Incident Field Amplitude Research Articles

Vortex harmonic generation in indium tin oxide thin film irradiated by a two-color field.

When a two-color Laguerre-Gaussian laser beam propagates through an indium tin oxide (ITO) material, the spatial distributions of odd- and even-order vortex harmonics carrying orbital angular momentum (OAM) are studied. The origin of vortex harmonics can be directly clarified by investigating their dependence on the incident laser field amplitude and frequency. In addition, it is shown that the spectral intensities of vortex harmonics are sensitive to the epsilon-near-zero nonlinear enhancing effects and the thickness of ITO materials. Thus the vortex harmonics can be conveniently tunable, which provides a wider potential application in optical communications based on high-order OAM coherent vortex beams.

Steerable photonic jet for super-resolution microscopy

A promising technique in optical super-resolution microscopy is the illumination of the sample by a highly localized beam, a photonic jet (also called photonic nanojet). We propose a method of computation of incident field amplitude and phase profiles that produce photonic jets at desired locations in the near field after interaction with a fixed micro-scale dielectric lens. We also describe a practical way of obtaining the incident field profiles using spatial light modulators. We expect our photonic jet design method to work for a wide range of lens shapes, and we demonstrate its application numerically using two-dimensional micro-lenses of circular and square cross-sections. We furthermore offer a theoretical analysis of the resolution of photonic jet design, predicting among other that a larger lens can produce a narrower photonic jet. Finally, we give both theoretical and numerical evidence that the waist width of the achieved designed jets is increasing linearly and slowly over a large interval of radial distances. With uniform plane wave illumination, the circular two-dimensional micro-lens produces a similar-sized jet at a fixed radial distance, while the square lens does not form a jet at all. We expect our steerable optical photonic jet probe to enable highly localized adaptive real-time measurements and drive advances in super-resolution optical microscopy and scatterometry, as well as fluorescence and Raman microscopy. Our relatively weak peak jet intensity allows application in biology and health sciences, which require high resolution imaging without damaging the sample bio-molecules.

Extreme enhancement of the quality (Q)-factor and mode field intensity in cavity-resonator gratings.

In this paper, dielectric Cavity-Resonant Integrated-Grating Filters (CRIGFs) are numerically optimized to achieve extremely high-quality factors, by optimizing the cavity in/out-coupling rate and by introducing apodizing mode-matching sections to reduce scattering losses. Q-factors ranging between 0.1 and 50 million are obtained and two different domains are distinguished, as a function of the perturbation parameter which controls the cavity in/out-coupling rate. When the cavity coupling Q-factor is lower than the Q-factor of the uncoupled Fabry-Perot cavity, corresponding to the over-coupling regime, the reflectivity response exhibits a high resonance maximum. On the contrary, in the under-coupling regime the resonant reflectivity maximum is much weaker since the scattering losses of the uncoupled cavity dominate. Between these two domains, the so-called critical coupling condition leads to very strong field enhancement inside the device, reaching up to 104 times the incident field amplitude. This theoretical work paves the way towards the practical implementation of CRIGFs with much higher Q-factors than currently demonstrated, potentially reaching performance on a par with other resonators such as photonic crystal cavities or whispering gallery mode resonators. These results can serve to optimize the design of narrow-band planar grating filters, particularly for application in non-linear optics.

Study of the Optical and Thermoplasmonics Properties of Gold Nanoparticle Embedded in Al2O3 Matrix.

