Abstract

In this paper complete photonic bandgap (PBG) and iso-frequency contours (IFCs) of two-dimensional modified annular photonic crystals (MAPC) for four different configurations are numerically studied and calculated by applying plane wave expansion method. The effects of opto-geometric parameters of the designed unit-cell structures are clearly demonstrated in terms of opening frequency gaps and appearing tilted band curves. Optimal structures with large PBGs are reported. The absolute gap can be increased to a maximum value of Δω/ω=0.1766(2πc/a), where a is the lattice constant and c is the speed of light. The incorporation of additional parameters inside the unit cell of photonic crystal enables an extra degree of freedom for controlling the flow of light even in the absence of structural defects. The finite-difference time-domain method is utilized to depict the MAPC’s light deflection and guiding characteristics. These proposed structures are likely to be promising candidates for applications that require polarization insensitivity due to providing large complete PBGs and possessing special IFCs.

© 2012 Optical Society of America

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2009 (2)

B. Rezaei and M. Kalafi, “Absolute band gap properties in two-dimensional photonic crystals composed of air rings in anisotropic tellurium background,” Opt. Commun. 282, 2861–2869 (2009).
[CrossRef]

J. Feng, Y. Chen, J. Blair, H. Kurt, R. Hao, D. S. Citrin, C. J. Summers, and Z. Zhou, “Fabrication of annular photonic crystals by atomic layer deposition and sacrificial etching,” J. Vac. Sci. Technol. B 27, 568–572 (2009).
[CrossRef]

2008 (4)

H. Kurt, R. Hao, Y. Chen, J. Feng, J. Blair, C. Summers, D. S. Citrin, and Z. Zhou, “Design of annular photonic crystal slabs,” Opt. Lett. 33, 1614–1616 (2008).
[CrossRef]

X. L. Yang, L. Z. Cai, Y. R. Wang, G. Y. Dong, X. X. Shen, X. F. Meng, and Y. Hu, “Large complete bandgaps in a two-dimensional square photonic crystal with isolated single-atom dielectric rods in air,” Nanotechnology 19, 025201 (2008).
[CrossRef]

X. Zhu, Y. Zhang, D. Chandra, S.-C. Cheng, J. M. Kikkawa, and S. Yang, “Two-dimensional photonic crystals with anisotropic unit cells imprinted from poly(dimethylsiloxane) membranes under elastic deformation,” Appl. Phys. Lett. 93, 161911 (2008).

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

2006 (2)

B. Rezaei and M. Kalafi, “Engineering absolute bandgap in anisotropic hexagonal photonic crystals,” Opt. Commun. 266, 159–163 (2006).
[CrossRef]

R. K. Sinha and Y. Kalra, “Design of optical waveguide polarizer using photonic band gap,” Opt. Express 14, 10790–10794 (2006).
[CrossRef]

2005 (5)

H. Kurt and D. S. Citrin, “Photonic crystals for biochemical sensing in the terahertz region,” Appl. Phys. Lett. 87, 041108 (2005).

H. Kurt and D. S. Citrin, “Coupled-resonator optical waveguide for biochemical sensing of nanoliter volumes of analyte in the terahertz region,” Appl. Phys. Lett. 87, 241119(2005).

H. Kurt and D. S. Citrin, “Annular photonic crystals,” Opt. Express 13, 10316–10326 (2005).
[CrossRef]

W. Kuang, Z. Hou, Y. Liu, and H. Li, “The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice,” J. Opt. A 7, 525–528 (2005).
[CrossRef]

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

2004 (1)

A. F. Matthews, S. F. Mingaleev, and Y. S. Kivshar, “Band-gap engineering and defect modes in photonic crystals with rotated hexagonal holes,” Laser Phys. 14, 631–634 (2004).

