S. Doyle, “Tuning curvature in flow lithography: a new class of concave/convex particles,” Langmuir 25, 5986–5992 (2009).
[CrossRef]

Egashira, M.

M. Hase, M. Egashira, N. Shinya, H. Miyazaki, K. M. Kojima, and S.-I. Uchida, “Optical transmission spectra of two-dimensional quasi-periodic photonic crystals based on Penrose-tiling and octagonal tiling systems,” J. Alloys Compd. 342, 455–459 (2002).
[CrossRef]

El Kurdi, M.

Elsesser, M. T.

G.-R. Yi, V. N. Manoharan, E. Michel, M. T. Elsesser, S.-M. Yang, and D. J. Pine, “Colloidal clusters of silica or polymer microspheres,” Adv. Mater. 16, 1204–1208 (2004).
[CrossRef]

Euliss, L. E.

J. P. Rolland, B. W. Maynor, L. E. Euliss, A. E. Exner, G. M. Denison, and J. M. DeSimone, “Direct fabrication and harvesting of monodisperse, shape-specific nanobiomaterials,” J. Am. Chem. Soc. 127, 10096–10100 (2005).
[CrossRef]

Exner, A. E.

J. P. Rolland, B. W. Maynor, L. E. Euliss, A. E. Exner, G. M. Denison, and J. M. DeSimone, “Direct fabrication and harvesting of monodisperse, shape-specific nanobiomaterials,” J. Am. Chem. Soc. 127, 10096–10100 (2005).
[CrossRef]

Fan, S.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Freund, R. M.

H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire, “Design of photonic crystals with multiple and combined bandgaps,” Phys. Rev. E 83, 046703 (2011).
[CrossRef]

Fung, E. Y.

E. K. Riley, E. Y. Fung, and C. M. Watson, “Buckled colloidal crystals with nonspherical bases for two-dimensional slab photonic bandgaps,” J. Appl. Phys. 111, 093504 (2012).
[CrossRef]

S. H. Lee, E. Y. Fung, E. K. Riley, and C. M. Liddell, “Asymmetric colloidal dimers under quasi-2D confinement,” Langmuir 25, 7193–7195 (2009).
[CrossRef]

Fung, E. Y. K.

E. Y. K. Fung, K. Muangnapoh, and C. M. L. Watson, “Anisotropic photonic crystal building blocks: colloids tuned from mushroom caps to dimers,” J. Mater. Chem. 22, 10507–10513 (2012).
[CrossRef]

Gajic, R.

R. Gajić, D. Jovanović, K. Hingerl, R. Meisels, and F. Kuchar, “2D photonic crystals on the Archimedean lattices [tribute to Johannes Kepler (1571–1630)],” Opt. Mater. 30, 1065–1069 (2008).
[CrossRef]

Gates, B.

Y. Xia, B. Gates, and Z.-Y. Li, “Self-assembly approaches to three-dimensional photonic crystals,” Adv. Mater. 13, 409–413 (2001).
[CrossRef]

Gong, T.

T. Gong and D. W. M. Marr, “Electrically switchable colloidal ordering in confined geometries,” Langmuir 17, 2301–2304 (2001).
[CrossRef]

Gu, B.-Y.

R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, “Effects of shapes and orientations of scatterers and lattice symmetries on the photonic bandgap in two-dimensional photonic crystals,” J. Appl. Phys. 90, 4307–4313 (2001).
[CrossRef]

Z.-Y. Li, J. Wang, and B.-Y. Gu, “Creation of partial bandgaps in anisotropic photonic-bandgap structures,” Phys. Rev. B 58, 3721–3729 (1998).
[CrossRef]

Hase, M.

M. Hase, M. Egashira, N. Shinya, H. Miyazaki, K. M. Kojima, and S.-I. Uchida, “Optical transmission spectra of two-dimensional quasi-periodic photonic crystals based on Penrose-tiling and octagonal tiling systems,” J. Alloys Compd. 342, 455–459 (2002).
[CrossRef]

Hatton, T. A.

P. Panda, K. P. Yuet, T. A. Hatton, and P. S. Doyle, “Tuning curvature in flow lithography: a new class of concave/convex particles,” Langmuir 25, 5986–5992 (2009).
[CrossRef]

Herlihy, K. P.

K. P. Herlihy, J. Nunes, and J. M. DeSimone, “Electrically driven alignment and crystallization of unique anisotropic polymer particles,” Langmuir 24, 8421–8426 (2008).
[CrossRef]

Hingerl, K.

R. Gajić, D. Jovanović, K. Hingerl, R. Meisels, and F. Kuchar, “2D photonic crystals on the Archimedean lattices [tribute to Johannes Kepler (1571–1630)],” Opt. Mater. 30, 1065–1069 (2008).
[CrossRef]

Hosein, I. D.

