Holography, Fourier Optics, and Beyond Photonic Crystals: Holographic Fabrications for Weyl Points, Bound States in the Continuum, and Exceptional Points

Since the 1990s, applications of holography and Fourier optics have been significantly expanded from the spatial modulation of light propagation to the nanofabrication of superlattices. Holographic mixing of multiple beams is found to be highly compatible with unprecedented engineering of 1D, 2D, and 3D superlattices, particularly at the nanoscales. This is essential for the development of champion photonic crystals working at optical frequencies. However, these extensive efforts toward holographic photonic crystals have declined with the failure to obtain a champion photonic crystal and the rapid rise of other important classes of optical modes in the 2010s such as Weyl points, bound state in continuum (BIC), and exceptional points (EPs). To obtain photonic crystals, the symmetric modulations of the sinusoidally distributed real part of permittivity (Re(ε)), that can be considered as waves of matter from the viewpoint of Fourier optics, are sufficient. However, Weyl points, BIC, and EPs demand more complicated and advanced modulation of such as asymmetrically distributed wave of Re(ε) and the coupled Re(ε) and imaginary ε (Im(ε)). It is, therefore, important to determine whether holographic fabrications can be an efficient solution to Weyl points, BIC, and EPs. In this review, a comprehensive overview of holography, Fourier optical surface/volume gratings, and their implementations for Weyl points, BIC, and EPs is presented. Holography and Fourier optics are ready to take the next step toward Weyl points, bound states in the continuum (BIC), and exceptional points (EPs), which are collectively beyond conventional diffractive optics (e.g., photonic crystals). In this review, a comprehensive overview of holography and Fourier optics is provided and then laid out why holographic fabrications can open up a generic opportunity for Weyl points, BIC, and EPs.