Diameter-bandwidth product limitation of isolated-object cloaking

We show that cloaking of isolated objects is subject to a diameter-bandwidth product limitation: as the size of the object increases, the bandwidth of good (small cross-section) cloaking decreases inversely with the diameter, as a consequence of causality constraints even for perfect fabrication and materials with negligible absorption. This generalizes a previous result that perfect cloaking of isolated objects over a nonzero bandwidth violates causality. Furthermore, we demonstrate broader causality-based scaling limitations on any bandwidth-averaged cloaking cross-section, using complex analysis and the optical theorem to transform the frequency-averaged problem into a single scattering problem with transformed materials.

[1]  Steven G. Johnson,et al.  General scaling limitations of ground-plane and isolated-object cloaks , 2011, 1102.3897.

[2]  T. Cui,et al.  Arbitrarily elliptical–cylindrical invisible cloaking , 2008 .

[3]  Sergei A. Tretyakov,et al.  Broadband Electromagnetic Cloaking Realized With Transmission-Line and Waveguiding Structures , 2011, Proceedings of the IEEE.

[4]  M. Qiu,et al.  Cylindrical invisibility cloak with simplified material parameters is inherently visible. , 2007, Physical review letters.

[5]  Grant E. Carichner,et al.  Fundamentals of Aircraft and Airship Design, Volume 2 – Airship Design and Case Studies , 2013 .

[6]  S. Guenneau,et al.  Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section. , 2008, Optics letters.

[7]  J. Pendry,et al.  Three-Dimensional Invisibility Cloak at Optical Wavelengths , 2010, Science.

[8]  T. Cui,et al.  Three-dimensional broadband and broad-angle transformation-optics lens. , 2010, Nature communications.

[9]  D. Smith,et al.  Designing three-dimensional transformation optical media using quasiconformal coordinate transformations. , 2010, Physical review letters.

[10]  I. Smolyaninov,et al.  Two-dimensional metamaterial structure exhibiting reduced visibility at 500 nm. , 2008, Optics letters.

[11]  Dispersive cylindrical cloaks under nonmonochromatic illumination. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  J. Pendry,et al.  Hiding under the carpet: a new strategy for cloaking. , 2008, Physical review letters.

[13]  Vladimir M. Shalaev,et al.  Optical cloaking with metamaterials , 2006, physics/0611242.

[14]  L. Landau,et al.  statistical-physics-part-1 , 1958 .

[15]  G. Barbastathis,et al.  Macroscopic invisibility cloak for visible light. , 2010, Physical review letters.

[16]  G. Sterman.  An Introduction To Quantum Field Theory , 1994 .

[17]  J. Pendry,et al.  Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect. , 2007, Optics letters.

[18]  M. Qiu,et al.  Ideal cylindrical cloak: perfect but sensitive to tiny perturbations. , 2007, Physical review letters.

[19]  David R. Smith,et al.  Full-wave simulations of electromagnetic cloaking structures. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  J. Lourtioz,et al.  Infrared cloaking based on the electric response of split ring resonators. , 2008, Optics express.

[21]  G. Milton,et al.  On the cloaking effects associated with anomalous localized resonance , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[22]  Hongsheng Chen,et al.  Practical Limitations of an Invisibility Cloak , 2009 .

[23]  Che Ting Chan,et al.  Extending the bandwidth of electromagnetic cloaks , 2007 .

[24]  J. Pendry,et al.  Calculation of material properties and ray tracing in transformation media. , 2006, Optics express.

[25]  A. E. Culhaoglu,et al.  Bistatic scattering characterization of a three-dimensional broadband cloaking structure , 2011, 1109.6150.

[26]  J. Hao,et al.  Gain-assisted transformation optics. , 2011, Optics express.

[27]  Yu Luo,et al.  Macroscopic invisibility cloaking of visible light , 2010, Nature communications.

[28]  J. Lee,et al.  Direct visualization of optical frequency invisibility cloak based on silicon nanorod array. , 2009, Optics express.

[29]  D. Miller,et al.  On perfect cloaking. , 2006, Optics express.

[30]  R. J. Crewther,et al.  Introduction to quantum field theory , 1995, hep-th/9505152.

[31]  Boubacar Kante,et al.  Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies , 2009, 0907.4416.

[32]  David R. Smith,et al.  Metamaterial Electromagnetic Cloak at Microwave Frequencies , 2006, Science.

[33]  David R. Smith,et al.  Controlling Electromagnetic Fields , 2006, Science.

[34]  坂井 典祐,et al.  M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory, Addison-Wesley, New York and Tokyo, xxii+842p., 23.5×16.5cm [東工大理] , 1996 .

[35]  Baile Zhang,et al.  Spherical cloaking using nonlinear transformations for improved segmentation into concentric isotropic coatings. , 2009, Optics express.

[36]  A. Ward,et al.  Refraction and geometry in Maxwell's equations , 1996 .

[37]  T. Cui,et al.  Loss compensation in external cloaks using a thin layer of gain media , 2010 .

[38]  Roger G. Newton,et al.  Optical theorem and beyond , 1976 .

[39]  Steven G. Johnson,et al.  Delay-bandwidth and delay-loss limitations for cloaking of large objects. , 2010, Physical review letters.

[40]  N. Engheta,et al.  Achieving transparency with plasmonic and metamaterial coatings. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  David R. Smith,et al.  Broadband Ground-Plane Cloak , 2009, Science.

[42]  Obtaining a nonsingular two-dimensional cloak of complex shape from a perfect three-dimensional cloak , 2008 .

[43]  M. Lipson,et al.  Silicon nanostructure cloak operating at optical frequencies , 2009, 0904.3508.

[44]  Tie Jun Cui,et al.  Compact-sized and broadband carpet cloak and free-space cloak. , 2009, Optics express.

[45]  G. Bartal,et al.  An optical cloak made of dielectrics. , 2009, Nature materials.

[46]  D. Werner,et al.  Two-dimensional eccentric elliptic electromagnetic cloaks , 2008 .

[47]  Rodney S. Tucker,et al.  Delay–bandwidth product and storage density in slow-light optical buffers , 2005 .

[48]  Yijun Feng,et al.  Electromagnetic cloaking by layered structure of homogeneous isotropic materials. , 2007, Optics express.

[49]  Huanyang Chen,et al.  Time delays and energy transport velocities in three dimensional ideal cloaking devices , 2007, 0712.3985.

[50]  Xiang Zhang,et al.  A carpet cloak for visible light. , 2011, Nano letters.

[51]  Hua Ma,et al.  The open cloak , 2009 .

[52]  W. Marsden.  I and J , 2012 .

[53]  Andrew G. Glen,et al.  APPL , 2001 .

[54]  Chao Li,et al.  Experimental verification of broadband invisibility using a cloak based on inductor-capacitor networks , 2009 .

[55]  N. Engheta,et al.  Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials. , 2009, Physical review letters.

[56]  T. Tyc,et al.  Broadband Invisibility by Non-Euclidean Cloaking , 2009, Science.

[57]  U. Leonhardt,et al.  Notes on conformal invisibility devices , 2006, physics/0605227.

[58]  Martin Wegener,et al.  Optical microscopy of 3D carpet cloaks:ray-tracing calculations. , 2010, Optics express.