Optical invisibility, which started in the pages of fiction before becoming an intriguing quest of humankind for over a century, has blossomed into a remarkable scientific journey toward reality over the last two decades. Perfect optical cloaking requires the total scattering of electromagnetic waves around an object at all angles, all polarizations, over a wide frequency range, irrespective of the medium. Such a device is still far-fetched, requiring the transformation of space around a cloaked region such that the phase velocity is faster than other areas to preserve the phase relationships. However, by simplifying the invisibility requirements, pioneering work on spherical transformation cloaks, carpet cloaks, plasmonic cloaks, and mantle cloaks has been realized in narrowband microwave, infrared, and even optical wavelengths. In this Tutorial, we review the theoretical basis for invisibility cloaking, from spherical transformational optics to non-Euclidian cases, and discuss their limitations. Subsequently, we highlight the recent trends in realizing reconfigurable intelligent cloaks to overcome the traditional limitations of wideband operation and parallel efforts in unidirectional cloaking. Because the human eye is insensitive to the phase and polarization of visible light, a class of ray optics cloaking devices has been recently developed by eliminating phase preservation requirements. Notably, we focus on the recent progress achieved on invisibility cloaks that function in natural incoherent light and can be realized using standard optical components. We conclude this Tutorial with a prospective of potential applications and the practicality of optical cloaks in everyday life.
The remarkable progress of electromagnetics over the last two decades is defined by the realization of metamaterials. Metamaterials are artificially structured materials exhibiting extraordinary properties that are not observed in natural materials. This is achieved by designing a new class of periodically arranged engineered macroscopic “atoms” of the desired physical property rather than being guided by their chemical composition. In 1968, Veselago first discussed the possibility of negative permeability and permittivity.1 The concept remained dormant until 1999, when Pendry et al. demonstrated a practical method of designing left-handed metamaterials that did not follow the conventional right-hand rule of electromagnetics.2,3 Since then, an explosion of various concepts and ideas occurred, resulting in a richer understanding of the permittivity–permeability plane. Notably, the intriguing technique of bending light led to the concepts of negative optical refraction and super-lensing, paving the way for the development of various metadevices.4,5
Light–matter interaction through metamaterials has enabled exciting technological developments that were not possible before. One of the most fascinating applications of metamaterials is the possibility of realizing an optical cloak around an object, making incoming light bypass it. The initial spherical transformation proposal by Pendry et al.6 and Leonhardt,7 although theoretically elegant, required an anisotropic variation of permeability and permittivity tensors that were virtually impossible to fabricate in practice. Subsequently, a simplified 2D cylindrical transformational cloak was proposed and experimentally verified for microwave frequencies by Schurig et al.; the dielectric and magnetic property variations were designed in a radial direction.8 Over the years, what started as the ultimate exemplification of the metamaterial concept, the science of optical cloaking has made progress beyond even the physics of metamaterials, eyeing breakthrough applications in optical shielding, blind-spot monitoring, non-invasive sensors, and so on. A chronological summary of major breakthroughs in this area over the last 20 years is shown in Fig. 1.
More recently, a class of cloaking devices has been proposed based on the initial transformational optics, namely, carpet cloaks that utilize a quasi-conformal mapping of transformational optics—with the advantages of more accessible material parameters for wider bandwidths.9 To that end, plasmonic and mantle cloaks have been theorized using scattering cancellation methods that do not aim to design a perfect cloak, but rather use scattering dominant terms in the multipole expansion of the scattered field, hence easing the material requirements.10,11 Many other types of passive and active cloaking devices have been proposed over the years;12,13 however, the realization of an ideal three-dimensional cloak over the whole visible wavelength spectrum remains challenging. Consequently, while such efforts continue, a class of ray optics cloaking devices has been proposed over the last decade with the aim of hiding an object.14,15 Because the human eye is insensitive to the polarization and phase of light, approximations that relax those requirements have enabled the development of broadband, large-size cloaks consisting of standard optical components such as lenses, prisms, and polarizers. This approach, while not as rich in physics as metamaterials, could be immensely useful for many practical applications in the future. Although previous reviews have covered metamaterial-based cloaking devices, the latter part of the more recent story has not been categorically compiled. In this Tutorial, although we cover major breakthroughs in optical cloaking science, starting with passive and active cloaking, we focus mainly on geometrical optics and its potential applicability. In the end, we present the latest optical cloaking research trends that utilize breakthroughs in other areas of science, including data science and machine learning.
Although it is beyond the scope of this review, it is worth mentioning that optical cloaking studies have inspired and helped other fields beyond electromagnetics—namely, transient thermal cloaking,16 thermal waves,17–19 elastic waves,20 sound waves,21 surface fluidic waves,22 and even quantum matter waves23—to envision invisibility possibilities. Beyond the bending of waves, the concept of temporal cloaking has also been explored, wherein the occurrence of an event is cloaked creating a “time hole” in the probe beam.24,25
II. METAMATERIAL-BASED CLOAKING
We present a brief overview of metamaterial cloaking, that is, transformation optics, metasurfaces, and scattering cancellation. The details of these techniques can be found in previous review papers.12,13,26,27
A. Transformation optics
We consider the electromagnetic field distribution in the virtual coordinate system and the transformed electromagnetic field distribution in the physical coordinate system, where and represent the permittivity and permeability tensors in the virtual and physical coordinate systems, respectively. Maxwell's equations have exactly the same form in any coordinate system; therefore, the electromagnetic field distributions between the virtual and physical coordinates can be transformed as
where is the Jacobian matrix, .
In principle, transformation optics allows one to hide a large object. In 2006, transformation optics for cloaking was independently presented by Pendry et al.6 and Leonhardt.7 The paths of electromagnetic waves in the physical coordinate system can be controlled within a metamaterial with an appropriate spatial distribution of permittivity and permeability. The transformation optics gives an ideal cloak, i.e., an object is cloaked for arbitrary polarization and no reflection occurs at the interface of the metamaterial and the background medium such as air. For example, we consider the hidden object to be a sphere of radius R1 and the cloaking region to be contained within the annulus R1 < r < R2 for an incident plane wave [Fig. 2(a)]. The coordinate transformation gives permittivity and permeability distributions in the region of R1 < r < R2 in the spherical coordinate system (r,θ,ϕ) as6
where . Equation (2) indicates that both permittivity and permeability are identical and anisotropic, ensuring no reflection for arbitrary polarization. In practice, it is challenging to implement such extreme permittivity and permeability parameters. In the pioneering experimental work on cloaking [Fig. 2(b)],8 a two-dimensional cloak prototype composed of split-ring resonators was designed for one polarization and non-zero reflection being allowed, that is, three components (, , and ) from six components in the cylindrical coordinate system were considered. Subsequently, the validity of cloaking an object was confirmed at frequencies around 8.5 GHz.
In the optics regime, however, such split-ring resonators can no longer be used. Cai et al.28 presented a two-dimensional optical metamaterial cloak consisting of metallic nanowires immersed in a cylindrical silica medium. Similarly, considering one polarization and non-zero reflection, the validity of cloaking was numerically confirmed at 632.8 nm, assuming a helium–neon laser.
In other words, in the cloaking design using transformation optics, allowing non-zero reflection and limiting the polarization avoid extreme parameters in practice. It has been reported29 that such cylindrical cloaks with simplified material parameters inherently allow the zeroth-order cylindrical wave to pass through the cloak; this is a factor failing invisibility.
Non-Euclidian transformation cloaking has been introduced, wherein the cloak does not preserve the phase of the incident wave and provides a wideband frequency response. Non-Euclidian cloaking remains difficult to practically implement, while it reduces the material parameter requirements.30
When there is an object on a reflector, an incident wave is scattered from the object. The aim of carpet cloaking is to make the reflection wave similar to that without the object by engineering the refractive index profile around the object [Fig. 3(a)].9 The carpet cloak relaxes the requirements of permittivity and permeability to cloak an object, allowing experimental demonstrations in the microwave31,32 and optical ranges.33–38 In one of these studies,31 a microwave carpet cloak consisted of non-resonant “H”-shaped metallic elements and concealed a bump from 13 to 16 GHz [Fig. 3(b)]. In another study,33 an optical carpet cloak was implemented on a silicon-on-insulator wafer, wherein the silicon slab served as a two-dimensional waveguide [Fig. 3(c)]. The refractive index profile was realized by varying the hole densities. The cloaking phenomenon was observed in the range of 1400–1800 nm.
B. Metasurface cloak
We consider a scenario in which a monochromatic plane wave is incident on an object placed on a flat plate, the object being covered by a metasurface. If each unit cell of the metasurface can control the phase by with unity-amplitude in the reflection wave, an arbitrary wavefront can be engineered. In other words, a proper phase profile over the metasurface can generate a reflection response that is the same as the case of the flat plate without the object.
The function of the carpet cloak was experimentally demonstrated using a metasurface with its thickness being much smaller than the operating wavelength in the microwave range in 2013.39 The unit cell consisted of a “H”-shaped metallic pattern and showed almost full coverage of the reflection phase by varying the size of the pattern, leading to an arbitrary phase profile over the metasurface. Various unit cells have been investigated, such as silver nanocavities40 for the visible range, metallic rings41,42 for the millimeter-wave and terahertz ranges, and dielectric cylinders43 for the microwave range. In 2015, a metasurface cloak composed of gold nanoantennas was experimentally demonstrated in the optics range (Fig. 4).44 The metasurface concealed a 3D shaped object including multiple bumps and dents at an operating wavelength of 730 nm for one polarization. Arbitrary polarization for a metasurface cloak was experimentally demonstrated using metallic rings in the microwave range.45 Metasurfaces with dual-frequency46 and multi-frequency operation47 have also been reported.
C. Scattering cancellation
We consider the scattering of a subwavelength spherical object in air for the incidence of a monochromatic plane wave. The electromagnetic field outside of the spherical object is expanded with different channels labeled (l, m, σ), where l, m, and σ represent the total angular momentum, the angular momentum component along one of the axes—for example, z (−l ≤ m ≤ l)—and the polarization, respectively. The expansion expression of spherical waves and the boundary condition of the spherical object to air determine the coefficients of the channels. The total scattering cross section is then given by48
where is the wavelength and the reflection coefficient is defined as , with and being the incoming wave and outgoing wave amplitudes, respectively. Equation (3) indicates that the scattering cross section of the spherical object at (l,σ) can be zero when . Owing to spherical symmetry, is a function of (l,σ), but not of m.
