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FUNCTIONAL MATERIALS

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Metamaterials: from waves to matter

Metamaterials are artificial media whose effective properties, whether they be of electromagnetic, acoustic or mechanical nature, can in principle be tailored at will. The interaction between these different fields is a key point of next generation of metamaterials. The aim of the symposium is to bring together researchers working on these various aspects of metamaterials from fundamental physics to applications.

Scope:

The possibility of designing matter properties at one’s will is a technological dream that has led to a tremendous research activity. Metamaterials are such artificial structures whose effective properties are not found in natural materials. The term metamaterials was originally coined for artificial media whose electromagnetic properties were considered. This led to new concepts and devices such as negative refraction, artificial magnetism, super lenses or invisibility cloaks. Recently the field of metasurfaces were initiated by F. Capasso, where one considers the bidimensional analogue of metamaterials, with the aim of realizing extended laws of diffraction, designing flat achromatic lenses, polarization and geometrical phases control devices, efficient solar cells etc. Very recently the concept of topological insulators was extended to metamaterials.

The field has in fact expanded far beyond the historical borders of electromagnetism and the concepts have been extended to acoustic waves, water waves and even seismic waves and thermal transport. There are now as well impressive works on mechanical metamaterials where one aims at designing the mechanical properties of artificial media. Totally unconventional properties such as a negative Poisson modulus have been obtained experimentally. An important direction of research is the tentative of controlling several different physical phenomena, leading to the concept of multiphysics metamaterials. Specifically, it is possible to imagine, e.g., the simultaneous control of heat flow and the emission of electromagnetic radiation by a metamaterials. Another interesting direction is that of quantum metamaterials where one introduces quantum degree of freedom inside a photonic mesostructure in order to control the effective permittivity through the quantum microstates inside the system. This leads to a “blurring” of the classical disciplines. This challenging yet extremely powerful interaction between different fields is one of the key drivers for further innovation.

The symposium will be intrinsically multi-disciplinary. It will bring together researchers from different horizons and provide a valuable forum to discuss the latest advances and issues in the design and modeling of optical, acoustic, mechanical and multiphysics metamaterials. The symposium will welcome both experimental and theoretical works.

Hot topics to be covered by the symposium:

  • Electromagnetic metamaterials;
  • Metasurfaces;
  • Quantum metamaterials;
  • Topological metamaterials;
  • Acoustic and mechanical metamaterials;
  • Multi-physics metamaterials;
  • Mathematical and numerical methods.

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Non photonic metamaterials : Philippe Ben Abdallah
13:00
Authors : M. Gandolfi (1,2,3), G. Mazza (4,5), M. Capone (6), G. Ferrini(1,2), C. Giannetti (1,2), F. Banfi (1,2)
Affiliations : 1 Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Brescia I-25121, Italy 2 I-LAMP (Interdisciplinary Laboratories for Advanced Materials Physics), Università Cattolica del Sacro Cuore, Brescia I-25121, Italy 3 Laboratory of Soft Matter and Biophysics, Department of Physics and Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Heverlee, Leuven, Belgium 4 Centre de Physique Theorique, Ecole Polytechnique, CNRS, Universite Paris-Saclay, 91128 Palaiseau, France 5 College de France, 11 place Marcelin Berthelot, 75005, Paris, France 6 CNR-IOM Democritos National Simulation Center and Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy

Resume : Coherent control of wave-like phenomena via metamaterials is driving a technological revolution in fields ranging from electronics, photonics, to phononics. Although temperature has been historically taken as the paradigmatic example of an incoherent field, undergoing diffusive as opposed to wave-like propagation, on short space and time scales Fourier law fails and the possibility for temperature wave propagation sets in [1]. Building on this rational we propose a new class of metamaterials allowing for coherent temperature control on the ultrafast time-scale. As a model example we propose and theoretically investigate the dispersion relation of a “Temperonic Crystal”, a periodicic structure made alternating two materials sustaining heat waves on short time-scales. For instance a Temperonic Crystal may act as a frequency filter for a temperature pulse triggered by an ultra-short laser pulse. The above concepts are then contextualized in the frame of Quantum Materials. The anisotropy inherent high temperatures superconductors makes them an ideal building block to engineer metamaterials encompassing coherent control capabilities of the wave-like nature of the temperature fields occurring on ultrafast time-scales [2,3]. [1] Tzou, “Macro- to Microscale Heat Transfer: the Lagging Behavior” (John Wiley & Sons, Inc., 2014) [2] Gandolfi et al., in press on Physica Scripta [3] Giannetti et al., Advances in Physics 65, 58-238 (2016)

Z.I.1
13:15
Authors : Pankaj Rajak, Rajiv K. Kalia, Aiichiro Nakano, and Priya Vashishta
Affiliations : Collaboratory for Advanced Computing and Simulations, Department of Physics & Astronomy, Department of Computer Science, Department of Chemical Engineering & Materials Science, University of Southern California, Los Angeles, CA 90089-0242, USA

Resume : Deformation behavior of an ultralight architecture consisting of hollow Ni nanotubes and solid nanorods arranged as a 3-D kagomé structure is studied using Molecular dynamics simulations. As a precursor, we have also investigated mechanical response of a single hollow Ni nanotube and nanorod under uniaxial compression. We observe that 1/6(112) Shockley partial dislocations and twin formation at 3.5% compression collapse the nanotube and nanorod. Kagomé structure made from solid nanorods shows deformation both near the node of kagomé lattice and the eight beams connected to it for compression above 5%. In the case of hollow nanotube architecture, most of the deformation is observed near the node of the kagomé structure for strains higher than 6%. At 8% and 12.5% compression, we observe plastic buckling of solid and hollow architecture, respectively. Hence hollow nanotube architecture can withstand much larger compression with very little deformation of the system than the solid nanorod architecture. The deformation in all these systems is caused by 1/6(112) Shockley partial and 1/2(110) dislocations.