In this paper, the optical and thermoplasmonics properties of nanocomposites consisting of spherical gold nanoparticles (AuNPs) integrated in {Al}_{2}{O}_{3} matrix are determined using the Finite Element Method (FEM). Firstly, the refractive index (n), extinction coefficient (kappa ), absorption coefficient {(mu }_{a}), and optical conductivity (sigma ) are calculated from the effective complex permittivity obtained by solving the Laplace’s equation for different size and concentration of nanoparticles. The surface plasmon resonance (SPR) properties of AuNPs are optimized from the peak presented in the absorption coefficient spectrum. The results show that the optical parameters n, kappa , {mu }_{a}, and sigma undergo a strong variation around the wavelength {lambda }_{max} corresponding to the SPR phenomenon. The value of {lambda }_{max} increases from 560 to 600 nm when the radius of the particles varies between r=5 and r=30 nm. The effect of the AuNP concentration on the band gap energy {E}_{g}(eV) of Au-{Al}_{2}{O}_{3} nanocomposites is also studied, a shift from Eg=5.34 to Eg=5.49 eV is observed when the concentration of the AuNPs increases from 0 to 0.82mathrm{%}. The electric field enhancement induced by the AuNPs at plasmonic resonance is also determined depending to the particle size; the results show that the enhancement factor increases from g=4.71 to g=6.95 when the radius of the AuNPs increases from r=5 to 30 nm. The thermal dissipation of the plasmonic energy of spherical of our system dispersed in the {Al}_{2}{O}_{3} matrix is determined considering the Joule effect which occurs by the oscillation of the charges at the plasmonic resonance. The generated thermal power by particles is calculated for different sizes, which allows to calculate the thermal power per gram of particles depending on the intensity of the incident electric field. The results show that the plasmonic thermal power is almost identical for small particles when the radius is less than r=15 nm and increases considerably when the size increases from r=15 to 30 nm. For a fixed size and incident field amplitude, we calculated the temperature change in the nanocomposites Au-{Al}_{2}{O}_{3} depending of time for different particle concentrations; the temperature variation curves obtained are linear as a function of time.

Nonlinear optical dynamics of two-dimensional super-lattices of quantum V-emitters

We study theoretically the nonlinear optical response of a super-lattice of regularly arranged three-level identical quantum emitters with a doublet in the excited state to the action of a monochromatic electromagnetic field quasi-resonant to optical transitions in the emitter, using into account the dephasing of the system. The total retarded dipole-dipole interaction of the emitters is accounted for in the mean-field approximation. This interaction plays the role of positive feedback, which (in combination with the immanent nonlinearity of emitters themselves) leads to multistability of the super-lattice response. The stability of different response branches is analyzed using the Lyapunov exponents’ method. Another important property of the super-lattice is its high reflectance in a certain frequency range; i.e., within this range, the super-lattice operates as a perfect nanometer mirror; moreover, reflection can be switched to transmission changing slightly the incident field amplitude (bistability). The possibility of the application of the above-mentioned super-lattice optical properties in nanophotonics is discussed.

Tapering the Incident Field When Solving Problems of Electromagnetic Wave Scattering Over Finite-Size Random Surfaces

Introduction. An analysis of radio wave scattering over random surfaces frequently involves integral equations, which are solved by numerical methods. These methods are feasible only provided limited dimensions of the surface. The requirement of surface limitation leads to the appearance of edge currents, resulting in significant errors when calculating the radar cross section (RCS), particularly for grazing incident angles. The influence of edge currents is reduced by a function tapering the incident field amplitude. This function should satisfy the following requirements: to provide a low suppression of the field along the entire finite-size surface between its edges at the same time as decreasing the incident field amplitude to negligible values when approaching the edges. The incident field under the application of the tampering function should satisfy the wave equation with a minimum error. Although various tapering functions are applied for incident field amplitude (i.e. Gaussian, Thorsos, integral), none of them satisfies the aforementioned requirements.Aim. To suggest a novel function for tapering the amplitude of an electromagnetic wave incident on a perturbed finite-size surface when calculating RCS. In comparison with the known functions, the proposed function must satisfy the entire set of requirements.Materials and methods. A comparison of the proposed tapering function for incident field amplitude with the known tapering functions was performed, including the estimation of the error of satisfying the wave equation. To prove the applicability of the proposed tapering function, a mathematical modeling of the bistatic scatter diagram of a two-dimensional sea-like finite surface with a spatial Elfouhaily spectrum was carried out using Monte Carlo calculations in the Matlab environment.Results. Compared to the known tapering functions, the proposed tapering function satisfies the entire set of requirements. The results of mathematical modeling showed that the proposed function for tapering the incident field amplitude provides acceptable accuracy of estimating the RCS of finite-size random surfaces.Conclusion. A novel function for tapering the incident field amplitude was derived. This function reduces the influence of edge currents on the accuracy of RCS estimation of two-dimensional finite-size random surfaces, thus being instrumental for solving scattering problems.

