Integrating cold plasma equations into the Fourier modal method to analyze second harmonic generation at metallic nanostructures

We introduce a computational scheme to analyze second harmonic generation in periodic metallic nanostructures, i.e. metamaterials, that are composed of multiple layers. To describe the nonlinear polarization by the metallic constituents, we rely on a hydrodynamic model for the conduction electrons. Our computational approach is based on the Fourier modal method into which we incorporate the hydrodynamic plasma model. We detail physical and numerical peculiarities of the algorithm and we access aspects of convergence in a comprehensive manner. Finally, we provide further insights into the characteristics of intrinsic nonlinearities of metamaterials.

[1]  Nicolae C. Panoiu,et al.  Second harmonic generation in metamaterials based on homogeneous centrosymmetric nanowires , 2010 .

[2]  F. Lederer,et al.  A numerical approach for analyzing higher harmonic generation in multilayer nanostructures , 2010 .

[3]  F. Lederer,et al.  Multipole nonlinearity of metamaterials , 2009, 0908.4019.

[4]  M. Wegener,et al.  Second-harmonic generation from split-ring resonators on a GaAs substrate. , 2009, Optics letters.

[5]  Andreas Tünnermann,et al.  Double-element metamaterial with negative index at near-infrared wavelengths. , 2009, Optics letters.

[6]  Harald Giessen,et al.  Matched coordinates and adaptive spatial resolution in the Fourier modal method. , 2009, Optics express.

[7]  A. Tünnermann,et al.  Polarization-independent negative-index metamaterial in the near infrared. , 2009, Optics letters.

[8]  E. Ulin-Avila,et al.  Three-dimensional optical metamaterial with a negative refractive index , 2008, Nature.

[9]  Stephan W. Koch,et al.  Classical theory for second-harmonic generation from metallic nanoparticles. Phys Rev B 79:235109 , 2008, 0807.3575.

[10]  Stefan Linden,et al.  Experiments on second- and third-harmonic generation from magnetic metamaterials. , 2008, Optics express.

[11]  D. de Ceglia,et al.  Enhanced transmission and second harmonic generation from subwavelength slits on metal substrates , 2008, SPIE Photonics Europe.

[12]  Carsten Rockstuhl,et al.  Resonances in complementary metamaterials and nanoapertures. , 2008, Optics express.

[13]  M. Larciprete,et al.  Second-harmonic generation from metallodielectric multilayer photonic-band-gap structures , 2008, 0801.0637.

[14]  Zhaoning Yu,et al.  Nonlinear optical spectroscopy of photonic metamaterials , 2007, 2008 Conference on Lasers and Electro-Optics and 2008 Conference on Quantum Electronics and Laser Science.

[15]  Kurt Busch,et al.  A Krylov‐subspace based solver for the linear and nonlinear Maxwell equations , 2007 .

[16]  Jari Turunen,et al.  Fourier modal method for the analysis of second-harmonic generation in two-dimensionally periodic structures containing anisotropic materials , 2007 .

[17]  Jari Turunen,et al.  Local field asymmetry drives second-harmonic generation in non-centrosymmetric nanodimers. , 2007, Nano letters.

[18]  M. Wegener,et al.  Second-Harmonic Generation from Magnetic Metamaterials , 2006, Science.

[19]  Kevin J. Malloy,et al.  Second harmonic generation from a nanopatterned isotropic nonlinear material , 2006 .

[20]  Y. Kivshar,et al.  Second-harmonic generation in nonlinear left-handed metamaterials , 2005, physics/0506092.

[21]  U. Chettiar,et al.  Negative index of refraction in optical metamaterials. , 2005, Optics letters.

[22]  Brian K. Canfield,et al.  Polarization effects in the linear and nonlinear optical responses of gold nanoparticle arrays , 2005 .

[23]  Y. Kivshar,et al.  Nonlinear properties of left-handed metamaterials. , 2003, Physical review letters.

[24]  Yeshaiahu Fainman,et al.  Analysis of enhanced second-harmonic generation in periodic nanostructures using modified rigorous coupled-wave analysis in the undepleted-pump approximation. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[25]  R. Shelby,et al.  Experimental Verification of a Negative Index of Refraction , 2001, Science.

[26]  J. Pendry,et al.  Negative refraction makes a perfect lens , 2000, Physical review letters.

[27]  R. W. Christy,et al.  Optical Constants of the Noble Metals , 1972 .

[28]  K. Sauer,et al.  Topics on nonlinear wave-plasma interaction , 1987 .