Photonic band gaps in two-dimensional square lattices: Square and circular rods

Villeneuve, Pierre R.; Piché, Michel

doi:10.1103/physrevb.46.4973

Cited by 109 publications

(56 citation statements)

References 6 publications

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“…Instead, the elements comprising the lattice may play a critical role in determining the maximum absolute gap that can be achieved for a given dielectric contrast. This observation is also supported by the work of Villeneuve and Piché in their study of the shape of the rod cross section [12]. Extending the concept of symmetry reduction to 3D crystals by changing the relative size of the elements comprising the lattice may also lead to increased 3D PBGs.…”

supporting

confidence: 56%

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Larger Two-Dimensional Photonic Band Gaps

1996

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Absolute photonic band gaps in two-dimensional square and honeycomb lattices of circular crosssection rods can be increased by reducing the structure symmetry. The addition of a smaller diameter rod into the center of each lattice unit cell lifts band degeneracies to create significantly larger band gaps. Symmetry breaking is most effective at filling fractions near those which produce absolute band gaps for the original lattice. Rod diameter ratios in the range 0.1-0.2 yield the greatest improvement in absolute gap size. Crystal symmetry reduction opens up new ways for engineering photonic gaps.[S0031-9007 (96) The last few years have witnessed an ongoing search for periodic dielectric structures which give rise to a photonic band gap (PBG)-a region of the frequency spectrum where propagating modes are forbidden. These "photonic crystals" could alter radiation-matter interactions and thus improve the efficiency of optical devices by controlling spontaneous emission [1]. Applications of these crystals in semiconductor lasers and solar cells [1], and high-quality resonant cavities and filters [2] have been proposed. Although three-dimensional (3D) PBG crystals suggest the most interesting ideas for novel applications, two-dimensional (2D) structures could also find several important uses, as a result of their strong angular reflectivity properties over a wide frequency band. For example, 2D PBG crystals with absolute band gaps provide a large stop band for use as a feedback mirror in laser diodes [3]. Photonic gaps at visible to near-infrared (IR) wavelengths could have the widest impact in applications. As the band gap frequency is directly related to the size of the scattering elements comprising the lattice, a near-IR band gap requires features with dimensions in the submicron size regime. Fabricating 3D periodic structures in this regime poses an overwhelming challenge, despite progress in microfabrication technology. Perhaps for this reason attention has been drawn towards 2D lattice structures. The successful fabrication of 2D crystals with near-IR band gaps has been recently reported [4,5].

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confidence: 56%

“…We start with the single-rod square lattice of air holes in a dielectric material, whose photonic properties have been previously studied by several groups [12][13][14], each reporting that band gaps for each of the two orthogonal polarizations occur. However, there has been some discrepancy as to whether an absolute PBG is present.…”

mentioning

confidence: 99%

Larger Two-Dimensional Photonic Band Gaps

1996

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“…(14) and (16), expanding it in terms of three basis vectors 3 (where m, n, l are independent integers), and employing these bases as…”

Section: Reciprocal Lattice Vector Gmentioning

confidence: 99%

“…After E. Yablonovitch and S. John reported their pioneer research in experiments [1][2][3], many others published their theoretical analyses, concerned with 3-D structures [4][5][6][7][8][9] or 2-D ones [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In classical analysis of a dielectric periodic structure, the eigenvalue equations are formulated by means of the plane wave expansion method of scalar field [5,12] or vector field [4,[6][7][8][9][10][11][13][14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

“…In classical analysis of a dielectric periodic structure, the eigenvalue equations are formulated by means of the plane wave expansion method of scalar field [5,12] or vector field [4,[6][7][8][9][10][11][13][14][15][16][17][18][19][20][21][22][23]. In numerical analysis, FDTD method is the first choice to carry out the wide-band frequency response of the periodic structure [24].…”

Section: Introductionmentioning

confidence: 99%

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Study on Bandwidth of 2-D Dielectric PBG Material

Zheng¹,

Zhang²

2003

PIER

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Abstract-Based on the eigenvalue equations of vector fields E and H by extending Bloch theorem to the vector field Maxwell equations, the characteristics of 2-D dielectric rod array with square cross-section elements arranged in square lattice is analyzed in detail. From the numerical results, empirical expressions for both the relative bandwidth of frequency band gap and the midgap frequency with respect to the average permittivity, under the optimal filling fraction of dielectric/air in cross-section for wider bandwidth, are formulated by means of data fit.

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Theoretical Band Gap Studies of Two-Dimensional Photonic Crystals with Varying Column Roundness

Hillebrand

Hergert

Harms

2000

phys. stat. sol. (b)

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The present contribution introduces theoretical studies of photonic crystals. On the basis of Maxwell's equations and a `plane wave expansion' band structures and densities of states are computed for triangular and square 2D lattices of air columns in silicon. The main topic of the paper are investigations of band gap modifications (TM-and TE-polarization) for pores of deteriorating roundness, approximated by ellipses of varying eccentricity. The presented computations include the consideration of background structures in the form of stripes (SiO 2 ) in the model. The results are compared with calculations for circular air columns of varying filling factors.Im vorliegenden Beitrag werden theoretische Untersuchungen zu photonischen Kristallen vorgestellt. Auf der Grundlage der Maxwellschen Gleichungen und einer `ebenen Wellen Entwicklung' werden fu È r triangulare und quadratische 2D Gitter Bandstrukturen und Zustandsdichten berechnet. Schwerpunkt der Publikation bilden Untersuchungen zu Vera È nderungen der Bandlu È cken (TM-und TE-Polarisation), wenn die Poren in Silizium nicht mehr exakt rund sind, sondern durch Ellipsen mit variabler Exzentrizita È t gena È hert werden. Die vorgestellten Berechnungen erlauben zusa È tzlich, streifenfo È rmige Hintergrundstrukturen (SiO 2 ) in den Modellen zu beru È cksichtigen. Die Ergebnisse werden mit Rechnungen fu È r kreisfo È rmige Luftsa È ulen bei variablem Fu È llfaktor verglichen.

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Photonic band gaps in two-dimensional square lattices: Square and circular rods

Cited by 109 publications

References 6 publications

Larger Two-Dimensional Photonic Band Gaps

Larger Two-Dimensional Photonic Band Gaps

Study on Bandwidth of 2-D Dielectric PBG Material

Theoretical Band Gap Studies of Two-Dimensional Photonic Crystals with Varying Column Roundness

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