Wave Propagation Part 6 potx

The Electrodynamic Properties of Structures with Thin Superconducting Film in Mixed State 167 great importance: thin Kerr nonlinear dielectric produces the soliton-like pulses, thin superconducting film gives the possibility of control, negative index material slab reduces the pulse velocity providing large interaction of pulses with a flux-line lattice in superconductor. 012345 1 . 10 6 1 . 10 6 BT v, m/s . Fig. 14. Magnitude of the pulse velocity as function of external magnetic field. The parameters of the structure are: t=40 nm, η=10 -8 N⋅s/m 2 , j y0 =10 9 A/m 2 , ω=20⋅10 11 rad/s, a=0.025 m, b=0/02 m, δ=100 μm, E s =10 3 V/m, α 3 =10 -15 C⋅m/V 2 7. Conclusion In this chapter the propagation of electromagnetic waves in structures with thin high temperature superconducting film is investigated. The interaction of electromagnetic wave with thin superconductor in the mixed state is studied. It is shown, that the presence of the moving magnetic vortex structure in superconductor can lead not only to attenuation, but also to amplification of electromagnetic waves. The condition of amplification consists in equality of velocity of electromagnetic wave and the moving vortex structure. It is shown, that the electromagnetic wave amplification takes place at the expense of energy of Abrikosov vortex lattice. The representation of thin superconducting film in the form of boundary condition has enabled us to understand the mechanism of electromagnetic wave interaction with moving vortex structure. This method allowed us to simplify the numerical calculation. In this study also the propagation of electromagnetic waves in periodic structures superconductor - dielectric is examined. The peculiarities of periodic structures with thin superconducting film in Larkin-Ovchinnikov state are revealed. The features of periodic structures superconductor - semiconductor are studied. The new pass bands and amplification bands are found. The possibility of the control of processes of attenuation and amplification is shown. The control can be realized by means of change of external magnetic field and transport current density. The dependence of coefficients of attenuation and amplification on the thickness of superconducting film and frequency enables us to make active devices which parameters can vary widely. The structures with thin superconducting film in mixed state and combination of dielectric layer and negative index material layer are considered. It is shown, that the combination of dielectric and negative index material acts as the slow-wave structure in limited structures. The combination of dielectric and negative index material with thin superconducting film can be used in different devices such as waveguides and resonators as the control section. As the example of such application the waveguide with nonlinear thin film is considered. It Wave Propagation 168 is shown, that the nonlinear film with Kerr like nonlinearity excites the nonlinear soliton- like pulses. And the presence in such waveguide of the control section on the base of thin superconducting film permits to change not only attenuation coefficient, but also the direction of pulse propagation. The properties of structures with thin high temperature superconducting films in the mixed state open the promissory perspective for their application in modern devices with control of parameters. 8. References Abrikosov, A. A. (2004). Type-II superconductors and the vortex lattice. Sov. Phys. Uspekhi, Vol. 174, No. 11, pp. 1234–1239. Artemov, Y. V.; Genkin, V. M.; Leviev, G. I. & Ovchinnikova, V. (1997). Nonlinear microwave losses in thin superconducting YBCO films. Superconductor Science and Technology, Vol. 10, No. 8, pp. 590-593. Baena, J. D.; Jelinek, L.; Marqués, R. & Medina, F. (2005). Near-perfect tunneling and amplifcation of evanescent electromagnetic waves in a waveguide filled by a metamaterial: Theory and experiment. Physical Review B, Vol. 72, pp. 075116–1–8. Bednorz, J.G.; Muller, K.A. (1986). Possible high T c superconductivity in the Ba-La-Cu-O system. Zeitschrift für Physik B, Vol. 64, No. 