I. D. Hosein and C. M. Liddell, “Convectively assembled asymmetric dimer-based colloidal crystals,” Langmuir 23, 10479–10485 (2007).
[CrossRef]

Ippen, E. P.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, “Guiding 1.5  μm light in photonic crystals based on dielectric rods,” Appl. Phys. Lett. 85, 6110–6112 (2004).
[CrossRef]

Joannopoulos, J. D.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, “Guiding 1.5  μm light in photonic crystals based on dielectric rods,” Appl. Phys. Lett. 85, 6110–6112 (2004).
[CrossRef]

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

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed (Princeton University, 2008).

Johnson, S. G.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, “Guiding 1.5  μm light in photonic crystals based on dielectric rods,” Appl. Phys. Lett. 85, 6110–6112 (2004).
[CrossRef]

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

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed (Princeton University, 2008).

Jovanovic, D.

R. Gajić, D. Jovanović, K. Hingerl, R. Meisels, and F. Kuchar, “2D photonic crystals on the Archimedean lattices [tribute to Johannes Kepler (1571–1630)],” Opt. Mater. 30, 1065–1069 (2008).
[CrossRef]

Katare, Y. K.

J. A. Champion, Y. K. Katare, and S. Mitragotri, “Particle shape: a new design parameter for micro- and nanoscale drug delivery carriers,” J. Controlled Release 121, 3–9 (2007).
[CrossRef]

Kim, S.-H.

S.-M. Yang, S.-H. Kim, J.-M. Lim, and G.-R. Yi, “Synthesis and assembly of structured colloidal particles,” J. Mater. Chem. 18, 2177–2190 (2008).
[CrossRef]

Kitagawa, H.

S.-I. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, “Experimental demonstration of complete photonic bandgap in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

Kojima, K. M.

M. Hase, M. Egashira, N. Shinya, H. Miyazaki, K. M. Kojima, and S.-I. Uchida, “Optical transmission spectra of two-dimensional quasi-periodic photonic crystals based on Penrose-tiling and octagonal tiling systems,” J. Alloys Compd. 342, 455–459 (2002).
[CrossRef]

Kolodziejski, L. A.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, “Guiding 1.5  μm light in photonic crystals based on dielectric rods,” Appl. Phys. Lett. 85, 6110–6112 (2004).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Kuchar, F.

R. Gajić, D. Jovanović, K. Hingerl, R. Meisels, and F. Kuchar, “2D photonic crystals on the Archimedean lattices [tribute to Johannes Kepler (1571–1630)],” Opt. Mater. 30, 1065–1069 (2008).
[CrossRef]

Lee, S. H.

S. H. Lee, E. Y. Fung, E. K. Riley, and C. M. Liddell, “Asymmetric colloidal dimers under quasi-2D confinement,” Langmuir 25, 7193–7195 (2009).
[CrossRef]

Li, Z.-Y.

Y. Xia, B. Gates, and Z.-Y. Li, “Self-assembly approaches to three-dimensional photonic crystals,” Adv. Mater. 13, 409–413 (2001).
[CrossRef]

Z.-Y. Li, J. Wang, and B.-Y. Gu, “Creation of partial bandgaps in anisotropic photonic-bandgap structures,” Phys. Rev. B 58, 3721–3729 (1998).
[CrossRef]

Liddell, C. M.

S. H. Lee, E. Y. Fung, E. K. Riley, and C. M. Liddell, “Asymmetric colloidal dimers under quasi-2D confinement,” Langmuir 25, 7193–7195 (2009).
[CrossRef]

I. D. Hosein and C. M. Liddell, “Convectively assembled asymmetric dimer-based colloidal crystals,” Langmuir 23, 10479–10485 (2007).
[CrossRef]

Lim, J.-M.

S.-M. Yang, S.-H. Kim, J.-M. Lim, and G.-R. Yi, “Synthesis and assembly of structured colloidal particles,” J. Mater. Chem. 18, 2177–2190 (2008).
[CrossRef]

Lim, K. M.

H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire, “Design of photonic crystals with multiple and combined bandgaps,” Phys. Rev. E 83, 046703 (2011).
[CrossRef]

Lin, Y.

K. Ohlinger, Y. Lin, and J. S. Qualls, “Maximum and overlapped photonic bandgaps in both transverse electric- and transverse magnetic-polarizations in two-dimensional photonic crystals with low symmetry,” J. Appl. Phys. 106, 063520 (2009).
[CrossRef]

Manoharan, V. N.