Z.I.2
13:30
Authors : Haedong Park1, Hyungho Kwon1, Yongsan An2, Woong-Ryeol Yu2, Myoung-Woon Moon1, and Kahyun Hur1
Affiliations : 1Computational Science Center, Korea Institute of Science and Technology, 02792 Seoul, Korea; 2Department of Materials Science and Engineering and Research Institute of Advanced Materials (RIAM), Seoul National University, 08826 Seoul, Korea

Resume : Poisson?s ratio is the negative ratio of deformed and lateral strains when a material gets mechanical load. For the material with negative value of Poisson?s ratio, it is called as auxetic metamaterial. A number of auxetic structures have been discovered or fabricated, although, most structures are actuated by contact force: mechanical load. Electric- or magnetic field and temperature are considered as non-contact force. Only few auxetic structures which deform by these interactions have been studied sporadically so that a mechanism of certain non-contact force responsive auxetic structure cannot be applied to others. Here, we propose a general rule to give non-contact force sensitive dynamics on arbitrary auxetic structure. Especially, we select temperature input and hexagonal auxetic structure to present new hexagonal auxetic structure which thermally and reversibly switches between in-plane honeycomb and auxetic structure. All these structures consist of their own auxetic frame and thermal expansible rods. Large differences of thermal expansion coefficients (CTE) between the frames and rods make this possible. Key points of understanding this study are (i) how thermal expansible rod with large CTE can be prepared, (ii) how the auxetic frame and the rods have to be combined to realize above phenomenon, and (iii) what the effect or application of this is. Detailed explanations on these are going to be discussed in the presentation.

Z.I.3
13:45
Authors : Romain FLEURY
Affiliations : Laboratory of Wave Engineering, EPFL, Switzerland

Resume : The recent discovery of topological phases of condensed matter has recently spawned a quest for their classical analogs in other branches of physics. In wave physics, in particular, several proposals have been put forward to obtain artificial periodic materials with a topologically nontrivial band structure, leading to metamaterial analogs of topological insulators. In particular, these materials support backscattering-immune chiral wave transport on their edges, along with a remarkable topological resilience against a large class of defects and disorder. In this presentation, we review our recent theoretical and experimental work on acoustic and electromagnetic topological insulators. We discuss our strategies to break time-reversal symmetry to induce a non-zero Chern invariant in nonreciprocal acoustic metamaterials, and pseudospin engineering methods to induce topologically nontrivial subwavelength acoustic and electromagnetic states without breaking time-reversal symmetry. Our results may lead to a novel class of system that exploit topological protection to guide and manipulate waves in unprecedented ways.

Z.I.4
 
Theoretical methods and modeling : Didier Felbacq
14:15
Authors : Alexander Zagoskin
Affiliations : University of Loughborough

Resume : Fragility of macroscopic quantum states severely restricts the realization of quantum simulations using the available hardware. Here we propose the "minimalist" approach using quantum metamaterials for the purpose, and discuss its possibilities and limits.

Z.II.1
14:45
Authors : Patrice Genevet
Affiliations : CHREA, France

Resume : Abrupt modifications of the fields across an interface can be engineered by depositing an array of subwavelength resonators specifically tailored to address local amplitude, phase and polarization changes. Physically, ultrathin nanostructure arrays, also called "optical metasurfaces", control light by engineeering artificial boundary conditions of Maxwell's equations. Metasurfaces can achieved various sorts of optical functionalities, ranging from the basic control of the transmission and reflection of light, to the control of the radiation patterns for comprehensive wavefront engineering and holography. After transmission or reflection through a metasurface, the amount of propagation phase shift required to achieve any optical function depends on the wavelength. This basic dispersion effect, which already affects bandwidth of conventional devices, is also limiting the operation of metasurfaces to a narrow bandwidth. In this presentation, we present a multi-wavelengths achromatic metasurface and we will talk about our recent results on free-standing dielectric metasurfaces and conclude with a discussion on the concept of conformal boundary optics: an analytical method based on novel, first principle derivations that allows us to engineer transmission and reflection at will for any interface geometry and any incident wave.

Z.II.2
15:15
Authors : Wei Yan and Philippe Lalanne
Affiliations : Laboratoire Photonique Numérique et Nanosciences, Université Bordeaux, IOGS, CNRS, France

Resume : We propose an efficient, rigorous and intuitive modal formalism (valid for lossy and dispersive resonators in inhomogeneous backgrounds) to model light interaction by a resonant metallic nanostructure. The formalism is the analogue of the modal waveguide formalism for electromagnetic resonators. Optical resonators play an essential role in many areas of modern photonics, from quantum plasmonics, optical metamaterials, integrated photonic circuits, to optical sensors. This predominant role is the outcome of the recent progress of bottom-up and top-down technologies that have allowed a proliferation of totally new resonator constructs with very distinct properties and dimensions, such as high-Q dielectric microcavities, plasmonic nanoantennas or associations of them. Comparatively, the resonator modelling has seen much less progress, and we enter an era where optical resonator technologies are limited by the lack of effective design tools rather than by creativity and fabrication. Here we elaborate a theoretical and numerical formalism that has the potential to bring a real difference in resonator design. Developed for the most general case of 3D plasmonic resonators in inhomogeneous backgrounds, the formalism differs markedly from classical methods. It is the equivalent of waveguide-mode-theory for resonators, and offers similar strengths: an intuitive modelling that sticks to the physics of the resonance and a high-performance with computational speeds that are several orders of magnitude faster than those presently available with classical methods.

Z.II.3
15:30
Authors : G. Demésy, A. Nicolet
Affiliations : Institut Fresnel (UMR 7249); Institut Fresnel (UMR 7249);

Resume : A new method is presented for the direct computation of the resonances associated with electromagnetic structures including media with highly dispersive permittivities.  A classical way to introduce dispersion is to use Drude or Lorentz models. All these models are in fact representations of a dispersive permittivity in the form of a rational function of the frequency f, i.e. N(f)/D(f) where N and D are polynomials in f. A direct way to obtain an eigenvalue problem is to multiply the equation by the denominator D(f). In this case, the discretization of the problem will lead to a generalized polynomial eigenvalue problem (of degree higher than 2). Very recent advances in linear algebra algorithms have provided efficient libraries able to directly tackle such problems (e.g. SLEPc). This model is applied to 2D periodic structures such as metamaterials where plasmons appear when the frequency of the mode is associated to a negative permittivity.

