Abstract

Carpet or ground-plane invisibility cloaks hide an object in reflection and inhibit transmission experiments by construction. This concept has significantly reduced the otherwise demanding material requirements and has hence enabled various experimental demonstrations. In contrast, free-space invisibility cloaks should work in both reflection and transmission. The fabrication of omnidirectional three-dimensional free-space cloaks still poses significant challenges. Recently, the idea of the carpet cloak has been carried over to experiments on unidirectional free-space invisibility cloaks that only work perfectly for one particular viewing direction and, depending on the design, also for one linear polarization of light only. Here, by using photorealistic ray tracing, we visualize the performance of four types of such unidirectional cloaks in three dimensions for different viewing directions and different polarizations of light, revealing virtues and limitations of these approaches in an intuitive manner.

© 2013 OSA

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References

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2013 (1)

J. Fischer and M. Wegener, “Three-dimensional optical laser lithography beyond the diffraction limit,” Laser Photon. Rev.7(1), 22–44 (2013).
[CrossRef]

2012 (4)

2011 (3)

T. Ergin, J. Fischer, and M. Wegener, “Optical phase cloaking of 700 nm light waves in the far field by a three-dimensional carpet cloak,” Phys. Rev. Lett.107(17), 173901 (2011).
[CrossRef] [PubMed]

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, “Cross-section comparisons of cloaks designed by transformation optical and optical conformal mapping approaches,” J. Opt.13(2), 024002 (2011).
[CrossRef]

J. C. Halimeh, R. Schmied, and M. Wegener, “Newtonian photorealistic ray tracing of grating cloaks and correlation-function-based cloaking-quality assessment,” Opt. Express19(7), 6078–6092 (2011).
[CrossRef] [PubMed]

2010 (6)

2009 (2)

Y. Luo, J. Zhang, H. Chen, L. X. Ran, B. I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antenn. Propag.57(12), 3926–3933 (2009).
[CrossRef]

J. C. Halimeh, T. Ergin, J. Mueller, N. Stenger, and M. Wegener, “Photorealistic images of carpet cloaks,” Opt. Express17(22), 19328–19336 (2009).
[CrossRef] [PubMed]

2008 (1)

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

2007 (1)

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett.99(18), 183901 (2007).
[CrossRef] [PubMed]

2006 (5)

G. Dolling, M. Wegener, S. Linden, and C. Hormann, “Photorealistic images of objects in effective negative-index materials,” Opt. Express14(5), 1842–1849 (2006).
[CrossRef] [PubMed]

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys.8(10), 247 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

Akbarzadeh, A.

Busch, K.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater.20(7), 1038–1052 (2010).
[CrossRef]

Chen, H.

Y. Luo, J. Zhang, H. Chen, L. X. Ran, B. I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antenn. Propag.57(12), 3926–3933 (2009).
[CrossRef]

Danner, A. J.

Dolling, G.

Ergin, T.

T. Ergin, J. Fischer, and M. Wegener, “Optical phase cloaking of 700 nm light waves in the far field by a three-dimensional carpet cloak,” Phys. Rev. Lett.107(17), 173901 (2011).
[CrossRef] [PubMed]

J. C. Halimeh, T. Ergin, N. Stenger, and M. Wegener, “Transformationsoptik – Massgeschneiderter optischer Raum,” Phys. Unserer Zeit41, 170–175 (2010).
[CrossRef]

T. Ergin, J. C. Halimeh, N. Stenger, and M. Wegener, “Optical microscopy of 3D carpet cloaks:ray-tracing calculations,” Opt. Express18(19), 20535–20545 (2010).
[CrossRef] [PubMed]

J. C. Halimeh, T. Ergin, J. Mueller, N. Stenger, and M. Wegener, “Photorealistic images of carpet cloaks,” Opt. Express17(22), 19328–19336 (2009).
[CrossRef] [PubMed]

Essig, S.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater.20(7), 1038–1052 (2010).
[CrossRef]

Fischer, J.

J. Fischer and M. Wegener, “Three-dimensional optical laser lithography beyond the diffraction limit,” Laser Photon. Rev.7(1), 22–44 (2013).
[CrossRef]

T. Ergin, J. Fischer, and M. Wegener, “Optical phase cloaking of 700 nm light waves in the far field by a three-dimensional carpet cloak,” Phys. Rev. Lett.107(17), 173901 (2011).
[CrossRef] [PubMed]

Greenleaf, A.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett.99(18), 183901 (2007).
[CrossRef] [PubMed]

Halimeh, J. C.

Hormann, C.

Kong, J. A.

Y. Luo, J. Zhang, H. Chen, L. X. Ran, B. I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antenn. Propag.57(12), 3926–3933 (2009).
[CrossRef]

Kundtz, N. B.