2, pp. 189-193. Bespyatykh, Y. I.; Wasilewski, W.; Gajdek, M.; Simonov, A. D. & Kharitonov, V. D. (1993). Dispersion and damping of surface magnetostatic waves in a ferromagnet-type II superconductor structure, Physics of the Solid State, Vol. 35, No. 11, pp.1466-1470. Bulgakov, A. A. & Shramkova, O. V. Dispersion and instability of electromagnetic waves in layered periodic semiconductor structures, Technical Physics, Vol. 48, No. 3, pp. 361- 369. Chiang, T C. (2004). Superconductivity in thin films. Science, Vol. 306, No. 5703, pp. 1900 - 1901. Dmitrenko, I. M. (1996). Resistive state of broad superconducting films and phase-slip lines, Low Temperature Physics, Vol. 22, pp. 648-665. Engheta, N. & Ziolkowski, R.W. (2006). Introduction, history, and selected topics in fundamental theories of metamaterials, In: Metamaterials, Ed. by Engheta, N. & Ziolkowski, R.W., John Wiley & Sons, ISBN 13978-0-47176102-0, New York. Gilmour, A. S. (1994). Principles of traveling wave tubes, Artech House, ISBN 0890067201, Boston. Glushchenko, A.G. & Golovkina, M.V. (1998 a). Electromagnetic wave propagation in superconductor-dielectric multilayers, Proceedings of International symposium on electromagnetic compatibility EMC'98, pp. 430-432, Italy, Rome. [25] Glushchenko, A.G. & Golovkina, M.V. (1998 b). Reflection of an electromagnetic wave by a layered superconductor-dielectric structure. Technical Physics Letters, Vol. 24, No. 4, pp.9-12. Glushchenko, A.G. & Golovkina, M.V. (2006). A nonlinear pulse propagation in a waveguide thin-layer superconductor-insulator structure with Kerr nonlinearity. Physics of Wave Processes and Radio Systems (in Russian), Vol. 9, No. 2, pp. 12-17. Glushchenko, A.G. & Golovkina, M.V. (2007). Propagation of electromagnetic waves in periodic structures with superconducting layers having electrodynamic parameters The Electrodynamic Properties of Structures with Thin Superconducting Film in Mixed State 169 in the nonlinearity range of the dynamic mixed state, Technical Physics, Vol. 52, No. 10, pp. 1366-1368. Golovkina, M.V. (2007). Two-layered waveguide containing a negative index material slab with resistive film., Proceedings of Metamaterials'2007, First International Congress on Advanced Electromagnetic Materials in Microwaves in Microwaves and Optics, pp. 377- 379, Italy , October 2007, Rome. Golovkina, M.V. (2008). Properties of pulses in the layered structure with negative index material slab and two-layered thin film superconductor-nonlinear dielectric, Proceedings of Second International Congress of Advanced Electromagnetic Materials in Microwaves and Optics Metamaterials, Spain , September 2008, Pamplona. Golovkina, M.V. (2009 a). Characteristics of electromagnetic waves propagation in multilayered structure semiconductor – superconductor, Vestnic Pomorskogo Universiteta, Vol. 3, pp.70-75, ISSN 1728-7340. Golovkina, M.V. (2009 b). Electromagnetic wave propagation in multilayered structures with negative index material, In: Wave propagation in materials for modern applications, Petrin, A. (Ed.), pp. 149-162, Intech, ISBN 978-953-7619-65-7. Golovkina, M.V. (2009 c). Electromagnetic wave propagation in waveguide with thin superconducting film and metamaterial slab, Progress in Electromagnetics Research Symposium, Russia, August 2009, Moscow. Gozar, A.; Logvenov, G.; Kourkoutis, L.F.; Bollinger, A. T.; Giannuzzi, L. A.; Muller, D. A. & Bozovic, I. (2008). High-temperature interface superconductivity between metallic and insulating copper oxides. Nature, Vol. 455, pp. 782-785. Gunji, T.; Unno, M.; Arimitsu, K.; Abe, Y.; Long, N. & Bubendorfer, A. (2005). Preparation of YBCO and BSCCO superconducting thin films by a new chemical precursor method. Bulletin of the Chemical Society of Japan, Vol. 78, , No. 1, pp.187-191. Gutliansky, E. D. (2005). Amplification of longitudinal ultrasonic waves by a moving vortex structure in type II superconductors. JETP Letters, Vol. 82, No. 2, pp. 72-76. Hein, M. (1999). High-Temperature-Superconductor Thin Films at Microwave Frequencies, Springer; ISBN 3540656464. Hohenwarter, G. K. G.; Martens, J. S.; Beyer, J. B.; Nordman, J. E. & McGinnis, D. P.