G.-R. Yi, V. N. Manoharan, E. Michel, M. T. Elsesser, S.-M. Yang, and D. J. Pine, “Colloidal clusters of silica or polymer microspheres,” Adv. Mater. 16, 1204–1208 (2004).
[CrossRef]

Marr, D. W. M.

T. Gong and D. W. M. Marr, “Electrically switchable colloidal ordering in confined geometries,” Langmuir 17, 2301–2304 (2001).
[CrossRef]

Marsal, L. F.

L. F. Marsal, T. Trifonov, A. Rodríguez, J. Pallares, and R. Alcubilla, “Larger absolute photonic bandgap in two-dimensional air-silicon structures,” Physica E 16, 580–585 (2003).
[CrossRef]

Maynor, B. W.

J. P. Rolland, B. W. Maynor, L. E. Euliss, A. E. Exner, G. M. Denison, and J. M. DeSimone, “Direct fabrication and harvesting of monodisperse, shape-specific nanobiomaterials,” J. Am. Chem. Soc. 127, 10096–10100 (2005).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed (Princeton University, 2008).

Meisels, R.

R. Gajić, D. Jovanović, K. Hingerl, R. Meisels, and F. Kuchar, “2D photonic crystals on the Archimedean lattices [tribute to Johannes Kepler (1571–1630)],” Opt. Mater. 30, 1065–1069 (2008).
[CrossRef]

Men, H.

H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire, “Design of photonic crystals with multiple and combined bandgaps,” Phys. Rev. E 83, 046703 (2011).
[CrossRef]

Michel, E.

G.-R. Yi, V. N. Manoharan, E. Michel, M. T. Elsesser, S.-M. Yang, and D. J. Pine, “Colloidal clusters of silica or polymer microspheres,” Adv. Mater. 16, 1204–1208 (2004).
[CrossRef]

Mitragotri, S.

J. A. Champion, Y. K. Katare, and S. Mitragotri, “Particle shape: a new design parameter for micro- and nanoscale drug delivery carriers,” J. Controlled Release 121, 3–9 (2007).
[CrossRef]

Miyazaki, H.

M. Hase, M. Egashira, N. Shinya, H. Miyazaki, K. M. Kojima, and S.-I. Uchida, “Optical transmission spectra of two-dimensional quasi-periodic photonic crystals based on Penrose-tiling and octagonal tiling systems,” J. Alloys Compd. 342, 455–459 (2002).
[CrossRef]

Mohraz, A.

A. Mohraz and M. J. Solomon, “Direct visualization of colloidal rod assembly by confocal microscopy,” Langmuir 21, 5298–5306 (2005).
[CrossRef]

Muangnapoh, K.

E. Y. K. Fung, K. Muangnapoh, and C. M. L. Watson, “Anisotropic photonic crystal building blocks: colloids tuned from mushroom caps to dimers,” J. Mater. Chem. 22, 10507–10513 (2012).
[CrossRef]

Neff, C. W.

C. W. Neff, T. Yamashita, and C. J. Summers, “Observation of Brillouin zone folding in photonic crystal slab waveguides possessing a superlattice pattern,” Appl. Phys. Lett. 90, 021102 (2007).
[CrossRef]

Nguyen, N. C.

H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire, “Design of photonic crystals with multiple and combined bandgaps,” Phys. Rev. E 83, 046703 (2011).
[CrossRef]

Noda, S.

S. Noda, “Recent progresses and future prospects of two- and three-dimensional photonic crystals,” J. Lightwave Technol. 24, 4554–4567 (2006).
[CrossRef]

S.-I. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, “Experimental demonstration of complete photonic bandgap in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

Nunes, J.

K. P. Herlihy, J. Nunes, and J. M. DeSimone, “Electrically driven alignment and crystallization of unique anisotropic polymer particles,” Langmuir 24, 8421–8426 (2008).
[CrossRef]

Ohlinger, K.

K. Ohlinger, Y. Lin, and J. S. Qualls, “Maximum and overlapped photonic bandgaps in both transverse electric- and transverse magnetic-polarizations in two-dimensional photonic crystals with low symmetry,” J. Appl. Phys. 106, 063520 (2009).
[CrossRef]

Pallares, J.

L. F. Marsal, T. Trifonov, A. Rodríguez, J. Pallares, and R. Alcubilla, “Larger absolute photonic bandgap in two-dimensional air-silicon structures,” Physica E 16, 580–585 (2003).
[CrossRef]

Panda, P.

P. Panda, K. P. Yuet, T. A. Hatton, and P. S. Doyle, “Tuning curvature in flow lithography: a new class of concave/convex particles,” Langmuir 25, 5986–5992 (2009).
[CrossRef]

Parrilo, P. A.

H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire, “Design of photonic crystals with multiple and combined bandgaps,” Phys. Rev. E 83, 046703 (2011).
[CrossRef]

Peraire, J.

