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Independent nonlinear modes in waveguides with finite-length layered superconductors

Young scientists conference  “Problems of Theoretical Physics” Bogolyubov Institute for Theoretical Physics. Independent nonlinear modes in waveguides with finite-length layered superconductors. Tetiana Rokhmanova A.Ya . Usikov Institute for Radiophysics and Electronics,

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Independent nonlinear modes in waveguides with finite-length layered superconductors

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  1. Young scientists conference “Problems of Theoretical Physics” Bogolyubov Institute for Theoretical Physics Independent nonlinear modes in waveguides with finite-length layered superconductors TetianaRokhmanova A.Ya. Usikov Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, 12, Proskurast., 61085 Kharkov, Ukraine. 24-27 December 2013, Kyiv

  2. 1. Layered superconductors - definition - perspectives of the study 2. Formulation of the problem 3. Field inside the layered superconductors - nonlinearity of equations - ordinary & extraordinary waves 4. Behavior of modes of I and II polarizations coming form vacuum 5. Principle of superposition 6. Conclusion Outline TetianaRokhmanova (IRE NASU) Kyiv-2013 2/16

  3. Layered superconductors are periodic structures, where thin superconductinglayers (about 0.2 nm) are separated by the thicker insulator ones (about 1.5 nm), and are electrodynamically related to each other due to the intrinsicJosephson effect. 1. Layered superconductors Natural strongly anisotropic high-Tc crystals Bi2 Sr2 Ca Cu2O8+δ or artificial compounds like Nb /Al – Al Ox / Nb aretheexamplesof such materials. Tetiana Rokhmanova (IRE NASU) Kyiv-2013 3/16

  4. Josephon plasma waves THz frequency range (from 300 GHz to 30 THz) technological perspectives Josephson plasma scientific perspectives 1. Why to study? Anisotropy of current-carrying capability: the currentsalongandacrossthe layers are of different nature. Tetiana Rokhmanova (IRE NASU) Kyiv-2013 4/16

  5. 2. Geometry of the problem Tetiana Rokhmanova (IRE NASU) Kyiv-2013 5/16

  6. 2. Polarization of the waves I polarization: in vacuum II polarization: in superconductor <<1 Tetiana Rokhmanova (IRE NASU) Kyiv-2013 6/16

  7. dielectric conductivity of the insulating layers 3. Field in the layered superconductor nonlinearity London penetration depth across the layers magnetic flux quantum ! Even waves of small amplitudes are considerably nonlinear. thickness of the dielectric layer Tetiana Rokhmanova (IRE NASU) Kyiv-2013 7/16

  8. z 3. Polarization in the layered superconductor ordinary mode: extraordinary mode: Az = 0 Az  0 linear attenuating nonlinear running Tetiana Rokhmanova (IRE NASU) Kyiv-2013 8/16

  9. in layered superconductor Ey Ez Hy Hz 0 0 in vacuum Ey Ez Hy Hz 3. Boundary conditions 0 Here α~1, β<<1, γ<<1, I polarization totally reflects II polarization partly reflects independently of I polarization Tetiana Rokhmanova (IRE NASU) Kyiv-2013 9/16

  10. Incident mode of the • I polarization: • fully reflects • does not convert • into II polarization 4. Behavior of I and II polarizations • Incident mode of the • II polarization: • partly reflects and partly transmits • does not convert • into I polarization Tetiana Rokhmanova (IRE NASU) Kyiv-2013 10/16

  11. The I polarization fully reflects. hIi = 2; hIIi = 0; 4. Behavior of I and II polarizations The II polarization partly reflects and transmits. hIi = 0; hIIi = 2; The I and IIpolarizationsbehaveindependently. hIi = 2; hIIi = 2; Tetiana Rokhmanova (IRE NASU) Kyiv-2013 11/16

  12. all the curves have • the same envelope curve; • period of oscillations • depends on the parameters; • the period increases with • decreasing D and increasing Ly and Lz; • full transmittance at • the special critical amplitude. different lateral dimensions and thickness of the sample 4. Dependence on parameters for II polarization different frequencies Tetiana Rokhmanova (IRE NASU) Kyiv-2013 12/16

  13. II polarization: 4. Critical point I polarization: Tetiana Rokhmanova (IRE NASU) Kyiv-2013 13/16

  14. 1st step II incident = + 5. Principle of superposition = = 2nd step + II reflected = reflected I reflected I incident incident + + 3rd step 0 = I transmitted II transmitted + = transmitted Tetiana Rokhmanova (IRE NASU) Kyiv-2013 14/16

  15. 5. TE & TM modes • both of them: • partly reflect and transmit; • partly convert one into the other; Tetiana Rokhmanova (IRE NASU) Kyiv-2013 15/16

  16. waveguide modes of two specific orthogonal polarizations • (I and II polarizations) reflectindependently; • the mode of I polarization fully reflects from the layered superconductor and excites only an evanescent mode inside of it, the mode of • II polarization partly reflectsand partly transmits through the sample; • the superposition principle is valid and it is convenient to represent a mode of any polarization via this two specific polarizations; • the superposition principle was demonstrated on • the TE and TM modes and it was shown that for a certain parameters • TE and TM modes can be converted one into the other. 6. Conclusions Tetiana Rokhmanova (IRE NASU) Kyiv-2013 16/16

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