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 [13], invisibility cloaks have recently attracted increasing interests in wide fields [49] 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 [1014] or even naturally available materials [15,16]. The sizes of the hidden objects also become from microscopic to macroscopic domain [1517]. 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 O1 with complex amplitude U1(x,y)=|U1(x,y)|exp[jϕ1(x,y)], where x and y are the components of position vectors, j is the imaginary unit, and ϕi(x,y) (subscript i is a variable) is the phase, one can use a time-reversal medium [21] produced conjugated wavefront U1*(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 functionH) and an object O1 (its AS can be read asH1=F[U1(x,y)], F denotes the Fourier transform operation), the AS of the transmitted light becomes to At=AHH1. As H and H1 are conjugated to each other, we get

At=AHH1=CA
where C is a real constant, which means that the information of object O1 is cancelled [2527].

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 P recording the information of object O1 in front of the plane Q and a plane reference wave R with the complex amplitudeR(x,y)=|R(x,y)|exp[jϕr(x,y)], we can get the transmittance of the hologram

t=β{[|U1(x,y)|2+|R(x,y)|2]+U1(x,y)R(x,y)*+U1*(x,y)R(x,y)}
(where superscript * indicates the conjugation, and β is a coefficient related to the recording medium and recording procedure of the hologram) [23], which can be divided into t=t1+t2+t3, wheret1=β[|U1(x,y)|2+|R(x,y)|2], t2=βU1(x,y)R*(x,y) and t3=βU1*(x,y)R(x,y), corresponding to 0, 1, and −1 diffraction orders of the hologram.

 figure: Fig. 1

Fig. 1 (color online) Sketch of optical path for concealing objects and creating illusions. P andQ are the cloaking and observing planes; O1, and O2 are objects; A and Bare the beam splitters; C, D, and E are the mirrors; and S1, S2, and S3 are the shutters. In the recording process, S1 and S2 are open while S3is closed; in the reconstruction process, S3 is open while S1 and S2 are closed.

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To conceal object O1, we consider term t3 of Eq. (2). Supposing that a light beam 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)t3=βR(x,y)R*(x,y)U1*(x,y). To avoid the influence of the diffracted light beams corresponding to terms t1 and t2 on the transmission light beam, the angle between the reference light R and the object light S can be chosen to be large enough. Let the transmission light pass through object O1 (still placed in front of the plane Q) once again, we get that the complex amplitude on the observing plane Q is

T'(x,y)=βR(x,y)R*(x,y)U1*(x,y)U1(x,y)=R'(x,y)U1*(x,y)U1(x,y)=C0R'(x,y)
where C0 is a real constant, R'(x,y)=βR(x,y)R*(x,y), which expresses a plane light without the information of object O1, is corresponding to A in Eq. (1), meaning that the information of object O1 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 T'(x,y)=C0R'(x,y)=C1 (C1 is a constant), the result of Eq. (3) indicates that the light field observed on the plane Q is a plane light field.

Note that for a phase-modulated recording medium, the transmittance t of the hologram is determined by the refractive index distribution n=n0+Δn(x,y) [31], wheren0>1,n0|Δn(x,y)|, and Δn(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 O1 [U1(x,y)] into another object O2 [U2(x,y)], we can first make a hologram of closely placed objects O1 and O2 [see Fig. 1]. In this case, Eq. (2) changes to

t=β{[|U1(x,y)U2(x,y)|2+|R(x,y)|2]+[U1(x,y)U2(x,y)]R(x,y)*+[U1(x,y)U2(x,y)]*R(x,y)}.

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 hologramT(x,y)=β[U1(x,y)U2(x,y)]*R(x,y)B(x,y)=β'[U1(x,y)U2(x,y)]*. Let the transmission light pass through the object O1 once again, we get that the complex amplitude on the observing plane Q is

T'(x,y)=β'[U1(x,y)U2(x,y)]*U1(x,y)=C3U2*(x,y)
where C3 is a real constant. As a result, we can only observe object O2.

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 (λ=632.8nm) is collimated into a plane wave and then split by beam splitters A and B into three parts: an object beam L, a reference beam R, and an illumination beam R*, which is a phase-conjugated beam of Rfor producing time-reversal signal. S1, S2, and S3 are shutters. In the recording process of cloak, S1 and S2 are open while S3 is closed. In this case, beam L propagates through an object (objects) and interferes with reference beam R on the cloak plane (P). After recording the cloak, S3 is open while S1 and S2 are closed for creating time-reversal wave to realize invisibility or create illusion. In this case, the cloak is illuminated by 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 Q after passing through an object placed in front of Q. For simplification, we assume O1 and O2 to be two-dimensional objects with the same size of 20mm×20mm. The distance between Q and P is d=1.23m.

