Electromagnetic Materials: Shield, Meta-Surface Absorber, and Clock

1.1 Metamaterials - The novel approach

At the macroscopic level, the complex behaviors of individual atoms in a material play a crucial role in its EM properties. To understand how these atoms align and bond to form the material, we need to consider how thermodynamic laws influence their interactions and arrangements. When analyzing how materials interact with EM radiation, it is essential to focus on the averaged responses of the material over time and space. This is particularly important when the wavelength of a wave is significantly greater than the distance between the atoms. Even if the intricate details of atomic interactions are not directly observed, this approach allows for a comprehensive understanding of the behavior of the material. This classic electrodynamic method was discovered long before the fundamental atomic structure of matter was understood. In this approach, we treat the material as a homogeneous medium, defined by its permeability (μ) and permittivity (ε). These fundamental properties play a crucial role in determining how the material interacts with external magnetic and electric fields. The theory of homogenization is particularly effective across a wide range of wavelengths within the EM spectrum. However, as we delve into scales that are close to atomic dimensions, the limitations of this method become apparent. At these minute scales, the arrangement and behavior of the matter are heavily influenced by thermodynamic principles, reflecting the complex interplay of forces that govern matter on a scale only slightly larger than the atomic level. In recent years, there has been a burgeoning interest in exploring the EM characteristics of synthetic materials containing “atom-like” inclusions designed to interact with incoming waves in unconventional manners, resulting in unattainable properties with natural substances. The term ‘Metamaterial’ was first coined by Rodger M. Walser in 1999. Metamaterials are macroscopic composites made of periodic or non-periodic structures, and their functionality is determined by both the cellular architecture and chemical composition [4].

1.2 Why meta?

The question comes, “Why Meta?”; the word ‘Meta’ has a Greek origin meaning ‘beyond’ or ‘after.’ So obviously, MMs are materials that show characteristics beyond natural materials. They are made with capabilities that are extraordinary and are fed with abilities to manipulate waves that are not possible with natural materials from the periodic table [5]. As we know, in the domain of materials science, pure substances are characterized by a homogeneous chemical composition, such as metals or semiconductors, whereas mixtures are assemblies of substances that maintain their individual properties. However, metamaterials blur this categorization [6], as they are frequently engineered as structured amalgamations of constituents (e.g., metals and dielectrics) that are combined to yield emergent properties. Now, when considering the metamaterial as an effective medium, it becomes necessary for the size of the cells to be either smaller than or equal to the wavelength of the incident radiation to exhibit the required characteristics, and that refers to its sub-wavelength features [7], where the sub-wavelength features denote the structural components of a metamaterial that are significantly smaller than the wavelength of the EM wave that interacts with the medium. This condition guarantees that the EM wave interprets the metamaterial as a homogeneous medium rather than as an assemblage of discrete elements [6]. If ‘a’ is the lattice and ‘λ’ is the wavelength of the incoming radiation, it must satisfy the condition that,

This helps in homogenization and tuning material response. Here, the equivalence of meta-atomic [8] structures with specific geometry and design can exhibit the same EM properties that are desired. The design flexibility in shape, size, and materials results in achieving emergent characteristics such as negative refractive index, unusual permeability, and permittivity values [9]. These materials have remarkable optical properties, like absorption, shielding, cloaking, and negative refraction.

1.3 The history behind the left-handed materials

The term “Meta” within the realm of a research subject concerning invisibility and “metamaterials” was initially brought into prominence by scholars in EM theory and optical engineering. The emergence of this concept gained widespread acknowledgment following the release of two seminal papers in 2006. The first one introduced to Ref. [10] entails directing EM waves around an entity to render it imperceptible. The second presented an alternative strategy employing conformal mapping [11] techniques to achieve invisibility using metamaterials. These materials are characterized by a dual negative index, which makes them left-handed materials (LHM) in the ε – μ domain [12] (the four quadrants of isotropic materials including double negative (DNG), Double positive (DPS), Epsilon negative (ENG), and μ-negative materials (MNG) [5]) a challenging feat to replicate in nature. Consequently, the approach involves artificially engineering these materials to possess the desired properties, but how was this done? The breakthrough in achieving this feat dates back to 1996 and 1999 with the invention of the split ring resonator (SRR) composed of both electric [13] and magnetic plasma [14]. Thus, it was understood that individual resonant structures of different sizes (wavelength range), shapes, designs, and patterns constitute bulk 3D MMs of desired behavior. For DNG materials, n also becomes negative. If the real part of ε and μ is negative, the refractive index will be positive as n = με. However, energy loss leads to an imaginary component in both permittivity and permeability, so that the real part of n in the complex plane is negative. For materials with n < 0, the wave vector (k) and Poynting vector point in opposite directions, while the parallel component of the wave vector remains the same (Figure 2) [15].

