屏蔽裝置(cloaking)是近年來極為熱門的研究，許多學者紛紛投入其中，各領域不乏此類研究，例如電磁學、光學、聲學、應力波、熱傳學等等，而本文將引入不完美介面概念來探討熱屏蔽問題。本文模型分為球型與圓柱兩種物體，考慮不完美介面效應發生在物體與斗篷兩者之間的介面，並探討在靜態與時諧這兩種熱傳方式下的異向性屏蔽裝置，在靜態問題中所推導出來的斗篷材料跟不完美介面參數、熱導係數、物體及斗篷尺寸有關，而時間諧合問題中在準靜態的假設下所推導出來的斗篷材料跟不完美介面參數、熱導係數、物體及斗篷尺寸、容積熱容有關，其中不完美介面參數為常數與位置無關。本文也將各設計屏蔽裝置有關的參數作數值分析，討論各參數對屏蔽效果的影響，從中可看到不完美介面在屏蔽裝置的應用，提出與以往不考慮不完美介面效應的屏蔽裝置有何不同之處。

In this thesis, we theoretically and numerically analyze thermal invisibility based on the concept of scattering cancellation and imperfect interface. We show that an anisotropic shell with imperfect interface may drastically suppress the scattering from cylindrical or spherical objects under static or time-harmonic conditions. The imperfect interface exists between object and shell. It means that the heat flow outside the object and the cloak made of the shell and interface behaves as if the object is not present. In static condition, we find that the cloak depends on the interface parameters, conductivity, and the size of the object and cloak. While, under time-harmonic condition, the cloak depends on not only the previous material and geometric properties, but also the volumetric heat capacity in quasi-static limit. In addition, we discuss each parameter how to influence the thermal invisibility. Unlike previous research, we consider the imperfect interface parameters so that we have more freedoms to design the thermal cloak.

Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical tables. Courier Corporation, (1964).

Alù, A., Mantle cloak: Invisibility induced by a surface, Physical Review B 80(24), 245115 (2009).

Alù, A., Viewpoint: Thermal cloaks get hot, Physics 7, 12 (2014).

Alù, A. and N. Engheta, Achieving transparency with plasmonic and metamaterial coatings, Physical Review E 72(1), 016623 (2005).

Arfken, G. B., H. J. Weber and F. E. Harris, Mathematical Methods for Physicists. Amsterdam ; Boston: Elsevier, (2011).

Balanis, C. A., Advanced Engineering Electromagnetics. Hoboken, N.J.: Wiley, (1989).

Benveniste, Y. and T. Miloh, The effective conductivity of composites with imperfect thermal contact at constituent interfaces, International Journal of Engineering Science 24(9), 1537-1552 (1986).

Brown, R. G., Classical electrodynamics-part II. Retrieved from http://www.thp.uni-koeln.de/alexal/pdf/electrodynamics.pdf (2007).

Brun, M., S. Guenneau and A. B. Movchan, Achieving control of in-plane elastic waves, Applied Physics Letters 94(6), 061903 (2009).

Cai, W., U. K. Chettiar, A. V. Kildishev and V. M. Shalaev, Optical cloaking with metamaterials, Nature Photonics 1(4), 224-227 (2007).

Chen, H. and C. Chan, Acoustic cloaking in three dimensions using acoustic metamaterials, Applied Physics Letters 91(18), 183518 (2007).

Chen, P.-Y., M. Farhat, S. Guenneau, S. Enoch and A. Alu, Acoustic scattering cancellation via ultrathin pseudo-surface, Applied Physics Letters 99(19), 191913 (2011).

Chen, T., Thermal conduction of a circular inclusion with variable interface parameter, International Journal of Solids and Structures 38(17), 3081-3097 (2001).

Chen, T., C.-N. Weng and J.-S. Chen, Cloak for curvilinearly anisotropic media in conduction, Applied Physics Letters 93(11), 114103 (2008).

Cheng, H. and S. Torquato, Effective conductivity of periodic arrays of spheres with interfacial resistance, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 453(1956), 145-161 (1997a).

Cheng, H. and S. Torquato, Effective conductivity of dispersions of spheres with a superconducting interface, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 453(1961), 1331-1344 (1997b).

Ergin, T., N. Stenger, P. Brenner, J. B. Pendry and M. Wegener, Three-dimensional invisibility cloak at optical wavelengths, Science 328(5976), 337-339 (2010).

Fan, C., Y. Gao and J. Huang, Shaped graded materials with an apparent negative thermal conductivity, Applied Physics Letters 92(25), 251907 (2008).

Farhat, M., P.-Y. Chen, H. Bagci, C. Amra, S. Guenneau and A. Alù, Thermal invisibility based on scattering cancellation and mantle cloaking, Scientific Reports 5, 9876 (2015).

Fleury, R. and A. Alù, Quantum cloaking based on scattering cancellation, Physical Review B 87(4), 045423 (2013).

Greenleaf, A., Y. Kurylev, M. Lassas and G. Uhlmann, Approximate quantum cloaking and almost-trapped states, Physical Review Letters 101(22), 220404 (2008).

Greenleaf, A., M. Lassas and G. Uhlmann, Anisotropic conductivities that cannot be detected by EIT, Physiological Measurement 24(2), 413-419 (2003a).

