General equation for directed electromagnetic wave propagation in 1D metamaterial: projectiong operator method

• Autorzy: Ampilogov D. , Leble S.

Identyfikatory

DOI

10.17466/TQ2016/20.2/B

• Języki publikacji: EN

Abstrakty

EN

We consider a boundary regime problem for 1D wave propagation in a metamaterial medium with simultaneously negative dielectric permittivity and magnetic permeability. We apply a projecting operator method to the Maxwell system in the time domain that allows the space of the linear propagation problem to be split into subspaces of directed waves for the relations of a given material with general dispersion. After projection, the equations for directed waves have a maximally simplified form, which is most convenient for numerical and analytical integration. Matrix elements of the projectors act as integral operators. For a given nonlinearity and dispersion we derive a general system of interacting right/left waves with combined (hybrid) amplitudes. The result is specified for the Drude metamaterial model for both permittivity and permeability coefficients and the Kerr nonlinearity. We also discuss and investigate singular solitary wave solutions of the system as a limit stationary elliptic system related to some boundary regimes.

Słowa kluczowe

EN

metamaterials; directed waves interactions; Drude dispersion; Kerr nonlinearity; solitary solutions

• Wydawca: Politechnika Gdańska
• Czasopismo: TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
• Rocznik: 2016
• Tom: Vol. 20, No 2
• Strony: 143--155
• Opis fizyczny: Bibliogr. 28 poz., rys.

Twórcy

autor

Ampilogov D.

• Immanuel Kant Baltic Federal University Al. Nevsky 14, Kaliningrad, Russia

autor

Leble S.

• Immanuel Kant Baltic Federal University Al. Nevsky 14, Kaliningrad, Russia

Bibliografia

• [1] Bose J C 1898 Proceedings of Royal Society 63 146
• [2] Mandelshtam L I 1950 Lectures on some problems of the theory of oscillations, in Complete Collection of Works, vol. 5, Academy of Sciences 428 (in Russian)
• [3] Malyuzhinets G D 1951 Zhurnal Technicheskoi Fiziki 21 940 (in Russian; english translation in Sov. Phys. Technical Physics)
• [4] Veselago V G 1966 FTT 8 3571; 1967 Soviet Phys. Solid State 8 2853; 1968 Soviet Phys. Usp. 10 509
• [5] Smith D R, Padilla W J, Vier D C, Nemat-Nasser S C and Schultz S 2000 Physical Review Letters 84 4184
• [6] Sihvola A 2007 Metamaterials 1 2
• [7] Shelby R A, Smith D R and Schultz S 2001 Science 292 (5514) 77
• [8] Lipworth G, Mrozack A, Hunt J, Marks D L, Driscoll T, Brady D and Smith D R 2013 Journal of the Optical Society of America A 30 1603
• [9] Sanada A, Caloz C and Itoh T 2003 Zeroth order resonance in composite right/left-handed transmission line resonators, Proc. Asia-Pacific Microw. Conf. 3 1588
• [10] Cheng C-Y and Ziolkowski R W 2003 IEEE Trans. Microw. Theory Tech. 51 (12) 2306
• [11] Chung Y, Jones C K R T, Schafer T and Wayne C E 2005 Nonlinearity 18 1351
• [12] Wen S, Xiang Y, Dai X, Tang Z, Su W and Fan D 2007 Phys. Rev. A 75, 033815
• [13] Leble S 1990 Nonlinear Waves in Waveguides, Springer
• [14] Fleck J A 1970 Phys. Rev. B 84 (1)
• [15] New G H C, Kinsler P and Radnor B P 2005 Phys. Rev. A 72
• [16] Amiranashvili Sh and Demircan A 2011 Advances in Optical Technologies 2011, ID 989515
• [17] Perelomova A A 2000 Applied Mathematics Letters 13 93
• [18] Belov V V, Dobrokhotov S Yu and Tudorovskiy T Ya 2006 J. Eng. Math. 55 (1-4) 183
• [19] Kuszner M and Leble S 2011 Journal of the Physical Society of Japan 80, 024002
• [20] Boyd R W 1992 Nonlinear Optics, Academic Press
• [21] Ziolkowski R W and Kipple A 2003 Phys. Rev. E 68, 026615
• [22] Milonni P W 2005 Fast Light, Slow Light and Left-Handed Light, Institute of Physics Publishing 184
• [23] Ziolkowski R 2003 Optical Society of America 11 662
• [24] Zhao Y, Argyropoulos C and Hao Y 2008 Optical Society of America 16 6717
• [25] Argyropoulos Ch. et al. 2013 Optics Express 21 (12) 15037
• [26] Ipatov M, Zhukova V, Panina L V and Zhukov A 2009 PIERS Online 5 (6) 586
• [27] Ampilogov D, Leble S 2016 Physics Letters A 380 2271
• [28] Pietrzyk M E and Kanatchikov I V On the Polysymplectic Integrator for the Short Pulse Equation, arXiv:1512.09105v1

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę