Abstract

The monochromatic aberrations produced by the phase distribution reflected by resonant sub-wavelength metallic structures are studied both analytically and numerically. Even for normal incidence, the angular dependence of the re-radiated wavefront disturbs the overall performance of the reflectarray. This effect is modelled as combination of a linear and a cubic dependence. A complete numerical simulation of a multilevel focusing reflectarray is performed using computational-electromagnetic and physical-optics-propagation methods. A modified Strehl ratio is defined to show the dependence of the focused spot behavior on aperture. The irradiance distribution is dependent on the polarization state. A small-aperture focusing reflectarray has been designed, fabricated, and tested. The irradiance distribution at the focusing plane is compared with the simulated one, showing a good agreement when residual wavefront aberrations are included.

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  15. V. Mahajan, “Aberration theory made simple,” SPIE Press (1991).
  16. Y. Li and E. Wolf, “Focal shift in diffracted converging spherical waves,” Opt. Commun. 39(4), 211–215 (1981).
    [CrossRef]

2009

F. González, J. Alda, J. Simón, J. Ginn, and G. Boreman, “The effect of metal dispersion on the resonance of antennas at infrared frequencies,” Infrared Phys. Technol. 52(1), 48–51 (2009).
[CrossRef]

2008

2007

J. Ginn, B. Lail, and G. Boreman, “Phase characterization of reflectarray elements at infrared,” IEEE Trans. Antenn. Propag. 55(11), 2989–2993 (2007).
[CrossRef]

J. S. Tharp, J. Alda, and G. D. Boreman, “Off-axis behavior of an infrared meander-line waveplate,” Opt. Lett. 32(19), 2852–2854 (2007).
[CrossRef] [PubMed]

2006

1993

D. Pozar and T. Metzler, “Analysis of a reflectarray antenna using microstrip patches of variable size,” Electron. Lett. 29(8), 657–658 (1993).
[CrossRef]

1981

Y. Li and E. Wolf, “Focal shift in diffracted converging spherical waves,” Opt. Commun. 39(4), 211–215 (1981).
[CrossRef]

1978

J. Montgomery, “Scattering by an infinite periodic array of microstrip elements,” IEEE Trans. Antenn. Propag. 26(6), 850–854 (1978).
[CrossRef]

1972

1963

D. Berry, R. Malech, and W. Kennedy, “The reflectarray antenna,” IEEE Trans. Antenn. Propag. 11(6), 645–651 (1963).
[CrossRef]

1960

Alda, J.

Berry, D.

D. Berry, R. Malech, and W. Kennedy, “The reflectarray antenna,” IEEE Trans. Antenn. Propag. 11(6), 645–651 (1963).
[CrossRef]

Boreman, G.

F. González, J. Alda, J. Simón, J. Ginn, and G. Boreman, “The effect of metal dispersion on the resonance of antennas at infrared frequencies,” Infrared Phys. Technol. 52(1), 48–51 (2009).
[CrossRef]

J. Ginn, B. Lail, J. Alda, and G. Boreman, “Planar infrared binary phase reflectarray,” Opt. Lett. 33(8), 779–781 (2008).
[CrossRef] [PubMed]

J. Ginn, B. Lail, and G. Boreman, “Phase characterization of reflectarray elements at infrared,” IEEE Trans. Antenn. Propag. 55(11), 2989–2993 (2007).
[CrossRef]

Boreman, G. D.

Ginn, J.

F. González, J. Alda, J. Simón, J. Ginn, and G. Boreman, “The effect of metal dispersion on the resonance of antennas at infrared frequencies,” Infrared Phys. Technol. 52(1), 48–51 (2009).
[CrossRef]

J. Ginn, B. Lail, J. Alda, and G. Boreman, “Planar infrared binary phase reflectarray,” Opt. Lett. 33(8), 779–781 (2008).
[CrossRef] [PubMed]

J. Ginn, B. Lail, and G. Boreman, “Phase characterization of reflectarray elements at infrared,” IEEE Trans. Antenn. Propag. 55(11), 2989–2993 (2007).
[CrossRef]

Ginn, J. C.