In conventional materials with a positive n, the electric field (E), magnetic field (H), and k form a right-handed coordinate system. On the other hand, − n materials form a left-handed coordinate system. This chapter delves into the intriguing applications of metamaterials, a class of engineered materials with unique properties. We will begin by exploring electromagnetic (EM) shielding, which effectively protects sensitive electronic equipment from interference. Next, we will examine the role of metamaterial absorbers, which are designed to capture and dissipate electromagnetic waves across a range of frequencies with remarkable efficiency. Finally, we will discuss cloaking technologies, which aim to render objects invisible to detection by manipulating how light and other waves interact with them. Although all these applications leverage the principles of metamaterials, the methodologies employed to achieve each result are distinctly varied and fascinating.

2.1 EMI shielding

EMI shielding refers to the practice of enclosing electronic components or systems with materials designed to block external EMI. EMI can disrupt or degrade the functionality of sensitive electronic devices, posing significant challenges in fields ranging from telecommunications to medical devices. The early twentieth century conductive enclosures meant to diminish radio frequency interference (RFI) in communication systems. Conductive metals such as copper and aluminum were used as the early shielding materials for their highly conductive features and ease of fabrication [17]. In modern shielding strategies, some combinations of conductive coatings, metal enclosures, ferrite beads, along with the latest materials to attenuate conductive and radiative coupling routes, are employed within EMI control strategies. These methods have been known to be a major part of the communications, aerospace, automotive, and consumer electronics industries, where integrity of the signal is key, and their understanding of EMI in both its modalities helps engineers design systems more resistant to EM disturbances. Materials such as composite and other non-metallic shielding solutions would provide better performance in certain applications. Carbon-based polymer and ferrite materials emerged as alternatives to metal, which are excellent conductors and can reflect or absorb EMI when employed as EMI shield.

There is rapid increase in the development of shielding standards; the IEC and FCC recently adopted standards detailing the parameters for shielding effectiveness (SE) and compliance benchmarks for different industries. Modern regulations impose a high degree of constraints, in addition to shielding efficiency, strong emphasis on the environmental aspects at large, such as recyclability, and diminished EM pollution [18].

2.2 Mechanism of shielding

The major mechanisms of shielding from EMI include absorption, reflection, and multiple reflections. Absorption occurs when EM waves penetrate a shielding material and dissipate some of their energy as heat through resistive and dielectric losses within the material [19]. This mechanism is very effective for materials with high electrical conductivity and high magnetic permeability, such as steel and nickel. Reflection, on the other hand, is charged up surfaces generating opposing currents in response to the incident EM wave, resulting in wave reflection. This mechanism has a very strong influence on the electrical and magnetic values of the shielding material and the frequency of incoming waves. Also, there is a possibility of multiple reflections whereby waves will bounce numerous times internally within the thin, porous layers, leading to cumulative attenuation in the propagation of EM field energy. Nevertheless, performance specifics of the EM shielding are dependent upon materials’ properties: conduction (σ), permeability (μ), and permittivity (ε). For example, copper materials are known for high conductivity and hence great reflection from high-frequency electromagnetic fields; mu-metal, Meta surfaces afford strong shielding inserts against lower-frequency magnetism [20].

2.3 Shielding effectiveness (SE)

SE describes a material’s capability to attenuate or block EM waves, using decibels (dB) as units. It incorporates three core components, which include reflection (R), absorption (A), and multiple reflections (M). The total shielding effectiveness is given by:

Reflection loss (R) is due to the impedance mismatch created between the incident waves and the shielding material. When the EM waves impinge on a medium of impedance dissimilar to that of free space (Z₀ ≈ 377 Ω), some of the energy will reflect back. The reflection loss can be calculated using the expression:

Where Z_S is the impedance of the shielding material defined as:

Here, μ is the permeability, while σ represents the electrical conductivity of the material. The higher the mismatch in impedances, the higher the reflections [21].