Z.II.4
15:45
Authors : Graeme W. Milton and Ornella Mattei
Affiliations : Department of Mathematics, The University of Utah

Resume : It is rare in science that a completely new type of wave is discovered. Field patterns represent such a discovery and occur in space-time microstructures (or in microstructures of hyperbolic materials), such that a disturbance propagating along a characteristic line does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is the field pattern. In one spatial direction plus time, the field patterns occur when the slope of the characteristics is, in a sense, commensurate with the space-time microstructure. Field patterns with different spatial shifts do not generally interact, but rather evolve as if they live in separate dimensions, as many dimensions as the number of field patterns. Alternatively one can view a collection as a multicomponent potential, with as many components as the number of field patterns. Presumably if one added a tiny nonlinear term to the wave equation one would then see interactions between these field patterns in the multidimensional space that one can consider them to live, or between the different field components of the multicomponent potential if one views them that way. As a result of PT-symmetry many of the complex eigenvalues of an appropriately defined transfer matrix have unit norm and hence the corresponding eigenvectors correspond to propagating modes. There are also modes that blow up exponentially with time.

Z.II.5
16:00 Coffee break    
16:15 Plenary Session    
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Fabrication and characterization : Agnès Maurel
09:00
Authors : Martin Wegener
Affiliations : Institute of Applied Physics and Institute of Nanotechnology Karlsruhe Institute of technology (KIT) 76128 Karlsruhe Germany

Resume : We review our recent experiments on microstructured metamaterials made by using 3D laser printing. This includes chainmail-like structures showing a sign reversal of the Hall coefficient, mechanical buckling metamaterials as reusable light-weight shock absorbers, and two-component metamaterials with near-zero or negative effective thermal length-expansion coefficient from positive constituents.

Z.III.1
09:30
Authors : F. Gonzalez-Posada, F. Omeis, R. Smaali, L. Cerutti, E. Centeno, T. Taliercio
Affiliations : F. G-P, L. C. and T.T are with the Univ. Montpellier - CNRS, IES UMR 5214 F-34000, Montpellier, France F.O., R.S. and E.C are with Institute Pascal ? UMR6602, Univ. Blaise Pascal - CNRS, BP 10448 ? 63000 Clermont-Ferrand, France

Resume : We demonstrate a periodic array of metallic-insulator-metallic (MIM) nano-resonators (NRs) using highly doped InAsSb semiconductors on GaSb substrates, which can be described as a high absorber in the infrared region. Our simulation approach permits to obtain analytically the optical properties of the absorption structure with rigorous coupled-wave analysis. These NRs sustain several gap-plasmon modes having high effective indices that allow the confinement of the electromagnetic waves at subwavelength scale. We establish a coherent fabrication geometry for an almost total absorption at certain wavelengths from 10 to 50 micrometers. The fabricated NR arrays show absorption peaks at different wavelengths in linear relationship with the NR width. A constant and variable loss dielectric function for the whole spectral range demonstrate a perfect matching between experimental results and theoretical calculations. However, the gap-plasmon space area under the resonators seems systematically higher than the physical resonator width. These theoretical and experimental results path the way to introduce highly doped semiconductors as a clear good candidate to realize MIM NRs as absorbing metasurfaces operating from the mid-IR until the THz range. The spectral control available varying the simple geometry of the NRs arrays will be basic building blocks for a growing number of promising applications, including thermal detectors, light sources, energy-harvesting systems and bio-sensors.

Z.III.2
09:45
Authors : Isabelle Rodriguez1, Raúl Perez-Ruiz1, Roberto Fenollosa1, Alejandro Manjavacas3, M. Consuelo Jiménez2, Guillermo Gonzalez-Rubio5, Judith Langer5, Andrés Cantarero4, Luis M. Liz-Marzán5, Miguel A. Miranda1,2 and Francisco Meseguer1
Affiliations : 1Instituto de Tecnología Química (CSIC-UPV), Universidad Politécnica de Valencia, Av. Los Naranjos s/n, 46022 VALENCIA, Spain 2Departamento de Química, Universitat Politècnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain 3Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA 4Molecular Science Institute, University of Valencia, PO Box 22085, 46071 Valencia, Spain 5Bionanoplasmonics Laboratory, CICbiomaGUNE, Paseo de Miramón 182, 20014 Donostia-San Sebastián, Spain

Resume : Photochemistry is rooted on the selection rules for optical transitions between atomic/molecular levels. As the magnetic component of light has a negligible contribution, the dipolar electric approximation has generally been assumed. This traditional understanding has been challenged by the recent discovery of metamaterials, where the contributions of both the electric and magnetic fields are comparable. Here we present preliminary experimental results on the generation of singlet oxygen, a paradigmatic example of dipole-forbidden optical transitions in photochemistry, through magnetic dipole allowed optical transition in gold nanorods. Both photochemical test reactions and decay kinetics of photosensitized singlet oxygen luminescence have been employed. SERS and Laser Flash Photolysis experiments are shown.

Z.III.3
10:00
Authors : Flavia Timpu*, Claude Renaut*, Morgan Trassin**, Manfred Fiebig**, Rachel Grange*
Affiliations : *Optical Nanomaterial Group, Institute for Quantum Electronics, Department of Physics, ETH Zürich, Auguste-Piccard-Hof 1, 8093 Zürich, Switzerland **Multifunctional Ferroic Materials, Department of Materials, ETH Zürich, Vladimir-Prelog-Weg 4, 8093 Zürich, Switzerland

Resume : Barium titanate (BaTiO3) is a very promising building block for metamaterials and other photonic devices. Such a perovskite material is transparent from the ultraviolet to the infrared and possess a high refractive index (n = 2.5 at 500 nm). In addition, BaTiO3 emits a strong second harmonic generation (SHG) signal due to its noncentrosymmetric crystal structure, even down to the nanoscale [1]. However, nonlinear optical processes are known to be weak in bulk materials and extremely small at the nanoscale since they mainly scale with the volume. Therefore, we develop strategies to enhance nonlinear effects without using metallic nanoantennas, but by using the properties of the BaTiO3 material itself. Here, we demonstrate Mie resonances in single BaTiO3 nanoparticles of 200 nm in diameter. We show that these resonances can be further used to enhance the SHG signal up to 4 orders of magnitude higher than in bulk crystal. We obtain strong correlation between the linear and the nonlinear optical responses of single BaTiO3 nanoparticles [2]. Since these particles are chemically synthesized and not well suited to build metasurfaces, we also show that thin films, deposited by pulsed laser can be structured with focused ion beam milling. And, we obtain the very first BaTiO3 meta-atoms. [1] E. Kim, A. Steinbrück, M. T. Buscaglia, V. Buscaglia, T. Pertsch and R. Grange, ACS Nano, 2013, 7, 5343–5349. [2] F. Timpu, A. Sergeyev, N. R. Hendricks and R. Grange, ACS Photonics, 2017, 4, 76–84.

