Fano Model Research Articles

Inhomogeneous crystallization of a‐Si thin films irradiated by femtosecond laser

AbstractRecently, we have carried out a detailed Raman analysis to investigate the inhomogeneous crystallization of a‐Si thin films irradiated by femtosecond (Fs) laser. As expected, there are many etched spots overlapping each other, which features the surface morphology of the irradiated films. It is observed clearly that there has generated an inhomogeneous crystallization inside a‐Si thin film induced by Fs laser, and the crystalline volume fraction in one irradiated spot varies depending on different areas from the center to the edge. It is hard to observe any crystallization at the spot center where maximum energy of Fs laser is injected; however, there is an increasing crystalline volume fraction when the site varies from the center to the edge of the irradiated spot. More importantly, as the site varies from the center to the edge, the TO mode of Si nanocrystals (NCs; first‐order Si–Si peak at ~520.5 cm−1) is asymmetrically broadened towards the low wavenumber and exhibits a dip on the high wavenumber. A model has been proposed to explain this inhomogeneous crystallization inside the a‐Si thin films induced by Fs laser, and both phonon confinement model and Fano model have been employed to discuss the origin of asymmetric line shapes of TO mode of Si NCs, and we prefer to attribute the asymmetry of TO mode to Fano effect. Our present research results provide a deep insight into the origin of asymmetric broadening for the Raman TO mode of Si NCs inside a‐Si thin films irradiated by Fs laser.

Anisotropic Flow Control and Gate Modulation of Hybrid Phonon-Polaritons.

Light-matter interaction in two-dimensional photonic or phononicmaterials allows for the confinement and manipulation of free-space radiation at sub-wavelength scales. Most notably, the van der Waals heterostructure composed of graphene (G) and hexagonal boron nitride (hBN) provides for gate-tunable hybrid hyperbolic plasmon phonon-polaritons (HP3). Here, we present the anisotropic flow control and gate-voltage modulation of HP3 modes in G-hBN on an air-Au microstructured substrate. Using broadband infrared synchrotron radiation coupled to a scattering-type near-field optical microscope, we launch HP3 waves in both hBN Reststrahlen bands and observe directional propagation across in-plane heterointerfaces created at the air-Au junction. TheHP3 hybridization is modulated by varying the gate voltage between graphene and Au. This modifies the coupling of continuum graphene plasmons with the discrete hBN hyperbolic phonon polaritons, which is described by an extended Fano model. This work representsthe first demonstration of the control of polariton propagation, introducing a theoretical approach to describe the breakingof the reflection and transmission symmetry for HP3 modes. Our findings augment the degree of control of polaritons in G-hBN and related hyperbolic metamaterial nanostructures, bringing new opportunities for on-chip nano-optics communication and computing.

In situ scattering of single gold nanorod coupling with monolayer transition metal dichalcogenides.

We investigated in situ the interaction between a single gold nanorod and monolayer transition metal dichalcogenides (TMDCs) by atomic force microscopy nanomanipulation and single-particle spectroscopy. We observed that the resonant scattering peak of the hybrid redshifted, the full width at half maximum of the scattering resonance narrowed and the scattering intensity increased compared with those of the same nanorod before coupling with monolayer TMDCs. These results were understood with the aid of finite-difference time-domain simulations, the Fano model, and the classical oscillator model. Also, the spectral features varied with the distance between the nanorod and TMDCs, and the interaction was mainly attributed to the resonant energy transfer effect. Our findings clarify the influence of TMDCs on the plasmonic resonance and contribute to a deeper understanding of the plasmon exciton interaction. These results are beneficial for the optimization of plasmonic nanostructure-TMDC hybrids and their corresponding applications.

The blow-up of $$\mathbb {P}^4$$ P 4 at 8 points and its Fano model, via vector bundles on a del Pezzo surface

Building on the work of Mukai, we explore the birational geometry of the moduli spaces $$M_{S,L}$$ of semistable rank two torsion-free sheaves, with $$c_1=-K_S$$ and $$c_2=2$$ , on a polarized degree one del Pezzo surface (S, L); this is related to the birational geometry of the blow-up X of $$\mathbb {P}^4$$ in 8 points. Our analysis is explicit and is obtained by looking at the variation of stability conditions. Then we provide a careful investigation of the blow-up X and of the moduli space $$Y=M_{S,-K_S}$$ , which is a remarkable family of smooth Fano fourfolds. In particular we describe the relevant cones of divisors of Y, the group of automorphisms, and the base loci of the anticanonical and bianticanonical linear systems.