Absorption loss (A) occurs when EM wave energy is converted to heat as it travels through a shielding material owing to resistive and dielectric losses. The absorption loss is proportional to the material’s thickness (t) and the wave penetration depth as described by the skin-depth (δ), which signifies how deep a wave can penetrate a conductor before it attenuates to 1/e of its initial amplitude shown in Figure 3. The skin depth is given by,

Here, ω is the angular frequency of the wave. It is because of high absorption loss with reduced skin depth that high-conductivity and permeability of materials like copper or steel are particularly effective at shielding. The absorption is given as:

It thus shows that thicker materials give larger absorption loss (A). With increase in frequency, the skin depth decreases, thereby causing current to be made to flow closer to the surface of the shielding material.

This ensures that high frequencies are prevented from getting more access to the shielding material as much lower thickness is required to prevent them, and thicker sheltering systems are employed for low frequencies or the deployment of more permeable shielding alloys. Multiple reflections (M) are, however, of lesser importance and contribute to attenuation where multilayered, porous, or granular materials cause EM waves to bounce internally multiple times [22].

2.4 Theoretical foundation of shielding

The behavior of EM waves in shielding materials is regulated by Maxwell’s equations, which explain the relationship between electric (E) and magnetic (H) fields. For time-varying fields, the equations become:

Where B= μH and D = εB; relate magnetic and electric fields to material properties, including permeability (μ) and permittivity (ε). Materials of high conductivity (ε) are excellent reflectors and are very effective against high-frequency waves. On the other hand, materials of high permeability (μ), such as mu-metal, are more effective in low-frequency magnetic field shielding [23].

Microwave-absorbing materials are noble and of utmost consideration in radar stealth technologies, communication system protection, and electromagnetic pollution control. Their capacity to convert energy of electromagnetic waves into heat or dissipate it as dielectric or magnetic losses turns them into essential materials considering worldwide engineering applications. Mathematically understood, the Maxwell-Wagner effect is related to the complex permittivity (ε*) of a material, any material that would possess energy storage and loss capabilities. With respect to this, it can be expressed as

where ε′ is the real part representing energy storage capacity, and ε′′ is the imaginary part associated with dielectric losses. This interfacial polarization is accordingly believed to increase the loss factor (ε′′) and consequently enhances microwave absorption.

Within the limits of effective medium theories, such as Maxwell-Garnett and Bruggeman models, explanations of the mechanism predicting the composite permittivity fix the level of interfacial polarization. These explained how the respective dielectric properties of their components determine the overall behavior of heterogeneous materials. By regulating the distribution and concentration of conductive fillers, interfacial polarization effects can be enhanced in microwave absorption [23, 24]. The combination of porous architecture, conductive nanostructures, and dielectric matrices has been paramount to the development of next-generation materials for telecommunications, defense, and electronics applications.

2.5 Materials being used for EMI shielding

Graphene and its derivatives—RGO genre—are gradually being looked at with favor for EMI shielding owing to their excellent conductivity and extremely high surface-to-volume ratio. Wave reflection can significantly take place because of graphene being an excellent conductor, while fine, thin, and flexible sheets provide lightweight protection for shielding. Combined with SF and PMMA, the RGO has shown to make a potent character in microwave absorbers as developed by Acharya et al. Subsequently, this produced a conductive network providing both dielectric and magnetic loss mechanisms. The optimized composite with 9 wt% RGO and 1 wt% SF offered absorption efficiencies exceeding 99% in the X-band (8–12 GHz) through magneto-dielectric coupling [24]. The Maxwell-Wagner effect plays a critical role in the absorption of microwaves by considering interfacial polarization in heterogeneous dielectric materials. This appears when an alternating EM field encounters a composite matured by components having different electrical properties (i.e., different σ and ϵ). When electromagnetic waves are penetrating a composite medium either thick or thin, there is a charge build-up occurring at the interfaces of materials with conductors and insulators as they do not instantaneously respond to the external field, which significantly varies with time. Due to slow motion of the charge, this relaxes fast enough to permit interaction with the quick field changing, which gives rise to localized polarization. This charge polarization dissipates energy from the incident wave, thus adding to the microwave absorption efficiency of such materials, which is much augmented in materials combining conducting nano supports-such as CNTs, MXene, and graphene-with dielectric matrices such as polymers, aerogels, or nanocellulose, as shown in Figure 4. This results in innumerable interfaces where charge builds up and realigns via microwaves. Nanocarbon-structured aerogels combined with CNTs showed far superior absorption power by capturing and dissipating EM waves because of the additional contributions from polarization effects [25].