Z.III.4
10:15
Authors : Xuan Wang, Alexandre Baron, Ashod Aradian, Philippe Barois, Virginie Ponsinet
Affiliations : CNRS, University of Bordeaux, CRPP UPR8641, F-33600 Pessac, France

Resume : Self-assembled metamaterials constitute a promising platform towards bulk optical materials with unusual effective properties. Reporting on several experimental systems, we show that they can reach unprecedented values of bulkiness and homogeneity figures of merit. This is achieved by assembling plasmonic nanoparticles into dense 3D structures, in which the localized surface plasmon resonances of the particles provide specific optical responses. We produce anisotropic nanocomposites by the assembly of gold nanoparticles within spontaneously ordered matrices of diblock copolymers. In particular, we study periodic lamellar stacks of layers of gold particles alternating with layers of pure polymer. Combining their detailed structural study and the measure of their anisotropic effective dielectric permittivity by spectroscopic ellipsometry, we show that they constitute hyperbolic metamaterials, allowing for the propagation of large magnitude wavevectors, which would be evanescent in a dielectric. We obtain plasmonic nanoclusters made of metallic satellites surrounding a dielectric core by colloidal engineering. We first show that the individual clusters present a strong magnetic scattering, using polarization resolved spectroscopic light scattering. The nanoclusters are subsequently assembled into a bulk material, with an effective magnetic permeability found by variable angle spectroscopic ellipsometry to take values between 0.8 and 1.4, over the visible light wavelength range.

Z.III.5
10:30 Coffee break    
 
Slabs and Metasurfaces : Didier Felbacq
11:00
Authors : F. Utel, L. Pattelli, K. Vynck, D.S. Wiersma
Affiliations : Univ. of Florence Italy, LP2N Institut d'Optique d'Aquitaine France

Resume : Disordered photonic systems are full of surprises, in particular if the spatial arrangement of scattering elements goes beyond a simple Gaussian distribution. Examples include photonic quasi-crystals, hyper-uniform structures, and structures in which the distribution is inhomogeneous. We will discuss recent developments regarding interference effects in Lévy glasses where contradicting predictions exist on the existence of a mobility edge in two-dimensions and the extent to which Lévy-alpha particle distributions can enhance or decrease the degree of localization of optical modes. [1] P. Barthelemy, J. Bertolotti, D. S. Wiersma, A lévy flight for light, Nature 453, 427 (2008). [2] D. S. Wiersma, Disordered Photonics 7, 188-196 (2013). [3] R. Savo, M. Burresi, T. Svensson, K.Vynck, D.S. Wiersma, Walk dimension for light in complex disoredered media, Phys. Rev. A 90, 023839 (2014)

Z.IV.1
11:30
Authors : H. Eghlidi, C. U. Hail, P. Richner, D. Poulikakos
Affiliations : Laboratory of Thermodynamics in Emerging Technologies, Institute of Energy Technology, Department of Mechanical and Process Engineering, ETH Zürich, CH-8092 Zürich, Switzerland

Resume : Sub-diffraction plasmonic rods have been studied as optical antennas and in metasurfaces. Their scattering cross-section and resonance can be largely tuned, and their fabrication, through chemical synthesis or electron-beam lithography is well established. However, the full potential of such simple plasmonic entities has not been exploited. In this presentation, we will introduce three novel examples of arrays of plasmonic nanorods which manipulate visible light in extraordinary manners: First, we show that out-of-plane metal-dielectric composite nanorods can act as very effective and broadband absorbers of light. We realize such nanorods by directly printing them using electrohydrodynamic printing in a rapid nanodripping mode [1,2]. We show that by controlling the height of the printed rods we can precisely control their level of absorption [2] and exploiting this, we print gray-scale images with ultimate diffraction-limited spatial resolution. Second, we demonstrate engineered in-plane nanorod arrays which generate vivid colors. By adjusting the dimensions and periodicity of such nanorod arrays, and combining rods with different sizes we can achieve a wide range of colors . Finally, we report on our concept of metasurfaces composed of nanorods with varying dimensions, which can manipulate the phase-front of light and bend it to a desired direction. We demonstrate a high light-bending efficiency (> 25%) and tunable bandwidth of the metasurface. References 1. P. Galliker, J. Schneider, H. Eghlidi, S. Kress, V. Sandoghdar, and D. Poulikakos, “Direct Printing of Nanostructures by Electrostatic Autofocussing of Ink Nanodroplets,” Nature Communications 3:890 (2012). 2. P. Richner, H. Eghlidi, S. J. P. Kress, M. Schmid, D.J. Norris, and D. Poulikakos, “Printable Nanoscopic Metamaterial Absorbers and Images with Diffraction-Limited Resolution,” ACS Appl. Mater. Interfaces, 8, 11690 (2016).

Z.IV.2
11:45
Authors : Antonio Capretti, Arnon Lesage and Tom Gregorkiewicz
Affiliations : University of Amsterdam

Resume : Nanoscale dielectric resonators and quantum-confined semiconductors have enabled an unprecedented control over light absorption and over excited electron states, respectively. In this work, we embed photoluminescent silicon nanocrystals (Si-NCs) into a 2D array of SiO2 nanocylinders, and experimentally prove a powerful concept: the resulting metamaterial preserve the luminescent properties of the Si-NCs, and inherit the spectrally-selective absorption properties of the nanocylinders. This hierarchical approach provides increased photoluminescence (PL) intensity, without utilizing any lossy plasmonic components. Specifically, our calculations predict such a metamaterial enables tunable absorption peaks up to 50% in the visible spectrum, when free-standing, and it can reach total absorption by using a back-reflector. We experimentally detect extinction spectral peaks in the metamaterial, which drive enhanced absorption in the Si-NCs. Consequently, we measure increased PL intensity, obtained without affecting the PL lifetime, angular pattern and extraction efficiency. The principle demonstrated here is general and the Si-NCs can be replaced with other semiconductor quantum dots, rare-earth ions or organic molecules. Similarly, the dielectric medium can be adjusted on purpose. We envision the use of this hierarchical design for efficient photovoltaic, photo-catalytic and artificial photosynthetic devices with spectrally selective absorption and enhanced efficiency.