H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire, “Design of photonic crystals with multiple and combined bandgaps,” Phys. Rev. E 83, 046703 (2011).
[CrossRef]

Petrich, G. S.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, “Guiding 1.5  μm light in photonic crystals based on dielectric rods,” Appl. Phys. Lett. 85, 6110–6112 (2004).
[CrossRef]

Pine, D. J.

G.-R. Yi, V. N. Manoharan, E. Michel, M. T. Elsesser, S.-M. Yang, and D. J. Pine, “Colloidal clusters of silica or polymer microspheres,” Adv. Mater. 16, 1204–1208 (2004).
[CrossRef]

Qi, L.

X. Ye and L. Qi, “Two-dimensionally patterned nanostructures based on monolayer colloidal crystals: controllable fabrication, assembly, and applications,” Nano Today 6(6), 608–631 (2011).
[CrossRef]

Qualls, J. S.

K. Ohlinger, Y. Lin, and J. S. Qualls, “Maximum and overlapped photonic bandgaps in both transverse electric- and transverse magnetic-polarizations in two-dimensional photonic crystals with low symmetry,” J. Appl. Phys. 106, 063520 (2009).
[CrossRef]

Rakich, P. T.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, “Guiding 1.5  μm light in photonic crystals based on dielectric rods,” Appl. Phys. Lett. 85, 6110–6112 (2004).
[CrossRef]

Riley, E. K.

E. K. Riley, E. Y. Fung, and C. M. Watson, “Buckled colloidal crystals with nonspherical bases for two-dimensional slab photonic bandgaps,” J. Appl. Phys. 111, 093504 (2012).
[CrossRef]

S. H. Lee, E. Y. Fung, E. K. Riley, and C. M. Liddell, “Asymmetric colloidal dimers under quasi-2D confinement,” Langmuir 25, 7193–7195 (2009).
[CrossRef]

Rodríguez, A.

L. F. Marsal, T. Trifonov, A. Rodríguez, J. Pallares, and R. Alcubilla, “Larger absolute photonic bandgap in two-dimensional air-silicon structures,” Physica E 16, 580–585 (2003).
[CrossRef]

Rolland, J. P.

J. P. Rolland, B. W. Maynor, L. E. Euliss, A. E. Exner, G. M. Denison, and J. M. DeSimone, “Direct fabrication and harvesting of monodisperse, shape-specific nanobiomaterials,” J. Am. Chem. Soc. 127, 10096–10100 (2005).
[CrossRef]

Schoenfeld, W. V.

M. D. Weed, H. P. Seigneur, and W. V. Schoenfeld, “Optimization of complete bandgaps for photonic crystal slabs through use of symmetry breaking hole shapes,” Proc. SPIE 7223, 72230Q (2009).
[CrossRef]

Seigneur, H. P.

M. D. Weed, H. P. Seigneur, and W. V. Schoenfeld, “Optimization of complete bandgaps for photonic crystal slabs through use of symmetry breaking hole shapes,” Proc. SPIE 7223, 72230Q (2009).
[CrossRef]

Shinya, N.

M. Hase, M. Egashira, N. Shinya, H. Miyazaki, K. M. Kojima, and S.-I. Uchida, “Optical transmission spectra of two-dimensional quasi-periodic photonic crystals based on Penrose-tiling and octagonal tiling systems,” J. Alloys Compd. 342, 455–459 (2002).
[CrossRef]

Smith, H. I.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, “Guiding 1.5  μm light in photonic crystals based on dielectric rods,” Appl. Phys. Lett. 85, 6110–6112 (2004).
[CrossRef]

Solomon, M. J.

A. Mohraz and M. J. Solomon, “Direct visualization of colloidal rod assembly by confocal microscopy,” Langmuir 21, 5298–5306 (2005).
[CrossRef]

Summers, C. J.

C. W. Neff, T. Yamashita, and C. J. Summers, “Observation of Brillouin zone folding in photonic crystal slab waveguides possessing a superlattice pattern,” Appl. Phys. Lett. 90, 021102 (2007).
[CrossRef]

Takayama, S.-I.

S.-I. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, “Experimental demonstration of complete photonic bandgap in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

Tanaka, Y.

S.-I. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, “Experimental demonstration of complete photonic bandgap in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

Trifonov, T.

L. F. Marsal, T. Trifonov, A. Rodríguez, J. Pallares, and R. Alcubilla, “Larger absolute photonic bandgap in two-dimensional air-silicon structures,” Physica E 16, 580–585 (2003).
[CrossRef]

Uchida, S.-I.

