An electromagnetic multipole expansion beyond the long-wavelength approximation

Abstract The multipole expansion is a key tool in the study of light–matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The multipole moments of the source. These numbers are frequently computed with expressions obtained after the long-wavelength approximation. Here, we derive exact expressions for the multipole moments of dynamic sources that resemble in their simplicity their approximate counterparts. We validate our new expressions against analytical results for a spherical source, and then use them to calculate the induced moments for some selected sources with a non-trivial shape. The comparison of the results to those obtained with approximate expressions shows a considerable disagreement even for sources of subwavelength size. Our expressions are relevant for any scientific area dealing with the interaction between the electromagnetic field and material systems.

[1]  N. Engheta,et al.  Cloaking a sensor. , 2009, Physical review letters.

[2]  C. Rockstuhl,et al.  On the dynamic toroidal multipoles from localized electric current distributions , 2015, Scientific Reports.

[3]  Vahid Sandoghdar,et al.  Design of plasmonic nanoantennae for enhancing spontaneous emission. , 2007, Optics letters.

[4]  F. Lederer,et al.  Multipole analysis of meta-atoms , 2011 .

[5]  Boris N. Chichkov,et al.  Nonradiating anapole modes in dielectric nanoparticles , 2015, Nature Communications.

[6]  S. Tretyakov,et al.  Phase-change material-based nanoantennas with tunable radiation patterns. , 2016, Optics letters.

[7]  F. Lederer,et al.  Analogue of electromagnetically induced transparency in a terahertz metamaterial , 2009, 0907.1937.

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

[9]  N I Zheludev,et al.  Electromagnetic toroidal excitations in matter and free space. , 2016, Nature materials.

[10]  N. Engheta,et al.  Multifrequency optical invisibility cloak with layered plasmonic shells. , 2008, Physical review letters.

[11]  Marta Castro-López,et al.  Multipolar interference for directed light emission. , 2014, Nano letters.

[12]  H. Doeleman,et al.  Antenna-cavity hybrids: matching polar opposites for Purcell enhancements at any linewidth , 2016, 1605.04181.

[13]  Nandini Bhattacharya,et al.  Excitation of the radiationless anapole mode , 2016 .

[14]  P. Nordlander,et al.  The Fano resonance in plasmonic nanostructures and metamaterials. , 2010, Nature materials.

[15]  J. Sáenz,et al.  Angle-suppressed scattering and optical forces on submicrometer dielectric particles. , 2012, Journal of the Optical Society of America. A, Optics, image science, and vision.

[16]  D. Sikdar,et al.  Optically resonant magneto-electric cubic nanoantennas for ultra-directional light scattering , 2015 .

[17]  J. P. Barton,et al.  Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam , 1989 .

[18]  C. Rockstuhl,et al.  Exact dipolar moments of a localized electric current distribution. , 2015, Optics express.

[19]  Andrea Alu,et al.  A subwavelength plasmonic metamolecule exhibiting magnetic-based optical Fano resonance , 2013, CLEO: 2013.

[20]  Shanhui Fan,et al.  Superscattering of light from subwavelength nanostructures. , 2010, Physical review letters.

[21]  C. Rockstuhl,et al.  Fundamental Limits of Optical Force and Torque , 2016, 1605.03945.

[22]  Lukas Novotny,et al.  Demonstration of zero optical backscattering from single nanoparticles. , 2012, Nano letters.

[23]  F. Lederer,et al.  Magnetoelectric coupling in nonidentical plasmonic nanoparticles: Theory and applications , 2015 .

[24]  Willie J Padilla,et al.  Perfect metamaterial absorber. , 2008, Physical review letters.

[25]  F Moreno,et al.  Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere , 2012, Nature Communications.

[26]  Yuri S. Kivshar,et al.  Fano Resonances in Nanoscale Structures , 2010 .

[27]  Z. Jacob,et al.  All-dielectric metamaterials. , 2016, Nature nanotechnology.

[28]  F. Lederer,et al.  A generalized Kerker condition for highly directive nanoantennas. , 2015, Optics letters.

[29]  P. Grahn,et al.  Electromagnetic multipole theory for optical nanomaterials , 2012, 1206.0530.

[30]  F. J. Rodríguez-Fortuño,et al.  Lateral forces on circularly polarizable particles near a surface , 2015, Nature Communications.

[31]  Boris N. Chichkov,et al.  Multipole analysis of light scattering by arbitrary-shaped nanoparticles on a plane surface , 2013 .

[33]  A. Polman,et al.  Directional emission from a single plasmonic scatterer , 2014, Nature Communications.

[34]  Jun Chen,et al.  Optical pulling force , 2011 .

[35]  Andrey E. Miroshnichenko,et al.  Directional visible light scattering by silicon nanoparticles , 2012, Nature Communications.

[36]  N. Bonod,et al.  Purcell factor of spherical Mie resonators , 2015 .