Z.IV.3
12:00
Authors : Silvia Romano (1), Gianluigi Zito (2), Stefano Managò (2), Erika Penzo (3), Simone Sassolini (3), Scott Dhuey (3), Stefano Cabrini (3), Anna Chiara De Luca (2), Vito Mocella (1)
Affiliations : (1) Institute for Microelectronics and Microsystems, National Research Council, CNR-IMM UoS Napoli, Italy (2) Institute of Protein Biochemistry, National Research Council, CNR-IBP, Napoli, Italy (3) Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, USA

Resume : Metasurfaces are artificial structures suitably designed to possess unexpected electromagnetic effects, such as beam-steering, anomalous refraction and optical-wavefront shaping. They can be considered as a 2D alternative to metamaterials and provide a novel and easier method for miniaturization of optical elements. A photonic crystal membrane can support bound states in the continuum of radiation modes, i.e. resonant states with theoretical infinite lifetime. Experimentally, fabrication imperfections and finite sample extension partially break the symmetry of the photonic crystal lattice and allow the coupling of external radiation with these symmetry-protected modes. This involves very narrow coupled resonances, with a high Q-factor and an extremely large field intensity enhancement, up to 6 orders of magnitude larger than the intensity of the incident beam. Here, we show that the enhanced field confined in proximity to the surface of a silicon nitride photonic crystal membrane can be applied to boost fluorescence emission of probe molecules dispersed on the surface. Our results provide new solutions for light manipulation at the nanoscale, especially for sensing and nonlinear optics applications.

Z.IV.4
12:15
Authors : Gianluigi Zito (1), Silvia Romano (2), Giuseppe Calafiore (3,4), Simone Sassolini (3), Scott Dhuey (3), Stefano Cabrini (3), Anna Chiara De Luca (1), Vito Mocella (2)
Affiliations : (1) Consiglio Nazionale delle Ricerche, IBP, Via P. Castellino 111, 80131, Napoli, Italy; (2) Consiglio Nazionale delle Ricerche, IMM, Via P. Castellino 111, 80131, Napoli, Italy; (3) Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA; (4) aBeam Technologies Inc., 22290 Foothill Blvd, St. 2 Hayward, CA, 94541, USA;

Resume : Electromagnetic waves of specific frequencies can be confined and controlled by photonic and plasmonic structures. Very recently, nearly perfect light confinement has been achieved in a photonic crystal (PhC) slab by virtue of resonant trapping in the continuum of radiation modes. This type of electromagnetic field localization is indicated as a bound state in the continuum (BIC). Herein, we experimentally demonstrate conversion of photon spin degrees of freedom to orbital angular momentum in a designer PhC slab with sub-wavelength thickness and BIC-based light confinement. Abrupt nonparaxial redirection of light is enabled by BIC excitation at normal incidence and imposes total spin-to-angular momentum conversion. Experimental results are in excellent agreement with our model based on geometric parallel transport of light polarization. Numerical modeling indicates that the electromagnetic field structure consists of a vortex-antivortex lattice characterized by transverse photonic spin. Circular dichroism is experimentally observed and discussed.

Z.IV.5
12:30
Authors : Agnès Maurel, Jean-Jacques Marigo, Kim Pham, Jean-Francois Mercier
Affiliations : Institut Langevin, ESPCI, 1 rue Jussieu, Paris, France

Resume : We present the homogenization of an array of locally resonant structures; the resonance is of the Mie type or of the Helmholtz type. In the low frequency regime, we define a small parameter kh, with k the wavenumber and h the array spacing; the array thickness e=O(h). For both resonators, an appropriate scaling of the physical parameters (material parameters or geometrical parameters) with respect to kh allows us to identify the source of the subwavelength resonance. The homogenization method is based on a two scale expansions and matched asymptotic technique is used. We end with effective jump conditions across the array involving effective parameters among which one is frequency dependent and encapsulates the resonances. Validations of our models will be presented by comparison with direct numerics.

Z.IV.6
12:45 Lunch    
 
Novel effects in metamaterials : Alexander Zagoskin
14:30
Authors : C. A. Downing and G. Weick
Affiliations : Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504, F-67000 Strasbourg, France

Resume : We consider a dimerized linear chain made of spherical metallic nanoparticles, where each nanoparticle supports a localized surface plasmon. The near-field dipolar interaction between the localized surface plasmons gives rise to collective plasmons, which are extended over the whole nanoparticle array. At the edge of the plasmonic bandstructure, we reveal a novel excitation which is described by a one-dimensional massive Dirac-like Hamiltonian, suggesting phenomena such as Klein tunnelling may be present. We also show that the bipartite chain is governed by a nontrivial Zak phase, which both predicts the manifestation of edge states and announces the system as the nanoplasmonic analogue of a topological insulator. When two dimerized chains with different topological phases are connected, we find the appearance of the bosonic version of a topologically protected Jackiw-Rebbi midgap state. We discuss the radiative and nonradiative losses of the collective plasmonic excitations, which is of crucial importance for plasmonic energy and information transport, and comment on the challenges for experimental realization of the effects found theoretically. [1] A. Brandstetter-Kunc, G. Weick, C. A. Downing, D. Weinmann, R. A. Jalabert, Nonradiative limitations to plasmon propagation in chains of metallic nanoparticles, Phys. Rev. B 94, 205432 (2016). [2] C. A. Downing and G. Weick, Topological collective plasmons in bipartite chains of metallic nanoparticles (arXiv:1611.03349).