2003 (2)

2002 (1)

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

2001 (1)

2000 (2)

M. Qiu and S. He, “Optimal design of a two-dimensional photonic crystal of square lattice with a large complete two-dimensional bandgap,” J. Opt. Soc. Am. B 17, 1027–1030(2000).
[CrossRef]

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. K. Park, D. H. Jang, and Y. H. Lee, “Continuous room-temperature operation of optically pumped two-dimensional photonic crystal lasers at 1.6 μm,” IEEE Photon. Technol. Lett. 12, 1295–1297(2000).
[CrossRef]

1999 (1)

1998 (1)

Z. Y. Li, B. Y. Gu, and G. Z. Yang, “Large absolute band gap in 2D anisotropic photonic crystals,” Phys. Rev. Lett. 81, 2574–2577 (1998).
[CrossRef]

1996 (1)

C. M. Anderson and K. P. Giapis, “Larger two-dimensional photonic band gaps,” Phys. Rev. Lett. 77, 2949–2952 (1996).
[CrossRef]

1994 (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

1993 (1)

E. Yablonovitch, “Photonic band-gap crystals,” J. Phys. Condens. Matter 5, 2443–2460 (1993).
[CrossRef]

1992 (1)

P. R. Villeneuve and M. Piche, “Photonic band gaps in two dimensional square and hexagonal lattices,” Phys. Rev. B 46, 4969–4972 (1992).
[CrossRef]

1987 (2)

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

S. John, “Strong localization of photons in certain dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

Anderson, C. M.

C. M. Anderson and K. P. Giapis, “Larger two-dimensional photonic band gaps,” Phys. Rev. Lett. 77, 2949–2952 (1996).
[CrossRef]

Asano, T.

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

Baba, T.

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

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Blair, J.

J. Feng, Y. Chen, J. Blair, H. Kurt, R. Hao, D. S. Citrin, C. J. Summers, and Z. Zhou, “Fabrication of annular photonic crystals by atomic layer deposition and sacrificial etching,” J. Vac. Sci. Technol. B 27, 568–572 (2009).
[CrossRef]

H. Kurt, R. Hao, Y. Chen, J. Feng, J. Blair, C. Summers, D. S. Citrin, and Z. Zhou, “Design of annular photonic crystal slabs,” Opt. Lett. 33, 1614–1616 (2008).
[CrossRef]

Boucaud, P.

Cai, L. Z.

X. L. Yang, L. Z. Cai, Y. R. Wang, G. Y. Dong, X. X. Shen, X. F. Meng, and Y. Hu, “Large complete bandgaps in a two-dimensional square photonic crystal with isolated single-atom dielectric rods in air,” Nanotechnology 19, 025201 (2008).
[CrossRef]

Chandra, D.

X. Zhu, Y. Zhang, D. Chandra, S.-C. Cheng, J. M. Kikkawa, and S. Yang, “Two-dimensional photonic crystals with anisotropic unit cells imprinted from poly(dimethylsiloxane) membranes under elastic deformation,” Appl. Phys. Lett. 93, 161911 (2008).

Checoury, X.

Chen, Y.

J. Feng, Y. Chen, J. Blair, H. Kurt, R. Hao, D. S. Citrin, C. J. Summers, and Z. Zhou, “Fabrication of annular photonic crystals by atomic layer deposition and sacrificial etching,” J. Vac. Sci. Technol. B 27, 568–572 (2009).
[CrossRef]

H. Kurt, R. Hao, Y. Chen, J. Feng, J. Blair, C. Summers, D. S. Citrin, and Z. Zhou, “Design of annular photonic crystal slabs,” Opt. Lett. 33, 1614–1616 (2008).
[CrossRef]

Cheng, S.-C.

X. Zhu, Y. Zhang, D. Chandra, S.-C. Cheng, J. M. Kikkawa, and S. Yang, “Two-dimensional photonic crystals with anisotropic unit cells imprinted from poly(dimethylsiloxane) membranes under elastic deformation,” Appl. Phys. Lett. 93, 161911 (2008).

Citrin, D. S.