González, F.

F. González, J. Alda, J. Simón, J. Ginn, and G. Boreman, “The effect of metal dispersion on the resonance of antennas at infrared frequencies,” Infrared Phys. Technol. 52(1), 48–51 (2009).
[CrossRef]

Kennedy, W.

D. Berry, R. Malech, and W. Kennedy, “The reflectarray antenna,” IEEE Trans. Antenn. Propag. 11(6), 645–651 (1963).
[CrossRef]

Lail, B.

J. Ginn, B. Lail, J. Alda, and G. Boreman, “Planar infrared binary phase reflectarray,” Opt. Lett. 33(8), 779–781 (2008).
[CrossRef] [PubMed]

J. Ginn, B. Lail, and G. Boreman, “Phase characterization of reflectarray elements at infrared,” IEEE Trans. Antenn. Propag. 55(11), 2989–2993 (2007).
[CrossRef]

Lail, B. A.

Li, Y.

Y. Li and E. Wolf, “Focal shift in diffracted converging spherical waves,” Opt. Commun. 39(4), 211–215 (1981).
[CrossRef]

Lopez-Alonso, J. M.

Malech, R.

D. Berry, R. Malech, and W. Kennedy, “The reflectarray antenna,” IEEE Trans. Antenn. Propag. 11(6), 645–651 (1963).
[CrossRef]

McLeod, J. H.

Metzler, T.

D. Pozar and T. Metzler, “Analysis of a reflectarray antenna using microstrip patches of variable size,” Electron. Lett. 29(8), 657–658 (1993).
[CrossRef]

Middleton, C. F.

Montgomery, J.

J. Montgomery, “Scattering by an infinite periodic array of microstrip elements,” IEEE Trans. Antenn. Propag. 26(6), 850–854 (1978).
[CrossRef]

Munk, B. A.

Pozar, D.

D. Pozar and T. Metzler, “Analysis of a reflectarray antenna using microstrip patches of variable size,” Electron. Lett. 29(8), 657–658 (1993).
[CrossRef]

Shen, F.

Simón, J.

F. González, J. Alda, J. Simón, J. Ginn, and G. Boreman, “The effect of metal dispersion on the resonance of antennas at infrared frequencies,” Infrared Phys. Technol. 52(1), 48–51 (2009).
[CrossRef]

Tharp, J. S.

Wang, A.

Wolf, E.

Y. Li and E. Wolf, “Focal shift in diffracted converging spherical waves,” Opt. Commun. 39(4), 211–215 (1981).
[CrossRef]

Young, M.

Appl. Opt.

Electron. Lett.

D. Pozar and T. Metzler, “Analysis of a reflectarray antenna using microstrip patches of variable size,” Electron. Lett. 29(8), 657–658 (1993).
[CrossRef]

IEEE Trans. Antenn. Propag.

J. Ginn, B. Lail, and G. Boreman, “Phase characterization of reflectarray elements at infrared,” IEEE Trans. Antenn. Propag. 55(11), 2989–2993 (2007).
[CrossRef]

D. Berry, R. Malech, and W. Kennedy, “The reflectarray antenna,” IEEE Trans. Antenn. Propag. 11(6), 645–651 (1963).
[CrossRef]

J. Montgomery, “Scattering by an infinite periodic array of microstrip elements,” IEEE Trans. Antenn. Propag. 26(6), 850–854 (1978).
[CrossRef]

Infrared Phys. Technol.

F. González, J. Alda, J. Simón, J. Ginn, and G. Boreman, “The effect of metal dispersion on the resonance of antennas at infrared frequencies,” Infrared Phys. Technol. 52(1), 48–51 (2009).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

Y. Li and E. Wolf, “Focal shift in diffracted converging spherical waves,” Opt. Commun. 39(4), 211–215 (1981).
[CrossRef]

Opt. Lett.

