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For a compact millimeter wave imaging system it is very important to design every component into small size, for the components in a millimeter wave system are usually much larger than those in an optical imaging system due to rela-tively long wave lengths. In this paper, we suggest a kind of binary diffractive lens (BDL) designed using double nega-tive materials (DNG) as the objective lens for a millimeter wave imaging system. The DNG-BDL has not only the ad-vantage of low profile but also small f number, which will be benefit for constructing a compact millimeter wave imaging system. Several DNG-BDL are designed and analyzed using the FDTD method. The numerical results of the focal plane field of the DNG-BDL are presented, which show that the DNG-BDL with small f number has relatively better focusing characteristic than that of a double positive BDL with same f number.

Since Veselago’s theory [

The basic characteristic of an imaging lens is that it can focus the plane wave to a focal point. In practice, imaging lens can not focus plane wave absolutely to a point, it can only focus the plane wave to a small region, and this will be represented by a main narrow lobe in the focal plane field (FPF) intensity distribution which is drawn versus a line perpendicular to the propagation direction, see

netic waves passing through a lens, and the reason why energies concentrate into the main beam is that the phases of the electromagnetic waves reaching to the focal point have nearly same phases. So the basic rule for design a focusing lens is that every wave path to the focal point should be equal, for example the wave path ABCO in

Following the design rule just mentioned, take a 1/2^{2} BDL (2^{2} sub-zones in each zone) as an example [

where r_{n} is the distance from the focal point to the lens , n is the number index of the sub-zones, f is the focal length, λ is the wavelength. It is clear that there is λ/2^{2} difference (phase difference is π/2) between two neighboring r_{n}.

Waves propagated in DNG medium generate negative wave path differences compared to waves propagated in the air, which is opposite to that in DPS medium. Dif-

ferent height of sub-zones will generate wave path difference and this will compensate for the difference among all r_{n}, then each wave path to the focal point will be equal. Accordingly, the sub-zone step height d is determined by the following equation

where k_{d} is the wave number in the DNG medium and according to [_{r }andε_{r} are both negative, so from equation (2) we get

i.e.(3)

For 1/2^{k} BDL, there are sub-zones in each zone, and the path difference between two neighboring subzones is λ/2^{k}, then the parameters of this BDL are:

Among numerous methods for solving DNG problems, FDTD method [

, (7)

where

ω_{p} is the material’s resonant frequency.

The perfect lens (μ_{r}_{ }= –1, ε_{r}_{ }= –1) proposed by Pendry in [

The BDL designed and analyzed here are axisymmetric, so a symmetry boundary (see

The FPF (f = 30e-3) of a 1/2 DPS-BDL (ε_{r}_{ }= 2.2, contains five zones) was computed using the FDTD code and compared with that obtained by boundary element method (BEM) as shown in

Then several DNG-BDL are designed and analyzed using the FDTD method. Shown in

structure of a 1/2^{2} DNG-BDL (μ_{r}_{ }= –1, ε_{r}_{ }= –1) with four zones, focal length f = 105 mm and diameter D = 105 mm (FN = 1). The FPF of the DNG-BDL was computed using the FDTD method and compared with that of a DPS-BDL (ε_{r}_{ }= 2.2), see

For BDL of small FN, the FPF side lobes of the DNG-BDL are relatively even much lower than that of the DPS-BDL, an example is shown in ^{2} DNG and DPS BDL (five zones) are f = 10 mm, diameter D = 47 mm (FN = 0.21). The FPF of two DNG-BDL with μ_{r}_{ }= ε_{r}_{ }= –2 and two DPS-BDL with ε_{r}_{ }= 3.78 were also computed. Shown in

The DNG-BDL which has good characteristics of low profile and small f number is studied in this paper. The design formulas of the DNG-BDL are presented and several DNG-BDL are designed and analyzed using the FDTD method. The focal plane fields of several DNGBDL are given and compared with that of DPS-BDL; the compared results show that the DNG-BDL with small f number has better focusing characteristics than that of DPS-BDL, and this property makes it very useful to be taken as the objective lens to construct a compact millimeter wave imaging system.