This interfacial polarization enables attenuation of the energy and dipole formation to further hamper the propagation of an electromagnetic wave. The composites built on this polarizing mechanism derive reinforcement through synergistic interfacial interaction from conducting fillers into insulating matrices. The MXene-polymer composites indicated innovations in dielectric properties, essentially having complementary needs for interfacial charge storage and dissipation. In that regard, Mendoza-Sánchez et al. cited that the performances would be phenomenal with harnessing the maximization of the parameter relating to texture and chemistry-based assemblies for otherwise crystallization in nano-dimensional fortified crystals. Its dispersed phase lengthened the path for microwave propagation through enhanced interfacial zones because of the porous architecture of high-open-cell anti-microbial advanced materials. They also make a significant contribution toward the scattering processes, which build up localized charges at interfaces [26]. Zhou et al. demonstrated that well-connected, dense sheet-like networks from carbon aerogels showed excellent absorption capabilities working at X-band frequencies due to their interfacial polarization capabilities [27].

Carbon nanomaterials, such as carbon black, multi-walled carbon nanotubes (MWCNTs), graphene, and graphene nanoribbons (GNRs), have also demonstrated their efficiency for EMI shielding. Tripathi et al. studied the absorption of microwave-perfect MWCNT and carbon black-reinforced lightweight polyurethane (PU) matrix nanocomposites. The optimized sample with a particular content of 75 mg MWCNT and 250 mg carbon black per gram of PU demonstrated a peak reflection loss of 16.14 dB at 11.92 GHz with about 90% absorption over the 11.03–13.00 GHz frequency range [28]. Yadav et al. examined the effects of carbon black-based composites containing cobalt and MoS₂. At a thickness of 2.5 mm, the incorporation of such materials allowed the arrangements to achieve a shielding efficacy of over 97% at 14 GHz with a 7.7 GHz absorption bandwidth. Performance absorption was enhanced by asymmetric polarization and magneto-dielectric coupling processes. This work reports high absorption performance because of the synergistic effect of conductive filler enhancement of the complex permittivity of the material, allowing for enhanced wave attenuation and the effective coupling mechanism between the magnetic and dielectric losses, which is crucial for broad microwave absorption [29]. The composite presented roughly 40 dB shielding effectiveness, reflecting more than 95% relative to the incoming EM wave. The work of Alegaonkar et al. pointed to edge effects of the GNRs, which, coupled with their ability to form conductively connecting clusters within the matrix, add to their performance shall be flashed into a braze by the conductively connecting clusters inside the matrix. GNRs increased the matrix’s dielectric and conductive properties, as well as the efficiency of microwave absorption. The polyurethanes-composite incorporated with nanocarbons showed improved absorption owing to strong interfacial interactions and multiple scattering mechanisms. Using hierarchical structures into a composite allowed one to trap electromagnetic waves by extending the path of its propagation toward relaxation into dielectric and conductivity losses. The underlying mechanisms that govern the microwave absorption processes in these nanocomposite systems are of a complex nature. Dielectric losses due to phenomena, such as dipole and interfacial polarization, are vital for energy dissipation. Besides, magnetic loss mechanisms due to natural and exchange resonance give up their contribution to absorption once magnetic inclusions occur, for instance, with cobalt nanoparticles. Eddy current losses, due to circular current movement within ferromagnetic materials, give additional channels for heat dissipation. The losses due to conduction are another major aspect of microwave absorption [30].