(1989). Single superconducting thin film devices for applications in high Tc materials circuits. IEEE Transactions on Magnetics, Vol. 25, pp. 954-956. Jakšić, Z.; Dalarsson, N. & Maksimović, M. (2006) Negative refractive index metamaterials: principles and applications. Microwave Review, Vol. 12, №o. 1, pp. 36–49. Itozaki, H.; Higaki, K.; Harada, K.; Tanaka, S.; Yazu, S.& Tada, K. (1989). Properties of high Jc BiSrCaCuO and TlBaCaCuO thin film. Physica C: Superconductivity, Vol. 162-164, Part 1, pp. 367-368. Korn, G. A. & Korn, T. M. (2000). Mathematical Handbook for Scientists and Engineers, Dover Publications, ISBN 0486411478. Koster, G.; Brinkman, A.; Hilgenkamp H.; Rijnders A.J.H.M. & Blank D.H.A. (2008). High-Tc superconducting thin films with composition control on a sub-unit cell level; the effect of the polar nature of the cuprates. Journal of Physics: Condensed Matter, Vol. 20, No. 26, pp. 264007-1-264007-6. Kurushin, E. P. & Nefedov, E. I. (1983). Electrodynamics of anisotropic waveguiding structures, Nauka, Moscow. Wave Propagation 170 Kurushin, E. P.; Nefedov, E. I. & Fialkovsky, A. T. (1975). Diffraction of electromagnetic waves in anisotropic structures, Nauka, Moscow. Kwak, M. H.; Tae Kim, Y. T.; Moon, S E.; Ryu, H C; Lee, S J. & Kang, K. Y. (2005). Microwave properties of tunable phase shifter using superconductor/ ferroelectric thin films. Integrated Ferroelectrics, Vol. 77, No. 1, pp. 79 - 85. Larkin, A.I. & Ovchinnikov, Y.N. (1975). Nonlinear conductivity of superconductors in the mixed state, Sov. Phys. JETP, Vol. 41, No. 5, pp. 960-965. Nefedov, I. S. & Tretyakov, S. A. (2003). Waveguide containing a backward-wave slab. Radio Science, Vol. 38, No. 6, pp. 9–1. Phillips, J. M. (1995). High temperature superconducting thin films, In: High-temperature superconducting materials science and engineering: new concepts and technology, Shi, D. (Ed.), pp. 305-325, ISBN 0080421512, Pergamon, Great Britain. Popkov, A.F. (1989). The magnetostatic wave amplification by magnetic vortex flux in structure ferrite - superconductor. Technical Physics Letters, Vol. 15, pp. 9-14. Schauer, W.; Xia, X.X.; Windte, V.; Meyera, O.; Linkera, G.; Lia, Q. & Geerk, J. (1990). Growth quality and critical current density of sputtered YBaCuO thin films. Cryogenics, Vol. 30,No. 7, pp. 586-592. Schilling, A.; Cantoni, M., Guo, J. C. & Ott, H. R. (1993)., Superconductivity above 130 K in the HgBaCaCuO system. Nature, Vol. 363, pp. 56-58. Schmidt, V.V. (2002). The physics of superconductors: introduction to fundamentals and applications, Springer, ISBN 3540612432. Shelby, A.; Smith, D. R. & Schultz, S. (2001). Experimental verification of a negative index of refraction. Science, Vol. 292, 77-79. Smith, D. R.; Padilla, W. J.; Vier, D. C.; Nemat-Nasser, S.C. & Schultz, S. (2000). Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett., Vol. 84, 4184-4187. Veselago, V. G. (1968) The electrodynamics of substances with simultaneously negative values of epsilon and mu. Sov. Phys. 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High temperature superconducting thin films for microwave filters. Science in China (Series A), Vol. 45, No. 9, pp. 1183-1191. Part 2 Light Wave Propagation and Nanofocusing 9 Detection and Characterization of Nano-Defects Located on Micro-Structured Substrates by Means of Light Scattering Pablo Albella, 1 Francisco González, 1 Fernando Moreno, 1 José María Saiz 1 and Gorden Videen 2 1 University of Cantabria 2 Army Research Laboratory 1 Spain 2 USA 1. Introduction Detection and characterization of microstructures is important in many research fields such as metrology, biology, astronomy, atmospheric contamination, etc. These structures include micro/nano particles deposited on surfaces or embedded in different media and their presence is typical, for instance, as a defect in the semiconductor industry or on optical surfaces. They also contribute to SERS and may contribute to solar cell performance [Sonnichsen et al., 2005; Stuart et al., 2005; Lee et al., 2007]. The central problem related to the study of morphological properties of microstructures (size, shape, composition, density, volume, etc.) is often lumped into the category of “Particle Sizing” and has been a primary research topic [Peña et al., 1999; Moreno and Gonzalez, 2000; Stuart et al., 2005; Lee et al., 2007]. There are a great variety of techniques available for the study of micro- and nano- structures, including profilometry and microscopy of any type: optical, electron, atomic force microscopy (AFM), etc. Those based on the analysis of the scattered light have become widely recognized as a powerful tool for the inspection of optical and non-optical surfaces, components, and systems. Light-scattering methods are fast, flexible and robust. Even more important, they are generally less expensive and non-invasive; that is, they do not require altering or destroying the sample under study [Germer et al., 2005; Johnson et al., 2002; Mulholland et al., 2003]. In this chapter we will focus on contaminated surfaces composed of scattering objects on or above smooth, flat substrates. When a scattering system gets altered either by the presence of a defect or by any kind of irregularity on its surface, the scattering pattern changes in a way that depends on the shape, size and material of the defect. Here, the interest lies not only in the characterization of the defect (shape, size, composition, etc.), but also on the mere detection of its presence. We will show in detail how the analysis of the backscattering patterns produced by such systems can be used in their characterization. This may be useful in practical situations, like the fabrication of a chip in the semiconductor industry in the case of serial-made microstructures, the performance of solar cells, for detection and Wave Propagation 174 characterization of contaminants in optical surfaces like telescope mirrors or other sophisticated optics, and for assessing surface roughness, etc. [Liswith, 1996; Chen, 2003]. Before considering the first practical situation, we find it convenient to describe the backscattering detection concept. Backscattering detection In a typical scattering experiment, a beam of radiation is sent onto a target and the properties of the scattered radiation are detected. Information about the target is then extracted from the scattered radiation. All situations considered in this work exploit this detection scenario in the backscattering direction. Although backscattered light may be the only possible measurement that can be made in some situations, especially when samples are crowded with other apparati, it also does have some advantages that make it a useful approach in other situations. Backscattering detection can be very sensitive to small variations in the geometry and/or optical properties of scattering systems with structures comparable to the incident wavelength. It will be shown how an integration of these, over either the positive or negative quadrant, corresponding to the defect side or the opposite one, respectively, yields a parameter that allows one not only to deduce the existence of a defect, but also to provide some information about its size and location on the surface, constituting a non-invasive method for detecting irregularities in different scattering systems. 2. System description Figure 1 shows an example of a typical practical situation of a microstructure that may or may not contain defects. In this case, the microstructure is an infinitely long cylinder, or fiber. Together with the real sample, we show the 2D modelling we use to simulate this situation and provide a 3D interpretation. This basic design consists on an infinitely long metallic cylinder of diameter D, placed on a flat substrate. We define two configurations: the Non-Perturbed Cylinder (NPC) configuration, where the cylinder has no defect and the Perturbed Cylinder (PC) configuration, which is a replica of the NPC except for a defect that can be either metallic or dielectric and can be located either on the cylindrical microstructure itself or at its side, lying on the flat substrate underneath. We consider the spatial profile of this defect to be cylindrical, but other defect shapes can be