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, “Cross-section comparisons of cloaks designed by transformation optical and optical conformal mapping approaches,” J. Opt.13(2), 024002 (2011).
[CrossRef]

Kurylev, Y.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett.99(18), 183901 (2007).
[CrossRef] [PubMed]

Landy, N.

N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. Mater.12(1), 25–28 (2012).
[CrossRef] [PubMed]

Lassas, M.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett.99(18), 183901 (2007).
[CrossRef] [PubMed]

Ledermann, A.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater.20(7), 1038–1052 (2010).
[CrossRef]

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys.8(10), 247 (2006).
[CrossRef]

Li, J.

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

Linden, S.

Luo, Y.

Y. Luo, J. Zhang, H. Chen, L. X. Ran, B. I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antenn. Propag.57(12), 3926–3933 (2009).
[CrossRef]

Mueller, J.

Pendry, J. B.

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, “Cross-section comparisons of cloaks designed by transformation optical and optical conformal mapping approaches,” J. Opt.13(2), 024002 (2011).
[CrossRef]

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, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

Philbin, T. G.

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys.8(10), 247 (2006).
[CrossRef]

Ran, L. X.

Y. Luo, J. Zhang, H. Chen, L. X. Ran, B. I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antenn. Propag.57(12), 3926–3933 (2009).
[CrossRef]

Schmied, R.

Schurig, D.

Smith, D. R.

Y. Urzhumov and D. R. Smith, “Low-loss directional cloaks without superluminal velocity or magnetic response,” Opt. Lett.37(21), 4471–4473 (2012).
[CrossRef] [PubMed]

N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. Mater.12(1), 25–28 (2012).
[CrossRef] [PubMed]

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, “Cross-section comparisons of cloaks designed by transformation optical and optical conformal mapping approaches,” J. Opt.13(2), 024002 (2011).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

Staude, I.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater.20(7), 1038–1052 (2010).
[CrossRef]

Stenger, N.

Thiel, M.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater.20(7), 1038–1052 (2010).
[CrossRef]

Uhlmann, G.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett.99(18), 183901 (2007).
[CrossRef] [PubMed]

Urzhumov, Y.

Urzhumov, Y. A.

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, “Cross-section comparisons of cloaks designed by transformation optical and optical conformal mapping approaches,” J. Opt.13(2), 024002 (2011).
[CrossRef]

von Freymann, G.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater.20(7), 1038–1052 (2010).
[CrossRef]

Wegener, M.

J. Fischer and M. Wegener, “Three-dimensional optical laser lithography beyond the diffraction limit,” Laser Photon. Rev.7(1), 22–44 (2013).
[CrossRef]

J. C. Halimeh and M. Wegener, “Photorealistic ray tracing of free-space invisibility cloaks made of uniaxial dielectrics,” Opt. Express20(27), 28330–28340 (2012).
[CrossRef] [PubMed]

J. C. Halimeh and M. Wegener, “Time-of-flight imaging of invisibility cloaks,” Opt. Express20(1), 63–74 (2012).
[CrossRef] [PubMed]

T. Ergin, J. Fischer, and M. Wegener, “Optical phase cloaking of 700 nm light waves in the far field by a three-dimensional carpet cloak,” Phys. Rev. Lett.107(17), 173901 (2011).
[CrossRef] [PubMed]

J. C. Halimeh, R. Schmied, and M. Wegener, “Newtonian photorealistic ray tracing of grating cloaks and correlation-function-based cloaking-quality assessment,” Opt. Express19(7), 6078–6092 (2011).
[CrossRef] [PubMed]

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater.20(7), 1038–1052 (2010).
[CrossRef]

T. Ergin, J. C. Halimeh, N. Stenger, and M. Wegener, “Optical microscopy of 3D carpet cloaks:ray-tracing calculations,” Opt. Express18(19), 20535–20545 (2010).
[CrossRef] [PubMed]

J. C. Halimeh, T. Ergin, N. Stenger, and M. Wegener, “Transformationsoptik – Massgeschneiderter optischer Raum,” Phys. Unserer Zeit41, 170–175 (2010).
[CrossRef]

R. Schmied, J. C. Halimeh, and M. Wegener, “Conformal carpet and grating cloaks,” Opt. Express18(23), 24361–24367 (2010).
[CrossRef] [PubMed]

J. C. Halimeh, T. Ergin, J. Mueller, N. Stenger, and M. Wegener, “Photorealistic images of carpet cloaks,” Opt. Express17(22), 19328–19336 (2009).
[CrossRef] [PubMed]

G. Dolling, M. Wegener, S. Linden, and C. Hormann, “Photorealistic images of objects in effective negative-index materials,” Opt. Express14(5), 1842–1849 (2006).
[CrossRef] [PubMed]

Wu, B. I.

