Tuning of band gaps for a two-dimensional piezoelectric phononic crystal with a rectangular lattice

In this paper, the elastic wave propagation in a two-dimensional piezoelectric phononic crystal is studied by considering the mechanic-electric coupling. The generalized eigenvalue equation is obtained by the relation of the mechanic and electric fields as well as the Bloch-Floquet theorem. The band structures of both the in-plane and anti-plane modes are calculated for a rectangular lattice by the planewave expansion method. The effects of the lattice constant ratio and the piezoelectricity with different filling fractions are analyzed. The results show that the largest gap width is not always obtained for a square lattice. In some situations, a rectangular lattice may generate larger gaps. The band gap characteristics are influenced obviously by the piezoelectricity with the larger lattice constant ratios and the filling fractions.

Numerical analysis of acoustic band gaps in two-dimensional periodic materials

Using the plane-wave expansion (PWE)method , the band gaps of the two-dimension phononic crystals composed of square, triangle and honeycomb arrays aluminum cylinders in the air are calculated numerically. The band structures of three lattices were compared and analyzed. It is concluded that the band-gap of honeycomb lattices is located at lower frequency fields, compared with square and triangle lattices. When the filling fraction is between 0.091 and 0.6046, the honeycomb lattices have larger band gaps and gain an advantage over square and triangle lattices. In addition, the gap map is introduced to illustrate the influences of filling fraction on the number, the relative width and the limit frequency of the band-gap.

Photonic band structures of two-dimensional photonic crystals with deformed lattices

Using the plane-wave expansion method, we have calculated and analysed the changes of photonic band structures arising from two kinds of deformed lattices, including the stretching and shrinking of lattices. The square lattice with square air holes and the triangular lattice with circular air holes are both studied. Calculated results show that the change of lattice size in some special ranges can enlarge the band gap, which depends strongly on the filling factor of air holes in photonic crystals; and besides, the asymmetric band edges will appear with the broken symmetry of lattices.

A Method for Increasing X-ray Protection Capability Based on Photonic Crystal Technology

In this paper, we propose a method to improve anti-radiation capability by coating heavy metal X-ray protection glass with compound photonic crystal layers, based on the unique property of photonic crystal that light cannot be propagated within the range of band gaps. Using the plane wave expansion method,we made a theoretical study of parameters affecting the band gap structures of one-dimensional photonic crystals. Based on the findings, we chose appropriate materials and compound structure of photonic crystal so as to get high X-ray reflection coating photonic crystal layers. By this method, the reflection rate within X-ray wavelength can reach the maximum value of 100%, and the average value of over 90%. Even low-cost heavy metal X-ray protection glass of absorption coefficient value can achieve the desired effect. Thus, this method greatly decreases the anti-radiation requirements of heavy X-ray protection glass.