This paper examines the binary Fresnel zone plate (FZP) lens frequency-harmonic and space-resolution focusing, and its application as a FZP lens antenna. A microwave FZP lens antenna (FZPA) radiates both at design (90 GHz) and terahertz (THz) odd harmonic frequencies. Frequency and space domain antenna operation are studied analytically by use of the vector diffraction integral applied to a realistic printed FZPA. It is found that all harmonic gain peaks are roughly identical in form, bandwidth, and top values. At each harmonic frequency, the FZPA has a beamwidth that closely follows the Rayleigh resolution criterion. If the lens/antenna resolution is of prime importance and the small aperture efficiency is a secondary problem the microwave-design FZP lens antenna can be of great use at much higher terahertz frequencies. Important feature of the microwave FZP lens is its broader-zone construction compared to the equal in resolution terahertz-design FZP lens. Thus, unique and expensive microtechnology for the microwave FZP lens fabrication is not required. High-order harmonic operation of the FZP lens or lens antenna could find space resolution and frequency filtering applications in the terahertz and optical metrology, imaging tomography, short-range communications, spectral analysis, synchrotron facilities, and so on.

During the last two decades, a rapid exploration of terahertz waves is taking place [

If the high lens resolution and small thickness are of prime importance, the binary FZP lens consisting of free-standing or printed skinny metal rings would be preferable. Such lenses have found a lot of applications in the areas of 3D imaging tomography, electron microscopy, sensing and security systems, and synchrotron radiation facilities for beam focusing [

Main objective of this paper is to clarify the harmonic action of binary FZP lens and antenna, and to examine them numerically in frequency and space domains with for grounding hypothetically their future employment as multiband focusing and filtering devices.

Section

Section

Section

The paper is completed by a general conclusion, acknowledgement, and list of references.

In general, a FZP lens centered in the origin of Cartesian coordinate system is transforming an axially incident spherical wave front of radius

Figure

Plane-wave illuminated binary negative Fresnel zone plate lens.

The normally illuminated by a plane wave planar FZP conmprises concentric half-wave zones with zone radii

In optics the following approximation of (

By definition, the so-called Rayleigh resolution criterion for the resolving power of a circular aperture of diameter

From (

In the case of a binary FZP, however, the constant value 1.22 of

Values of

10 | 20 | 30 | 40 | 50 | ||

pFZP | 1.275 | 1.245 | 1.235 | 1.230 | 1.227 | |

nFZP | 1.125 | 1.165 | 1.185 | 1.195 | 1.200 |

From Table

The resolving angle

The ending zone width

Next, we clarify the multiple frequency-domain behavior of the binary FZP lens illuminated by a plane wave. This phenomenon is analogious to the axial multiple focusing of the same lens. Both phenomena are linked by (

Next, it is clarified that the multifrequency phenomenon taking as an example a binary FZP lens of four Fresnel (or half-wave) zones designed for a focal length

The maintenance of same aperture diameter

Harmonic-action FZP lens at (a) 3rd harmonic frequency

Similarly, for an illuminating plane wave with a frequency

The field intensities provided at the primary focal point by all real open zones corresponding to

Taking into account the basic lens/antenna relation between the focusing gain and radiating aperture

Consider the geometry of binary FZP lens antenna consisting of feed-horn and positive binary FZP of concentric metal rings (in grey) obstructing the even zones (Figure

Radiation geometry of FZP lens antenna.

The antenna radiation characteristics have been computed by use of the vector Kirchhoff’s diffraction integral solved explicitly for the axially symmetric binary FZP lens antenna [

The feed-horn field is approximated theoretically by the broadly used aperture directive gain function

The microwave FZP lens antenna design studied in this paper is marked by the acronym FZPA-M-10, which stands for FZP Antenna designed at the Microwave frequency

Binary FZP lens of FZPA-M-10 designed at microwave frequency of 90 GHz with all even zones covered by thin metal (in grey) printed on dielectric substrate (in light brown).

The FZP lens is made as a printed construction with metal rings of thickness

In the studied FZP lens structure, the Teflon substrate plate is 1 mm thick, while the metal rings have a width of 0.1 mm and are supposed infinitely conductive.

The outmost (10th) zone is obstructed by a metal ring of width

Frequency analysis of the FZP lens antenna is based on the variation of far-field directive gain versus frequency in the normal direction

The FZPA-M-10 has been examined numerically in the frequency band 50–1550 GHz. Figure

Frequency-domain harmonic action of binary FZP antenna: directive gain versus frequency.

The multiband FZP antenna is considered as a multitude of individual harmonic-frequency antennas radiating all or each at a time. The analysis is made on the assumption that each individual harmonic antenna is fed by a feed located at the same focal point

Practically, the harmonic-frequency feeds could be also located off axis on a circular arc, which is the scan curve of the FZP lens antenna [

The essential frequency-domain parameters of the antenna FZPA-M-10 are listed in Table

Frequency-domain radiation parameters of FZP lens antennas: microwave (M) and terahertz (T) designs.

