Abstract

The quality of the image produced by optical reflectarrays as a function of the F/#, polarization, and wavelength is analyzed in this paper. The results are expressed as monochromatic and polychromatic modulation transfer functions. They show that large aperture multilevel reflectarrays perform quite close to the diffraction-limited case. The chromatic aberrations make these elements highly wavelength-selective.

© 2011 Optical Society of America

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References

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  1. J. Ginn, B. Lail, and G. Boreman, “Phase characterization of reflectarray elements at infrared,” IEEE Trans. Antennas Propag. 55, 2989–2993 (2007).
    [CrossRef]
  2. J. Ginn, B. Lail, J. Alda, and G. Boreman, “Planar infrared binary phase reflectarray,” Opt. Lett. 33, 779–781 (2008).
    [CrossRef] [PubMed]
  3. J. Ginn, J. Alda, J. A. Gómez-Pedrero, and G. Boreman, “Monochromatic aberrations in resonant optical elements applied to a focusing multilevel reflectarray,” Opt. Express 18, 10931–10940 (2010).
    [CrossRef] [PubMed]
  4. B. Munk, Finite Antenna Arrays and FSS (Wiley, 2006).
  5. J. Tharp, J. M. Lopez-Alonso, J. Ginn, C. Middleton, B. Lail, B. Munk, and G. Boreman, “Demonstration of a single-layer meanderline phase retarder at infrared,” Opt. Lett. 31, 2687–2689 (2006).
    [CrossRef] [PubMed]
  6. J. Tharp, J. Alda, and G. Boreman, “Off-axis behavior of an infrared meanderline waveplate,” Opt. Lett. 32, 2852–2854(2007).
    [CrossRef] [PubMed]
  7. D. Berry, R. Malech, and W. Kennedy, “The reflectarray antenna,” IEEE Trans. Antennas Propag. 11, 645–651 (1963).
    [CrossRef]
  8. D. Pozar and T. Metzler, “Analysis of a reflectarray antenna using microstrip patches of variable size,” Electron. Lett. 29, 657–658 (1993).
    [CrossRef]
  9. J. Huang and J. A. Encinar, Reflectarray Antennas(Wiley–IEEE, 2007).
    [CrossRef]
  10. F. J. González, J. Alda, J. S. Rodríguez, J. Ginn, and G. Boreman, “The effect of metal dispersion on the resonance of antennas at infrared frequencies,” Infrared Phys. Technol. 52, 48–51 (2009).
    [CrossRef]
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  13. J. W. GoodmanIntroduction to Fourier Optics, 3rd ed.(Roberts, 2005).
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    [CrossRef]

2010 (1)

2009 (1)

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

2008 (1)

2007 (2)

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

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

2006 (2)

1993 (1)

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

1982 (1)

1963 (1)

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

Alda, J.

Berry, D.

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

Boreman, G.

Encinar, J. A.

J. Huang and J. A. Encinar, Reflectarray Antennas(Wiley–IEEE, 2007).
[CrossRef]

Ginn, J.

Gómez-Pedrero, J. A.

González, F. J.

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

Goodman, J. W.

J. W. GoodmanIntroduction to Fourier Optics, 3rd ed.(Roberts, 2005).

Hristov, H.

H. Hristov, Fresnel Zones in Wireless Links, Zone Plates Lenses and Antennas (Artech, 2000).

Huang, J.

J. Huang and J. A. Encinar, Reflectarray Antennas(Wiley–IEEE, 2007).
[CrossRef]

Kennedy, W.

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

Lail, B.

Lopez-Alonso, J. M.

Mahajan, V. N.

Malech, R.

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

Metzler, T.

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

Middleton, C.

Munk, B.

Pozar, D.

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

Rodríguez, J. S.

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

Shen, F.

Tharp, J.

Wang, A.

Appl. Opt. (1)

Electron. Lett. (1)

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

IEEE Trans. Antennas Propag. (2)

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

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

Infrared Phys. Technol. (1)

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

J. Opt. Soc. Am. (1)

Opt. Express (1)

Opt. Lett. (3)

Other (4)

J. Huang and J. A. Encinar, Reflectarray Antennas(Wiley–IEEE, 2007).
[CrossRef]

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

H. Hristov, Fresnel Zones in Wireless Links, Zone Plates Lenses and Antennas (Artech, 2000).

J. W. GoodmanIntroduction to Fourier Optics, 3rd ed.(Roberts, 2005).

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Figures (6)

Fig. 1
Fig. 1

Complex reflection coefficient for the eight different resonant structures used in this study. (a) and (c) represent the magnitude of the reflection coefficient. (b) and (d) represent the phase. The dependence with the angle for both polarization states is given in (a) and (b), meanwhile, the spectral behavior is presented in (c) and (d). The SQ labels are for square patches being the number of the value of the side of the square in nanometers. The SS labels are for square patch elements with slots introduced into the center of the element being the number of the size of the square slot in nanometers. GP denotes the ground plane. It is worth noticing that (a) and (b) have been computed using a finite-element method (HFSS by Ansoft) while (c) and (d) have been determined through a method-of-moments algorithm (Designer by Ansoft), which may explain the slight differences found for normal incidence and 10.6 μm wavelength.

Fig. 2
Fig. 2

Typical layout of a reflectarray focusing onto a plane. The resonant element is represented as the dark gray square on a circular ring at the reflectarray plane. The angle θ describes the location of a given point of the reflectarray with respect to the focal point of the system.

Fig. 3
Fig. 3

(a) PSF and (b) MTF for a large aperture reflectarray as a function of the polarization state of the incident radiation. The cutoff frequency is the same for the two polarizations but the MTF behaves differently.

Fig. 4
Fig. 4

(a) Horizontal profile of the MTF for horizontal linear polarization as a function of the F / # . (b) Ratio between the area under the calculated MTF and the diffraction-limited MTF as a function of the F / # .

Fig. 5
Fig. 5

(a) Irradiance map as a function of the axial coordinate z and λ. The white cross represents the point corresponding to the design conditions. (b) Plot of the evolution of the irradiance at the location given by Eq. (3).

Fig. 6
Fig. 6

(a) MTF for different wavelengths at the location of the nominal focus. MTF for a multilevel reflectarray at the focal planes for different wavelengths. (b) Chromatic dependence of the MTF at 6.95 cycles / mm for two axial positions.

Equations (8)

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E r ( x , y , z ) = A E r 0 ( x 0 , y 0 ) · exp ( j k r ) 2 π · r z r × ( 1 r j k ) d x 0 d y 0 ,
PSF ( x , y , z ) = E r ( x , y , z ) 2 | O P ,
E 0 ( x 0 , y 0 ) = [ E 0 x ( x 0 , y 0 ) E 0 y ( x 0 , y 0 ) ] .
[ E r 0 x E r 0 y ] = R 1 ( β ( x 0 , y 0 ) ) · [ ρ | | ( x 0 , y 0 ) 0 0 ρ ( x 0 , y 0 ) ] · R ( β ( x 0 , y 0 ) ) [ E 0 x ( x 0 , y 0 ) E 0 y ( x 0 , y 0 ) ] ,
H ( ν x , ν y ) = PSF ( x , y , z ) exp ( i · 2 π · ( ν x x + ν y y ) ) d x d y .
f ( λ ) = f d λ d λ ,
I ( λ ) = I d + I λ | λ = λ max Δ λ + 1 2 2 I λ 2 | λ = λ max ( Δ λ ) 2 .
S = 1 + 1 2 I d 2 I λ 2 | λ = λ max ( Δ λ ) 2 .

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