To conceal an object, we insert object O1 in front of the observing plane Q in both recording process and cloaking process. For a phase-only object O1 [Fig. 2(a) ] with complex amplitude

U1(x,y)={exp(j7π60),(yellowarea)exp(j163π180),(redarea)
which are shown in Figs. 2(b)-2(c), the calculated results reveal that the observed real part and imaginary part of complex amplitude of O1 on Q plane fluctuate less than 2.0e14 around 1 [Fig. 2(d)] and 0 [Fig. 2 (e)], respectively, indicating that object O1 is invisible. As O1 is a complex phase- and amplitude-modulated object, its complex amplitude is assumed to be
U1'(x,y)={exp(j7π60),(yellowarea)0.5exp(j163π180),(redarea)
[the absolute value |U1'(x,y)| is shown in Fig. 3(a) ], the calculated absolute value of complex amplitude of light on Q plane [Fig. 3(b)] is closely related to |U1'(x,y)|2[see Fig. 3(a)]. Obviously, the object is detectable. However, as an amplitude-modulated plate, silver halide plate for example, with transmittance proportional to |U1'(x,y)|2 is inserted in front of O1, the absolute value of amplitude distribution of O1 [Fig. 3(c)] approaches 1 [with fluctuation less than 2.0e14], meaning that O1 is invisible now.

 figure: Fig. 2

Fig. 2 (color online) Simulated results of concealing a phase-only object O1[U1(x,y)]. (a) Scheme of object O1; (b), (c) real and imaginary parts of U1(x,y); (d), (e) fluctuation of observed real and imaginary parts of complex amplitude of O1 on Qplane around 1 and 0, respectively.

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 figure: Fig. 3

Fig. 3 (color online) Simulated results of concealing a complex phase- and amplitude-modulated object O1[U1'(x,y)]. (a) Absolute value of U1'(x,y); (b) observed absolute values of complex amplitude of O1 on Q plane without amplitude modulated plate; (c) fluctuation of absolute values of the output complex amplitude on Q plane around 1 with amplitude modulated plate.

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Then, we consider transforming object O1 to O2 [Fig. 4(a) ], here O2 is assumed to be a complex phase- and amplitude-modulated object with complex amplitude

U2(x,y)={exp(j7π60),(yellowarea)0.5exp(j163π180),(redarea)
and its absolute value, real and imaginary parts are shown in Figs. 4(b)-4(d), respectively. In this case, O1 and O2 are located in front of plane Q in the recording process and then O2 is removed in the process of creating illusion. For a phase-only object O1 [see Eq. (9) and Figs. 2(b)-2(c)], the calculated complex amplitude distribution of light on Q plane [real part, Fig. 4(e) and imaginary part, Fig. 4 (f)] is almost the same as U2(x,y) [Figs. 4(c) and 4(d)], implying that object O1 is indeed observed as O2. The negative value of the calculated imaginary part of light [Fig. 4 (f)] is due to the conjugation between the calculated light field and U2(x,y). For the detector on the plane Q, only the intensity |U2(x,y)|2 is considered, meaning there is no influence that the calculated light field and U2(x,y) are conjugated. If O1 is a complex phase- and amplitude-modulated object [see Eq. (10) and Fig. 3(a)], the complex amplitude distribution of light on Q plane [Fig. 5(a) ] is strongly modulated by object O1, meaning that object O1 is not hidden completely. Inserting an amplitude-modulated plate with amplitude transmittance proportional to |U1'(x,y)|2 in front of O1, we can see that the absolute value of complex amplitude of light [Fig. 5(b)] is the same as |U2(x,y)| [see Fig. 4 (b)], indicating that only O2 is now detectable.

 figure: Fig. 4

Fig. 4 (color online) Simulated results of creating illusion of transforming a phase-only object O1 [U1(x,y)] into O2 [U2(x,y)]. (a) Scheme of object O2; (b), (c), (d) absolute value, real and imaginary parts of U2(x,y); (e), (f) observed real and imaginary parts of complex amplitude of light on Q plane.

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 figure: Fig. 5

Fig. 5 (color online) Simulated results of creating illusion of transforming a complex phase- and amplitude-modulated object O1[U1'(x,y)] into O2[U2(x,y)]. (a), (b) Observed absolute values of complex amplitude of light on Q plane without (a) and with (b) an amplitude modulated plate, respectively.

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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).

References

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  • |

  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).

2011 (6)

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

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]

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]

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

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]

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]

2010 (5)

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]

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]

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]

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]

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

2009 (6)

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]

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]

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]

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]

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]

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]

2008 (4)

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]

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

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

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

2007 (2)

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]

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

2006 (3)

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

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

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]

2004 (1)

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

1996 (1)

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

1969 (1)

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

Alu, A.

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

Barbastathis, G.

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

Bartal, G.

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]

Brenner, P.

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]

Cai, W.

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

Cardenas, J.

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]

Chan, C. T.

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

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]

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]

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]

Chen, H.

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

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]

Chen, H. Y.

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]

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]

Chen, X.

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]

Cheng, Q.

Chettiar, U. K.

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

Chin, J. Y.

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]

Cui, T. J.

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]

Cummer, S. A.

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]

Danner, A. J.