M. Hase, M. Egashira, N. Shinya, H. Miyazaki, K. M. Kojima, and S.-I. Uchida, “Optical transmission spectra of two-dimensional quasi-periodic photonic crystals based on Penrose-tiling and octagonal tiling systems,” J. Alloys Compd. 342, 455–459 (2002).
[CrossRef]

Villeneuve, P. R.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Wang, J.

Z.-Y. Li, J. Wang, and B.-Y. Gu, “Creation of partial bandgaps in anisotropic photonic-bandgap structures,” Phys. Rev. B 58, 3721–3729 (1998).
[CrossRef]

Wang, R.

R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, “Effects of shapes and orientations of scatterers and lattice symmetries on the photonic bandgap in two-dimensional photonic crystals,” J. Appl. Phys. 90, 4307–4313 (2001).
[CrossRef]

Wang, X.-H.

R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, “Effects of shapes and orientations of scatterers and lattice symmetries on the photonic bandgap in two-dimensional photonic crystals,” J. Appl. Phys. 90, 4307–4313 (2001).
[CrossRef]

Watson, C. M.

E. K. Riley, E. Y. Fung, and C. M. Watson, “Buckled colloidal crystals with nonspherical bases for two-dimensional slab photonic bandgaps,” J. Appl. Phys. 111, 093504 (2012).
[CrossRef]

Watson, C. M. L.

E. Y. K. Fung, K. Muangnapoh, and C. M. L. Watson, “Anisotropic photonic crystal building blocks: colloids tuned from mushroom caps to dimers,” J. Mater. Chem. 22, 10507–10513 (2012).
[CrossRef]

Weed, M. D.

M. D. Weed, H. P. Seigneur, and W. V. Schoenfeld, “Optimization of complete bandgaps for photonic crystal slabs through use of symmetry breaking hole shapes,” Proc. SPIE 7223, 72230Q (2009).
[CrossRef]

Wen, F.

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed (Princeton University, 2008).

Xia, Y.

Y. Yin and Y. Xia, “Self-assembly of monodispersed spherical colloids into complex aggregates with well-defined sizes, shapes, and structures,” Adv. Mater. 13, 267–271 (2001).
[CrossRef]

Y. Xia, B. Gates, and Z.-Y. Li, “Self-assembly approaches to three-dimensional photonic crystals,” Adv. Mater. 13, 409–413 (2001).
[CrossRef]

Yamashita, T.

C. W. Neff, T. Yamashita, and C. J. Summers, “Observation of Brillouin zone folding in photonic crystal slab waveguides possessing a superlattice pattern,” Appl. Phys. Lett. 90, 021102 (2007).
[CrossRef]

Yang, G.-Z.

R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, “Effects of shapes and orientations of scatterers and lattice symmetries on the photonic bandgap in two-dimensional photonic crystals,” J. Appl. Phys. 90, 4307–4313 (2001).
[CrossRef]

Yang, S.-M.

S.-M. Yang, S.-H. Kim, J.-M. Lim, and G.-R. Yi, “Synthesis and assembly of structured colloidal particles,” J. Mater. Chem. 18, 2177–2190 (2008).
[CrossRef]

G.-R. Yi, V. N. Manoharan, E. Michel, M. T. Elsesser, S.-M. Yang, and D. J. Pine, “Colloidal clusters of silica or polymer microspheres,” Adv. Mater. 16, 1204–1208 (2004).
[CrossRef]

Ye, X.

X. Ye and L. Qi, “Two-dimensionally patterned nanostructures based on monolayer colloidal crystals: controllable fabrication, assembly, and applications,” Nano Today 6(6), 608–631 (2011).
[CrossRef]

Yethiraj, A.

A. Yethiraj, “Tunable colloids: control of colloidal phase transitions with tunable interactions,” Soft Matter 3, 1099–1115 (2007).
[CrossRef]

Yi, G.-R.

S.-M. Yang, S.-H. Kim, J.-M. Lim, and G.-R. Yi, “Synthesis and assembly of structured colloidal particles,” J. Mater. Chem. 18, 2177–2190 (2008).
[CrossRef]

G.-R. Yi, V. N. Manoharan, E. Michel, M. T. Elsesser, S.-M. Yang, and D. J. Pine, “Colloidal clusters of silica or polymer microspheres,” Adv. Mater. 16, 1204–1208 (2004).
[CrossRef]

Yin, Y.

Y. Yin and Y. Xia, “Self-assembly of monodispersed spherical colloids into complex aggregates with well-defined sizes, shapes, and structures,” Adv. Mater. 13, 267–271 (2001).
[CrossRef]

Yuet, K. P.

P. Panda, K. P. Yuet, T. A. Hatton, and P. S. Doyle, “Tuning curvature in flow lithography: a new class of concave/convex particles,” Langmuir 25, 5986–5992 (2009).
[CrossRef]

Adv. Mater.