FZP antenna | |||||

(GHz) | (dBi) | (GHz) | (%) | (%) | |

FZPA-M-10 | 90 | 28.9 | 18.4 | 9.63 | |

( | 270 | 28.6 | 6.1 | 1.07 | |

1350 | 28.5 | 1.22 | 0.05 | ||

FZPA-T-150 | |||||

( | 1350 | 52 | 16.3 | 1.20 | 7.92 |

Here by a space-domain antenna study, the FZP lens radiation pattern analysis at the design and harmonic frequencies is understood. Figure

Radiation characteristics of FZPA-M-10 versus angle

The half-power (or −3 dB) antenna beamwidth

For the FZP design wavelength

Thus, for a known design FZP resolving angle

Similarly, for the

Table

Theoretical beamwidth matches very well the Rayleigh resolution criterion for all working frequencies. For example, at

At all microwave and terahertz harmonics, the studied FZP lens antenna preserves roughly constant the peak gain values (

Radiation pattern parameters of FZP lens antennas: microwave (M) and terahertz (T) designs.

FZP antenna | ||||||

(GHz) | (deg) | (deg) | ( | (dB) | (dB) | |

FZPA-M-10 | 90 | 2.4 | 2.43 | 2835 | ||

( | 270 | 0.78 | 0.81 | 945 | 11 | −25 |

1350 | 0.15 | 0.16 | 189 | |||

FZPA-T-150 | ||||||

( | 1350 | 0.15 | 0.155 | 226 | 22 | −56 |

The quick drop of the FZP lens/antenna focusing/radiation efficiency with the rise of harmonic frequency deserves more discussions. The aperture antenna radiation efficiency less than 40–50% is not satisfactory, and less than 10–20% is considered small. In principle, the binary FZP lens/antenna belongs to the latter efficiency category because of noneffective amplitude and phase aperture utilization. By exploiting a proper phase correction of the aperture field like in the grooved dielectric or multidielectric FZP lenses, for instance, the corresponding FZP lens antenna easy reaches at its design (first-order) frequency the radiation efficiency of the classical aperture antennas (horn, parabolic-reflector, etc.), though in a rather smaller frequency band.

The low efficiency might be considered as a price for the unique features of the binary FZP lens or antenna: precise harmonic filtering and resolution characteristics that the usual directive-aperture antennas do not possess. Especially valuable is the big potential resolution at the much higher harmonic frequencies as it is discussed above. Similar “give and take” is met in many natural phenomena, and also in many other radioelectronic devices. Very appropriate example with a similar to the FZP multifrequency action is the harmonic-frequency multiplier. In particular, a big power-efficiency loss is produced in the process of harmonic-frequency multiplication of microwave frequencies to much higher terahertz frequencies. The output of the solid-state terahertz generators based on the frequency multiplication drops with harmonic frequency increase as about

It is clear that at THz harmonic frequencies, the microwave FZP lens/antenna aperture is not utilized efficiently for a focusing or radiation. Such low aperture radiation efficiency, however, is also typical for all planar frequency-independent antennas like the Archimedean and equiangular. For example, the Archimedean spiral antenna, which can radiate in a frequency band greater than

Next are described terahertz FZP lens and antenna, designed at the terahertz frequency of 1350 GHz (Figure

Terahertz-design FZP lens of FZPA-T-150 lens antenna designed at 1350 GHz.

The computed copolar and cross-polar radiation patterns of terahertz-design FZPA-T-150 versus angle

Radiation patterns of terahertz-design FZPA-T-150 versus angle

At the same working terahertz frequency of 1350 GHz, both antennas, the microwave antenna FZPA-M-10 and terahertz antenna FZPA-T-150, have the following radiation parameters:

similar absolute and relative bandwidths of about 16.5 GHz (absolute) and 1.2% (relative), respectively;

comparable radiation pattern beamwidths (or angular resolutions) of about 0.15 degrees;

Naturally, the terahertz-design antenna FZPA-T-150 has a much higher gain and aperture efficiency, but a similar radiation to those of FZPA-M-10 at its design frequency of 90 GHz. At FZPA-T-150 harmonic frequencies like 4.05 THz (3rd terahertz harmonic) and 20.25 THz (15th harmonic, located in the low-infrared band), the aperture utilization efficiency of the FZPA-T-150 will again become low, about 1% and 0.05%, correspondingly.

With regards to the structural, technological, and other lens qualities, the contrast between the microwave- and terahertz-design FZP lenses shows:

FZP lens used in the FZPA-T-150 antenna has very narrow ending zones. As was pointed out above, the last or the 150th zone is only 185

microwave-design FZP lens in the FZPA-M-10 antenna working at high-terahertz harmonics has a much simpler construction and can be easily fabricated, while the terahertz-design FZP lens needs sophisticated, precise, and costly microtechnology for its production;

narrow-zone terahertz-design FZP lenses are more fragile electrically and might not withstand high-energy illumination [

It is fascinating that the big microwave-design antenna FZPA-M-10 could operate at frequency harmonics much higher than the terahertz frequencies or in the infrared band, for instance, for which the antenna aperture efficiency will be really extremely low (at about

Instead, the terahertz lens/antenna FZPA-T-150 could be chosen for reaching the low infrared range. As is pointed out above, its 15th harmonic is the infrared frequency of 20250 GHz (or 20.25 THz) that corresponds to wavelength of 14.81

The study exposes for the first time a number of intriguing features related to the binary microwave FZP lens and antenna operating at harmonic terahertz frequencies. The harmonic gain versus frequency pattern shows a strict appearance of the peak gains in proportion to the frequency harmonic sequence

The high-order harmonic operation of the FZP lens and antenna could find space resolution and frequency filtering applications in terahertz and optical metrology, imaging tomography, spectral analysis, short-range communications, synchrotron radiation and focusing facilities, and radio astronomy, among others

The author acknowledges the Support received from the Chilean Science Agency CONICYT within the Fondecyt Project 1095012/2009 and Anillos ACT-53/2010 Project.