Z.V.1
14:45
Authors : Sylvain Lannebère, Mário G. Silveirinha
Affiliations : Department of Electrical Engineering, University of Coimbra and Instituto de Telecomunicações, 3030-290 Coimbra, Portugal; Department of Electrical Engineering, University of Coimbra and Instituto de Telecomunicações, 3030-290 Coimbra, Portugal University of Lisbon – Instituto Superior Técnico, Department of Electrical Engineering, 1049-001 Lisboa, Portugal

Resume : In recent works it has been shown that wave instabilities may build up when two closely spaced perfectly smooth parallel surfaces are sheared past one another with a velocity exceeding some threshold value [1-3]. This phenomenon is the counterpart of Cherenkov radiation but for neutral and polarizable matter. It occurs because of the coupling between the guided modes supported by each surface and is accompanied by a friction force due to the conversion of kinetic energy into electromagnetic energy. The conditions required for the emergence of the instabilities in planar or cylindrical geometries as well as their relation with a broken PT-symmetry and negative Doppler shifted frequencies were studied in [1-10]. Interestingly, it was demonstrated in Ref. [3] that similar instabilities and spontaneous light emission can also occur for an isolated classical dipole moving in the close vicinity of a plasmonic slab. Here, we extend this problem to quantum mechanics and study the time dynamics of a moving two-level atom interacting with the quantized field of a plasmonic surface. It is shown that for a certain range of parameters the system is characterized by a negative spontaneous emission, meaning that the transition rate to the excited state exceeds the transition rate to the ground state and is associated with a quantum friction force. However, different from the classical case, the instabilities saturate due to the peculiar energy spectrum of the two-level atom [11]. References: [1] M. G. Silveirinha, “Quantization of the electromagnetic field in nondispersive polarizable moving media above the Cherenkov threshold,” Physical Review A, vol. 88, p. 043846, Oct. 2013. [2] M. G. Silveirinha, “Theory of quantum friction,” New Journal of Physics, vol. 16, p. 063011, June 2014. [3] M. G. Silveirinha, “Optical Instabilities and Spontaneous Light Emission by Polarizable Moving Matter,” Physical Review X, vol. 4, p. 031013, July 2014. [4] P. P. Meyer, “A quantum Cerenkov effect,” Journal of Physics A: Mathematical and General, vol. 18, no. 12, p. 2235, 1985. [5] S. A. R. Horsley, “Canonical quantization of the electromagnetic field interacting with a moving dielectric medium,” Phys. Rev. A, vol. 86, p. 023830, 2012. [6] S. I. Maslovski and M. G. Silveirinha, “Quantum friction on monoatomic layers and its classical analog,” Physical Review B, vol. 88, p. 035427, July 2013. [7] M. G. Silveirinha, “Spontaneous parity-time-symmetry breaking in moving media,” Physical Review A, vol. 90, p. 013842, July 2014. [8] Y. Guo and Z. Jacob, “Singular evanescent wave resonances in moving media,” Optics express, vol. 22, pp. 26193–26202, 2014. [9] S. A. R. Horsley and S. S. Bugler-Lamb, “Negative frequencies in wave propagation: a microscopic model,” Phys. Rev. A, vol. 93, p. 063828, 2016. [10] S. Lannebère and M. G. Silveirinha, “Wave instabilities and unidirectional light flow in a cavity with rotating walls,” Physical Review A, vol. 94, p. 033810, Sept. 2016. [11] S. Lannebère and M. G. Silveirinha, “Negative spontaneous emission by a moving two-level atom,” Journal of Optics, vol. 19, no. 1, p. 014004, 2016.

Z.V.2
15:15
Authors : François Fernique, Guillaume Weick
Affiliations : Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, Strasbourg, France

Resume : Since a few years, plasmonic nanostructures have witnessed a boost of interest due to their ability to perform subwavelength optics. Plasmonic metamaterials indeed present extraordinary features such as the possibility to trap and control light at the nanoscale. Periodic arrays of metallic nanoparticles are of particular interest since they support collective plasmonic modes which extend over the whole metasurface. Such collective modes arise due to the dipolar interaction between localized surface plasmons on each nanoparticle, opening a new way to transport light at the nanoscale. A crucial quantity to evaluate for future applications is the lifetime of the collective excitations. For a single nanoparticle, the plasmon suffers from both radiative and nonradiative damping processes which strongly depend on the nanoparticle size. However, in 2D arrays, the interactions between the nanoparticles significantly modifiy the decay rates. We present a theoretical framework to evaluate the damping mechanisms for arbitrary 2D periodic arrays of metallic nanoparticles. We apply our results to arrays with various geometries. Among them, we concentrate on the cases of the honeycomb, Lieb and Kagomé arrays which present interesting topological features such as Dirac-like plasmons [1,2] and nondispersive bands that can be used to localize light onto metasurfaces. [1] G. Weick et al, PRL 110, 106801 (2013) [2] T. J. Sturges et al, 2D Materials 2, 014008 (2015)

Z.V.3
15:30
Authors : Charles A. Downing, Eros Mariani, Guillaume Weick
Affiliations : School of Physics and Astronomy Exeter, IPCMS Strasbourg

Resume : We study the effect of the electromagnetic environment on the resonance frequency of localized surface plasmons in dimers of interacting metallic nanoparticles. While this shift (analogous to the Lamn shift in atomic physics) is usually not measurable in an isolated nanoparticle, we show that it leads to sizeable corrections to the level splitting induced by interactions in nanoparticle dimers. The ratio between the level splitting for the longitudinal and transverse hybridized modes takes a universal form dependent only on the interparticle distance. We discuss the possibility to successfully realize the proposed measuremt in experiments with state-of-the-art nanoplasmonic devices.

Z.V.4
15:45
Authors : G. P. Tsironis
Affiliations : Department of Physics, University of Crete, Greece

Resume : Superconducting metamaterials comprised of rf Superconducting QUantum Interference Devices (SQUIDs) form a complex nonlinear medium with interesting tuneability and dynamic multistability properties. Depending on the parameter regime the SQUID metamaterial may operate in a negative permeability regime, induce intrinsic nonlinear localized modes, tame disorder through hysteretic loops or transmit through nonlinear frequency bands. They can also enter into a partially coherent regime and form stable chimera states. In the quantum realm, on the other hand, SQUIDs may be used as qubits and thus building blocks of quantum computers. The superconducting qubit “meta-atoms” may interact through an injected electromagnetic field and form a propagating “quantum breather”, i.e. a compound semiclassical propagating mode induced by the nonlinearity of the interaction. In this presentation we will first focus on the classical results and outline the nonlinear dynamics aspects of the SQUID metamaterial and then switch to the quantum regime and describe the dynamics of the collective mode and its properties.