Y. Xia, B. Gates, and Z.-Y. Li, “Self-assembly approaches to three-dimensional photonic crystals,” Adv. Mater. 13, 409–413 (2001).
[CrossRef]

Y. Yin and Y. Xia, “Self-assembly of monodispersed spherical colloids into complex aggregates with well-defined sizes, shapes, and structures,” Adv. Mater. 13, 267–271 (2001).
[CrossRef]

G.-R. Yi, V. N. Manoharan, E. Michel, M. T. Elsesser, S.-M. Yang, and D. J. Pine, “Colloidal clusters of silica or polymer microspheres,” Adv. Mater. 16, 1204–1208 (2004).
[CrossRef]

Appl. Phys. Lett.

C. W. Neff, T. Yamashita, and C. J. Summers, “Observation of Brillouin zone folding in photonic crystal slab waveguides possessing a superlattice pattern,” Appl. Phys. Lett. 90, 021102 (2007).
[CrossRef]

S.-I. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, “Experimental demonstration of complete photonic bandgap in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 87, 061107 (2005).
[CrossRef]

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, “Guiding 1.5  μm light in photonic crystals based on dielectric rods,” Appl. Phys. Lett. 85, 6110–6112 (2004).
[CrossRef]

J. Alloys Compd.

M. Hase, M. Egashira, N. Shinya, H. Miyazaki, K. M. Kojima, and S.-I. Uchida, “Optical transmission spectra of two-dimensional quasi-periodic photonic crystals based on Penrose-tiling and octagonal tiling systems,” J. Alloys Compd. 342, 455–459 (2002).
[CrossRef]

J. Am. Chem. Soc.

J. P. Rolland, B. W. Maynor, L. E. Euliss, A. E. Exner, G. M. Denison, and J. M. DeSimone, “Direct fabrication and harvesting of monodisperse, shape-specific nanobiomaterials,” J. Am. Chem. Soc. 127, 10096–10100 (2005).
[CrossRef]

J. Appl. Phys.

K. Ohlinger, Y. Lin, and J. S. Qualls, “Maximum and overlapped photonic bandgaps in both transverse electric- and transverse magnetic-polarizations in two-dimensional photonic crystals with low symmetry,” J. Appl. Phys. 106, 063520 (2009).
[CrossRef]

R. Wang, X.-H. Wang, B.-Y. Gu, and G.-Z. Yang, “Effects of shapes and orientations of scatterers and lattice symmetries on the photonic bandgap in two-dimensional photonic crystals,” J. Appl. Phys. 90, 4307–4313 (2001).
[CrossRef]

E. K. Riley, E. Y. Fung, and C. M. Watson, “Buckled colloidal crystals with nonspherical bases for two-dimensional slab photonic bandgaps,” J. Appl. Phys. 111, 093504 (2012).
[CrossRef]

J. Controlled Release

J. A. Champion, Y. K. Katare, and S. Mitragotri, “Particle shape: a new design parameter for micro- and nanoscale drug delivery carriers,” J. Controlled Release 121, 3–9 (2007).
[CrossRef]

J. Lightwave Technol.

J. Mater. Chem.

S.-M. Yang, S.-H. Kim, J.-M. Lim, and G.-R. Yi, “Synthesis and assembly of structured colloidal particles,” J. Mater. Chem. 18, 2177–2190 (2008).
[CrossRef]

E. Y. K. Fung, K. Muangnapoh, and C. M. L. Watson, “Anisotropic photonic crystal building blocks: colloids tuned from mushroom caps to dimers,” J. Mater. Chem. 22, 10507–10513 (2012).
[CrossRef]

J. Optoelectron. Adv. Mater.

C. G. Bostan and R. M. de Ridder, “Design of photonic crystal slab structures with absolute gaps in guided modes,” J. Optoelectron. Adv. Mater. 4, 921–928 (2002).

Langmuir

I. D. Hosein and C. M. Liddell, “Convectively assembled asymmetric dimer-based colloidal crystals,” Langmuir 23, 10479–10485 (2007).
[CrossRef]

S. H. Lee, E. Y. Fung, E. K. Riley, and C. M. Liddell, “Asymmetric colloidal dimers under quasi-2D confinement,” Langmuir 25, 7193–7195 (2009).
[CrossRef]

T. Gong and D. W. M. Marr, “Electrically switchable colloidal ordering in confined geometries,” Langmuir 17, 2301–2304 (2001).
[CrossRef]

A. Mohraz and M. J. Solomon, “Direct visualization of colloidal rod assembly by confocal microscopy,” Langmuir 21, 5298–5306 (2005).
[CrossRef]