Guenneau, S., C. Amra and D. Veynante, Transformation thermodynamics: cloaking and concentrating heat flux, Optics Express 20(7), 8207-8218 (2012).

Han, T., T. Yuan, B. Li and C.-W. Qiu, Homogeneous thermal cloak with constant conductivity and tunable heat localization, Scientific Reports 3, 1593 (2013).

Hildebrand, F. B., Advanced calculus for applications. Englewood Cliffs, N.J: Prentice-Hall (1962).

Hu, J., X. Zhou and G. Hu, Design method for electromagnetic cloak with arbitrary shapes based on Laplace’s equation, Optics Express 17(3), 1308-1320 (2009).

Huy, H. P. and E. Sánchez-Palencia, Phénomènes de transmission à travers des couches minces de conductivitéélevée, Journal of Mathematical Analysis and Applications 47(2), 284-309 (1974).

IEEE., Standard Dictionary of Electrical and Electronics Terms. New York: Wiley-Interscience, (1972).

Jiang, W. X., J. Y. Chin, Z. Li, Q. Cheng, R. Liu and T. J. Cui, Analytical design of conformally invisible cloaks for arbitrarily shaped objects, Physical Review E 77(6), 066607 (2008b).

Jiang, W. X., T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng and J. Y. Chin, Arbitrarily elliptical–cylindrical invisible cloaking, Journal of Physics D: Applied Physics 41(8), 085504 (2008a).

Kapitza, P., The study of heat transfer in helium II, J. Phys.(USSR) 4(1-6), 181-210 (1941).

Knott, E. F., J. F. Shaeffer and M. T. Tuley, Radar Cross Section. Boston: Artech House, (1993).

Kubo, R., Thermodynamics Amsterdam: North-Holland, (1968).

Leonhardt, U., Optical conformal mapping, Science 312(5781), 1777-1780 (2006).

Leonhardt, U., Applied physics: Cloaking of heat, Nature 498(7455), 440-441 (2013).

Li, C. and F. Li, Two-dimensional electromagnetic cloaks with arbitrary geometries, Optics Express 16(17), 13414-13420 (2008).

Lipton, R., Influence of interfacial surface conduction on the DC electrical conductivity of particle reinforced composites, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 454(1973), 1371-1382 (1998).

Lipton, R. and B. Vernescu, Composites with imperfect interface, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 452(1945), 329-358 (1996).

Maldovan, M., Sound and heat revolutions in phononics, Nature 503(7475), 209-217 (2013).

Miloh, T. and Y. Benveniste, On the effective conductivity of composites with ellipsoidal inhomogeneities and highly conducting interfaces, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 455(1987), 2687-2706 (1999).

Milton, G. W., M. Briane and J. R. Willis, On cloaking for elasticity and physical equations with a transformation invariant form, New Journal of Physics 8(10), 248 (2006).

Monti, A., A. Alù, A. Toscano and F. Bilotti, Optical Scattering Cancellation through Arrays of Plasmonic Nanoparticles: A Review, Photonics 2(2), 540-552 (2015).

Narayana, S. and Y. Sato, Heat flux manipulation with engineered thermal materials, Physical Review Letters 108(21), 214303 (2012).

Nicolet, A., F. Zolla and S. Guenneau, Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section, Optics Letters 33(14), 1584-1586 (2008).

Norris, A. and A. Shuvalov, Elastic cloaking theory, Wave Motion 48(6), 525-538 (2011).

Norris, A. N., Acoustic cloaking theory, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 464(2097), 2411-2434 (2008).

Pendry, J. B., D. Schurig and D. R. Smith, Controlling electromagnetic fields, Science 312(5781), 1780-1782 (2006).

Rahm, M., D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith and J. B. Pendry, Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations, Photonics and Nanostructures-fundamentals and Applications 6(1), 87-95 (2008).

Sanchez-Palencia, E., Comportement limite d’un probleme de transmissiona travers une plaque faiblement conductrice, CR Acad. Sci. Paris Ser. A 270, 1026-1028 (1970).

Schittny, R., M. Kadic, S. Guenneau and M. Wegener, Experiments on transformation thermodynamics: molding the flow of heat, Physical Review Letters 110(19), 195901 (2013).

Schurig, D., J. Pendry and D. R. Smith, Calculation of material properties and ray tracing in transformation media, Optics Express 14(21), 9794-9804 (2006).

Torquato, S. and M. Rintoul, Effect of the interface on the properties of composite media, Physical Review Letters 75(22), 4067 (1995).

Wu, Q., K. Zhang, F.-y. Meng and L.-W. Li, Material parameters characterization for arbitrary N-sided regular polygonal invisible cloak, Journal of Physics D: Applied Physics 42(3), 035408 (2008).

Xu, H., X. Shi, F. Gao, H. Sun and B. Zhang, Ultrathin three-dimensional thermal cloak, Physical Review Letters 112(5), 054301 (2014).

Zhang, J., Y. Luo, H. Chen and B.-I. Wu, Cloak of arbitrary shape, Journal of the Optical Society of America B 25(11), 1776-1779 (2008).

Zhang, S., D. A. Genov, C. Sun and X. Zhang, Cloaking of matter waves, Physical Review Letters 100(12), 123002 (2008).

Zhang, S., C. Xia and N. Fang, Broadband acoustic cloak for ultrasound waves, Physical Review Letters 106(2), 024301 (2011).