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Zone Plates

Acronym: FZP

Definition: an optical device for focusing light (or other electromagnetic radiation) based on diffraction

Alternative terms: Fresnel zone plates, operation principle, diffraction, chromatic aberrations

German: Zonenplatte

Category: general optics

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URL: https://www.rp-photonics.com/zone_plates.html

A zone plate is an optical device which can be used for focusing light. In contrast to a lens, it is based on diffraction rather than on refraction. It is usually flat (and can thus be considered as an example for flat optics) and exhibits a radially varying transmissivity:

  • The most simply produced (and therefore most frequently used) zone plates are binary zone plates, where the transmissivity at each location can only be either 0 (fully opaque) or some constant value – possibly 1 (fully transparent). For example, one may use a reflecting metal film on a glass surface, which is etched away at suitable positions, using a lithographic technique.
  • There are also zone plates with a gradually varying transmissivity (continuous zone plates) – in particular, sinusoidal zone plates.

Zone plates may also be used in reflection rather than in transmission, e.g. when they are realized with reflecting metal films.

Zone plates are sometimes called Fresnel zone plates (FZP), emphasizing the important contributions of Augustin-Jean Fresnel [1]. Another term is diffractive lenses; zone plates can to some extent be used like lenses, even though their operation principle is completely different.

Zone plates can be regarded as a special kind of diffraction gratings, where one does not have straight grating lines, but rather circular structures.

Example for a Fresnel Lens Design

Considering the simple case where incident light has flat wavefronts (example: a collimated Gaussian beam), one can design a binary zone plate quite simply: for a given focal length, one can consider the optical phase of light reaching the intended beam focus from a radial position r at the zone plate. One chooses full transmission if that optical phase change (modulo 2π) is between 0 and π, for example, and zero transmission otherwise. Essentially, one blocks all those light components which would have “wrong” phase values, thus reducing the total optical intensity. It is also possible to use a different range of phase values, e.g. from π/2 to +π/2. For good performance, a substantial number of rings should be covered by the input beam profile.

Zone plate designs can also be adjusted to other focusing conditions, e.g. for incident diverging beams.

Figure 1 shows the structure of a zone plate designed for 100 mm focal length for an optical wavelength of 632.8 nm (for light from a helium–neon laser).

zone plate
Figure 1: Structure of a Fresnel zone plate.

Figure 2 shows how the beam intensity profile evolves when a Gaussian input beam (w0 = 0.5 mm) is used. One sees the intended beam focus in the middle (for z = f), and in addition there are intensity maxima at z = f / 3, z = f / 5, z = f / 7 etc. That feature is observed for binary zone plates, but is avoided for sinusoidal zone plates.

zone plate
Figure 2: Evolution of intensity profile for focusing a Gaussian beam with a Fresnel zone plate. The simulation has been done with the RP Fiber Power software.

Zone plates exhibit strong chromatic aberrations – as many other diffractive optical elements do. Figure 3 shows an example for that.

zone plate
Figure 3: Same as Figure 2, but with a 20% longer optical wavelength. The beam focus appears at an earlier location, and has a much wider diameter.

Applications of Zone Plates

For focusing visible and infrared light, one usually prefers ordinary lenses, because they offer better performance in various respects. However, their operation principle is hard to utilize in some extreme spectral regions, where most materials exhibit strong absorption. For example, lenses for extreme UV, X-rays and other short-wavelength synchrotron radiation are hard to realize, and Fresnel zone plates can then be a good solution. They may be used not only for focusing radiation, but also for imaging purposes.

There are modified designs of zone plates, e.g. the Zernike zone plate, where a Zernike phase filter is integrated. Such devices are used for phase contrast imaging.

For some applications, one may profit from the possible very flat design of a zone plate. However, there are other types of flat optics realized with photonic metasurfaces.

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Bibliography

[1]A. J. Fresnel, “Calcul de l'intensité de la lumière au centre de l'ombre d'un ecran et d'une ouverture circulaires eclairés par un point radieux”, in: Œuvres Complètes d'Augustin Fresnel, Imprimerie Impériale, Paris (1866)
[2]K. Miyamoto, “The phase Fresnel lens”, J. Opt. Soc. Am. 51 (1), 17 (1961), doi:10.1364/JOSA.51.000017
[3]M. Young, “Zone plates and their aberrations”, J. Opt. Soc. Am. 62 (8), 972 (1972), doi:10.1364/JOSA.62.000972
[4]J. Kirz, “Phase zone plates for x rays and the extreme uv”, J. Opt. Soc. Am. 64 (3), 301 (1974), doi:10.1364/JOSA.64.000301

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See also: diffraction, diffractive optics, diffraction gratings, lenses, flat optics
and other articles in the category general optics

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