Z.V.5
16:15
Authors : A.Slobozhanyuk, S. H. Mousavi, X. Ni, D. Smirnova, Y. S. Kivshar, and A. B. Khanikaev
Affiliations : Department of Electrical Engineering, The City College of New York, NY 10031, USA Nonlinear Physics Centre, Australian National University, Canberra ACT 0200, Australia Department of Nanophotonics and Metamaterials, ITMO University, St. Petersburg 197101, Russia

Resume : The discovery of two-dimensional topological photonic systems has transformed our views on propagation and scattering of electromagnetic waves, and a quest for similar states in three dimensions has been put forward. Here we demonstrate that symmetry protected three-dimensional topological states can be engineered in an all-dielectric platform with the electromagnetic duality between electric and magnetic fields ensured by the structure design. Magneto-electric coupling playing the role of a synthetic gauge field leads to a topological transition to an “insulating” regime with a complete three-dimensional photonic bandgap. An emergence of surface states with conical Dirac dispersion and spin-locking is unimpeded. Robust propagation of surface states along two-dimensional domain walls is confirmed numerically by first principle studies. The proposed system represents a table-top platform for emulating relativistic physics of massive Dirac fermions and the surface states can be interpreted as Jackiw-Rebbi states bound to the interface separating domains with opposite particle masses.

Z.V.6
16:45 Coffee break    
 
Poster session : -
17:00
Authors : Ion Sandu1, Ana-Maria Banici(Niculescu)1,2, Iuliana Urzica1 , Gabriel Cojocaru1, Iulia Anghel1, Marius Dumitru1, Maria Badiceanu3
Affiliations : 1National Institute for Lasers, Plasma and Radiation Physics, Lasers Dept, Bucharest-Magurele, 409, Atomistilor Street, 077125, Romania; 2University of Craiova, Faculty of Mathematics and Natural Sciences, RO-200585, Craiova, Romania; 3University of Bucharest, Faculty of Physics;

Resume : Nanosphere lithography (NSL) called also and natural lithography is an inexpensive technique capable of producing well-ordered 2D nanosphere arrays. The major problem of the nanosphere lithography is the lack of control over defects, dislocations and the low size of 2D nanosphere crystal domains. Nanosphere arrays typically consist of numerous microscopic (few hundreds of square micrometers) domains, with little or no correlation between them. In phenomena which involves a coherent light beam (laser) in interaction with patterned surfaces, and applications in which usually the measured signal is proportional with the interaction area and the intensity of the input signal, a larger 2D crystal domain would allowed a cheaper sensor or a more accurate measurements. Also, a single domain (even small) is preferable than numerous, small, not correlated, forming a close packed monolayer; uncorrelated nanoparticles will generate a decorrelate output signal. Through the so called ''coffee ring'' effect we can turn the particle ring in a ribbon by imposing geometric constrains on the drop. The drying of a large, flat, pinned, and elongated microsphere suspension drop deposited onto substrate, has as result a photonic crystal which presents a reduced number of missing spheres and dislocations. By using polystyrene nanosphere (0.7, 1.5, and 3.0 μm), ribbons of 25 mm in length and few tens of micrometers width were obtained. The method is simple, cheap, and fast.

Z.VI.1
17:00
Authors : Soonmin Yim, Yeon Sik Jung
Affiliations : Korea Advanced Institute of Science and Technology (KAIST)

Resume : Recently, the fabrication of high-density subwavelength nanohole array has been attempted due to its promising applications. However, typical high-resolution fabrication methods based on serial patterning processes suffer from low throughput and high cost. We introduce a facile and cost-effective fabrication method for high-resolution and high-density nanohole with sub-50 nm periodicity. We used solvent-assisted nano-transfer printing to fabricate densely packed and well-aligned Cr nanowires from duplication of cylindrical block copolymer template. Then, Au nanohole array was obtained via evaporation of Au onto patterned Si master template. Fabricated Au nanohole array was transferred to quartz substrate, resulting in square-aligned 18-nm-diameter holes with a density over 400 holes/μm2. In addition, it is shown that transmission characteristics of Au film is changed by forming nanohole structures. A resonance peak around 650 nm, which is not present in the transmittance spectrum of a flat Au film, is observed for Au nanohole array film, suggesting that the new peak may stem from plasmonic effect induced by the densely packed nanohole structures. The resonance peak shows clear sensitivity against the change of the refractive index of surrounding medium (115 nm/RIU), indicating its potential for sensor application.

Z.VI.2
17:00
Authors : Matthias Pauly, Hebing Hu, Sribharani Sekar, Vincent Lemaire, and Gero Decher
Affiliations : Université de Strasbourg, CNRS, Institut Charles Sadron, F-67000 Strasbourg, France

Resume : Recently there has been great interest in developing metamaterials that can control the flow of electromagnetic waves in unprecedented ways. These metamaterials need to have subwavelength dimensions, i.e. in the range of tens of nm for optical applications, and have mostly been manufactured by top-down technologies that have the disadvantage of being quite expensive and slow. Obtaining large areas and regular (3D) ordering is difficult, and nanoparticle self-assembly appears to be a promising alternative. A big challenge, however, still resides in the hierarchical organization of these nanoscale building blocks into two- or three-dimensional structures with well-controlled location, orientation, and spacing across multiple length scales. In particular, chiral assemblies of plasmonic nanoparticles are proposed as an alternate route for the fabrication of optical metamaterials[1]. I will present a novel technique, called Grazing Incidence Spraying, that we have developed for the self-assembly of anisotropic nanoparticles as mono- and multilayer thin films.[2-3] It allows aligning anisotropic nano-objects on large areas with tunable particle density and orientation, and the combination with the Layer-by-Layer assembly technique[4] is used to build helical (and thus chiral) multilayer thin films in which the composition and orientation can be controlled independently in each layer. The optical properties as function of the thin film geometry will be detailed, with a special emphasis on oriented mono- and multilayers and on helical plasmonic superstructures, which display very high chiroptical activity. [1] V. K. Valev, J. J. Baumberg, C. Sibilia, T. Verbiest, Adv. Mater. 2013, 25, 2517-2534. [2] S. Sekar, V. Lemaire, H. Hu, G; Decher, M. Pauly, Faraday Discuss. 2016, 191, 373-389. [3] H. Hu, M. Pauly, O. Felix, G. Decher, Nanoscale 2017, DOI: 10.1039/C6NR08045F [4] G. Decher, Science 1997, 277, 1232-1237.