Y. Luo, J. Zhang, H. Chen, L. X. Ran, B. I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antenn. Propag.57(12), 3926–3933 (2009).
[CrossRef]

Zhang, J.

Y. Luo, J. Zhang, H. Chen, L. X. Ran, B. I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antenn. Propag.57(12), 3926–3933 (2009).
[CrossRef]

Adv. Funct. Mater. (1)

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater.20(7), 1038–1052 (2010).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

Y. Luo, J. Zhang, H. Chen, L. X. Ran, B. I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antenn. Propag.57(12), 3926–3933 (2009).
[CrossRef]

J. Opt. (1)

Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, “Cross-section comparisons of cloaks designed by transformation optical and optical conformal mapping approaches,” J. Opt.13(2), 024002 (2011).
[CrossRef]

J. Opt. Soc. Am. A (1)

Laser Photon. Rev. (1)

J. Fischer and M. Wegener, “Three-dimensional optical laser lithography beyond the diffraction limit,” Laser Photon. Rev.7(1), 22–44 (2013).
[CrossRef]

Nat. Mater. (1)

N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. Mater.12(1), 25–28 (2012).
[CrossRef] [PubMed]

New J. Phys. (1)

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys.8(10), 247 (2006).
[CrossRef]

Opt. Express (9)

J. C. Halimeh and M. Wegener, “Time-of-flight imaging of invisibility cloaks,” Opt. Express20(1), 63–74 (2012).
[CrossRef] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14(21), 9794–9804 (2006).
[CrossRef] [PubMed]

J. C. Halimeh, R. Schmied, and M. Wegener, “Newtonian photorealistic ray tracing of grating cloaks and correlation-function-based cloaking-quality assessment,” Opt. Express19(7), 6078–6092 (2011).
[CrossRef] [PubMed]

J. C. Halimeh and M. Wegener, “Photorealistic ray tracing of free-space invisibility cloaks made of uniaxial dielectrics,” Opt. Express20(27), 28330–28340 (2012).
[CrossRef] [PubMed]

J. C. Halimeh, T. Ergin, J. Mueller, N. Stenger, and M. Wegener, “Photorealistic images of carpet cloaks,” Opt. Express17(22), 19328–19336 (2009).
[CrossRef] [PubMed]

T. Ergin, J. C. Halimeh, N. Stenger, and M. Wegener, “Optical microscopy of 3D carpet cloaks:ray-tracing calculations,” Opt. Express18(19), 20535–20545 (2010).
[CrossRef] [PubMed]

A. J. Danner, “Visualizing invisibility: metamaterials-based optical devices in natural environments,” Opt. Express18(4), 3332–3337 (2010).
[CrossRef] [PubMed]

G. Dolling, M. Wegener, S. Linden, and C. Hormann, “Photorealistic images of objects in effective negative-index materials,” Opt. Express14(5), 1842–1849 (2006).
[CrossRef] [PubMed]

R. Schmied, J. C. Halimeh, and M. Wegener, “Conformal carpet and grating cloaks,” Opt. Express18(23), 24361–24367 (2010).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. Lett. (3)

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. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett.99(18), 183901 (2007).
[CrossRef] [PubMed]

T. Ergin, J. Fischer, and M. Wegener, “Optical phase cloaking of 700 nm light waves in the far field by a three-dimensional carpet cloak,” Phys. Rev. Lett.107(17), 173901 (2011).
[CrossRef] [PubMed]

Phys. Unserer Zeit (1)

J. C. Halimeh, T. Ergin, N. Stenger, and M. Wegener, “Transformationsoptik – Massgeschneiderter optischer Raum,” Phys. Unserer Zeit41, 170–175 (2010).
[CrossRef]

Science (2)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

Other (3)

U. Leonhardt and T. G. Philbin, Geometry and Light: The Science of Invisibility (Dover, 2010).

http://www.youtube.com/watch?v=RwgIr06OJLo

S. Andrew, Glassner, An Introduction to Ray Tracing (Morgan Kaufmann, 1989).

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Figures (9)

Fig. 1
Fig. 1

Illustration showing the virtual camera (blue eye) observing either (a) the piecewise homogeneous anisotropic unidirectional free-space cloak for designs (i)-(iii) or (b) the inhomogeneous isotropic unidirectional free-space cloak for design (iv). The model stands behind the cloak. The cloak in (a) has a square cross section of side length 14.1 cm enveloping a rhombic cloaked region of side length 11.51 cm. In the inset, the local u-axis (v-axis) makes an angle of 33.54 degrees counterclockwise with respect to the y-axis (x-axis). The cloak in (b) has a rectangular cross section of width 50 cm and height 57.14 cm, enveloping a roughly Gaussian cloaked region [12]. Each cloaked region has an area of 114.83 cm2 in the center vertical plane. The axis of either cloak is 50 cm away from the model.

