We introduce and numerically demonstrate a kind of isotropic dielectric macroscopic cloaks for hiding objects and creating illusions at visible frequencies. The cloaks are designed by angular spectrum theory and their working principle is based upon time reversal and conjugation operation. We will demonstrate that the cloaks are capable of hiding both phase-only and lossy objects. The size of the object to be hidden and the distance between the object and the cloak can be in range of millimeter and meter scale, respectively. The results are demonstrated by computer generated holography. Our work may provide a new way for pushing invisibility cloaks a big step toward more realistic fields.
©2011 Optical Society of America
As a result of the pioneer works by Pendry and Leonhardt [1–3], invisibility cloaks have recently attracted increasing interests in wide fields [4–9] due to their possible realizations from microwaves and THz to IR wavelengths and even visible frequencies. The cloaks can be constructed with manmade anisotropic structures or isotropic dielectric materials [10–14] or even naturally available materials [15,16]. The sizes of the hidden objects also become from microscopic to macroscopic domain [15–17]. However, such cloaks must enclose or cover the objects to be hidden and the cloaks not just prevent the objects from visible to the outside observers, but also make the outside invisible to the cloaked region. To overcome these shortcomings, complementary medium-based cloaks were proposed to hide distant objects outside the cloaks  and further to create optical illusions . Recently, a test experiment on creating illusions was also demonstrated .
Physically, complementary medium layer is in fact a time reversal device to produce conjugated signal of the objects to be hidden . However, such cloaks designed by transformation optics require the constitutive materials with simultaneously negative permittivity and permeability, which means strong dispersion, loss, and narrow band as well as a challenge to the fabrication technologies of physical realization of the cloaks especially in optical wavelengths . Here, based on classical angular spectrum (AS) theory, we propose a kind of isotropic dielectric cloaks for realizing invisibility and creating illusions at visible frequencies. Each cloak is equivalent to a time reversal device, which produces a phase-conjugated wave to cancel the influence of an object on light field and hence makes the object invisible. This kind of cloaks is capable of hiding both lossy and phase-only macroscopic objects and even creating illusions. The distance between the cloak and the object is in a range of meter scale. The results are demonstrated by computer generated holography simulations.
2. Theoretical analysis
For an object with complex amplitude , where and are the components of position vectors, is the imaginary unit, and (subscript is a variable) is the phase, one can use a time-reversal medium  produced conjugated wavefront to cancel it, which is equivalent to a complementary medium-based distant cloak. This process can be understood by AS theory [23,24]. As a light beam (AS = ) passes through a cloak (with transfer function) and an object (its AS can be read as, denotes the Fourier transform operation), the AS of the transmitted light becomes to . As and are conjugated to each other, we get25–27].
To get a time-reversal light wave, holography is widely employed and has been successfully applied to get super-resolution images through scattering media [28, 29] and even been proposed to realize negative refraction . As sketched in Fig. 1 , for a hologram on the plane recording the information of object in front of the plane and a plane reference wave with the complex amplitude, we can get the transmittance of the hologram23], which can be divided into , where, and , corresponding to 0, 1, and −1 diffraction orders of the hologram.
To conceal object , we consider term of Eq. (2). Supposing that a light beam with complex amplitude is used to illuminate the hologram, we get a transmission light field . To avoid the influence of the diffracted light beams corresponding to terms and on the transmission light beam, the angle between the reference light and the object light can be chosen to be large enough. Let the transmission light pass through object (still placed in front of the plane ) once again, we get that the complex amplitude on the observing plane isEq. (1), meaning that the information of object is cancelled completely. For a plane light, the wave field on a plane, which is perpendicular to the direction of propagation of the light, is a constant at a certain moment. Therefore, although ( is a constant), the result of Eq. (3) indicates that the light field observed on the plane is a plane light field.
Note that for a phase-modulated recording medium, the transmittance of the hologram is determined by the refractive index distribution , where,, and is determined by the interference terms of Eq. (2). This is to say that the refractive index of the hologram is always positive, indicating that the cloak (here is a hologram) used to hide an object discussed above is with absolute positive refractive index.
On the other hand, to create an optical illusion for transforming object  into another object , we can first make a hologram of closely placed objects and [see Fig. 1]. In this case, Eq. (2) changes to
Suppose that the illumination light is still a conjugated wave of reference beam, meaning , from term 3 of Eq. (4) we get the transmission light field of the hologram. Let the transmission light pass through the object once again, we get that the complex amplitude on the observing plane is
3. Numerical simulations
In the following, we will employ computer generated holography  to demonstrate the above results. The proposed optical scheme for the simulation is sketched in Fig. 1. Light from a laser source () is collimated into a plane wave and then split by beam splitters and into three parts: an object beam , a reference beam , and an illumination beam , which is a phase-conjugated beam of for producing time-reversal signal. , , and are shutters. In the recording process of cloak, and are open while is closed. In this case, beam propagates through an object (objects) and interferes with reference beam on the cloak plane (). After recording the cloak, is open while and are closed for creating time-reversal wave to realize invisibility or create illusion. In this case, the cloak is illuminated by (the amplitude is assumed to be 1) and then produces a phase-conjugated light of the same object (objects) in the recording process [23,32]. The amplitude of the output light is calculated on the observing plane after passing through an object placed in front of . For simplification, we assume and to be two-dimensional objects with the same size of . The distance between and is .
To conceal an object, we insert object in front of the observing plane in both recording process and cloaking process. For a phase-only object [Fig. 2(a) ] with complex amplitudeFigs. 2(b)-2(c), the calculated results reveal that the observed real part and imaginary part of complex amplitude of on plane fluctuate less than around [Fig. 2(d)] and [Fig. 2 (e)], respectively, indicating that object is invisible. As is a complex phase- and amplitude-modulated object, its complex amplitude is assumed to beFig. 3(a) ], the calculated absolute value of complex amplitude of light on plane [Fig. 3(b)] is closely related to [see Fig. 3(a)]. Obviously, the object is detectable. However, as an amplitude-modulated plate, silver halide plate for example, with transmittance proportional to is inserted in front of , the absolute value of amplitude distribution of [Fig. 3(c)] approaches [with fluctuation less than ], meaning that is invisible now.
Then, we consider transforming object to [Fig. 4(a) ], here is assumed to be a complex phase- and amplitude-modulated object with complex amplitudeFigs. 4(b)-4(d), respectively. In this case, and are located in front of plane in the recording process and then is removed in the process of creating illusion. For a phase-only object [see Eq. (9) and Figs. 2(b)-2(c)], the calculated complex amplitude distribution of light on plane [real part, Fig. 4(e) and imaginary part, Fig. 4 (f)] is almost the same as [Figs. 4(c) and 4(d)], implying that object is indeed observed as . The negative value of the calculated imaginary part of light [Fig. 4 (f)] is due to the conjugation between the calculated light field and . For the detector on the plane , only the intensity is considered, meaning there is no influence that the calculated light field and are conjugated. If is a complex phase- and amplitude-modulated object [see Eq. (10) and Fig. 3(a)], the complex amplitude distribution of light on plane [Fig. 5(a) ] is strongly modulated by object , meaning that object is not hidden completely. Inserting an amplitude-modulated plate with amplitude transmittance proportional to in front of , we can see that the absolute value of complex amplitude of light [Fig. 5(b)] is the same as [see Fig. 4 (b)], indicating that only is now detectable.
4. Conclusions and discussions
To conclude, we have introduced and numerically demonstrated a kind of dielectric macroscopic cloaks for cloaking objects and creating illusions at visible frequencies. The working principle of the cloaks, which is designed by Fourier optics approach, is based upon time reversal and conjugation operation. We have shown that the cloaks are capable of hiding macroscopic phase-only and lossy objects as the distance between each object and its cloak is in a range of meter, which are numerically demonstrated by computer generated holography.
It should be pointed out that, to make sure that the light illuminating on the object to be concealed is strictly conjugated with the object light, our cloaks demonstrated here are limited in one direction and single wavelength. But they are easily extended, at least in principle, to work in large angle by, for example, using multiple reference-beam holography . Obviously, this multi-direction cloaking system is more complex than the cloaking system discussed in our paper. To simplify the process of analysis and calculation, the objects to be hidden are transparent or semi-transparent in our paper. In fact, reflection or scattering light of the opaque object can also be used as the object light to create the hologram to conceal the object. Therefore, the present method may open a new way for invisibility cloaks to work in more realistic fields.
This work is supported by 973 Program (Grants 2007CB935300 and 2011CB933600), NSFC (Grants 60925020 and 60736041), and Science and Technology Bureau of Wuhan City, Hubei, China (Grant No. 200951830552). K. D. W. is also supported by the academic award for excellent Ph. D. Candidates funded by Ministry of Education of China and the PhD candidates’ self-research program of Wuhan University (Grant 20082020101000013).
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