Theoretical bandgap modeling of two-dimensional triangular photonic crystals formed by interference technique of three-noncoplanar beams

Anomalous refractive effects in honeycomb lattice photonic crystals formed by holographic lithography

We have investigated for the first time the anomalous refractive effects of a photonic crystal (PhC) formed by holographic lithography (HL) with triangular rods arranged in a honeycomb lattice in air. Possibilities of left-handed negative refraction and superlens are discussed for the case of TM2 band with the index contrast n = 3.4:1. In contrast to the conventional honeycomb PhC made of regular rods in air, the HL PhCs show left-handed negative refraction over a wider and higher frequency range with high transmissivity (>90%), and the effective indices quite close to -1 for a wide range of incident angles with a larger all-angle left-handed negative refraction (AALNR) frequency range (Deltaomega/omega approximately 14.8%). Calculations and FDTD simulations demonstrate the high-performance negative refraction properties can happen in the holographic structures for a wide filling ratio and can be modulated by changing the filling ratio easily.

Improvement of transmission properties through two-bend resonance by holographic design for a two-dimensional photonic crystal waveguide

We have investigated the transmission properties of a photonic crystal waveguide (PCW) formed by holographic lithography for the first time with a two-dimensional (2D) triangular holographic photonic crystal (PhC) including a line defect with two 60 masculine bends. Calculations have shown that for this PCW high transmission (>90%) through sharp corners can be obtained in a wide frequency range from 0.298 to 0.310 (omega alpha/2pi c) with the relative band gap of 4% when the dielectric contrast is 7.6:1. As far as we know, this result should be the widest frequency range with high transmission (>90%) in the waveguide of similar 2D triangular PhCs ever reported. We have also found that the specific holographic designs of PhC have strong influence on the resonance between the two waveguide bends, and thus this fact can be used as an effective means to improve the transmission property of 2D holographic PCW. In addition to the simplicity and low cost of holographic fabrication of PhCs, these features may reveal the possibly better guiding ability of holographic PCW than the conventional waveguide and the promising potential of the former in the application of photonic integrated circuits.

Analysis of a two-dimensional photonic bandgap structure fabricated by an interferometric lithographic system

An interferometric lithographic technique and double exposure method are applied to theoretically and experimentally investigate several kinds of 2D periodic structures. The shape, lattice symmetries, and lattice constants of the 2D structures, for different substrate rotational angles, are obtained from the simulated predictions. The shape of the 2D structures can be varied by controlling the rotational angle of the substrate and the development process, and they are validated experimentally. The variation of the lattice symmetry of the 2D structure with the substrate rotational angle is discussed in detail in relation to the axial angle and lattice constant. It is found that square, circular, rectangular, and elliptical scatterers which are arranged in parallelogram, triangular, and square lattices (with different lattice constants) can be obtained. The photonic bandgaps for each condition are also investigated. When the substrate rotational angles are the same, the normalized frequency (omega a/2 pi c) of photonic bandgap structures with an equal filling factor are very similar regardless of the interference angle. The results are helpful in designing the forbidden frequency when the lattice constant and the scatterer shape can be controlled by the interferometric lithographic technique.

Holographic design and band gap evolution of photonic crystals formed with five-beam symmetric umbrella configuration

We propose a holographic design of five-beam symmetric umbrella configuration, where there are a central beam and four ambient beams symmetrically scattered around the central one with the same apex angle, for fabrication of three-dimensional photonic crystals with tetragonal or cubic symmetries, and systematically analyzed the band gap properties of resultant photonic crystals when the apex angle is continuously increased. Our calculations reveal that large complete photonic band gaps exist in a wide range of apex angle for a relatively low refractive index contrast. Specifically, the face-centered cubic structure with a relative band gap of 25.1% for epsilon = 11.9 can be obtained with this recording geometry conveniently where all the beams are incident from the same half-space. These results will provide us with more understanding of this important recording geometry and give guidelines to its use in experiments.