## Abstract

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

## 1. Introduction

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 [18] and further to create optical illusions [19]. Recently, a test experiment on creating illusions was also demonstrated [20].

Physically, complementary medium layer is in fact a time reversal device to produce conjugated signal of the objects to be hidden [21]. 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 [22]. 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 ${\text{O}}_{\text{1}}$ with complex amplitude ${U}_{1}(x,y)=\left|{U}_{1}(x,y)\right|\mathrm{exp}[-j{\varphi}_{1}(x,y)]$, where $x$ and $y$ are the components of position vectors, $j$ is the imaginary unit, and ${\varphi}_{i}(x,y)$ (subscript $i$ is a variable) is the phase, one can use a time-reversal medium [21] produced conjugated wavefront ${U}_{1}{}^{*}(x,y)$ 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 = $A$) passes through a cloak (with transfer function$H$) and an object ${\text{O}}_{\text{1}}$ (its AS can be read as${H}_{1}=F[{U}_{1}(x,y)]$, $F$ denotes the Fourier transform operation), the AS of the transmitted light becomes to ${A}_{t}=AH{H}_{1}$. As $H$ and ${H}_{1}$ are conjugated to each other, we get

where $C$ is a real constant, which means that the information of object ${\text{O}}_{\text{1}}$ is cancelled [25–27].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 [30]. As sketched in Fig. 1 , for a hologram on the plane $\text{P}$ recording the information of object ${\text{O}}_{\text{1}}$ in front of the plane $\text{Q}$ and a plane reference wave $\text{R}$ with the complex amplitude$R(x,y)=\left|R(x,y)\right|\mathrm{exp}[-j{\varphi}_{r}(x,y)]$, we can get the transmittance of the hologram

To conceal object ${\text{O}}_{\text{1}}$, we consider term ${t}_{3}$ of Eq. (2). Supposing that a light beam ${\text{R}}^{*}$ with complex amplitude $B(x,y)={R}^{*}(x,y)$ is used to illuminate the hologram, we get a transmission light field $T(x,y)=B(x,y){t}_{3}=\beta R(x,y){R}^{*}(x,y){U}_{1}{}^{*}(x,y)$. To avoid the influence of the diffracted light beams corresponding to terms ${t}_{1}$ and ${t}_{2}$ on the transmission light beam, the angle between the reference light $\text{R}$ and the object light $\text{S}$ can be chosen to be large enough. Let the transmission light pass through object ${\text{O}}_{\text{1}}$ (still placed in front of the plane $\text{Q}$) once again, we get that the complex amplitude on the observing plane $\text{Q}$ is

Note that for a phase-modulated recording medium, the transmittance $t$ of the hologram is determined by the refractive index distribution $n={n}_{0}+\Delta n(x,y)$ [31], where${n}_{0}>1$,${n}_{0}\gg \left|\Delta n(x,y)\right|$, and $\Delta n(x,y)$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 ${\text{O}}_{1}$ [${U}_{1}(x,y)$] into another object ${\text{O}}_{\text{2}}$ [${U}_{2}(x,y)$], we can first make a hologram of closely placed objects ${\text{O}}_{1}$ and ${\text{O}}_{\text{2}}$ [see Fig. 1]. In this case, Eq. (2) changes to

Obviously, Eq. (4) expresses the same form of Eq. (2). Hence the hologram is with a positive refractive index.

Suppose that the illumination light is still a conjugated wave of reference beam, meaning $B(x,y)={R}^{*}(x,y)$, from term 3 of Eq. (4) we get the transmission light field of the hologram$T(x,y)=\beta {[{U}_{1}(x,y){U}_{2}(x,y)]}^{*}R(x,y)B(x,y)=\beta \text{'}{[{U}_{1}(x,y){U}_{2}(x,y)]}^{*}$. Let the transmission light pass through the object ${\text{O}}_{\text{1}}$ once again, we get that the complex amplitude on the observing plane $\text{Q}$ is

## 3. Numerical simulations

In the following, we will employ computer generated holography [32] to demonstrate the above results. The proposed optical scheme for the simulation is sketched in Fig. 1. Light from a laser source ($\lambda =632.8\text{nm}$) is collimated into a plane wave and then split by beam splitters $\text{A}$ and $\text{B}$ into three parts: an object beam $\text{L}$, a reference beam $\text{R}$, and an illumination beam ${\text{R}}^{*}$, which is a phase-conjugated beam of $\text{R}$for producing time-reversal signal. ${\text{S}}_{\text{1}}$, ${\text{S}}_{\text{2}}$, and ${\text{S}}_{3}$ are shutters. In the recording process of cloak, ${\text{S}}_{\text{1}}$ and ${\text{S}}_{\text{2}}$ are open while ${\text{S}}_{3}$ is closed. In this case, beam $\text{L}$ propagates through an object (objects) and interferes with reference beam $\text{R}$ on the cloak plane ($\text{P}$). After recording the cloak, ${\text{S}}_{3}$ is open while ${\text{S}}_{\text{1}}$ and ${\text{S}}_{\text{2}}$ are closed for creating time-reversal wave to realize invisibility or create illusion. In this case, the cloak is illuminated by ${\text{R}}^{*}$ (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 $\text{Q}$ after passing through an object placed in front of $\text{Q}$. For simplification, we assume ${\text{O}}_{\text{1}}$ and ${\text{O}}_{2}$ to be two-dimensional objects with the same size of $20\text{\hspace{0.17em}}\text{mm}\times 20\text{\hspace{0.17em}}\text{mm}$. The distance between $\text{Q}$ and $\text{P}$ is $d=1.23\text{\hspace{0.17em}}\text{m}$.

To conceal an object, we insert object ${\text{O}}_{\text{1}}$ in front of the observing plane $\text{Q}$ in both recording process and cloaking process. For a phase-only object ${\text{O}}_{\text{1}}$ [Fig. 2(a) ] with complex amplitude

Then, we consider transforming object ${\text{O}}_{\text{1}}$ to ${\text{O}}_{\text{2}}$ [Fig. 4(a) ], here ${\text{O}}_{\text{2}}$ is assumed to be a complex phase- and amplitude-modulated object with complex amplitude

## 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 [32]. 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.

## Acknowledgments

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).

## References and links

**1. **A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. **43**(4), 773–793 (1996). [CrossRef]

**2. **J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science **312**(5781), 1780–1782 (2006). [CrossRef] [PubMed]

**3. **U. Leonhardt, “Optical conformal mapping,” Science **312**(5781), 1777–1780 (2006). [CrossRef] [PubMed]

**4. **H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. **9**(5), 387–396 (2010). [CrossRef] [PubMed]

**5. **A. J. Danner, T. Tyc, and U. Leonhardt, “Controlling birefringence in dielectrics,” Nat. Photonics **5**(6), 357–359 (2011). [CrossRef]

**6. **J. Fischer, T. Ergin, and M. Wegener, “Three-dimensional polarization-independent visible-frequency carpet invisibility cloak,” Opt. Lett. **36**(11), 2059–2061 (2011). [CrossRef] [PubMed]

**7. **A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Phys. Rev. Lett. **100**(11), 113901 (2008). [CrossRef] [PubMed]

**8. **Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. **99**(11), 113903 (2007). [CrossRef] [PubMed]

**9. **W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics **1**(4), 224–227 (2007). [CrossRef]

**10. **J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. **101**(20), 203901 (2008). [CrossRef] [PubMed]

**11. **R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science **323**(5912), 366–369 (2009). [CrossRef] [PubMed]

**12. **J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. **8**(7), 568–571 (2009). [CrossRef] [PubMed]

**13. **L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics **3**(8), 461–463 (2009). [CrossRef]

**14. **T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science **328**(5976), 337–339 (2010). [CrossRef] [PubMed]

**15. **X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun **2**, 176 (2011). [CrossRef] [PubMed]

**16. **B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. **106**(3), 033901 (2011). [CrossRef] [PubMed]

**17. **D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science **314**(5801), 977–980 (2006). [CrossRef] [PubMed]

**18. **Y. Lai, H. Y. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. **102**(9), 093901 (2009). [CrossRef] [PubMed]

**19. **Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z.-Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. **102**(25), 253902 (2009). [CrossRef] [PubMed]

**20. **C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. **105**(23), 233906 (2010). [CrossRef] [PubMed]

**21. **G. A. Zheng, X. Heng, and C. H. Yang, “A phase conjugate mirror inspired approach for building cloaking structures with left-handed materials,” New J. Phys. **11**(3), 033010 (2009). [CrossRef] [PubMed]

**22. **J. B. Pendry and D. R. Smith, “Reversing light with negative refraction,” Phys. Today **57**(6), 37–43 (2004). [CrossRef]

**23. **J. W. Goodman, *Introduction to Fourier Optics,* 3rd ed. (McGraw-Hill, 2005).

**24. **M. Born and E. Wolf, *Principles of Optics* (Pergamon, 1970).

**25. **K. Wu and G. P. Wang, “General insight into the complementary medium-based camouflage devices from Fourier optics,” Opt. Lett. **35**(13), 2242–2244 (2010). [CrossRef] [PubMed]

**26. **K. Wu and G. Ping Wang, “Hiding objects and creating illusions above a carpet filter using a Fourier optics approach,” Opt. Express **18**(19), 19894–19901 (2010). [CrossRef] [PubMed]

**27. **K. Wu, Q. Cheng, and G. P. Wang, “Fourier optics theory for invisibility cloaks,” J. Opt. Soc. Am. B **28**(6), 1467–1474 (2011). [CrossRef]

**28. **X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics **5**(3), 154–157 (2011). [CrossRef] [PubMed]

**29. **Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics **2**(2), 110–115 (2008). [CrossRef] [PubMed]

**30. **J. B. Pendry, “Time reversal and negative refraction,” Science **322**(5898), 71–73 (2008). [CrossRef] [PubMed]

**31. **H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. **48**, 2909–2947 (1969).

**32. **T. Kreis, *Handbook of Holographic Interferometry Optical and Digital Methods* (Wiley-VCH, 2004).