Ubiquity of Beutler-Fano profiles: From scattering to dissipative processes

Fano models - consisting of a Hamiltonian with discrete-continuous spectrum - are one of the basic toy models in spectroscopy. They have been succesfull in explaining the lineshape of experiments in atomic physics and condensed matter. These models however have largely been out of the scope of dissipative dynamics, with ony a handful of works considering the effect of a thermal bath. Yet in nanostructures and condensed matter systems, dissipation strongly modulates the dynamics. In this article, we present an overview of the theoretical works dealing with Fano interferences coupled to a thermal bath and compare them to the scattering formalism. We provide the solution to any discrete-continuous Hamiltonian structure within the wideband approximation coupled to a Markovian bath. In doing so, we update the toy models that have been available for unitary evolution since the 1960s. We find that the Fano lineshape is preserved as long as we allow a rescaling of the parameters, and an additional Lorentzian contribution that reflects the destruction of the interference by dephasings. We discuss the pertinence of each approach - dissipative and unitary - to different experimental setups: scattering, transport and spectroscopy of dissipative systems. We finish by discussing the current limitations of the theories due to the wideband approximation and the memory effects of the bath.

Investigation the hexagonal cylindrical absorber for bio-sensing in optical regime

Optical absorber is important for various applications like solar-cell or optical sensing such as optical imaging. This paper has investigated the various formations of the cylindrical hollow structure such as triangular, rectangular and hexagonal cross-section and shows the benefit of the hexagonal absorber for 150 THz and the parametric studies investigated for the hexagonal structure. For achieving the multiband absorber, we have used another hexagonal particle inside of the first model the same as the co-axial formation and obtained dual-band characteristic. We show that by the asymmetric model we have the ability to obtain Fano response for the prototype absorber which can be noticed for the wideband application. The electric field shows that the prototype absorber has dipole mode. Finally, we have checked the external material effect on frequency shift as a factor for material recognition. We have compared the frequency shift in hexagonal, co-axial and Fano model for various refractive indexes. The studies show that the co-axial model is more suitable for material recognition, in comparison to hexagonal and Fano models.

Electron impact ionization of O2 and the interference effect from forward–backward asymmetry

Absolute double differential cross sections (DDCSs) of secondary electrons emitted from O2 under the impact of 7 keV electrons were measured for different emission angles between 30° and 145° having energies from 1–600 eV. The forward–backward angular asymmetry was observed from angular distribution of the DDCS of secondary electrons. The asymmetry parameter, thus obtained from the DDCS of two complementary angles, showed a clear signature of interference oscillation. The Cohen–Fano model of Young type electron interference at a molecular double slit is found to provide a good fit to the observed oscillatory structures. The present observation is in qualitative agreement with the recent results obtained from photoionization.

Coherent two-dimensional spectroscopy of a Fano model

The Fano lineshape arises from the interference of two excitation pathways to reach a continuum. Its generality has resulted in a tremendous success in explaining the lineshapes of many one-dimensional spectroscopies - absorption, emission, scattering, conductance, photofragmentation - applied to very varied systems - atoms, molecules, semiconductors and metals. Unravelling a spectroscopy into a second dimension reveals the relationship between states in addition to decongesting the spectra. Femtosecond-resolved two-dimensional electronic spectroscopy (2DES) is a four-wave mixing technique that measures the time-evolution of the populations, and coherences of excited states. It has been applied extensively to the dynamics of photosynthetic units, and more recently to materials with extended band-structures. In this letter, we solve the full time-dependent third-order response, measured in 2DES, of a Fano model and give the new system parameters that become accessible.

Nonlinear Fano interferences in open quantum systems: An exactly solvable model

We obtain an explicit solution for the stationary-state populations of a dissipative Fano model, where a discrete excited state is coupled to a continuum set of states; both excited sets of states are reachable by photoexcitation from the ground state. The dissipative dynamic is described by a Liouville equation in Lindblad form and the field intensity can take arbitrary values within the model. We show that the population of the continuum states as a function of laser frequency can always be expressed as a Fano profile plus a Lorentzian function with effective parameters whose explicit expressions are given in the case of a closed system coupled to a bath as well as for the original Fano scattering framework. Although the solution is intricate, it can be elegantly expressed as a linear transformation of the kernel of a $4\ifmmode\times\else\texttimes\fi{}4$ matrix which has the meaning of an effective Liouvillian. We unveil key notable processes related to the optical nonlinearity and which had not been reported to date: electromagnetic-induced transparency, population inversions, power narrowing and broadening, as well as an effective reduction of the Fano asymmetry parameter.