J. Feng, Y. Chen, J. Blair, H. Kurt, R. Hao, D. S. Citrin, C. J. Summers, and Z. Zhou, “Fabrication of annular photonic crystals by atomic layer deposition and sacrificial etching,” J. Vac. Sci. Technol. B 27, 568–572 (2009).
[CrossRef]

H. Kurt, R. Hao, Y. Chen, J. Feng, J. Blair, C. Summers, D. S. Citrin, and Z. Zhou, “Design of annular photonic crystal slabs,” Opt. Lett. 33, 1614–1616 (2008).
[CrossRef]

H. Kurt and D. S. Citrin, “Annular photonic crystals,” Opt. Express 13, 10316–10326 (2005).
[CrossRef]

H. Kurt and D. S. Citrin, “Photonic crystals for biochemical sensing in the terahertz region,” Appl. Phys. Lett. 87, 041108 (2005).

H. Kurt and D. S. Citrin, “Coupled-resonator optical waveguide for biochemical sensing of nanoliter volumes of analyte in the terahertz region,” Appl. Phys. Lett. 87, 241119(2005).

David, S.

Dong, G. Y.

X. L. Yang, L. Z. Cai, Y. R. Wang, G. Y. Dong, X. X. Shen, X. F. Meng, and Y. Hu, “Large complete bandgaps in a two-dimensional square photonic crystal with isolated single-atom dielectric rods in air,” Nanotechnology 19, 025201 (2008).
[CrossRef]

El Kurdi, M.

Feng, J.

J. Feng, Y. Chen, J. Blair, H. Kurt, R. Hao, D. S. Citrin, C. J. Summers, and Z. Zhou, “Fabrication of annular photonic crystals by atomic layer deposition and sacrificial etching,” J. Vac. Sci. Technol. B 27, 568–572 (2009).
[CrossRef]

H. Kurt, R. Hao, Y. Chen, J. Feng, J. Blair, C. Summers, D. S. Citrin, and Z. Zhou, “Design of annular photonic crystal slabs,” Opt. Lett. 33, 1614–1616 (2008).
[CrossRef]

Giapis, K. P.

C. M. Anderson and K. P. Giapis, “Larger two-dimensional photonic band gaps,” Phys. Rev. Lett. 77, 2949–2952 (1996).
[CrossRef]

Gu, B. Y.

Z. Y. Li, B. Y. Gu, and G. Z. Yang, “Large absolute band gap in 2D anisotropic photonic crystals,” Phys. Rev. Lett. 81, 2574–2577 (1998).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

Han, I. Y.

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. K. Park, D. H. Jang, and Y. H. Lee, “Continuous room-temperature operation of optically pumped two-dimensional photonic crystal lasers at 1.6 μm,” IEEE Photon. Technol. Lett. 12, 1295–1297(2000).
[CrossRef]

Hao, R.

J. Feng, Y. Chen, J. Blair, H. Kurt, R. Hao, D. S. Citrin, C. J. Summers, and Z. Zhou, “Fabrication of annular photonic crystals by atomic layer deposition and sacrificial etching,” J. Vac. Sci. Technol. B 27, 568–572 (2009).
[CrossRef]

H. Kurt, R. Hao, Y. Chen, J. Feng, J. Blair, C. Summers, D. S. Citrin, and Z. Zhou, “Design of annular photonic crystal slabs,” Opt. Lett. 33, 1614–1616 (2008).
[CrossRef]

He, S.

Hou, Z.

W. Kuang, Z. Hou, Y. Liu, and H. Li, “The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice,” J. Opt. A 7, 525–528 (2005).
[CrossRef]

Hu, Y.

X. L. Yang, L. Z. Cai, Y. R. Wang, G. Y. Dong, X. X. Shen, X. F. Meng, and Y. Hu, “Large complete bandgaps in a two-dimensional square photonic crystal with isolated single-atom dielectric rods in air,” Nanotechnology 19, 025201 (2008).
[CrossRef]

Hwang, J. K.

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. K. Park, D. H. Jang, and Y. H. Lee, “Continuous room-temperature operation of optically pumped two-dimensional photonic crystal lasers at 1.6 μm,” IEEE Photon. Technol. Lett. 12, 1295–1297(2000).
[CrossRef]

Jang, D. H.

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. K. Park, D. H. Jang, and Y. H. Lee, “Continuous room-temperature operation of optically pumped two-dimensional photonic crystal lasers at 1.6 μm,” IEEE Photon. Technol. Lett. 12, 1295–1297(2000).
[CrossRef]

Joannopoulos, J.

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals Modeling the Flow of Light (Princeton University, 1995).

John, S.

S. John, “Strong localization of photons in certain dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

Johnson, S.

Kalafi, M.

B. Rezaei and M. Kalafi, “Absolute band gap properties in two-dimensional photonic crystals composed of air rings in anisotropic tellurium background,” Opt. Commun. 282, 2861–2869 (2009).
[CrossRef]

B. Rezaei and M. Kalafi, “Engineering absolute bandgap in anisotropic hexagonal photonic crystals,” Opt. Commun. 266, 159–163 (2006).
[CrossRef]

Kalra, Y.

Kikkawa, J. M.

X. Zhu, Y. Zhang, D. Chandra, S.-C. Cheng, J. M. Kikkawa, and S. Yang, “Two-dimensional photonic crystals with anisotropic unit cells imprinted from poly(dimethylsiloxane) membranes under elastic deformation,” Appl. Phys. Lett. 93, 161911 (2008).

Kitagawa, H.

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

Kivshar, Y. S.

A. F. Matthews, S. F. Mingaleev, and Y. S. Kivshar, “Band-gap engineering and defect modes in photonic crystals with rotated hexagonal holes,” Laser Phys. 14, 631–634 (2004).

Kuang, W.

W. Kuang, Z. Hou, Y. Liu, and H. Li, “The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice,” J. Opt. A 7, 525–528 (2005).
[CrossRef]

Kurt, H.

J. Feng, Y. Chen, J. Blair, H. Kurt, R. Hao, D. S. Citrin, C. J. Summers, and Z. Zhou, “Fabrication of annular photonic crystals by atomic layer deposition and sacrificial etching,” J. Vac. Sci. Technol. B 27, 568–572 (2009).
[CrossRef]

H. Kurt, R. Hao, Y. Chen, J. Feng, J. Blair, C. Summers, D. S. Citrin, and Z. Zhou, “Design of annular photonic crystal slabs,” Opt. Lett. 33, 1614–1616 (2008).
[CrossRef]

H. Kurt and D. S. Citrin, “Annular photonic crystals,” Opt. Express 13, 10316–10326 (2005).
[CrossRef]

H. Kurt and D. S. Citrin, “Photonic crystals for biochemical sensing in the terahertz region,” Appl. Phys. Lett. 87, 041108 (2005).

H. Kurt and D. S. Citrin, “Coupled-resonator optical waveguide for biochemical sensing of nanoliter volumes of analyte in the terahertz region,” Appl. Phys. Lett. 87, 241119(2005).

Lee, Y. H.

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. K. Park, D. H. Jang, and Y. H. Lee, “Continuous room-temperature operation of optically pumped two-dimensional photonic crystal lasers at 1.6 μm,” IEEE Photon. Technol. Lett. 12, 1295–1297(2000).
[CrossRef]

Li, H.

W. Kuang, Z. Hou, Y. Liu, and H. Li, “The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice,” J. Opt. A 7, 525–528 (2005).
[CrossRef]

Li, Z. Y.

Z. Y. Li, B. Y. Gu, and G. Z. Yang, “Large absolute band gap in 2D anisotropic photonic crystals,” Phys. Rev. Lett. 81, 2574–2577 (1998).
[CrossRef]

Liu, Y.

W. Kuang, Z. Hou, Y. Liu, and H. Li, “The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice,” J. Opt. A 7, 525–528 (2005).
[CrossRef]

Matthews, A. F.

A. F. Matthews, S. F. Mingaleev, and Y. S. Kivshar, “Band-gap engineering and defect modes in photonic crystals with rotated hexagonal holes,” Laser Phys. 14, 631–634 (2004).

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals Modeling the Flow of Light (Princeton University, 1995).

Meng, X. F.

X. L. Yang, L. Z. Cai, Y. R. Wang, G. Y. Dong, X. X. Shen, X. F. Meng, and Y. Hu, “Large complete bandgaps in a two-dimensional square photonic crystal with isolated single-atom dielectric rods in air,” Nanotechnology 19, 025201 (2008).
[CrossRef]

Mingaleev, S. F.

A. F. Matthews, S. F. Mingaleev, and Y. S. Kivshar, “Band-gap engineering and defect modes in photonic crystals with rotated hexagonal holes,” Laser Phys. 14, 631–634 (2004).

Nakamura, M.

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

Noda, S.

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

Painter, O.

Park, H. K.

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. K. Park, D. H. Jang, and Y. H. Lee, “Continuous room-temperature operation of optically pumped two-dimensional photonic crystal lasers at 1.6 μm,” IEEE Photon. Technol. Lett. 12, 1295–1297(2000).
[CrossRef]

Piche, M.

P. R. Villeneuve and M. Piche, “Photonic band gaps in two dimensional square and hexagonal lattices,” Phys. Rev. B 46, 4969–4972 (1992).
[CrossRef]

Qiu, M.

Rezaei, B.

B. Rezaei and M. Kalafi, “Absolute band gap properties in two-dimensional photonic crystals composed of air rings in anisotropic tellurium background,” Opt. Commun. 282, 2861–2869 (2009).
[CrossRef]

B. Rezaei and M. Kalafi, “Engineering absolute bandgap in anisotropic hexagonal photonic crystals,” Opt. Commun. 266, 159–163 (2006).
[CrossRef]

Ryu, H. Y.

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. K. Park, D. H. Jang, and Y. H. Lee, “Continuous room-temperature operation of optically pumped two-dimensional photonic crystal lasers at 1.6 μm,” IEEE Photon. Technol. Lett. 12, 1295–1297(2000).
[CrossRef]

Scherer, A.

Scheuer, J.

Shen, X. X.

X. L. Yang, L. Z. Cai, Y. R. Wang, G. Y. Dong, X. X. Shen, X. F. Meng, and Y. Hu, “Large complete bandgaps in a two-dimensional square photonic crystal with isolated single-atom dielectric rods in air,” Nanotechnology 19, 025201 (2008).
[CrossRef]

Sinha, R. K.

Song, D. S.

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. K. Park, D. H. Jang, and Y. H. Lee, “Continuous room-temperature operation of optically pumped two-dimensional photonic crystal lasers at 1.6 μm,” IEEE Photon. Technol. Lett. 12, 1295–1297(2000).
[CrossRef]

Summers, C.

Summers, C. J.

J. Feng, Y. Chen, J. Blair, H. Kurt, R. Hao, D. S. Citrin, C. J. Summers, and Z. Zhou, “Fabrication of annular photonic crystals by atomic layer deposition and sacrificial etching,” J. Vac. Sci. Technol. B 27, 568–572 (2009).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

Takayama, S.

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

Tanaka, Y.

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Figures (9)

Fig. 1.
Fig. 1.

The geometry of the unit cell and the relevant opto-geometric parameters ( R , r , θ , δ ) utilized in the study.

Fig. 2.
Fig. 2.

The schematic diagrams of the MAPCs under consideration. (a) and (b) designate square- and triangular-lattice etched dielectric rods in air background, respectively. (c) and (d) show the complementary cases such that square- and triangular-lattice dielectric pillars embedded inside air holes in air background, respectively. The unit-cells of square- and triangular-lattice with a lattice periodicity a are indicated in (a) and (b), respectively.