Graphene nanoribbons are another potential option for EM shielding owing to their architecture and larger aspect ratios. Joshi et al. synthesized a hybrid composite consisting of GNRs, polyaniline (PANI), and epoxy resin, showing a shielding effectiveness greater at X-band. Materials such as carbon black and MWCNTs organize themselves into conductive paths through which EM energy can be directly converted to heat via the motion of electrons. Photothermal conversion properties of materials like MXenes allow this to be much more pronounced and would be extremely beneficial for broadband absorption [31]. Added to this is the hierarchical porous structure, such as that found in nanocarbon aerogels and composites, which enables multiple scattering of electromagnetic waves. Providing an extended path for wave propagation enhances absorption efficiency by capturing and distributing wave energy. Analysis of EMI shielding characteristics of hybrid composites manufactured using a large number of polymer hosts by incorporating a variety of fillers such as graphene, graphene derivatives, magnetic nanoparticles, conductive polymers to obtain shield with optimal efficiency and payload has been reported extensively. Between absorption efficiency and density, this question remains largely unanswered; however, derivatives and other modalities comes off as very promising in its scope of application range covering domains from stealth technologies to defense systems and devices of commercial electronics.

3.1 Metasurface as EM absorber

The modern world is profoundly reliant on a vast array of technologies that harness EM radiation, a fundamental force of nature that underpins many aspects of our daily lives. Pioneering physicist James Clerk Maxwell made groundbreaking contributions to the study of electromagnetism in the nineteenth century, laying the groundwork for numerous innovations that have transformed modern society. His work led to the creation of radio, television, wireless communication, global navigation, radar systems, and other technologies that support our rapidly evolving civilization [35]. One important aspect of aeronautical engineering is EM absorption, which plays a crucial role in stealth technology. The goal is to create a thin, lightweight material that effectively absorbs a wide range of frequencies. When EM energy from radar is absorbed by this material, the amount of energy reflected back decreases. As a result, an aircraft can become less detectable by radar by utilizing materials that are more effective at absorbing EM waves. Microwave absorbers are highly sought after because of their applications in both the military and civilian sectors. In the defense industry, these absorbers serve covert purposes, such as reducing radar cross-section (RCS) and providing protection against microwave radiation. A specific area within electronic warfare countermeasures, known as “stealth technology,” employs various techniques to make military systems such as tanks, battleships, missiles, and aircraft less detectable, or even invisible, to enemy radar. To reduce the RCS of an object, its external features can be shaped to minimize the backscattering of EM waves toward the radar source. Additionally, coating the target surface with radar-absorbing materials can also lower the RCS [36]. The increasing use of electronic devices such as computer local area networks, ovens, palmtops, medical equipment, Wi-Fi systems, and satellite communications has led to a greater focus on microwave absorbers in the civil sector. These devices generate more EM noise each day, which can result in cross-talk and contribute to environmental pollution from microwave radiation. To address these issues, EM compatibility (EMC) and the use of microwave absorbers are essential [37].

3.2 Progress in EM wave absorber

All incident electromagnetic waves, regardless of their frequency, polarization, or direction, can be absorbed by a perfect wave absorber. This type of absorber does not produce any reflected waves. However, a truly perfect EM wave absorber does not exist in reality. As a result, the effectiveness of material that absorbs EM waves is evaluated based on predetermined acceptable values for reflection coefficients. Typically, reflection coefficients of −20 dB or less are used as standards, while for applications requiring high performance, a coefficient of −30 dB or less is expected. A reflection coefficient of −20 dB indicates that the wave absorber absorbs 99% of the incident electromagnetic wave energy, while −30 dB indicates 99.9% [38].

Due to the high demand for wave absorbers in military applications, research began during World War II. Two different kinds of absorbers were architected as part of the German Schornsteinfeger Project and were mounted on the periscope and snorkel of a submarine to help conceal radar signals [39]. One of them was made from a material called Wesch, which consists of a rubber sheet infused with carbonyl iron. The second type, known as the Jaumann absorber, was created by alternating layers of dielectric material and a resistance sheet [40]. Additionally, the Salisbury screen absorber has been proposed [41]. The structure of this resonant-type wave absorber was made up of a resistance sheet that had a resistivity of 377 Ω and was positioned λ/4 from the rear metal plate. Figure 5 shows the design of the proposed absorber.