Transmission properties of terahertz waves through asymmetric rectangular aperture arrays on carbon nanotube films

Transmission spectra of terahertz waves through a two-dimensional array of asymmetric rectangular apertures on super-aligned multi-walled carbon nanotube films were obtained experimentally. In this way, the anisotropic transmission phenomena of carbon nanotube films were observed. For a terahertz wave polarization parallel to the orientation of the carbon nanotubes and along the aperture short axis, sharp resonances were observed and the resonance frequencies coincided well with the surface plasmon polariton theory. In addition, the minima of the transmission spectra were in agreement with the location predicted by the theory of Wood’s anomalies. Furthermore, it was found that the resonance profiles through the carbon nanotube films could be well described by the Fano model.

Large near-to-far field spectral shifts for terahertz resonances

We have performed far-field extinction measurements and near electric field measurements on gold bowtie antennas resonant at THz frequencies. These measurements show a very large shift between the resonant frequencies of the near-field and the far-field spectra. We use the established damped-driven harmonic oscillator model for resonators to model the far-field response of the antennas from the near-field spectrum and show that there is a large discrepancy between the predicted and measured far-field response. We were able to explain this discrepancy by improving the oscillator model with a Fano model. This large shift makes the prediction of the near-field response of resonant structures at THz frequencies very imprecise, provided that only information of the far-field response is available and establishes the necessity of measuring near fields for a correct and accurate characterization of these structures.

Spoof surface plasmon polaritons in terahertz transmission through subwavelength hole arrays analyzed by coupled oscillator model.

Both the localized resonance and excitation of spoof surface plasmon polaritons are observed in the terahertz transmission spectra of periodic subwavelength hole arrays. Analyzing with the coupled oscillator model, we find that the terahertz transmission is actually facilitated by three successive processes: the incident terahertz field first initiates the localized oscillation around each hole, and then the spoof surface plasmon polaritons are excited by the localized resonance, and finally the two resonances couple and contribute to the transmission. Tailoring the localized resonance by hole size, the coupling strength between spoof surface plasmon polaritons and localized resonances is quantitatively extracted. The hole size dependent transmittance and the coupling mechanism are further confirmed by fitting the measured spectra to a modified multi-order Fano model.

Fano-Liouville Spectral Signatures in Open Quantum Systems

The scattering amplitude from a set of discrete states coupled to a continuum became known as the Fano profile, characteristic for its asymmetric line shape and originally investigated in the context of photoionization. The generality of the model and the proliferation of engineered nanostructures with confined states gives immense success to the Fano line shape, which is invoked whenever an asymmetric line shape is encountered. However, many of these systems do not conform to the initial model worked out by Fano in that (i)they are subject to dissipative processes and (ii)the observables are not entirely analogous to the ones measured in the original photoionization experiments. In this Letter, we work out the full optical response of a Fano model with dissipation. We find that the exact result for the excited population, Raman, Rayleigh, and fluorescence emission is a modified Fano profile where the typical line shape has an additional Lorentzian contribution. Expressions to extract model parameters from a set of relevant observables are given.

Effects of surface-bulk hybridization in three-dimensional topological metals

Identifying the effects of surface-bulk coupling is a key challenge towards exploiting the topological nature of the surface states in many available three-dimensional topological `metals'. Here we combine an effective-model calculation and an ab-initio slab calculation to study the effects of the lowest order surface-bulk interaction: the hybridization. In the effective-model study, we discretize an established low-energy effective four-band model and introduce the hybridization between the surface bands and bulk bands in the spirit of the Fano model. We find that the hybridization enhances the energy gap between bulk and Dirac surface states and preserves the latter's spin texture qualitatively albeit with a reduced spin-polarization magnitude. Our ab-initio study finds the energy gap between the bulk and surface states to grow upon an increase in the slab thickness, very much in qualitative agreement with the effective model study. Comparing the results of our two approaches, we deduce that the experimentally observed low magnitude of spin polarization can be attributed to a hybridization-type surface-bulk interaction. We discuss evidences for such hybridization in existing ARPES data.