considered without difficulty. The cylinder axis is parallel to the Y direction and the X-Z plane corresponds to both the incidence and scattering planes. This restricts the geometry to the two-dimensional case, which is adequate for the purpose of our study [Valle et al., 1994; Moreno et al., 2006; Albella et al.,2006; Albella et al., 2007]. The scattering system is illuminated by a monochromatic Gaussian beam of wavelength λ (633nm) and width 2ω 0 , linearly polarized perpendicular to the plane of incidence (S-polarized). In order to account for the modifications introduced by the presence of a defect in the scattering patterns of the whole system, we use the Extinction theorem, which is one of the bases of modern theories developed for solving Maxwell’s Equations. The primary reason for this choice is that it has been proven a reliable and effective method for solving 2D light- scattering problems of rounded particles in close proximity to many kinds of substrates [Nieto-Vesperinas et al., 1992; Sanchez-Gil et al., 1992; Ripoll et al., 1997; Saiz et al., 1996]. Detection and Characterization of Nano-Defects Located on Micro-Structured Substrates by Means of Light Scattering 175 Fig. 1. Example of a contaminated microstructure (top figure) and its corresponding 2D and 3D models. The Extinction theorem is a numerical algorithm. To perform the calculations, it is necessary to discretize the entire surface contour profile (substrate, cylinder and defect) into an array of segments whose length is much smaller than any other length scale of the system, including the wavelength of light and the defect. Bear in mind that it is important to have a partition fine enough to assure a good resolution in the high curvature regions of the surface containing the lower portion of the cylinder and defect. Furthermore, and due to obvious computing limitations, the surface has to be finite and the incident Gaussian beam has to be wide enough to guarantee homogeneity in the incident beam but not so wide as to produce undesirable edge effects at the end of the flat surface. Consequently, in our calculations, the length of the substrate has been fixed to 80λ and the width (2ω 0 ) of the Gaussian beam to 8λ. 3. Metallic substrates In this section we initially discuss the case of metallic cylinders, or fibers, deposited on metallic substrates and with the defect either on the cylinder itself or on the substrate but near the cylinder. Defect on the Cylinder As a first practical situation, Figure 2 shows the backscattered intensity pattern, as a function of the incident angle θ i , for a metallic cylinder of diameter D = 2λ. We consider two different types of defect materials of either silver or glass and having diameter d = 0.15λ. It can be seen how the backscattering patterns measured on the unperturbed side of the cylinder (corresponding to θ s < 0) remain almost unchanged from the reference pattern. In this case, we could say that the defect was hidden or shadowed by the incident beam. If the scattering angle is such that the light illuminates the defect directly, a noticeable change in the positions and intensity values of the maxima and minima results. The number of maxima and minima observed may even change if the defect is larger than 0.4λ. This means that there is no change in the effective size of the cylinder due to the presence of the defect. This result can be explained using a phase-difference model [Nahm & Wolf, 1987; Albella et al., 2007], where the substrate is replaced by an image cylinder located opposite the [...]... A 9, (1992) 424–4 36 Peña, J.L., J M Saiz, P Valle, F González, and F Moreno, “Tracking scattering minima to size metallic particles on flat substrates,” Particle & Particle Systems Characterization 16, (1999) 113–118 Ripoll, J., A Madrazo, and M Nieto-Vesperinas, “Scattering of electromagnetic waves from a body over a random rough surface,” Opt Comm 142, (1997) 173–178 192 Wave Propagation Saiz, J.M.,... 