Second- and third-harmonic generation in metal-based structures

We present a theoretical approach to the study of second- and third-harmonic generation from metallic structures and nanocavities filled with a nonlinear material in the ultrashort pulse regime. We model the metal as a two-component medium, using the hydrodynamic model to describe free electrons and Lorentz oscillators to account for core electron contributions to both the linear dielectric constant and harmonic generation. The active nonlinear medium that may fill a metallic nanocavity, or be positioned between metallic layers in a stack, is also modeled using Lorentz oscillators and surface phenomena due to symmetry breaking are taken into account. We study the effects of incident TE- and TM-polarized fields and show that a simple reexamination of the basic equations reveals additional, exploitable dynamical features of nonlinear frequency conversion in plasmonic nanostructures.

[1]  Steve Blair,et al.  Second-harmonic generation from an array of sub-wavelength metal apertures , 2005 .

[2]  E. Adler,et al.  Nonlinear Optical Frequency Polarization in a Dielectric , 1964 .

[3]  A. Georges,et al.  Theory of multiple harmonic generation in reflection from a metal surface , 2005 .

[4]  Michael E. Crenshaw,et al.  A beam propagation method that handles reflections , 1994 .

[5]  Shen,et al.  Local and nonlocal surface nonlinearities for surface optical second-harmonic generation. , 1987, Physical review. B, Condensed matter.

[6]  Jennifer J. Quinn,et al.  Hydrodynamic model for surface plasmons in metals and degenerate semiconductors , 1976 .

[7]  Robert E. Parks,et al.  Magnetic-Dipole Contribution to Optical Harmonics in Silver , 1966 .

[8]  A. I. Maaroof,et al.  Bulk and surface plasmons in highly nanoporous gold films , 2007 .

[9]  F. Haas,et al.  Self-consistent fluid model for a quantum electron gas , 2001, cond-mat/0203394.

[10]  Steve Blair,et al.  Third-harmonic generation from arrays of sub-wavelength metal apertures. , 2009, Optics express.

[11]  Sudhanshu S. Jha,et al.  Nonlinear optical reflection from a metal surface , 1965 .

[12]  H. Ehrenreich,et al.  Optical Properties of Semiconductors , 1963 .

[13]  Igor V. Mel'nikov,et al.  Second-harmonic generation by a reflecting metal surface , 1994, Photonics West - Lasers and Applications in Science and Engineering.

[14]  G. Grimvall.  Many-body corrections to the effective electron mass in the noble metals , 1970 .

[15]  Reuven Gordon,et al.  Enhanced second harmonic generation from nanoscale double-hole arrays in a gold film , 2006 .

[16]  Sudhanshu S. Jha,et al.  Theory of optical harmonic generation at a metal surface , 1965 .

[17]  Charles T. Rogers,et al.  Optical surface second harmonic measurements of isotropic thin-film metals: Gold, silver, copper, aluminum, and tantalum , 2004 .

[18]  Ernest G. Linder,et al.  Effect of Electron Pressure on Plasma Electron Oscillations , 1936 .

[19]  Sudhanshu S. Jha,et al.  OPTICAL SECOND HARMONIC GENERATION IN REFLECTION FROM MEDIA WITH INVERSION SYMMETRY. , 1968 .

[20]  N. Bloembergen,et al.  Optical Nonlinearities of a Plasma , 1966 .

[21]  H. Ehrenreich,et al.  Optical Properties of Ag and Cu , 1962 .

[22]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[23]  Joseph Zyss,et al.  Enhanced second-harmonic generation by metal surfaces with nanoscale roughness: nanoscale dephasing, depolarization, and correlations. , 2004, Physical review letters.

[24]  S. S. Jha,et al.  Interband Contributions to Optical Harmonic Generation at a Metal Surface , 1967 .

[25]  D. Maystre,et al.  Optical second‐harmonic generation from silver at 1.064‐μm pump wavelength , 1987 .

[26]  V V Moshchalkov,et al.  Plasmonic ratchet wheels: switching circular dichroism by arranging chiral nanostructures. , 2009, Nano letters.

[27]  T. Ishikawa,et al.  The prominent 5d-orbital contribution to the conduction electrons in gold , 2010, 1003.3294.

[28]  H. Lezec,et al.  Extraordinary optical transmission through sub-wavelength hole arrays , 1998, Nature.

[29]  Robert E. Parks,et al.  Nonlinear Optical Reflection from a Metallic Boundary , 1965 .

