3.1. Introductory RemarksPhotonic bandgap (PBG) materials, more commonly known as photonic crystals, represent a class of synthetic composite optical materials in which their complex refractive index is spatially varied [54,55,56]. Most often it is alternating periodically and with large enough contrast between the segments with a low and a high real part of the complex refractive index (typical contrasts range between 1.5 and 2). The spatial periodicity of the photonic crystals for the visible wavelengths is of the order of few hundred of nanometers, the size comparable with a quarter of the operating wavelength (mesoscopic structures). The spatial variations can be along one, two, or three dimensions. Photonic crystal properties can even be variable with time (the co-called spatiotemporal photonic crystals [57]).Typically, dielectric materials are used to build photonic crystals, although metal-dielectric combinations are also met. Figure 5 illustrates the 1D, 2D, and 3D geometry of photonic crystals. The pioneer of photonic crystals rejected the opinion that 1D structures are actually photonic crystals and opined that they do not have a photonic bandgap, but actually only a bandstop, and that they should be described simply as Bragg mirrors or dielectric mirrors. The question has remained debatable since, but it appears that the majority of the scientific community nevertheless adopted the term “1D photonic crystal” in spite of dissenting opinions.Photonic crystals may be regarded as a generalization of common 1D multilayer dielectric mirrors [58] since the higher dimensionality of photonic crystals ensures either confinement of electromagnetic waves within a plane as in 2D structures or in full 3D, making them behave as real omnidirectional mirrors. In all cases (1D, 2D, or 3D), a range of frequencies appears where the propagation of light is prevented by multiple internal reflections within the structure. This is a behavior similar to what the semiconductor crystal lattice does with charge carriers where the lattice also creates a band of energies and the charge carrier propagation modes within that range are prohibited. Since that band is the well-known energy bandgap of semiconductors, its equivalent in photonic crystals has been denoted as the photonic bandgap (PBG).

There are numerous similarities and analogies between the semiconductor crystals and photonic crystals. Among other things, both exhibit defect modes, can have acceptor and donor dopants (in PBG structures these are the building blocks with either different size or different refractive index than the rest of the structure, so that they also have their own kind of “donors” and “acceptors”), exhibit surface states and surface waves, etc. Their crystal structure has its unit cells with the order of magnitude of the operating wavelength.

The methods of calculation of the relation between the PBG and the refractive index values are numerous and include both analytic and numerical ones. While the simple transfer matrix method [59] can be used for 1D photonic crystals, 2D and 3D structures are usually calculated by commercial software packages based on, e.g., Finite Element Method, Finite Difference Time Domain Method, boundary elements method, etc. (a more in-depth approach can be found in [60]. 3.3. Some Practical ApplicationsNanomembrane-based 2D photonic crystals are usable in a large number of practical applications. Among these are passive ultracompact waveguide components [64], like channel waveguides used for mostly lossless beam bending at distances comparable to the operating wavelength, i.e., vastly smaller than in conventional photonics, other kinds of optical waveguide structures with micro dimensions, various kinds of optical filters, beam splitters, multiplexers/demultiplexers, various optical couplers [65], different types or resonators electrically, mechanically, or optically tunable in real time, coupled resonator optical waveguide (CROW) [66] that may use defect cavities in the photonic crystal, dielectric microdisks, microrings or microcavities, polarization converters, passive optical limiters [67], on-chip optical true time delay lines [68], etc. Figure 6 shows top views of some examples of passive waveguide-based components in 2D photonic crystal nanomembranes.Active PBG waveguide components include various advanced light sources like ultralow threshold lasers, microlasers, VCSELs (vertical-cavity surface-emitting lasers) [69], ultrahigh efficiency LEDs, but also nonlinear frequency converters, nonlinear optical switches, etc. The use of gain media as the constitutive parts of ultrathin PBG emitters with emission control implemented through an increase of the light extraction efficiency provided another boost to this branch of applications. PBG structures are also used to enhance photocatalytic processes [70].Photonic crystals are also used a lot in conjunction with Fano-resonance enhancement. Fano resonance in nanophotonics generally is a resonant electromagnetic effect that occurs when a discrete quantum state couples with a continuum band of states through interference [71], resulting in the characteristic asymmetric line shape. This phenomenon is common in a large number of other branches of physics as well. In general nano-optics, the sharp asymmetric resonant shape is observed in absorption, transmission, and other spectral dispersions [71].Fano resonance in 2D photonic crystals has been a popular topic of research [72]. There are different Fano-resonance based 2D photonic crystals applications [73], most notably slow light devices for optical waveguide delay lines and with large dispersion enhancement [74], ultra-broadband reflectors, optical filters, nonlinear devices, light emitters and optical detectors, and various cavity-enhanced devices.

A large group of devices enabled by ultrathin photonic structures are various photodetectors, mostly those of intrinsic photonic type where the PBG width can be tailored to coincide with the bandgap of the semiconductor. Most notably, they include resonant cavity enhanced (RCE) and photonic crystal enhanced (PCE) devices, but also different types of solar cells.

The inventor of photonic crystals himself, Eli Yablonovitch, came up with the idea of photonic crystals while investigating the conditions of light trapping within the photodetector active area. He was analyzing ways to push the detector quantum efficiency closer to the fundamental performance limits, also known as the conventional limit, the ray-optics limit, the ergodic light trapping limit or the Lambertian limit. The idea was to enclose the photodetector within a cavity with omnidirectional reflection (full 3D). Such optical path enhancement was the actual goal of his seminal paper that introduced photonic crystals to the world [54].There is a body of literature dedicated to various methods of photodetector performance enhancement. An attempt to classify and systematize in detail different approaches, generally including the use of photonic crystals and nanophotonics, can be found in [75].