A scattering cancellation technique for cloaking a subwavelength spherical or cylindrical object was reported by Alù and Engheta.10 The scattering cross section of a dielectric sphere with positive permittivity is significantly reduced by a plasmonic coating with negative permittivity, that is, the dipole moment contributions from the core and the shell are cancelled out [Fig. 5(a)]. This concept was experimentally verified in the microwave range;49 a dielectric cylinder was surrounded by a plasmonic shell consisting of metallic fins immersed in liquid (acetone) and placed in a parallel-plate waveguide. The scattering cross section of a test sample with a total radius of 31.3 mm was effectively reduced at approximately 2 GHz.
Sensors and detectors are occasionally required to be less disturbing to the surrounding environment, for example, near-field scanning optical microscopy. The scattering cancellation technique has been extended to the concept of a “cloaking sensor” [Fig. 5(b)],50 wherein the incoming wave interacts with the inner sphere or the cylinder. The incoming wave can be measured by the inner object, while its presence is not perceived by the surroundings. A cloaked optical microscope tip has been reported.51
A mantle cloaking has also been presented, where a thin patterned surface having a properly designed surface impedance hides a subwavelength object (Fig. 6).11,52 Chen and Alù reported that a graphene monolayer was used for the mantle cloak in the terahertz range.53 The concept of the mantle cloak was experimentally verified in the microwave range.54
D. Reconfigurable and intelligent cloak
A reconfigurable metasurface cloak was experimentally demonstrated in the microwave range. The metasurface was composed of unit cells with each having a variable capacitor,57 and the reflection response in each unit cell was tuned using a bias voltage. The metasurface not only hid a bump but also mimicked other virtual shapes for the reflection response.
Machine learning has been widely explored in various research fields, and sophisticated algorithms allow the realization of various intelligent metasurfaces. Consequently, an intelligent metasurface cloak was experimentally demonstrated in the microwave range (Fig. 7).58 Similarly, in the aforementioned case, where each unit cell has a variable capacitor, the reflection response was used as a bias voltage. A deep learning technique controls the bias voltages of variable capacitors over the metasurface based on the information of the incident wave and the reflected spectrum. The metasurface cloak hides an object without any human intervention when the background is varied.
E. UNIDIRECTIONAL INVISIBLE CLOAK
Bender and Boettcher presented the notion of non-Hermitian parity-time (PT) symmetry in 1998, where the eigenvalues of a system could be real and positive through the combination of gain and loss.59 Non-Hermitian PT symmetry has been applied to periodic structures, revealing unidirectional invisibility at the exceptional point.60 A one-way invisible cloak was theoretically explored by means of the transformation optics of parity-time symmetric optical materials using the unidirectional feature at the exceptional point.61 A grating of wide metallic strips with active elements62 and antennas with active elements in a cylindrical arrangement, as physical implementations of such PT symmetric unidirectional cloaks, was discussed.63
Amemiya et al. presented the concept of an effective electromagnetic field for photons and a design of nonreciprocal invisibility cloaks using a photonic lattice model.64 A one-way invisible cloak was observed in a numerical model of a photonic crystal composed of yttrium–iron–garnet asymmetrically shaped semi-cylinders when an external direct current (DC) magnetic field was applied.65 It has been argued that if the spatial distributions of the real and imaginary parts of the permittivity in a planar medium are related to one another using the Kramers–Kronig relationships, unidirectional invisibility can be achieved.66
Transformation optics presents ideal conditions to hide a large object, namely, non-reflection, both polarizations, full-visible range, and omni-direction. While transformation-optics-based cloaks have opened up and boosted the research field of optical cloaks, the realization of optical cloak devices that require extreme parameters remains challenging. As an alternative approach, geometrical optics has garnered substantial interest with the development of practical devices able to operate across the full-visible wavelength range—for example, angle-dependent cloaking—by abandoning the omni-directional characteristic, although practical scenarios are limited.
The function of the carpet cloak, which can hide a bump, is achieved using metasurfaces. In particular, metasurfaces are compatible with tunable functions because only the amplitude and the phase of an electromagnetic field on a metasurface need to be controlled, compared with bulk metamaterials. The scattering cancellation technique has an intrinsic limitation on the size of an object that can be cloaked, while they remain attractive for hiding subwavelength objects. Beyond the optical cloaks discussed in Secs. II A–II C, several proposals—including the use of active unit cells driven by machine learning algorithms in Sec. II D and borrowing analogies from the physics community in Sec. II E—have achieved new cloaking devices breakthroughs.
