Larger Two-Dimensional Photonic Band Gaps

Abstract

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].

Photonic crystals in the optical regime — past, present and future

“…lattices that consist of two types of feature (e.g. di!erently sized holes etched into the material) have already been evaluated theoretically [136] and show larger band gaps than their`monoatomica counterparts.…”

Band gaps from ring resonators and structural periodicity

“…Both two-and three-dimensional PCs have been developed and studied extensively in the past decades [5][6][7][8][9]. Compared with the two-dimensional PC structure, the three-dimensional PC structure has the advantage of having stop bands in a broader range of incident angles; however, realization of a three-dimensional PC structure is extremely difficult on the scale of the visible frequency regime.…”

Study on Bandwidth of 2-D Dielectric PBG Material

“…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].…”

“…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].…”