Diffraction characteristics of general dielectric planar (slab) gratings and surface-relief (corrugated) gratings are reviewed. Applications to laser-beam deflection, guidance, modulation, coupling, filtering, wavefront reconstruction, and distributed feedback in the fields of acoustooptics, integrated optics, holography, and spectral analysis are discussed. An exact formulation of the grating diffraction problem without approximations (rigorous coupled-wave theory developed by the authors) is presented. The method of solution is in terms of state variables and this is presented in detail. Then, using a series of fundamental assumptions, this rigorous theory is shown to reduce to the various existing approximate theories in the appropriate limits. The effects of these fundamental assumptions in the approximate theories are quantified and discussed.

Analysis and applications of optical diffraction by gratings

Publisher Summary This chapter describes the self-imaging phenomenon and its applications. The self-imaging phenomenon requires a highly spatially coherent illumination. It disappears when the lateral dimensions of the light source are increased. When the source is made spatially periodic and is placed at the proper distance in front of the periodic structure, a fringe pattern is formed in the space behind the structure. The chapter discusses the theoretical and applicational aspects of the self-imaging phenomenon—that is, the property of the Fresnel diffraction field of some objects illuminated by a spatially coherent light beam. The applications of self-imaging are summarized in four main groups—namely, (1) image processing and synthesis, (2) technology of optical elements, (3) optical testing, and (4) optical metrology. The chapter describes the double diffraction systems using spatially incoherent illumination. The first periodic structure plays the role of a periodic source composed of a multiple of mutually incoherent slits. Depending on whether the periods of two periodic structures are equal, the Lau or the generalized Lau effect is discussed. Various applications of incoherent double-grating systems are described in the fields of optical testing, image processing, and optical metrology. After examining some cases of coherent and incoherent illumination, the general issue of spatial periodicities of optical fields and its relevance to the replication of partially coherent fields in space is discussed.

I The Self-Imaging Phenomenon and its Applications

As nanofabrication technology progresses, the emerging metasurface has offered unique opportunities for holography, such as an increased data capacity and the realization of polarization-sensitive functionality. Multicolor three-dimensional (3D) meta-hologram imaging is one of the most pursued applications for meta-hologram not yet realized. How to reduce the cross-talk among different colors in broad bandwidth designs is a critical question. On the basis of the off-axis illumination method, we develop a novel way to overcome the cross-talk limitation and achieve multicolor meta-holography with a single type of plasmonic pixel. With this method, the usable data capacity can also be improved. It not only leads to a remarkable image quality, with a signal-to-noise ratio (SNR) five times better than that of the previous meta-hologram designs, but also paves the way to new meta-hologram devices, which mark an advance in the field of meta-holography. For example, a seven-color meta-hologram can be fabricated with a color gamut 1.39 times larger than that of the red, green, and blue (RGB) design. For the first time, a full-color meta-holographic image in the 3D space is also experimentally demonstrated. Our approach to expanding the information capacity of the meta-hologram is unique, which extends broad applications in data storage, security, and authentication.

Multicolor 3D meta-holography by broadband plasmonic modulation

Binary phase elements in photoresist have been implemented which transform a uniform beam of light into an array of output light spots by means of the fractional Talbot effect. Arrays of more than 30 x 30 light spots with varying spot shapes have been achieved with compression ratios of up to 1:9.

Making an array illuminator based on the Talbot effect

Diffractive lenses have been traditionally designed with the first diffracted order. The spectral characteristics of diffractive lenses operating in higher diffracted orders differ significantly from the first-order case. Multiorder diffractive lenses offer a new degree of freedom in the design of broadband and multispectral optical systems that include diffractive optical elements. It is shown that blazing the surface-relief diffractive lens for higher diffraction orders enables the design of achromatic and apochromatic singlets. The wavelength-dependent optical transfer function and the associated Strehl ratio are derived for multiorder diffractive lenses. Experiments that illustrate lens performance in two spectral bands are described, and the results show excellent agreement with the theoretical predictions.

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Spectral properties of multiorder diffractive lenses

Special phase gratings are described by means of which the red, green, and blue color components of colored objects are generated side by side around the optical axis in the image plane of a lens. An analysis of these color separation gratings is given, and theoretical and experimental results for some grating samples are presented.

Color separation gratings.

Restoration of Faulty Images of Periodic Objects by Means of Self-Imaging

Prisms and gratings are practicable, individual optical components for many applications. However, their use often leads to an inconvenient off-axis light path in the optical setup. This can be avoided if, instead of a single prism or grating, a combination of such components is used. The well-known direct-vision prism is a combination of different prisms with a mutual compensation of the deflection

H. Dammann

Papers

Color separation gratings.

Restoration of Faulty Images of Periodic Objects by Means of Self-Imaging

From prism-prism via grating-prism to grating-grating compounds.