Cascades of Fano resonances in Mie scattering

The interference nature of resonant Mie scattering, which is described within the Fano model, has been demonstrated. The interference is caused by interaction of an incident electromagnetic wave with reemitted waves that correspond to eigenmodes of a scattering particle. Mie scattering due to the interference can be represented in the form of cascades of resonance lines of different shapes, each of which is described by the classical Fano formula. The effect is observed in resonant light scattering by an arbitrary body of revolution and discussed in detail using the example of scattering by an infinite homogeneous dielectric cylinder.

Surface plasmonic contribution to SEIRA and asymmetrical band

The Surface Enhanced InfraRed Absorption (SEIRA) band reaches its the maximum intensity and the band shape becomes asymmetric at the just percolated metal thin films. To explain for them, various models (e.g. the Fano model) have been proposed. However, no model can explain them completely. In this paper, we conducted a classical model calculations (Fresnel’s formula and the Bruggemann effective medium theory) for SEIRA and asymmetric bands. The calculated SEIRA spectra were good agreement with the experimentally spectra. Therefore, the asymmetrical SEIRA band might not be attributable to Fano model. Moreover, we specifically addressed the relation between effective dielectric constants of a metal–insulator composite thin film and SEIRA band shape change. Although the sign of the real part switched from positive to negative and although the imaginary part became metallic, the asymmetrical band shape did not change. The sign of the real part is

Pulse propagation in an autoionization medium with double Fano profile

We discuss the propagation of a short laser pulse in an auto- ionizing (AI) medium with degenerate double Fano model. By solving numerically the coupled equations for atoms and fields we show that by the proper choice of Fano parameters involved in the problem (contrary to the case considered in (E. Paspalakis, N. J. Kylstra, and P. L. Knight, Phys. Rev. A60 (1999)) we have now two Fano asymmetry parameters) one can eliminate almost completely the absorption in the pulse propagation. It means that we have the transparency in the medium. From the connection between population trapping in short pulsed laser field and transparency in the propagation of the laser pulse which has been fixed by Paspalakis et al., Phys. Rev. A60 (1999) we conclude that this proper choice leads to the presence of the population trapping (or the existence of the “dark” states) in the atomic system. Moreover, instead of one value of the laser detuning for which the dark states exist in the case of one AI level, we find numerically two such values in the case of two AI levels.

Influence of transfer residue on the optical properties of chemical vapor deposited graphene investigated through spectroscopic ellipsometry

In this study, we have examined the effects of transfer residue and sample annealing on the optical properties of chemical vapor deposited graphene, transferred onto a sapphire substrate. The optical absorption of graphene was obtained from point-by-point inversion of spectroscopic ellipsometry measurements in the visible and ultraviolet ranges (250–800 nm). Measured spectra were analyzed by optical models based on the Fresnel coefficient equations. The optical models were supported by correlated Raman, scanning electron microscopy, and atomic force microscopy measurements. The obtained data were phenomenologically described by a Fano model. Our results show that a residue layer left on graphene can significantly increase its optical absorption in the visible range, compared to an annealed sample.

Modular compactifications of the space of marked trigonal curves

We construct a sequence of modular compactifications of the space of marked trigonal curves by allowing the branch points to coincide to a given extent. Beginning with the standard admissible cover compactification, the sequence first proceeds through contractions of the boundary divisors and then through flips of the so-called Maroni strata, culminating in a Fano model for even genera and a Fano fibration for odd genera. While the sequence of divisorial contractions arises from a more general construction, the sequence of flips uses the particular geometry of triple covers. We explicitly describe the Mori chamber decomposition given by this sequence of flips.

Plasmon-assisted high reflectivity and strong magneto-optical Kerr effect in permalloy gratings

We demonstrate experimentally a strong plasmon-assisted enhancement of the transverse magneto-optical Kerr effect in permalloy gratings. The enhanced transverse magneto-optical Kerr effect is accompanied by an increased grating reflectivity with the maximum of enhancement being correlated with plasmonic Fano resonances. This correlation was confirmed by an intuitive Fano model and also through full-vectorial optical simulations. Simultaneously high reflectivity and transverse magneto-optical Kerr effect as well as narrowest ferromagnetic resonance linewidth and vanishing anisotropy make permalloy nanostructures attractive for applications in spintronics and nano-optics such as, for example, all-optical excitation of propagating spin waves and spectral tuning of optical nanoantennas.