In the realm of metamaterials, specific frequency bands have been deliberately targeted in the design of conductive absorbers [43]. However, the pursuit of wideband or broadband absorption can impose limitations on the selectivity of these frequency bands. Numerous absorbers have been developed that enhance the bandwidth of absorption, including innovative designs such as resistive sheets and lumped resistors. While these solutions can significantly improve performance, incorporating many lumped resistors often leads to increased manufacturing costs and adds complexity to the production process [44]. An intriguing alternative to traditional methods is the use of resistive ink, which can be applied to dielectric surfaces to achieve broad absorption bands. Although resistive paint tends to be more cost-effective, its successful application demands precise control over a uniformly thick dielectric base. Fortunately, modern processing techniques like screen printing and economical liquid-jet printing make it easier to achieve this precision, ensuring that the resistive ink is evenly distributed for optimal performance [45, 46, 47].

3.3 Mechanism of EM/ microwave absorber

5.1 Evolutions and foundations of cloaking technology

An EM cloak fundamentally operates as a device that induces a state of “invisibility” for an object concerning EM radiation within a designated frequency range [50]. The concept of a device that can render objects imperceptible to the unaided eye is deeply entrenched in a rich historical narrative prevalent in numerous cultures’ folklore, including the renowned cloak associated with Harry Potter from the literary works of J. K. Rowling [50]. Although early researchers were unable to attain genuine invisibility, their investigations catalyzed modern advancements in metamaterials and cloaking technologies, wherein the manipulation of light facilitates the perceived “disappearance” of objects by redirecting light around them. Nonetheless, the viability of attaining genuine invisibility, albeit within a limited spectrum of frequencies [1], has persistently been a focal point of investigation. Several scholarly works, including those by Leonhardtand [11] Pendry [51, 52], explored the foundational principles of invisibility mechanisms for objects. The inception of a novel domain emerged, integrating linear and non-linear optical concepts encompassing various principles from optics and wave analysis, such as Snell’s laws [52], Fermat’s principle, and so on [53]. An entity is rendered undetectable when it does not reflect waves to the source, refrains from dispersing waves through alternate pathways, and avoids generating any shadow. In other words, the entity must not disrupt the surrounding fields, or the fields should propagate undisturbed such that no object obstructs their path [50]. In EM wave scattering theory, the notion of “cloaking” pertains to the attenuation of an object’s overall scattering cross section (SCS) [50, 54] to ideally reduce it to zero.

Where SCS is the scattering cross-section. Accomplishing this entails either surrounding the object with an absorbing medium or altering its geometry to diminish the scattering field aimed toward the illumination source. Optimal cloaking encompasses the potential to render the entire object imperceptible, with both backscattering and shadow being completely or partially mitigated. This accounts for the background of the cloaking technology.

5.2 Foundational concepts

Each type of wave interacts with matter through mechanisms such as absorption, reflection, refraction, and scattering, making specific regions of the spectrum crucial for tailoring cloaking technologies. Longer wavelengths, including radio and microwaves, are extensively utilized within stealth technologies [55]. Infrared cloaking is centered on the reduction of thermal signatures, a critical capability within military surveillance frameworks to evade thermal imaging techniques [56]. In the visible spectrum, the challenge of cloaking becomes most pronounced, necessitating meticulous manipulation of light scattering and refraction to achieve invisibility to the human eye, leading to intricate lambda-d correlation issues [57]. By leveraging advanced materials like metamaterials, which help to manipulate and control EM waves in extraordinary manners, cloaking technologies can be tailored to function across designated wavelengths, thereby transmuting concepts that were once relegated to the realm of science fiction into tangible reality.

5.3 RC delays v/s sub-diffraction limit

As we investigate the practical execution of cloaking devices more thoroughly, an additional pivotal factor emerges—the “temporal” response of these materials to EM waves. This response is shaped by inherent characteristics such as resistance and capacitance [58], which together contribute to RC delays [5]. While optics is primarily concerned with the manipulation of spatial wave propagation, RC delays underscore the significance of overseeing time-dependent behavior within synthetic materials. Comprehending and mitigating these delays are essential for the proficient real-time functionality of cloaks, especially when dynamic or broadband performance is needed [59]. RC delay refers to the time constant indicated by,

Where R is the resistance, and C is the capacitance.

It should be understood that high RC delays will slow response, limiting the cloaking device’s operating bandwidth and creating energy loss. As a result, cloaking structures should be designed in such a way that minimizes the RC delay values within the ‘sub-diffraction limit’ [60]. Sub-diffraction control of light waves is necessary for the seamless bending and propagation of light. However, incorporating minimum RC delay and residing within the sub-diffraction limit seems challenging for the cloaking to be in effect [61]. More advanced materials with low-loss characteristics, high conductivity, and low resistance can minimize RC delays, while advanced nanofabrication techniques for the designing of novel materials to enable sub-diffraction precision are also in consideration for higher frequencies involving visible light.

