Effects of thermal annealing of W/SiO 2 multilayer Bragg reflectors on resonance characteristics of film bulk acoustic resonator devices with cobalt electrodes, J Vac Sci Technol A 22 (2004), 465-471. 6 a lens composed of a dielectric filled planar parallel-plate operating in the TEM mode was described. This time the dielectric gradation was achieved by a combination of circular and triangular dispersed equivalent volume-averaged relative permittivity control as well as transverse resonance guided permittivity thickness control. However, all of the methods above require considerable fabrication process duration due to numerous holes or posts having to be machined; in addition the lenses realized can be difficult to integrate with active circuits. In this article we detail the design and performance of a surface wave Luneburg lens operated in TE 01 mode in Ka band. The lens gradient dielectric constant is realized by photo lithographically etching holes of different sizes into one side of a standard PCB ground plane. In this way we introduce local inductive variation which partially neutralizes the intrinsic permittivity of the material in prespecified localized regions of the lens, i.e. gives local permittivity gradation control. For verification, a prototype lens was designed and fabricated; measurement and simulation results show good agreement.
LUNEBURG LENS DESIGNThe lens plane of a planar Luneburg lens is a circle of unit radius whose index of refraction n varies with the radius r according to, [1]:The lens n is maximum at its center r ϭ 0 (n ϭ ͱ2), and decreases gradually to the periphery r ϭ 1 (n ϭ 1), i.e. total variation of ⌬n ϭ ͱ2 Ϫ 1 Ϸ 0.414.A dielectric filled parallel holey metal plate operated in TE 01 mode could in principle be used in Luneburg Lens applications since this structure is capable of providing a refractive index from nearly zero to a value approaching the square root of the dielectric between the plates, [5]. This method relies on the theory that a waveguide with holes drilled in it can yield variation of equivalent refractive index, [6]. When circular holes arranged in rectangular lattice are introduced into one of the metal plates as shown in Figure 1, the equivalent refractive index n holes is given by [5] as:Here, b and c are the spacing between the neighboring holes along X ជ and Y ជ direction, respectively. For isotropy approximation c is made equal to b and both are restricted to be smaller than g /2, d is the diameter of the holes; r is the permittivity of the filled dielectric, g is the guided wavelength of the solid ground parallel plate, and a is the plate spacing. The electric field polarized in Y ជ direction, propagates along X ជ .The lens was designed according to [7] using only three discrete concentric cylindrical layers of respective values n ϭ 1.22, 1.34, 1.4. This was done to ease the demand on the (2) it can be seen that the value of n can only be increased by the introduced holes, thus the operating frequency is chosen such that we have n equal to 1.22 in the le...