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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 23 — Nov. 7, 2011
  • pp: 23240–23248

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All dielectric macroscopic cloaks for hiding objects and creating illusions at visible frequencies

Qiluan Cheng, Kedi Wu, and Guo Ping Wang  »View Author Affiliations


Optics Express, Vol. 19, Issue 23, pp. 23240-23248 (2011)
http://dx.doi.org/10.1364/OE.19.023240


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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 OSA

1. Introduction

As a result of the pioneer works by Pendry and Leonhardt [1

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

–3

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

], invisibility cloaks have recently attracted increasing interests in wide fields [4

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

] 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

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

–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]

] or even naturally available materials [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]

]. The sizes of the hidden objects also become from microscopic to macroscopic domain [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]

–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]

]. 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

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]

] and further to create optical illusions [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]

]. Recently, a test experiment on creating illusions was also demonstrated [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]

].

Physically, complementary medium layer is in fact a time reversal device to produce conjugated signal of the objects to be hidden [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]

]. 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

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

]. 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 U 1(x,y)= | U 1(x,y)|exp[−j ϕ1(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

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]

] 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

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

,24

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

]. As a light beam (AS = A) passes through a cloak (with transfer function H) and an object O1 (its AS can be read as H1=F[ U 1(x,y)], F denotes the Fourier transform operation), the AS of the transmitted light becomes to At= AH H1. As H and H1 are conjugated to each other, we get
At= AH H1=C A
(1)
where C is a real constant, which means that the information of object O1 is cancelled [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]

–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]

].

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

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]

] and even been proposed to realize negative refraction [30

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

]. 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 amplitude R(x,y)= | R(x,y)|exp[−j ϕr(x,y)], we can get the transmittance of the hologram
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)}
(2)
(where superscript * indicates the conjugation, and β is a coefficient related to the recording medium and recording procedure of the hologram) [23

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

], which can be divided into t= t1+ t2+ t3, where t1=β[ | U 1(x,y)|2+ | R(x,y)|2], t2=β U 1(x,y) R *(x,y) and t3=β U 1 *(x,y) R(x,y), corresponding to 0, 1, and −1 diffraction orders of the hologram.

Fig. 1 (color online) Sketch of optical path for concealing objects and creating illusions. P and Q 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.

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=β R(x,y) R *(x,y) U 1 *(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)=β R(x,y) R *(x,y) U 1 *(x,y) U 1(x,y)= R'(x,y) U 1 *(x,y) U 1(x,y)= C0 R'(x,y)
(3)
where C0 is a real constant, R'(x,y)=β R(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)= C0 R'(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

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

], where n0>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 [ U 1(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{[ | 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)} .
(4)

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)=β [ U 1(x,y) U 2(x,y)] * R(x,y) B(x,y)=β' [ U 1(x,y) U 2(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' [ U 1(x,y) U 2(x,y)] * U 1(x,y)= C3 U 2 *(x,y)
(5)
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

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

] 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

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

,32

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

]. 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 20 mm×20 mm. The distance between Q and P is d=1.23 m.

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
U 1(x,y)= { exp(−j 7π 60),  (yellow area) exp(−j 163π 180),  (red area)
(6)
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 2.0e−14 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
U 1 '(x,y)= { exp(−j 7π 60),    (yellow area) 0.5exp(−j 163π 180),  (red area)
(7)
[the absolute value | U 1 '(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 | U 1 '(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 | U 1 '(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 2.0e−14], meaning that O1 is invisible now.

Fig. 2 (color online) Simulated results of concealing a phase-only object O1[ U 1(x,y)]. (a) Scheme of object O1; (b), (c) real and imaginary parts of U 1(x,y); (d), (e) fluctuation of observed real and imaginary parts of complex amplitude of O1 on Qplane around 1 and 0, respectively.
Fig. 3 (color online) Simulated results of concealing a complex phase- and amplitude-modulated object O1[ U 1 '(x,y)]. (a) Absolute value of U 1 '(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.

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
U 2(x,y)= { exp(−j 7π 60),       (yellow area) 0.5exp(−j 163π 180), (red area)
(8)
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 U 2(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 U 2(x,y). For the detector on the plane Q, only the intensity | U 2(x,y)|2 is considered, meaning there is no influence that the calculated light field and U 2(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 | U 1 '(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 | U 2(x,y)| [see Fig. 4 (b)], indicating that only O2 is now detectable.

Fig. 4 (color online) Simulated results of creating illusion of transforming a phase-only object O1 [ U 1(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.
Fig. 5 (color online) Simulated results of creating illusion of transforming a complex phase- and amplitude-modulated object O1[ U 1 '(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.

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

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

]. 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).

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(090.1760) Holography : Computer holography
(230.3205) Optical devices : Invisibility cloaks

ToC Category:
Physical Optics

History
Original Manuscript: August 1, 2011
Revised Manuscript: September 30, 2011
Manuscript Accepted: October 18, 2011
Published: November 1, 2011

Citation
Qiluan Cheng, Kedi Wu, and Guo Ping Wang, "All dielectric macroscopic cloaks for hiding objects and creating illusions at visible frequencies," Opt. Express 19, 23240-23248 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-23-23240


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References

  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,” Science312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
  3. U. Leonhardt, “Optical conformal mapping,” Science312(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]
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