III. GEOMETRICAL OPTICS-BASED CLOAKING
Although various metamaterial cloaking methods based on scattering cancellation, transformation optics, and metasurfaces have been demonstrated, hiding a large spatial object over a broad range of wavelengths in the visible region has been challenging. Ray optics cloaking has attracted considerable attention because of its great promise in achieving a broad bandwidth (covering the entire visible spectrum) and scaling to arbitrarily large sizes using off-the-shelf optics. In contrast to transformation optics, where both the amplitude and the phase of light are preserved, the amplitude and the direction of light are preserved in the ray optics cloak scheme. Many optical components, such as mirrors, lenses, and prisms, are commercially available and operate over a broad range of wavelengths. In addition to its broad bandwidth, the large-scale implementation of a cloaking structure with optical elements is much simpler and more cost-effective than is the case with a metamaterial cloak. We provide an overview of ray optics cloaking that exploits optical components, such as mirrors, prisms, lenses, and digital technology.
A. Mirror-based cloaking designs
Reflection is the change in the direction of propagation of a wave at a boundary between two different media, thereby allowing the wave to return into the medium from which it began propagating. High reflection can be achieved by using a metallic mirror and a dielectric mirror, which can be employed to construct a cloaking device. The simplest cloaking design would be a plane mirror only cloak structure where two flat mirrors are separated and rotated by 45°, with another set of two flat mirrors reversing the effect of the first set, as shown in Fig. 8(a),68 where the collimated light is reflected twice using the first set of mirrors, creating a transverse displacement with respect to the starting trajectory. Next, the second set of mirrors retroreflects the light to return it to its initial path. Any object with a nearly arbitrary size cannot be seen between the top two plane mirrors.
The cloaked region can be extended longitudinally by making the separation between the two plane mirrors large after the light rays are collimated with transverse displacement using the two mirrors. An aerial view of the implemented cloak device is shown in Fig. 8(b), where two sets of right-angled mirrors redirect light around the cloaked region. As shown in Fig. 8(c), a trashcan can be clearly seen, while a chair located in the cloaked region is invisible.
The plane mirrors in the cloak device, as shown in Fig. 8(a), can be replaced by a right-angle prism where the total internal reflection (TIR) of the prisms is utilized to bend the light rays around the cloaked region. Figure 9(a) depicts a schematic of a right-angle prism-based cloaking device. The collimated light rays undergo TIR twice through the two successive right-angle prisms and are thus transversely shifted from their original trajectory, the second set of two right-angle prisms causing the light rays to return to their original path. An object can be cloaked between two sets of right-angle prisms, and a longitudinally extended cloaking region can be attained by creating a large distance between the two sets of prisms. For experimental demonstrations, commercially available right-angle glass prisms are assembled to create a prism-based optical cloak device, as shown in Fig. 9(b). An image of the experimental setup of the cloaking structure along the optical axis is shown in Fig. 9(c), demonstrating that a toy car placed behind the cloak device can be clearly seen through the cloak device without seeing a metallic bar in the cloaking area. The glass prism can be replaced by a plastic prism so that both the weight and cost of the implemented cloaking device can be significantly reduced.
Figure 10(a) shows a cloak device with 12 ports comprising off-the-shelf mirrors and beam-splitting polarizers, where the viewing zones are labeled I–IV69 and the light for the vertical polarization in regions II and III being reflected by a plane mirror rotated by 45°; this is then reflected again by the beam-splitting polarizer, leading to a displacement relative to its initial route, that is, any object can be cloaked in the middle of the displacement. Another set of the polarizer and the plane mirror can reflect light back to the original trajectory with the same degree of transverse shift. Conversely, light for horizontal polarization in regions I and IV can be transmitted through the two successive polarizers. 50% of the incident light passes through the cloak device for the observation of the background image behind the cloak structure owing to splitting the polarization of light, while an image projection is enabled by using the other 50% of the light.
For the white number “1” that is positioned at port 4 with the polarizer (Pn,1) that transmits vertical polarization, the horizontally polarized light is blocked by the polarizer while the vertical polarization of light gets reflected by another polarizer (Po,2) so that the number “1” appears only in region I. Conversely, the number “2” is located at port 9 without the polarizer (Pn,1) so that the polarizer (Po,3) transmits horizontal polarization that is then reflected by mirror (M3), but the polarizer (Po,3) reflects the vertical polarization, thereby allowing the image “2” to appear in regions III and IV. Figure 10(b) shows the experimental implementation of the cloak device, where a toy car can be viewed through the cloak structure without viewing a yellow cylindrical object that is located in the middle of the displacement.
In addition to the optical cloaking devices outlined above, mirrors can also be used to hide an acoustic absorber consisting of a sparse arrangement of sound-resonators.70 Each resonator has a diamond shape with each plane having a reflective mirror. The light paths in the presence of the sound absorber are recovered with an even number of light reflections at the mirrors on neighboring resonators; thus, there is no overall image flip. The image behind the sound absorber is seen for the view angle of the near-normal direction, while the sound absorption performance is preserved.
B. Prism-based cloaking designs
Refraction is the change in direction of wave propagation when it passes from one medium to another in which it has a different speed. The refractive indices of two different media determine the degree of wave bending, which is described by Snell's law. Redirecting light by refraction can be obtained using prisms, magnifying glasses, and lenses. An object can be concealed by bending light around a cloaked region, which is also easily achievable using refracting optical elements such as prisms.68 Figure 11(a) shows the top view of the setup of a cloak structure based on Snell's law, consisting of two L-shaped water-filled tanks. The direction of the collimated light rays parallel to the optical axis is shifted away from the optical axis at the first interface with water based on Snell's law and is then shifted back parallel to the optical axis at the second interface of the first tank by means of a transverse shift relative to the original path.
Any object can be concealed in the middle of the transversely shifted region. The effect of the first water tank is offset by the second tank, thereby transversely shifting the rays with the same displacement while allowing them to be parallel to the optical axis. Figures 11(b) and 11(c) show the aerial and front views of the experimental observation of the cloak device based on Snell's law, which demonstrates that a helicopter can be hidden in the middle of the displacement (i.e., cloak region) and a truck can be viewed below the waterline, while the helicopter appears in front of the truck above the waterline. The water-filled tanks guide light to be bent around the bottom of the helicopter, bending it back to its initial trajectory, allowing the truck to appear in its place.
Although many carpet cloaks have been designed based on the quasi-conformal mapping approach,9 the carpet-cloaking scheme can also be demonstrated by linear homogeneous transformations where a virtual coordinate space is divided into many triangular segments and a linear transformation in each segment is applied. This results in homogeneous material parameters in each segment so that a cloak structure can be realized at optical wavelengths simply using anisotropic materials. A macroscopic cloaking device operating over the entire visible spectrum has been demonstrated utilizing birefringence in a natural uniaxial crystal calcite.71,72 Figure 12(a) shows a schematic of an anisotropic cloak structure designed by homogeneous coordinate transformation, where the incident light rays can be reflected without distortion by restoring both their angle and position for a certain polarization state of light. Figure 12(b) shows a schematic view of the experimental setup. Images captured using a camera when an anisotropic cloak is placed on the top of the wedge to be concealed under laser irradiation at (c) 561 nm, (d) 488 nm, and (e) 650 nm with an incident angle of 18° are shown in Figs. 12(c)–12(e).
As the anisotropic cloak structure is designed for green light, the cloaking effect is clearly shown without distortion as shown in Fig. 12(c), wherein the “MIT” image appears at the same height, as if the bottom surface of the anisotropic cloak was flat. The color aberration causes the images obtained for the blue and red light to be slightly shifted, which can be minimized by using complementary dispersion.73
Another cloaking scheme that utilizes anisotropy is an isolated polygonal cloak for concealing a large object for the entire visible spectrum by applying the linear polygonal transformation.74 Several sections form the polygon in a virtual space, and a linear homogeneous coordinate transformation in individual sections enables the electromagnetic parameters of the cloak to be homogeneous, finite, and spatially independent.
For the experimental demonstration of a hexagonal cloak structure, six natural birefringent crystals with a trapezoidal shape are cemented together, where each crystal operates in the incident direction. The side and top views of the cloaking device are shown in Fig. 13(a). The experimental setup, where a glass tank which filled with a translucent liquid contains a yellow pillar as a concealed object placed at the center of the hexagonal cloaking structure, is shown in Fig. 13(b). Figure 13(c) shows the captured image without distortion, which is placed in the same location as the objects. A symmetric pattern of the cloak structure allows the hexagonal cloak to work for incident rays from the other five directions. The proposed polygonal cloaking device works for light rays from all observation angles.
Because anisotropy in a birefringent crystal is required for the two aforedescribed cloak structures, they work for a specific polarization. This difficulty can be resolved by employing the linear polygonal transformation with the ray optics approximation, where only isotropic materials are needed for experimental demonstration.14 Consequently, it works for arbitrary polarizations in multiple directions of incident light and also for a wide range of optical wavelengths using incoherent natural light.
A six-directional, phase-preserving hexagonal cloak with a central hexagon region as the cloak area, which can hide a fish in an aquatic environment, comprises six isosceles triangles of an isotropic glass with α = 13° at the apex and six isosceles triangles of air with β = α + 60° at the apex, as shown in Fig. 14(a). Figure 14(b) shows the experimental setup where a fish tank is filled with water. Dynamic scenes of the fish swimming inside and outside the cloak region of the aquatic environment are shown in Fig. 14(c). The fish become undetectable, and the green plants behind the cloak region are not obstructed when the fish swim inside the cloak, which works for incident rays from six different observation angles. A 3D cloak that can conceal macroscopic objects for fully polarized visible light has also been demonstrated by applying a 3D homogeneous polyhedral transformation and a spatially invariant refractive index discretization method.74
C. Lens-based cloaking designs
The beam diameter of the propagation light can be squeezed by using a lens to significantly reduce the overall dimensions of the cloak device (i.e., a higher cloaking ratio) compared to previous designs constructed with mirrors and prisms. A perfect cloak system in the paraxial approximation—assuming that the rays show a minimum deviation with respect to the center axis of the system—can generate an image with unity magnification, zero transverse and longitudinal shifts, and no aberrations as compared to an actual object. “ABCD” matrices can describe the propagation of rays through the optical system,15
where L is the length of the cloaking device and n is the refractive index of the surrounding medium.
Figure 15(a) shows a ray trace through a perfect cloak75 structure in paraxial approximation, requiring at least four lenses. Light is guided around a cloak region by the lenses, and an extended cylindrical area between the lenses where no rays pass (shaded orange) represents the cloaked region. For the experimental demonstration, a perfect paraxial cloak system is constructed using off-the-shelf achromatic doublets consisting of a combination of positive and negative lenses capable of drawing focal points at various wavelengths closer to each other, that is, by means of the opposite chromatic aberration behaviors of the two constitutive lenses with anti-reflection coatings at visible frequencies to mitigate the aberrations of the image. Figure 15(b) presents an on-axis view of a practical paraxial cloak, revealing that the background grid image is seen while a hand is cloaked in varying directions. Figure 15(c) shows the experimental setup of a rotationally symmetric lens-only paraxial cloak system.
By adding plane mirrors to the four-lens cloak system described above, the overall cloak system can be significantly compacted with a modified cloak region shape. Achromatic doubles are used to minimize both chromatic and spherical aberrations. Considering that light rays between side lenses are parallel, the most straightforward solution to further correct the chromatic aberration is to elongate the cloak system along the y-direction to obtain an optimized layout with the least aberration.
Ray-tracing simulation using commercial software (Zemax OpticStudio), where achromatic cylindrical lenses are employed, has been conducted. In the simulation setup, light rays are incident from the left-hand side to the detector on the right-hand side along the y-axis. A schematic top view of the cloaking design is shown in Fig. 16(a). For simplicity, the plane mirrors are assumed to be thin planes of negligible thickness in the simulation, the mirrors having an orientation of 45° with respect to the x- or y-direction.
As an experimental demonstration, a cloak system was built using commercially available spherical achromatic lenses (AC508-080-A and AC080-010-A, Thorlabs Inc.), as shown in Figs. 16(b) and 16(c), where a part of the background Toyota emblem can be seen through the cloak without aberrations, which is consistent with the simulation results.
The mass and volume of a lens material can be significantly reduced with easy scalability by using Fresnel lenses, although it is found to be difficult to achieve a clear image using a Fresnel lens due to diffraction occurring at the edges of concentric rings on the lens surface as compared to the conventional lenses.68 Figure 17(a) depicts a schematic consisting of four converging Fresnel lenses in series, where the separation distance between two Fresnel lenses is twice the focal length and two sets of Fresnel lenses are used to create an upright image. Figure 17(b) shows another schematic view, where two diverging lenses are used in the middle of the cloaking device so that light cannot pass through a focal point, leading to the correct image. As one set comprising the Fresnel lens and a diverging lens allows the light to be collimated with a reduced spot size, the distance between the two sets of lenses can be large; thus, being able to achieve a longitudinal extension of the cloaking region. The schematic shown in Fig. 17(a) experimentally demonstrates the two Fresnel lenses in the middle of the cloak device mounted together, where the tail of the helicopter is placed in the cloaked region and a red truck is located behind the cloak structure. Figure 17(c) displays the on-axis view showing that the tail of the helicopter is not visible as it is in the cloaked region, while the rear part of the truck behind the helicopter can be seen.
D. Digital technology-based cloaking designs
Although many interesting cloaking schemes have been proposed and experimentally demonstrated, it has been difficult achieving broad bandwidth and a large field-of-view (FOV) simultaneously. This problem can be addressed by employing widely available digital cameras and digital displays that allow information to be separated into discrete sections.76 After scanning the background with a camera, the captured data are encoded so that a distinctive view of a particular point in the background is provided by each pixel on the screen for a specific location of an observer. Performing this for many views with lenticular lenses can create numerous images of the background corresponding to the observer at different positions.
Figures 18(a) and 18(b) show a schematic of a digital integral cloak. It consists of an input surface—comprising a combination of the lenslet array and detector plate to capture the incident rays—and an output surface encompassing the lens array and the display array to display the light rays as if they pass through ambient space. Any macroscopic object in the visible light can be hidden when it is placed between the input and output surfaces. A superpixel that is located at the focusing plane of the lenslet array corresponds to every discretization in space, and isolated pixels for identifying individual ray angles are included in every superpixel.
The display plate reverses the effect of the detection scheme described above. Digital imaging and display technologies positioned on the surface of the cloak structure are enabled by discretized cloaking, which is called “digital cloaking.” The experimental setup, where the incident rays are captured by horizontally scanning the background with the input camera—the output rays being emitted from the lenslet array on the display screen along with the cloak region between the input and output planes—is shown in Figs. 18(c) and 18(d). Figures 18(e)–18(h) show screenshot images by a viewer moving horizontally at various viewing angles ranging from −4.1° to 6.7°, while Figs. 18(e′)–18(h′) show the same background images without the cloak system, representing 10.8° of the total 13.4° viewing range.