[30]  V V Moshchalkov,et al.  Asymmetric optical second-harmonic generation from chiral G-shaped gold nanostructures. , 2010, Physical review letters.

[31]  S Enoch,et al.  Strong modification of the nonlinear optical response of metallic subwavelength hole arrays. , 2006, Physical review letters.

[32]  Andrew G. Glen,et al.  APPL , 2001 .

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

[34]  M. Centini,et al.  Experimental study of Bloch vector analysis in nonlinear, finite, dissipative systems , 2010 .

[35]  A. Belardini,et al.  Second-harmonic generation from metallodielectric multilayer photonic-band-gap structures , 2008 .

[36]  Edward A. Stern,et al.  Second-Harmonic Radiation from Metal Surfaces , 1971 .

[37]  Henry Ehrenreich,et al.  Optical Properties of Noble Metals. II. , 1965 .

[38]  Mendoza,et al.  Simple model of second-harmonic generation. , 1992, Physical review. B, Condensed matter.

[39]  H. Teng,et al.  Chirp effects in femtosecond laser-induced surface second-harmonic generation from metals , 2004 .

[40]  N. Crouseilles,et al.  Quantum hydrodynamic model for the nonlinear electron dynamics in thin metal films , 2008 .

[41]  A. Lösch.  Nano , 2012, Ortsregister.

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

[43]  Shuang Zhang,et al.  Second harmonic generation from patterned GaAs inside a subwavelength metallic hole array. , 2006, Optics express.

[44]  Corvi,et al.  Hydrodynamic-model calculation of second-harmonic generation at a metal surface. , 1986, Physical review. B, Condensed matter.

[45]  John E. Sipe,et al.  Surface and bulk contributions to the second-order nonlinear optical response of a gold film , 2009 .

[46]  Simon,et al.  Second-harmonic generation from silver and aluminum films in total internal reflection. , 1985, Physical review. B, Condensed matter.

[47]  V V Moshchalkov,et al.  Linearly polarized second harmonic generation microscopy reveals chirality. , 2010, Optics express.

[48]  K. A. O'Donnell,et al.  Characterization of the second-harmonic response of a silver–air interface , 2005 .

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

[50]  H. Sonnenberg,et al.  Experimental Study of Optical Second-Harmonic Generation in Silver* , 1968 .

[51]  Juh Tzeng Lue,et al.  Optical second harmonic generation from thin silver films , 1997 .

[52]  Liebsch.  Second-harmonic generation at simple metal surfaces. , 1989, Physical review letters.

[53]  Mario Bertolotti,et al.  Engineering the second harmonic generation pattern from coupled gold nanowires , 2010 .

[54]  M. Vincenti,et al.  Extraordinary transmission in the UV range from sub-wavelength slits on semiconductors , 2009, CLEO/QELS: 2010 Laser Science to Photonic Applications.

[55]  M. Straub,et al.  Second harmonic generation from the Cu(001) surface , 1996 .

[56]  Lue,et al.  Nonlinear optical generation from noble metals and aluminum films in various geometric configurations. , 1989, Physical review. A, General physics.

[57]  S. Martellucci,et al.  Wavelength dependence of second-harmonic generation at the copper surface , 1993 .

[58]  H. Aronsson,et al.  The conduction electron optical mass in pure silver , 1972 .

[59]  N. Bloembergen.  Wave propagation in nonlinear electromagnetic media , 1963 .

[60]  E. Palik.  Handbook of Optical Constants of Solids , 1997 .

[61]  Pierre-François Brevet,et al.  Optical second harmonic generation of single metallic nanoparticles embedded in a homogeneous medium. , 2010, Nano letters.

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

[63]  Yaochun Shen.  Principles of nonlinear optics , 1984 .

[64]  J. Sambles,et al.  Simultaneous observation of surface plasmons on both sides of thin silver films , 1999 .

[65]  Pierre-Michel Adam,et al.  Role of surface plasmon in second harmonic generation from gold nanorods , 2007 .

[66]  U. Chettiar,et al.  The Ag dielectric function in plasmonic metamaterials. , 2008, Optics express.

[67]  A. Czapla,et al.  Free-electron parameters of sputtered noble metal films , 1985 .

[68]  M. Neviere,et al.  Nonlinear polarisation inside metals: A mathematical study of the free-electron model , 1986 .

[69]  John E. Sipe,et al.  Analysis of second-harmonic generation at metal surfaces , 1980 .