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

Engheta, N.

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

Ergin, T.

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]

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]

Fang, G.

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]

Feld, M. S.

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]

Fischer, J.

Gabrielli, L. H.

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]

Han, D. Z.

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]

Heng, X.

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]

Ji, C.

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]

Jiang, K.

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]

Justice, B. J.

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]

Kildishev, A. V.

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

Kogelnik, H.

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

Lai, Y.

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]

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]

Leonhardt, U.

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

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

Li, C.

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]

Li, F.

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]

Li, J.

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]

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

Lipson, M.

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]

Liu, H.

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]

Liu, R.

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]

Liu, X.

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

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]

Luo, Y.

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

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]

Meng, X.

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]

Mock, J. J.

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]

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]

Neff, C. W.

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]

Ng, J.

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]

Pendry, J. B.

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]

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]

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

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

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

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]

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

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

Poitras, C. B.

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]

Psaltis, D.

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]

Qiu, M.

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]

Ruan, Z.

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]

Schurig, D.

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

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]

Shalaev, V. M.

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

Sheng, P.

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

Smith, D. R.

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]

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

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]

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

Starr, A. F.

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]

Stenger, N.

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]

Tyc, T.

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

Valentine, J.

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]

Wang, G. P.

Wang, G. Ping

Wang, L. V.

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]

Ward, A. J.

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

Wegener, M.

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]

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]

Wu, K.

Xiao, J. J.

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]

Xu, X.

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]

Yan, M.

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]

Yang, C.

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]

Yang, C. H.

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]

Yaqoob, Z.

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]

Zentgraf, T.

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]

Zhang, B.

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

Zhang, J.

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]

Zhang, S.

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]

Zhang, X.

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]

Zhang, Z.-Q.

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]

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]

Zheng, G. A.

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]

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Figures (5)

Fig. 1
Fig. 1 (color online) Sketch of optical path for concealing objects and creating illusions. P andQ are the cloaking and observing planes; O 1 , and O 2 are objects; A and Bare the beam splitters; C, D, and E are the mirrors; and S 1 , S 2 , and S 3 are the shutters. In the recording process, S 1 and S 2 are open while S 3 is closed; in the reconstruction process, S 3 is open while S 1 and S 2 are closed.
Fig. 2
Fig. 2 (color online) Simulated results of concealing a phase-only object O 1 [ U 1 ( x , y ) ]. (a) Scheme of object O 1 ; (b), (c) real and imaginary parts of U 1 ( x , y ) ; (d), (e) fluctuation of observed real and imaginary parts of complex amplitude of O 1 on Qplane around 1 and 0, respectively.
Fig. 3
Fig. 3 (color online) Simulated results of concealing a complex phase- and amplitude-modulated object O 1 [ U 1 '(x,y) ]. (a) Absolute value of U 1 '(x,y) ; (b) observed absolute values of complex amplitude of O 1 on Q plane without amplitude modulated plate; (c) fluctuation of absolute values of the output complex amplitude on Q plane around 1 with amplitude modulated plate.
Fig. 4
Fig. 4 (color online) Simulated results of creating illusion of transforming a phase-only object O 1 [ U 1 (x,y) ] into O 2 [ U 2 (x,y) ]. (a) Scheme of object O 2 ; (b), (c), (d) absolute value, real and imaginary parts of U 2 (x,y) ; (e), (f) observed real and imaginary parts of complex amplitude of light on Q plane.
Fig. 5
Fig. 5 (color online) Simulated results of creating illusion of transforming a complex phase- and amplitude-modulated object O 1 [ U 1 '(x,y) ] into O 2 [ U 2 (x,y) ]. (a), (b) Observed absolute values of complex amplitude of light on Q plane without (a) and with (b) an amplitude modulated plate, respectively.

Equations (8)

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A t =AH H 1 =CA
t=β{[ | U 1 (x,y) | 2 + | R(x,y) | 2 ]+ U 1 (x,y)R (x,y) * + U 1 * (x,y)R(x,y)}
T'(x,y)=βR(x,y) R * (x,y) U 1 * (x,y) U 1 (x,y)=R'(x,y) U 1 * (x,y) U 1 (x,y)= C 0 R'(x,y)
t=β{[ | U 1 (x,y) U 2 (x,y) | 2 + | R(x,y) | 2 ]+[ U 1 (x,y) U 2 (x,y)]R (x,y) * + [ U 1 (x,y) U 2 (x,y)] * R(x,y)} .
T'(x,y)=β' [ U 1 (x,y) U 2 (x,y)] * U 1 (x,y)= C 3 U 2 * (x,y)
U 1 (x,y)={ exp(j 7π 60 ),(yellow area) exp(j 163π 180 ),(red area)
U 1 '(x,y)={ exp(j 7π 60 ),(yellow area) 0.5exp(j 163π 180 ),(red area)
U 2 (x,y)={ exp(j 7π 60 ),(yellow area) 0.5exp(j 163π 180 ),(red area)

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