31, 1744-17 46, (20 06) Albella, P., F Moreno, J M Saiz, and F González, “Backscattering of metallic microstructures will small defects located on flat substrates.” Opt Exp 15, (2007) 68 57 68 67 Albella, P., F Moreno, J M Saiz, and F González, “2D double interaction method for modeling small particles contaminating microstructures located on substrates.” J Quant Spectrosc Radiative Trans 1 06, 4–10 (2007)... directions perpendicular to the boundary Remembering the quantum character of the surface wave they say about surface plasmons and surface plasmon polaritons (SPPs) as quasi-particles associated with the wave The dispersion of the surface wave has the following important feature [Economou (1 969 ), Barnes (20 06) ]: the wavelength tends to zero when the frequency of the SPPs tends to some critical (cut off)... possible to decrease the wavelength of the SPPs to the values substantially 194 Wave Propagation smaller than the wavelength of visible light in vacuum and use the SPPs for trivial focusing by creation a converging wave [Bezus (2010)] In this case there is no breaking the diffraction Raleigh’s limitation and the energy of the wave is focused into the region with dimensions of the order of wavelength of the... function of wavelength in vacuum of exciting laser The curve starts from the lowest wavelength (in vacuum) of SPPs spectrum for silver: ( λsp )cr = 2 2π c ωp ≈ 1 96 nm As an example of application of the obtained results we consider the experiment on local Raman’s microscopy [De Angelis (2010)] A silver tip with angle γ ≈ 12° in the vicinity of 200 Wave Propagation the apex was used The wavelength of... scattering by submicrometer spherical particles on silicon and oxidized silicon surfaces,” Opt Eng 35, 858- 869 (19 96) Mittal, K L (editor) Particles on surfaces: Detection, Adhesion and Removal VSP, Utrech (1999) Moreno, F and F González Eds Light scattering from microstructures Springer Verlag (2000) Moreno, F., F González, and J M Saiz, “Plasmon spectroscopy of metallic nanoparticles above flat dielectric... (2004), Kawata (2001), Naber (2002), Babadjanyan (2000), Nerkararyan (20 06) , Novotny (1995), Mehtani (20 06) , Anderson (20 06) ] It is also important for the development of new optical sensors and delivery of strongly localized photons to tested molecules and atoms (for local spectroscopic measurements [Mehtani (20 06) , Anderson (20 06) , Kneipp (1997), Pettinger (2004), Ichimura (2004), Nie (1997), Hillenbrand... subwavelength waveguides, interconnectors, and nanooptical devices [Gramotnev (2005)] There are two phenomena of exceptional importance which make it possible nanofocusing The first is the phenomenon of propagation with small attenuation of electromagnetic energy of light along metal-vacuum or metal-dielectric boundaries This propagation exists in the form of strictly localized electromagnetic wave. .. defect on the substrate On the top are results for a dielectric substrate ε = 1 .6 and on the bottom for a gold substrate ε = 11 + 1.5i Finally, to illustrate this enhancement, Figure 12 shows some examples of the near-field pattern obtained for two different substrates illuminated at normal incidence The figures on 1 86 Wave Propagation the left correspond to the reference case having no defect and on... represent the components directly scattered by the particles to 188 Wave Propagation Fig 13 Multiple interaction model for two structures illuminated at normal incidence Inset shows the flat substrate approximation and image theory applied to the defect the detector; and arrows labelled (2) and (4) correspond to the components scattered downwards by the particles and then reflected towards the observation . Matter, Vol. 20, No. 26, pp. 264 007-1- 264 007 -6. Kurushin, E. P. & Nefedov, E. I. (1983). Electrodynamics of anisotropic waveguiding structures, Nauka, Moscow. Wave Propagation 170 Kurushin,. Superconductivity, Vol. 162 - 164 , Part 1, pp. 367 - 368 . Korn, G. A. & Korn, T. M. (2000). Mathematical Handbook for Scientists and Engineers, Dover Publications, ISBN 04 864 11478. Koster, G.;. Electromagnetic wave propagation in multilayered structures with negative index material, In: Wave propagation in materials for modern applications, Petrin, A. (Ed.), pp. 149- 162 , Intech, ISBN 978-953- 761 9 -65 -7.