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Indoor Signal Focusing by Means of Fresnel Zone Plate Lens Attached to Building Wall

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Indoor Signal Focusing by Means of Fresnel Zone Plate Lens Attached to Building Wall
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  INDOOR SIGNAL FOCUSING BY MEANS OF FRESNEL ZONE PLATE LENS ATTACHED TO BUILDING WALL Hristo D. Hristov, Rodolfo Feick, Walter Grote and Pablo Fernandez Abstract Simple and cheap FZP lens for indoor focusing of communication signals at the 2-GHz frequency band is proposed and studied. It consists of concentric metal rings, mounted outside on exterior building wall. The on-wall zone lens is illuminated normally by a spherical wave, srcinating at a outer focal distance of 7.15m. The inner focal distance was set to 1.7m. The focussing diffraction theory of the free-space FZP lens is modified and used for on-wall FZP lens examination. The presence of the wall does not deteriorate significantly the FZP lens focusing efficiency. Also, it is proved that the defocusing effect is smaller for lenses made by bigger number of rings and for walls with smaller thickness. The wall has a strong axial defocusing effect. It is more  pronounced for spherical wave illumination and less for plane wave incidence. The axial defocusing exhibits small dependence on the wave polarization. The zone plate lens construction comprising three metal rings, made of thin anti-mosquito mesh, has a focusing efficiency of about 15 dB (measured) and 14 dB (calculated), and defocusing of 14cm.  Key words: wireless communications, propagation, wave focusing, microwave lenses INTRODUCTION The idea behind the zone plate lens of alternate open and opaque annuli srcinated from the Fresnel zone principle and was first implemented by Soret in 1875 [1]. This lens has  found many diverse applications in optics [2], acoustics [3], microwave and millimiter-wave technique [4], etc., for signal/energy focusing and object imaging, special  processing, filtering and sensing. In the wireless engineering, the Fresnel zone concept has been applied to propagation link design and for building of radio relay directing and repeating constructions and microwave/millimetre-wave Fresnel zone plate (FZP) antennas [5]. In this work we utilize a simple and cheap FZP lens for indoor focusing (or local increase) of communication signals at the 2-GHz frequency band. It consists of concentric metal rings, mounted outside on thick exterior wall. The focusing action of this on-wall lens, illuminated normally by a spherical or plane wave incident from outside, was studied theoretically and well confirmed experimentally. A zone plate lens construction comprising three metal rings, made of thin anti-mosquito mesh, has shown a focusing efficiency or local signal increase of about 15 dB (measured) and 14 dB (calculated). 2. THEORY OF THROUGH-WALL INDOOR FOCUSING OF METAL FZP LENS: QUASI-OPTICAL APPROACH  Normally, the microwave FZP lens, consisting of circular metal rings, is mounted on thin low-loss dielectric plate, which does not disturb considerably its focusing  properties. But if the lens is attached to a thick lossy wall, at plane 0  z   = , as shown in Fig. 1, the rays diffracted at the open annular zones travel through the wall. Because of the refraction on the inner wall plane  z d  =  the rays change their initial directions and the lens indoor focal area moves slightly closer to the wall. Here the building wall is modelled as a homogeneous lossy dielectric plate of thickness d   and complex  permittivity ¨¨ r r r   j ε ε ε  ′ ′′= −  .   A A n  A n-1 CF 0 z SS n b n FZPring y l n l φ tn φ t b n-1 ∆ b n ∆ y ε 0 Inner planeOuter planed z-dzF ε 0 ε r  dSBr  n r r  n-1 φφ n B n-1 B n FZPringl n-1 φ t E   hy E h φ b' n ~ yz -horizontalplane S n-1 y F 1 P 1   Figure 1 Cross-section geometry of FZP lens on building wall: spherical-wave illumination From the above ray-tracing description follows that the focusing theory can be a combination of the physical optics (Fresnel-Kirchhoff´s diffraction) and geometric optics (Snell´s refraction law). Fig. 1 is a cross-sectional view of the on-wall Fresnel zone plate lens and illustrates the ray-tracing corresponding to the n-th zone. The current ray path rl   shows how the incident ray is converging to the point C or to the focal point 2 P  after diffraction at  point A (or at the elementary surface dS  ) and refraction at point B. The diffracted ray l   is propagating in the wall under a diffraction angle t  φ  , while the converging indoor ray r   is oriented to the current point C()  z   under an angle φ  . These angles are connected by the Snell’s law (sinsin r t  φ ε φ  ′= ) Similar paths follow the zone-   boundary rays n n n l r   and 111 n n n l r  − − − . The n -th Fresnel zone on the outer wall  plane has a design radius n b , which can be calculated by [5], [6] ( ) 22 22221211212 oo oo  F F nb F F F F nn F F  λ λ  −= + + + − ++ +            (1) where 1  F   and o  F   are the design focal distances (lengths) of the FZP lens located in free space. The equation gives the zone radii for a FZP lens, located in a free space (or for 0 d   = ). The projection of the n-th zone on the inner wall plane is of smaller size, with a zone radii bn ′  given by b b bn n n ∆ ′ = −  (2) where the radius difference n b ∆  can be obtained from the Fresnel zone ray-path difference in the presence of the wall 1 ()(())2 n r n n r o  s l r F d F d n λ ε ε  ′ ′+ + − + + − =  (3) or ( ) ( ) 2222221  n r n o n n  F b d b F d b b ε ∆ ∆  ′+ + + + − + −     1 02 r o  F d F d n λ ε  ′− − − + − =  (4) We then approximate (4) taking into account that 22 /1 n b d  ∆  <<  and 1 d F  <<  and o  F  . These conditions are well consistent with the typical wall thicknesses and focal distances For the above conditions we easy reach to the following equation for n b ∆    2 42 n n n nnn  A B A Bb A ∆ − + −=  (5) with 2 r n  Ad  ε  ′=  (5a) 22 /2 n n o o n  B b F dF b = − +  (5b) and 222211 /2 n n o n o C F b F b F F n λ  = + + + − − −  (5c) For finding the on-axis focusing characteristics of the FZP lens, mounted on a building wall we modify the field diffraction expression for the FZP lens located in free space (or when d=0). [5], taking into account the amplitude, phase and ray-direction changes due to the wall. For a spherical-wave illumination (Fig. 1), the field produced by the n -th inner zone is obtained in the form ( ) 1 ,, e()(coscos) nn b j s r  , v hn n i t 0b  j E z E T y dy sr   β  π φ φ λ  − ′ − +⊥⊥′ ′ ′= + ∫   (6) where 1 cos/ i  F s φ   = , ( ) 222cos1/()  y z d yt r  φ ε  ′ ′ ′= − − + , 221  s F y ′≅ +  and 22() r z d y ′= − +  are expressed as functions of  y ′ . 1,,0 -e 11  F  E E  F   β  ⊥ ⊥ =    (7) where , 1  E  ⊥    is the spherical wave amplitude around its srcin 1  P   and ,0  E  ⊥    is its value at point O (on the outer wall plane).
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