Although metamaterial- and metasurface-based cloaks are demonstrated using a series of complex and expensive fabrication methods over a very small area within a narrow wavelength range, easy implementation using commercially available optical elements is one of the key points in favor of ray optics-based cloaks. The mirrors, prisms, and polarizers work effectively across the entire visible wavelength spectrum and are easily available from vendors. The mirror-, prism-, and polarizer-based cloaking designs offer a more efficient method for cloaking in terms of simplicity and cost. Moreover, the cloaking ratio—defined as the ratio of the area of the cloaked region to the area of the entire cloak device for metamaterial- and metasurface-based cloaking structures—is relatively small, making them difficult to apply to practical applications as compared to mirror-, prism-, and polarizer-based cloaking devices. To further improve the cloaking ratio, the beam diameter of the propagating light can be compressed using a lens to minimize the total size of the cloak structure relative to the previous cloaking designs constructed from mirrors and prisms. However, the acceptance angle of the lens is very narrow, so a cloak system implemented with lenses offers a narrow FOV that can be improved by utilizing digital integral cloaking. While reducing the reflection in metamaterial- and metasurface-based cloaking devices is one of the biggest challenges, convenient broadband anti-reflection coatings with high efficiency are readily available for ray optics-based cloaks.
IV. SUMMARY AND PROSPECTS
In this Tutorial, we highlight some of the significant developments in the area of optical cloaking. Progress in optical cloaking should be examined against the backdrop of the development of metamaterials in electromagnetism. At the same time, it is important to capture how, when a roadblock appears, ideas have branched out into proposals backed by new physics. The quest started with an understanding of a negative refraction medium where the permeability and permittivity are simultaneously negative.1 Although not available in nature, with the realization of artificial materials combining negative and positive indices, intriguing devices were realized.77 In addition to invisibility, the pioneering early works by Veselago and Pendry et al. also provided methods of realizing perfect imaging that beat the diffraction limit, branching out to become an area of research examining subwavelength focusing.78 Subsequently, the pioneering work by Schurig et al. afforded a practical path to negative refractive index materials at microwave frequencies by integrating metallic wires and split-ring-resonators on printed circuit boards.8 With the confirmation of the very existence of negative refractive indices, a new world of metamaterials emerged—that of exotic material properties with subwavelength design parameters. These are significant milestones that led to a better understanding of subwavelength physics, not limited to electromagnetism:
The need for the anisotropic and complex functional dependences of material parameters;
The requirement for optical magnetism, which means the magnetic response should be equivalent to the electrical response, leading to significant loss at visible frequencies; and
The requirement that the phase velocity should be faster than the speed of light in a vacuum, leading to a singularity clause requiring operation at a single frequency with zero bandwidth.
All these issues are fundamental limitations of the underlying physics yet attempts to solve them for a specific situation at the expense of losing generality has led to remarkable progress. For example, the complexity of the parameters and the requirement of optical magnetism are somewhat simplified by introducing the all-dielectric carpet-cloaking concept. Its operation is limited to 2D applications and has strict limitations on angular and polarization responses, compromising phase conservation. Significant progress has been made in this direction over the years, including the reduction of anisotropy to a minimum, the broadening of the operating bandwidth, and the elimination of the ground plane to hide a free-standing object.31,35 More recently, carpet-cloaking devices have been represented as graded inhomogeneous metasurfaces,44 the introduction of which has immense potential to envision low-profile skin-like ultrabroadband cloaking devices in the future. Conversely, mantle and plasmonic cloaks use simplistic isotropic materials that can achieve a broader operational bandwidth compared to transformation optics methods. Both methods reduce the dominant terms in the multipole expansion of the scattered field using a shell with opposite polarizability.79 The main limitation of this approach remains the size of the cloaked region, which has been addressed by combining active metasurfaces, such as non-Foster elements that have shown potential to realize a thin low-profile cloak with broadband and no limitation on angles.80
We should point out challenge (3)—the requirement that the phase velocity should be faster than the speed of light in a vacuum, while reducing singularities in transformation optics cloaks—remains one of the most challenging issues. To that end, Leonhardt and Tyc proposed a non-Euclidian transformation approach that completely removes the requirement of superluminal propagation to achieve broader bandwidth and all-angle operation.30 This approach compromises the phase conservation requirement, which is only noticeable using precise interferometric measurements, making it potentially useful for applications where the human eye is the primary detector. However, no experimental work has been reported to confirm this concept owing to the complexity of practical design challenges.
Challenge (2) is a major barrier in the design of cloaks at visible frequencies. Strong optical magnetism is necessary to engineer the permeability at these frequencies. However, in typical metamaterials, the resonant frequency is linearly dependent on the size of the unit cells (such as a split-ring-resonator), requiring extremely miniaturized fabrication at higher frequencies. Such proposals with paired nanorod and metal-dielectric-metal fishnet structures are predicted to suffer from significant loss; consequently, they have never been directly observed.
The preceding discussion suggests that despite invisibility cloaking being a breakthrough in modern electromagnetics, a human-scale perfect cloak functional across the entire visible spectrum is still a pipe dream. In this respect, Alu et al. concluded that the main issues are related to fundamental causality and passivity limitations irrespective of specific cloaking techniques; that is, it would be impossible to realize ultimate stealth-like devices in this way.81 Inherent limitations in terms of linearity, time-invariant, and passive media can be addressed by utilizing active and non-linear systems.62,82 Several proposals have been made, although the applicability of these cloaks to daily life remains questionable. Consequently, the class of ray optics cloaking devices outlined in Sec. III, although not perfect, appears practical for many applications where a large object needs to be rendered invisible. However, the compactness of these devices remains a challenge, making it essential that new ideas continue to be developed.