5.4 Core principles of cloaking

The Maxwell equations are four mathematical equations delineating the characteristics of EM waves. Maxwell’s equations for plane waves can be written as,

But for the left-handed metamaterials or DNG materials,

Here, the light propagation will be opposite to what happens in natural materials.

Snell’s Law: Using Snell’s Law is essential in metamaterial engineering, particularly in cloaking. It is common knowledge that materials in the third quadrant of the material profile exhibit a negative refractive index [62]. Consequently, when an incident ray interacts with such materials, it experiences negative refraction or diffraction [63]. The refractive index of metamaterials will be thus;

Where μ is the permeability, and ε is the permittivity of the medium.

5.5 Development of cloaking technology

As mentioned, the root of cloaking technology traces back to the early twenty-first century, driven by advancements in EM theory and material science. The practical demonstrations of novel methods were truly influenced and initiated by the TO method and the advent of metamaterials. Over time, researchers focused on more efficient methods for the attainment of less bulky, less-lossy, high-performance cloaks. They refined these principles and incorporated new ideas, achieving breakthroughs in various frequency ranges, from microwaves to visible light. With the advent of these technological advancements, a diverse array of cloaking methodologies has emerged, employing distinctive techniques for the manipulation of interacting waves.

5.5.3 Research advancements

Ongoing research activities show advancements in the field of carpet technique with more efficient performances. Herein we produce the efficient working of a carpet cloak made up of dielectric resonators and substrate with a one-order mismatch in their epsilon values. The simulations utilize the full wave solver, CST Microwave Studio Suite, using the Time Domain Solver within the 4–5 GHz frequency range. The excitation mode applied consists of plane waves exhibiting various polarizations, such as linear, circular, and elliptical. These waves were generated at a frequency of 4.15 GHz. To assess the similarity between the designed cloak-attached scatterer and the ground plane, E-field and far-field monitors were utilized at the frequency of 4.15 GHz. The results of the E-field distributions of plane-polarized waves are visually represented in the graphical illustrations presented in Figure 6. Here it is evident from the simulation results [69], the cloak attached to the surface minimizes the distortions caused by the scatterer, thus making it more similar to the pattern of a ground plane. It has been observed that the metasurface cloak can conceal the scatterer to a certain degree, thereby replicating the characteristics of the ground plane across all modes of plane wave excitation. The distortion, as mentioned earlier, introduced by the scatterer, is effectively mitigated by the same, resulting in a reflection profile akin to a quasi-plane wave [53]. Consequently, it is now apparent that discerning the scatterer from the ground plane is challenging for any observer. The reflection pattern of the electric field provides insight into the cloaking effect achieved by the metasurface [69].

Another significant outcome enhancing the cloaking efficiency is the Radar Cross Section (RCS), demonstrated by the relevant structures. The RCS values exhibited by the scatterer attached to the cloak are similar to those of the ground plane for various polarization scenarios, including circular and elliptical as our investigations [69], as shown in Figure 7(a), (b), and 7(c).

The carpet cloak presented compelling evidence of the manageability of EM waves through metamaterial technology and TO. Utilizing these non-resonant metamaterials can significantly enhance bandwidth and reduce loss performance. Despite being in the initial stages, the process of cloaking signifies a novel method to govern EM wave propagation through complex media, holding substantial potential for diverse RF and optical applications in the future.

5.6 Ongoing research and challenges

The field of cloaking expands by focusing on improving efficiency, scalability, and adaptability. Current research focuses more on broadband cloaking [10] apart from cloaking in some specific ranges or frequencies, [68]. Also, methods that would reduce material loss and anisotropic issues in the design of metamaterials are of concern [68]. The emergence of low-cost, versatile, less bulky, lightweight, and flexible cloaks is a major concern. Challenges also persist in dynamic or non-homogenous environments where the cloaks are exposed to changes in temperature, pressure, and so on. Research is now deepening roots in the fields of quantum cloaking and 4D metamaterials. But these advances should also pave the way for reducing the challenges that pertain because apart from theoretical predictions, our ultimate aim is to make the technology practically possible for humanity.