K. P. Herlihy, J. Nunes, and J. M. DeSimone, “Electrically driven alignment and crystallization of unique anisotropic polymer particles,” Langmuir 24, 8421–8426 (2008).
[CrossRef]

P. Panda, K. P. Yuet, T. A. Hatton, and P. S. Doyle, “Tuning curvature in flow lithography: a new class of concave/convex particles,” Langmuir 25, 5986–5992 (2009).
[CrossRef]

Nano Today

X. Ye and L. Qi, “Two-dimensionally patterned nanostructures based on monolayer colloidal crystals: controllable fabrication, assembly, and applications,” Nano Today 6(6), 608–631 (2011).
[CrossRef]

Opt. Express

Opt. Mater.

R. Gajić, D. Jovanović, K. Hingerl, R. Meisels, and F. Kuchar, “2D photonic crystals on the Archimedean lattices [tribute to Johannes Kepler (1571–1630)],” Opt. Mater. 30, 1065–1069 (2008).
[CrossRef]

Phys. Rev. B

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Z.-Y. Li, J. Wang, and B.-Y. Gu, “Creation of partial bandgaps in anisotropic photonic-bandgap structures,” Phys. Rev. B 58, 3721–3729 (1998).
[CrossRef]

Phys. Rev. E

H. Men, N. C. Nguyen, R. M. Freund, K. M. Lim, P. A. Parrilo, and J. Peraire, “Design of photonic crystals with multiple and combined bandgaps,” Phys. Rev. E 83, 046703 (2011).
[CrossRef]

Physica E

L. F. Marsal, T. Trifonov, A. Rodríguez, J. Pallares, and R. Alcubilla, “Larger absolute photonic bandgap in two-dimensional air-silicon structures,” Physica E 16, 580–585 (2003).
[CrossRef]

Proc. SPIE

M. D. Weed, H. P. Seigneur, and W. V. Schoenfeld, “Optimization of complete bandgaps for photonic crystal slabs through use of symmetry breaking hole shapes,” Proc. SPIE 7223, 72230Q (2009).
[CrossRef]

Soft Matter

A. Yethiraj, “Tunable colloids: control of colloidal phase transitions with tunable interactions,” Soft Matter 3, 1099–1115 (2007).
[CrossRef]

Other

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed (Princeton University, 2008).

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Figures (16)

Fig. 1.
Fig. 1.

Schematics depicting unit cells (top) and corresponding Brillouin zones (bottom) for structure parameters: (a)–(b) rl=0.5 (tangent), L*=0.9, S=0.90, and (c)–(d) rl=0.25, L*=0.5, S=0.34. The high symmetry points are labeled and the irreducible Brillouin zone is highlighted in gray.

Fig. 2.
Fig. 2.

Maximum odd mode gaps in dimer cylinder and dimer particle bases for rl values of (a) 0.30, (b) 0.35, (c) 0.40, (d) 0.45, and (e) 0.50 (tangent). The left column pair corresponds to the 3-4 bandgap and the right column pair corresponds to the 4-5 bandgap. Within column pairs, the cylinder motif is modeled on the left and dimer bases on the right.

Fig. 3.
Fig. 3.

Schematics of dimer structures at rl value of 0.35. Ordinate values are S and abscissa values are L* shape parameters. The parameter space corresponding to contour plots and gap maps in Figs. 2, 47, and 14 is tiled.

Fig. 4.
Fig. 4.

Dielectric filling fraction comparison for cylinder morphology (left) and dimer morphology (right) for rl values of (a) 0.25, (b) 0.30, (c) 0.35, (d) 0.40, (e) 0.45, and (f) 0.50.

Fig. 5.
Fig. 5.

Maximum even mode gaps in dimer cylinder and dimer particle bases for rl values of (a) 0.25, (b) 0.30, (c) 0.35, (d) 0.40, (e) 0.45, and (f) 0.50 (tangent). The left column pair corresponds to the 1-2 bandgap, the center column pair corresponds to the 2-3 bandgap, and the right column pair corresponds to the 3-4 bandgap. Within column pairs, the cylinder motif is modeled on the left and dimer bases on the right.

Fig. 6.
Fig. 6.

(left to right) Contour plots of maximum polarization-independent gap indices 4 odd -5 odd from overlapping 4-5 odd and 3-4 even gaps, 3 odd -3 even from overlapping 3-4 odd and 2-3 even gaps, 4 odd -4 even from overlapping 4-5 odd and 3-4 even gaps, 3 even -5 odd from overlapping 4-5 odd and 3-4 even gaps, 2 even -3 even from overlapping 3-4 odd and 2-3 even gaps, and 3 even -4 even from overlapping 3-4 even and odd gaps for rl values of (a) 0.30, (b) 0.35, and (c) 0.40.