Despite the many challenges outlined herein, it is undeniable that in recent years, optical invisibility has become a fact rather than ideas from fiction books. Useful cloaking devices have been successfully realized beyond electromagnetics including acoustics, thermal, and fluidic devices, owing to their low-loss physical characteristics compared to optical devices. While most of the studies focus on fundamental physics and cloaking device proof of concept designs, it is worth pointing out that the need for invisibility in modern society will remain high in the future. Starting from obvious applications in areas such as modern warfare, surveillance, blind-spot removal in vehicles, spacecraft, and highly efficient solar cells, applications in sensing and display devices are virtually endless. While limitations in causality and passivity require fundamental breakthroughs in physics, there is great potential in taking advantage of recent developments in artificial intelligence and additive manufacturing to improve low-profile practical passive or active cloaks tuned for specific application scenarios.
The design of metamaterials and metasurfaces is a multi-dimensional complex optimization of the shapes and sizes of constituent materials that define the meta-atom for a specific operation. Typically, these designs originate intuitively but are limited by the frameworks of computationally expensive full-wave electromagnetic simulators and traditional nanofabrication techniques. The same can be said of large cloaks made using geometrical optics, where geometrical elements such as lenses, prisms, polarizers, and Fresnel optics must be optimized to reduce spherical and chromatic aberrations for all angles while maintaining a low physical profile.
In recent years, the growth in computational power and improvements in algorithms, combined with unparalleled surges in the collection and storage of large datasets, have led to renewed interest in the topic of artificial intelligence. Machine learning algorithms have become smarter in discovering hidden patterns in multi-dimensional datasets, resulting in classification, regression, clustering, and problem dimension reduction, all of which is practically impossible by human means alone. Consequently, machine learning algorithms have been successfully implemented in complex situations such as navigating self-driving vehicles, natural language processing to read and interpret text and images, and the discovery of new drugs.83 In research fields such as biology, medicine, and materials, the use of these algorithms is expanding our horizons with faster discoveries by leveraging existing fundamental models and traditional know-how.
More recently, the area of metamaterials has also followed this trend and rightfully so.84–88 Machine learning techniques are already being adopted in other areas of optics and nanophotonics.89 In the context of designing a practical cloaking device, in addition to solving an inverse design problem, algorithms can be powerful tools to predict and analyze the optical responses of cloaking devices or detectors without time-consuming and expensive simulations, which will permit the possibility of “intelligent invisibility” that is adaptive to movements, shapes, and the environment. Recently, in a pioneering work, Qian et al. demonstrated an artificial-neural-network-embedded active metasurface microwave cloak capable of responding to changing incident wave-fronts and backgrounds in milliseconds without any human intervention.58 Machine learning methods can also be used to design optical elements that have improved and tailored properties so that they can be used without aberrations for the entire visible spectrum over large areas. This is particularly true for the geometric optics-based cloaks outlined in Sec. III.
In ray optics cloaking devices, optical components such as mirrors, prisms, lenses, etc., have a limited range of refractive media. Consequently, the flexibility of the acceptance angle remains narrow. While bulk optics helps to confirm life-size cloaking concepts at a theoretical level, actual implementation usually suffers from a small cloaking ratio. To that end, the use of active components such as displays has been adopted in some cases. Moreover, each optical component of various design geometries can also be replaced using these optimized metamaterial- and metasurface-based elements, thereby significantly reducing the overall size of the existing bulk ray optics cloak structures. In addition, materials (active or passive), properties, geometries, and their combinations can be realized using artificial intelligence.
It is worth mentioning that in addition to the design challenges, rapid prototyping and manufacturing of metamaterial devices may appear to be an obstacle to the adoption of these devices in daily life. With the development of both design and manufacturing capabilities, it is foreseeable that flexible cloaks that can function effectively at all incident angles with a high cloaking ratio and a wide FOV could be mass produced at a low cost and with high efficiency using roll-to-roll (R2R) methods. These foldable or rollable devices are predicted to be applicable in all situations by wrapping them around objects of arbitrary shape, making cloaking devices practical in more common applications. Based on the requirements of emerging cloaking technologies, materials with the desired refractive indices and transparency within target wavelength ranges may be developed for metamaterial- or metasurface-based devices to replace current artificial materials that require complicated fabrication methods.
Moreover, the FOV of large cloaks using geometrical optics can be improved if constituent materials with even higher refractive indices become available in the future. To that end, additive manufacturing, which is a type of rapid digital manufacturing of parts based on layer-by-layer construction, offers great flexibility in fabricating complex parts with minimum lead times and waste.90 With an increasing number of materials—from plastics to metals—and the continuing improvement in manufacturing precision at a micro-scale, 3D printed optics shows promise for future adoption.91 In future, we may see interplay between these seemingly unrelated areas of research to pave the way to enjoy optical cloaking technology in everyday life.
This work was supported by Toyota Motor Corporation Research Grant. This work was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1F1A1062380). This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2020R1A4A1017915).
The data that support the findings of this study are available from the corresponding author upon reasonable request.