Photon management in a detector can be done by maximizing light concentration within the active region (which may be done through refractive and reflective concentrators, i.e., lenses or mirrors, but also diffractive structures like diffractive optical elements and holographic optical elements and finally through plasmonic light localization). The second approach is to use antireflection structures and includes interference multilayers, graded index dielectric films, diffractive structures, biomimetic structures like biomimetic moth-eye elements, random surface corrugations, subsurface or topside scatterers which in case of plasmonic nanoparticles or gratings enhancers additionally cause extreme light localizations, nanoantennas, and metamaterials (including superabsorbers). The third approach is to increase the optical path within the active region, and it includes the use of reflective structures such as backside mirrors, total internal reflection structures, radiative shields, resonant cavity enhancement (RCE), and photonic crystal enhancement (PCE).

Pan et al. designed and fabricated photodetectors based on roughened (surface-sculpted) silicon nanomembranes [76]. They demonstated significant dark current suppressions due to surface depletion and Schottky barrier modulations. A vast number of other works dedicated to this area of research have been published until now.Besides increasing the quantum efficiency enhancement of photodetectors and being building blocks for various types of resonant cavities including tailorable ones, photonic crystal nanomembranes serve as a basis for the detectors themselves as their function-enabling part. Moein et al. described a photodetector with an optically thin broadband graphene-monolayer on silicon nitride nanomembrane [77]. In their recent book chapter, Kim et al. described high-performance flexible photodetectors based on silicon, germanium, and III–V compound semiconductor nanomembranes [78]. Strain-engineered germanium-nanomembranes can be tailored to convert the indirect bandgap of Ge to a direct one and be utilized for different purposes, among others to make use of nanomembrane transferability to make germanium on silicon photodetectors [79].

Obviously, depending on the constitutive materials, the optical properties of PBG materials may be tunable by different external stimuli. For instance, as seen in the previous paragraph, the presence of external mechanical influences such as pressure, strain, and flexure will modify the properties of photonic crystals. Temperature changes or heat gradients may also influence their optical behavior, as well as absorption or adsorption of chemical or biochemical analytes. This is of importance for multitudinous sensing applications of photonic crystals.

A prominent place among them belongs to ultrasensitive biological sensing of disease biomarkers, antibiotics and similar analytes [80]. Some of these devices are based on electrochemiluminescence. The photonic crystal nanomembrane is typically used for signal amplification utilizing various strategies, most often light scattering. Xiao-Yan Wang et al. [18] used silicon dioxide photonic crystal nanomembranes as the electrochemiluminescent electrodes to selectively detect SFTSV (Severe Fever with Thrombocytopenia Syndrome Virus, also known as Huaiyangshan Banyangvirus or Dabie bandavirus). Using the scheme they proposed, the team achieved a 7-fold increase of the electrochemiluminescent intensity. The same principal author with a different team used electrochemiluminescence with their gold-filled polystyrene nanomembranes to detect tetracycline antibiotic [81]. Chemical and biological sensing using photonic crystals was considered in [82]. PBG structures containing hydrogel as sensitive material responding to pH factor, humidity and temperature changes, and chemical and biological analytes were described in [83].

Mechanic tunability of optical characteristics of photonic crystals is often used in mechanical sensing, as well as in cavity-based nanoresonator fabrication. It is also used for mechanical tuning of characteristics of different membrane-based optoelectronic devices. Nanomembrane-based 2D photonic crystals are typically both stretchable and flexible. This enables altering of their mechanical and structural properties. In this manner their optical properties are modified proportionally to the applied mechanical force.

Manjeshwar et al. [84] manufactured mechanical resonators out of 100 nm-thin freestanding GaAs nanomembranes structured as 2D photonic crystals. The resonators were intended for optomechanical microcavities on chip and for multi-element cavity optomechanical devices. Lu et al. [85] fabricated photonic crystal nanocavities from periodically stacked 1D nanorods embedded in a polydimethylsiloxane membrane. Their structure served as a sensor for strain analysis, since it can recognize different planar strains, including their type, direction, and amplitude. Chen et al. [86] showed through finite element simulations that strain in photonic crystals can induce photonic topological insulator states, thus pointing towards possible future uses in in quantum computing. Zhang et al. reviewed various applications of mechanochromic photonic crystals [87]. They also considered biomimetic inspiration for tuning of structural coloring of such nanophotonic composites. They observed applicability of mechanochromic PBG structures in such diverse fields as civil engineering (visual observation of defects and structural damages through strain-induced coloring), household appliances, biomedical sensors, fingerprint sensors, and multitudinous applications where a color-changing miniature strain sensor can be of use. Earlier, Rindorf and Bang [88] investigated photonic crystal fiber grating sensors in various sensing application including temperature measurement, refractometry, biological sensing, and strain measurement. Mechanically reconfigurable membrane-based photonic crystals based on shape memory copolymers were also proposed [89]. Due to their use of photonic crystals and the choice of the materials, their complete programming and recovery processes are done at room temperature, contrary to the traditional shape memory materials which are highly thermoresponsive and require the application of heat.

There are numerous other applications that make use of stretchability and flexibility of photonic crystal membranes. Many of them draw their inspiration from nature.