Fig. 2
Fig. 2

The piecewise homogeneous positive-uniaxial birefringent unidirectional free-space cloak under view along the transformation axis. (a) The bare field of view (FOV) as viewed by the virtual camera (see Fig. 1). (b) A rhombic mirror structure is placed in between the model and the virtual camera. (c) The cloak is placed around this structure and viewed for unpolarized light. (d) A horizontal linear polarizer is placed in front of the virtual camera, showing good cloaking behavior as extraordinary light dominates this setting, despite nontrivial ordinary contributions. (e) A vertical linear polarizer is placed in front of the virtual camera, showing bad cloaking behavior as ordinary light is dominant for this setting.

Fig. 3
Fig. 3

The piecewise homogeneous positive-uniaxial birefringent unidirectional free-space cloak under views away from the transformation axis. The bare mirror structure is shown and the corresponding cloaking result for horizontally linear polarized light, respectively for rotations of (a), (b) 5 degrees, (c), (d) 10 degrees, and (e), (f) 20 degrees around the axis of the cloak. The behavior of the unidirectional cloak for views not along the transformation axis is akin to a carpet cloak. Note the strong Fresnel reflections (b), (d), and (f) and the significant ordinary-light contributions particularly present in (b).

Fig. 4
Fig. 4

Same as Fig. 2, but for the negative-uniaxial variant of the piecewise homogeneous birefringent unidirectional free-space cloak. For horizontally polarized light, the cloaking behavior of this cloak is formidable as shown in (d). The step-like behavior of the vertically polarized light is due to ordinary light getting trapped in the corresponding segment of the cloak and escaping only after several total internal reflections. This is due to the fact that for this design μ o =3.271 in the corresponding cloak segment. Fresnel-reflection coefficients for this cloak are of the order of less than 3%.

Fig. 5
Fig. 5

Same as Fig. 3, but for the negative-uniaxial variant of the piecewise homogeneous birefringent unidirectional free-space cloak. Note how here the Fresnel reflections are much diminished in contrast to Fig. 3. This cloak acts as a very good three-dimensional polarization dependent carpet cloak for views away from the transformation axis, leading to the illusion of a flat mirror rotated at the same angle the cloak is rotated at.

Fig. 6
Fig. 6

Cloaking behavior of the piecewise homogeneous singly refracting unidirectional free-space cloak for a view along the transformation axis. This is a perfect cloak for this viewing direction. In (b), a rhombic mirror structure is introduced that hides the model and leads to a significant distortion of the bare FOV shown in (a). Upon introducing the singly refracting unidirectional cloak, the original bare FOV is retrieved perfectly, as shown in (c). Wave-cloaking behavior depicted in (d) by relative TOF difference is also perfect and limited only by machine precision, where the values are in the range of yoctoseconds (1 ys = 10−24 s). Note the superiority of this design to its uniaxial approximations in cloaks (i) and (ii).

Fig. 7
Fig. 7

Cloaking behavior of the piecewise homogeneous singly refracting unidirectional free-space cloak for views away from the transformation axis. The bare mirror structure is visualized along with its corresponding cloaked view for rotations of (a), (b) 5 degrees, (c), (d) 10 degrees, and (e), (f) 20 degrees. It is observed that this cloak acts as a perfect carpet cloak for views away from the transformation axis.

Fig. 8
Fig. 8

The inhomogeneous locally isotropic double-Gaussian unidirectional free-space cloak for a view along the transformation axis. The Gaussian-like corrugation in (b) is cloaked amazingly well upon introduction of the cloak in (c). Worthy to note is that the cloaking performance in 3D is also very good. Moreover, the wave cloaking of this device is also formidable as shown in (d), where the TOF-difference map indicates a maximum relative error of 6% with values smaller than 0.1 nanosecond (1 ns = 10−9 s). Fresnel-reflection coefficients for this setting are of the order of 0.01% or less.

Fig. 9
Fig. 9

The inhomogeneous locally isotropic double-Gaussian unidirectional free-space cloak for views away from the transformation axis. The mirror corrugation and its cloaking are shown for rotations of (a), (b) 5 degrees, (c), (d) 10 degrees, and (e), (f) 20 degrees. It is seen that the double-Gaussian unidirectional cloak behaves similarly to the Gaussian carpet cloak [12,19] for views away from the transformation axis. Fresnel-reflection coefficients for the above settings are 0.2% or less.

Tables (1)

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Table 1 List of Photorealistic Renderings of Various Devices

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