Fig. 3.
Fig. 3.

Brillouin zones for (a) square and (b) triangular lattices of MAPCs. The symmetry points are labeled.

Fig. 4.
Fig. 4.

Dispersion relations of the TM mode (solid-line) and TE mode (dotted-line) are shown. (a) Square lattice APC in air background with ( R , r , f ) = ( 0.360 a , 0.150 a , 0.336 ) . (b) MAPC in air background with ( R , r , δ , θ , f ) = ( 0.360 a , 0.150 a , 0.030 a , 45 ° , 0.336 ) . (c) MAPC in air background with parameters ( 0.400 a , 0.230 a , 0.050 a , 60°, 0.389). (d) MAPC in dielectric background with parameters ( 0.490 a , 0.125 a , 0.150 a , 45°, 0.295). (e) MAPC in dielectric background with parameters ( 0.480 a , 0.010 a , 0.150 a , 60°, 0.165). Shaded frequency regions correspond to the complete PBGs. The insets in each figure designate the unit cell of the corresponding photonic crystal.

Fig. 5.
Fig. 5.

IFCs plot of MAPC and regular PC are shown. (a) and (b) show the schematic representations of MAPC and regular PC, respectively. IFCs of first, second, third and fourth bands of MAPC with opto-geometric parameters of ( R , r , δ , θ , f ) = ( 0.360 a , 0.150 a , 0.030 a , 45 ° , 0.336 ) are shown in (c), (e), (g) and (j), respectively. IFCs of first, second, third and fourth bands of regular PC with radius r = 0.360 a are shown in (d), (f), (h) and (i), respectively.

Fig. 6.
Fig. 6.

Complete PBG variation Δ ω / ω with respect to the changes of the relative permittivity ε r of the dielectric medium. The graph is drawn to compare the complete PBG variation of both the square lattice of regular PC with inner radius, R = 0.49 a , and MAPC with the specified parameters ( R , r , δ , θ , f ) = ( 0.490 a , 0.125 a , 0.150 a , 45 ° , 0.295 ) in dielectric background. The two insets represent the dispersion diagrams of MAPCs when ε r = 14 and ε r = 16 .

Fig. 7.
Fig. 7.

(a) The complete PBG map by scanning the ratio of ( r / a ) for the square lattice of MAPC structure in air background with outer radius ( R = 0.360 a ). (b) The complete PBG map by scanning the ratio of ( r / a ) for the square lattice of MAPC in dielectric background with outer radius ( R = 0.490 a ). The unit-cells of the specified MAPCs are given as insets in the figures.

Fig. 8.
Fig. 8.

Iso-frequency contours of the second TM band for the square lattice MAPC in air background with the rotation angle θ of θ = 0 ° in (a), θ = 45 ° in (b) and θ = 45 ° in (c). For the three cases, the other parameters are fixed, i.e. ( R , r , δ ) = ( 0.360 a , 0.150 a , 0.03 a ) . (d), (e) and (f) represent steady-state electric field ( E z ) distributions of TM modes for the foregoing MAPC configurations when the operating frequency is centered at a / λ = 0 . 337 . The red and blue colors represent the maximum and minimum field values, respectively.

Fig. 9.
Fig. 9.

(a) Steady-state electric field ( E z ) distribution of TM mode and (b) steady-state magnetic field ( H z ) distribution of TE mode for the waveguide made up of triangular lattice MAPCs in dielectric background. The operating frequency is at a / λ = 0 . 47 . The related parameters for the aforementioned MAPCs are ( R , r , δ , θ ) = ( 0.480 a , 0.060 a , 0.150 a , 60 ° ) . The red and blue colors represent the maximum and minimum e - field / h - field values, respectively.

Tables (1)

Tables Icon

Table 1. Maximum Gap-Midgap Ratios and the Corresponding Complete PBG Frequency Intervals of the Proposed MAPC and APC Structures with Determined Optimum Geometrical Parameters

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