Fig. 7.
Fig. 7.

Gap maps with odd mode gaps (blue), even mode gaps (red), and overlapped gaps (purple) for asymmetric dimer cylinder structures with rl values of 0.35.

Fig. 8.
Fig. 8.

(Top) Gap maps with odd mode gaps (blue), even mode gaps (red), and overlapped gaps (purple) for dimer cylinder structures with rl value of 0.30. (Bottom) Gap maps with odd mode gaps (blue), even mode gaps (red), and overlapped gaps (purple) for dimer cylinder structures with rl value of 0.40.

Fig. 9.
Fig. 9.

Minimum dielectric contrasts for odd mode gaps in dimer cylinder and dimer particle bases at rl values of (a) 0.30, (b) 0.35, (c) 0.40, (d) 0.45, and (e) 0.50 (tangent). The left column pair corresponds to the 3-4 bandgap and the right column pair corresponds to the 4-5 bandgap. Within column pairs, the cylinder motif is modeled on the left and dimer bases on the right.

Fig. 10.
Fig. 10.

Minimum dielectric contrasts for even mode gaps in dimer cylinder and dimer particle bases at rl values of (a) 0.25, (b) 0.30, (c) 0.35, (d) 0.40, (e) 0.45, and (f) 0.50 (tangent). The left column pair corresponds to the 1-2 bandgap, the center column pair corresponds to the 2-3 bandgap and the right column pair corresponds to the 3-4 bandgap. Within column pairs, the cylinder motif is modeled on the left and dimer bases on the right.

Fig. 11.
Fig. 11.

Relative gap width variation with slab height h*. (a) Odd modes for rl=0.30, L*=0.1, S=0.83, and ϵc=10, where gap indices are 3-4 (open squares), 4-5 (filled squares), 6-7 (open circles), and 9-10 (filled circles). (b) Even modes for rl=0.40, L*=0.7, S=0.7, and ϵc=16, where gap indices are 2-3 (open squares), 3-4 (filled squares), 4-5 (open circles), 6-7 (filled circles), and 8-9 (open triangles). The corresponding band diagrams of (c) maximum odd mode bandgap and (d) even mode bandgap structures at slab height h*=1.0.

Fig. 12.
Fig. 12.

Gap maps for rl=0.35, L*=0.1, and S=0.83 at slab heights (a) h*=0.5, (b) h*=0.6, (c) h*=0.7, (d) h*=0.8, (e) h*=0.9, and (f) h*=1.0.

Fig. 13.
Fig. 13.

Displacement field (i.e., dielectric constant × electric field) at the K symmetry point for dimer cylinders at structure parameters rl=0.35, L*=0.1, S=0.83, and ϵc=14. (a) 3rd odd band, h*=0.5, (b) 4th odd band, h*=0.5, (c) 3rd odd band, h*=0.7, and (d) 4th odd band, h*=0.7.

Fig. 14.
Fig. 14.

Contour plots of maximum polarization-independent gap indices 3 odd -4 odd from (left) overlapping 3-4 odd and 3-4 even gaps, 3 odd -4 even from (left center) overlapping 3-4 odd and 3-4 even gaps, 6 odd -6 even from (center) overlapping 6-7 odd and 5-6 even gaps, 3 even -4 odd from (right center) overlapping 3-4 odd and 3-4 even gaps, 3 even -4 even from (right) overlapping 3-4 odd and 3-4 even gaps for h*=0.5 and rl values of (a) 0.30, (b) 0.35, and (c) 0.40.

Fig. 15.
Fig. 15.

(Top) Contour plots of odd mode gaps for gap indices 2-3 (left), 3-4 (center left), 5-6 (center right), and 6-7 (right) at slab height h*=0.5 and rl values of (a) 0.30, (b) 0.35, and (c) 0.40. (Bottom) Contour plots of largest even gaps for gap indices 1-2 (left), 2-3 (left center), 3-4 (right center), and 5-6 (right) at h*=0.5 and rl values of (a) 0.30, (b) 0.35, and (c) 0.40.

Fig. 16.
Fig. 16.

(Top) Gap maps with odd mode gaps (blue), even mode gaps (red), and overlapped gaps (purple) for direct dimer cylinder structures at h*=0.5 with rl value of 0.40. (Bottom) Gap maps with odd mode gaps (blue), even mode gaps (red), and overlapped gaps (purple) for inverted dimer cylinder structures at h*=0.5 with rl value of 0.45.

Tables (1)

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Table 1. Shape, Structural Parameters, and Dielectric Contrasts for Maximum Gap Sizes and Corresponding Minimum Dielectric Contrasts for Opening the Gapsa

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