Other

B. Munk, “Finite Antenna Arrays and FSS,” Wiley (2006)

V. Mahajan, “Aberration theory made simple,” SPIE Press (1991).

H. Hristov, “Fresnel zones in wireless links, zone plates lenses and antennas,” Artech (2000)

M. Y. Kiang, “Neural networks,” in Encyclopedia of Information Systems, Academic Press (2002), 303–315.

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Figures (6)

Fig. 1
Fig. 1

The unit cell for an individual resonant element is sketched on the left of the figure. The visible microscope photographs show two geometries for the metallic patches of the resonant elements: squares, and slotted squares.

Fig. 2
Fig. 2

Typical layout of a reflectarray focusing onto a plane. The resonant element is represented as the red square on a circular ring at the reflectarray plane having coordinates (x,y) with respect to the origin of the reflectarray O. The focal plane is situated at a distance f ’ from the reflectarray plane. Angles θ and β are the elevation and azimuth angles respectively. They describe the location of a given point of the reflectarray with respect to the focal point of the system, F’. The angle α is the angle of incidence of the incoming beam with respect to the optical axis.

Fig. 3
Fig. 3

Magnitude (top) and phase shift (bottom) produced by the eight elements of the subzone as a function of the angle and the polarization state (TE, perpendicular, and TM, parallel, components). The color coding is the same for both graphs. The labels are GP for the ground plane, and SQ for the square patches, being the number the size of the patch in nm, and SS for square slotted patches, being the number the size of the slot in a 4500 nm square patch. The vertical lines correspond with the maximum value of θ for the small aperture (red) and large aperture (blue) reflectarrays referred in the text.

Fig. 4
Fig. 4

Modified Strehl ratio as a function of the aperture angle θ. On the left (a) we have represented the small-aperture reflectarray. The maximum reflection angle is 4.77°. The figure at the right (b) is for the larg- aperture reflectarray that reaches an angle of 64.66°. The modified Strehl ratio has been calculated at discrete points, represented by circles. The solid line joining the circles has been validated numerically, and represents the smoothness and continuity of the dependence.

Fig. 5
Fig. 5

Irradiance distribution at the focal plane of a large-aperture reflectarray for three different cases. a) No polarization dependence, b) linear polarization at an azimuth of 0°, and c) linear polarization with azimuth of 45°. The colormap is the same for the three figures and it is normalized to the maximum of the irradiance.

Fig. 6
Fig. 6

Experimental (a) and calculated (b) irradiance distribution onto a pyroelectric camera.

Equations (8)

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Φ = 2 π λ { r sin α + f ' [ 1 + ( tan α r f ' ) 2 1 + tan 2 α ] } 2 π λ [ r 2 2 f ' r 4 8 f ' 3 + r 3 α 2 f ' 2 3 r 3 α 2 4 f ' ] ,
Φ a d d i t i o n a l = Φ ( α ) + Φ ( θ ) .
θ = tan 1 ( r f ' ) r f ' 1 3 ( r f ' ) 3 ,
Φ ( θ ) = Φ 0 + A 1 + exp ( | θ B | ) ,
Φ ( θ ) = Φ 0 + A [ 1 4 θ B 1 48 ( θ B ) 3 ] ,
Φ ( r ) = Φ 0 + A [ 1 4 r B f 4 B 2 + 1 48 B 3 ( r f ' ) 3 ] .
Φ = Φ ( x , y , λ , θ , s ) ,
( E x , o u t ( x , y ) E y , o u t ( x , y ) ) = R ( β ( x , y ) ) ( ρ , ( x , y ) ρ , ( x , y ) ρ , ( x , y ) ρ , ( x , y ) ) R ( β ( x , y ) ) ( E x , i n ( x , y ) E y , i n ( x , y ) ) .

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