Periodic dielectric structure for production of photonic band gap and devices incorporating the same

A periodic dielectric structure which exhibits a photonic band gap comprising, in combination:

• a plurality of elongate rods of a material of a given dielectric constant, the rods being arranged in planar layers with a given spacing between the rods in each layer, the spacing between the rods comprising a material of a different and contrasting refractive index to the material of the rods, the layers being stacked one on the other to form a three dimensional structure having a four-layer periodicity,
• a first layer comprising equally spaced parallel rods with the axis of all of the rods being in a given axial direction,
• the second layer comprising equally spaced parallel rods with the axes of the rods being perpendicular to the given axial direction of the first layer,
• a third layer comprising equally spaced parallel rods with the axes of the rods being parallel to the given axial direction of the first layer, the rods in the third layer being offset to about the midpoint between the rods in the first layer,
• a fourth layer comprising equally spaced parallel rods with the axes of the rods being perpendicular to the given axial direction of the first layer the rods of the fourth layer being offset to about the midpoint between the rods in the second layer,
• the dimension of the rods, the spacing therebetween, the refractive index contrast and the filling ratio being related to each other to produce a photonic band gap at a predetermined frequency.