Z.VI.3
17:00
Authors : Fakiri Fethallah, Rahmoun Khadidja
Affiliations : Department of Physics, Faculty of Science, Research Unit Materials and Renewable Energies U.R.M.E.R, University Abou Bekr Belkaid, BP 119, 13000 Tlemcen, Algeria

Resume : A numerical study is performed to investigate heat transfer and pressure drop in a rectangular channel with alternating porous baffles mounted on both upper and lower walls. Time-dependent three-dimensional turbulent flow with constant thermo physical properties is assumed for air and Reynolds number ranging from 10000 to 50,000. A detailed analysis is carried out to investigate flow pattern, Nusselt number, and friction factor for various obstacle height, width, and spacing. The results show a transition to unsteady flow at a moderate value of the Reynolds number. For the unsteady case, the flow becomes periodic in time with vortex-shedding oscillations.

Z.VI.4
17:00
Authors : Dong Wang and Peter Schaaf
Affiliations : Institute of Materials Engineering and Institute of Micro- and Nanotechnologies MacroNano®, Technische Universität Ilmenau, 98693 Ilmenau, Germany

Resume : Nanoporous gold nanoparticles (NPG-NPs) with controlled particle size and pore size can be fabricated via a combination of solid-state dewetting of Au/Ag bilayers and a subsequent dealloying process [1, 2]. Due to the combined effects of size and porosity, the NPG-NPs exhibit greater plasmonic tunability as compared to solid NPs [3]. For instance, for the NPG-NPs with sizes from 54 to 393 nm, the plasmon peak can be shifted in a wide spectral range from 685 to 1070 nm. It is obvious that there is a clear red-shift of plasmon peak with increasing porosity. However, the influences of both porosity and pore size on the plasmonic properties are very complicated and clearly different for small particles with dominated dipole mode and large particles with dominated quadrupole mode. In addition, the plasmonic property can be further tuned by fabricating the related hybrid NPs through filling other materials into the porous structure of the NPG-NPs. For instance, Au/Al2O3 hybrid porous NPs with controlled porosity and composition ratio are fabricated through plasma enhanced atomic layer deposition of Al2O3 into the porous structure. A further red-shift of the plasmon peak is observed in the hybrid NPs due to the change of the environmental refractive index. Moreover, Ag-Au hybrid porous NPs can be fabricated through the cyclic electroless deposition of Ag into the NPG-NPs [4]. In the Ag-Au hybrid porous NPs, both Au and Ag components with mesoscaled ligament size are bi-continuously percolated over the entire NP. Two distinct plasmon peaks are observed which can be attributed to Au and Ag components, respectively. The plasmonic properties can be well tuned by controlling the cycles of Ag deposition. Both plasmon peaks attributed to Au and Ag components blue shift with increasing amount of Ag. The Ag-Au hybrid NPs exhibit higher sensitivity in surface-enhanced Raman spectroscopy (SERS) detection of butter yellow (BY) than the NPG-NPs due to the presence of Ag and of the porous structure. Financial support was provided by the Deutsche Forschungsgemeinschaft (DFG, grant SCHA 632/20 and grant SCHA 632/24). References [1] D. Wang and P. Schaaf, “Nanoporous gold nanoparticles”, J. Mater. Chem., 22, 5344 (2012). [2] D. Wang, R. Ji, A. Albrecht, and P. Schaaf, “Ordered arrays of nanoporous gold nanoparticles”, Beilstein J. Nanotechnol., 3, 651 (2012). [3] C. Vidal, D. Wang, P. Schaaf, C. Hrelescu, and T. A. Klar, “Optical Plasmons of Individual Gold Nanosponges”, ACS Photonics, 2, 1436 (2015). [4] Y. Yan, A. I. Radu, W. Rao, H. Wang, G. Chen, K. Weber, D. Wang, D. Cialla-May, J. Popp and P. Schaaf, “Mesoscopically bi-continuous Ag-Au hybrid nanosponges with tunable plasmon resonances as bottom-up substrates for surface-enhanced Raman spectroscopy”, Chem. Mater., 8, 7673 (2016).

Z.VI.5
17:00
Authors : Minseok Seo, Jeeyoung Lee, Yoonseok Oh, Harim Oh, Jaeyong Kim, Myeongkyu Lee
Affiliations : Yonsei unversity

Resume : Plasmonic coloration of metal surface has mostly been based on the coating of noble metal nanoparticles like Au and Ag. However, these materials are difficult to use for practical applications because they are very expensive and also easily damaged. Bulk stainless steel is a widely used, cost-effective, durable, and corrosion-resistive metal. Various approaches have been suggested to obtain colored stainless steel, which include oxidation by laser irradiation [1], surface structuring by laser irradiation [2], [3], and chemical reaction to control passive film property [4]. In this study, we fabricated nano-scale patterns on the surface of stainless steel using soft lithography and electrochemical etching and analyzed their surface plasmon resonance characteristics. We fabricate a surface line pattern of 500 nm period. For this 1D structure, the surface plasmonic resonance strongly depended on the polarization state of the incident light. As the incident angle varied, the resonance absorption peak also shifted. All these can be explained by the grating-assisted emission of surface plasmons [5]. While angle and polarization-dependent coloration was possible by this periodic grating structure, localized surface plasmon resonance remained very weak, probably because the feature size of the pattern is still too large. It would be necessary to reduce the pattern size less than 100 nm in order to produce more prominent colors that are independent of the incident angle and polarization.

Z.VI.6

No abstract for this day


Symposium organizers
Andrea ALUUniversity of Texas

1616 Guadalupe St. UTA 7.215, Austin TX 78701, USA

alu@mail.utexas.edu
Didier FELBACQUniversity of Montpellier

Laboratory Charles Coulomb, Place Bataillon Bât. 21 CC074, 34095 Montpellier, France

didier.felbacq@umontpellier.fr
Pavel BELOVState University of Information Technologies, Mechanics and Optics (ITMO)

Sablinskaya st. 14, 197101, St. Petersburg, Russia

belov@phoi.ifmo.ru
Philippe BEN-ABDALLAHInstitut d’Optique

2 Av. Augustin Fresnel, 91127 Palaiseau cedex, France

pba@institutoptique.fr