Nonlinear Optical Dynamics and High Reflectance of a Monolayer of Three-Level Quantum Emitters with a Doublet in the Excited State

We study theoretically the nonlinear optical response of a monolayer of regularly arranged three-level identical quantum emitters with a doublet in the excited state to the action of a monochromatic electromagnetic field quasi-resonant to optical transitions in the emitter. The total retarded dipole–dipole interaction of the emitters is accounted for in the mean-field approximation. This interaction plays the role of a positive feedback, which (in combination with the immanent nonlinearity of emitters themselves) leads to multistability of the monolayer response. The stability of different response branches is analyzed using the Lyapunov exponents method. It is found that the instability type depends on the doublet splitting and changes from self-oscillations to chaos upon increasing the splitting. Another important property of the monolayer is its high (almost 100%) reflectance in a certain frequency range; i.e., within this range, the monolayer operates as a perfect nanometer mirror; moreover, reflection can be switched to transmission changing slightly the incident field amplitude (bistability). The possibility of application of the above mentioned monolayer optical properties in nanophotonics is discussed.

Ultrafast re-structuring of the electronic landscape of transparent dielectrics: new material states (Die-Met)

The swift excitation of the transparent dielectrics by intense short laser pulse produces ultra-fast re-structuring of the electronic landscape generating a wealth of material states continuously changing in space and in time in accord with the variations of the intensity. These unconventional transient material states combine simultaneously dielectric and metal properties (Die-Met). The laser excitation transforms a transparent dielectric into electrically inhomogeneous state early in the pulse time [1]. The permittivity of excited material varies in time and in space changing from positive to negative values that strongly affects the interaction process. The interplay between the transient permittivity gradient and polarisation of the incident laser becomes the major process of the new interaction mode. In a particular relation between the polarization and the permittivity gradient the incident field amplitude grows up while the wave is approaching to the surface where the real part of permittivity turns to zero. That results in the local increase in the absorbed energy density. The complex 3D structure of the permittivity makes a transparent part of excited dielectric (at ${\epsilon}0 > {\epsilon}re > 0$) optically active. The electro-magnetic wave passing through such a medium gets a twisted trajectory and accrues the geometric phase [2]. The plane of polarisation rotation and phase depends on the 3D permittivity structure [3]. Measuring the polarisation and phase of the probe beam allows quantitatively identify this new transient state. We discuss the revelations of this effect in different experimental situations and possible applications.

Relaxation times and symmetries in the nonlinear optical properties of a two-level system

In this work we introduce a methodology for the determination of the longitudinal and transversal relaxation times in a two-level system using symmetry properties of the optical responses in the frequency space εΔ1,Δ2. Employing the density matrix formalism and a perturbative scheme for the incident field amplitudes in the Four-wave mixing spectroscopy, the nonlinear macroscopic polarization is determined. The collective effects of the thermal reservoir are modeled as a time dependent frequency, whose manifestation is the broadening of the upper level according to a prescribed random function.

Domain wall motions in BST ferroelectric thin films in the microwave frequency range

The existence of domain wall motion at microwave frequencies and its contribution to the ferroelectric complex permittivity is shown by evaluating the dielectric properties of BaSrTiO3 (BST) thin films as a function of the incident power. Even at low AC field amplitudes, the presence of the domain walls and the correlated motions (vibration and jumps) result in sensitivity of the dielectric properties to the incident field amplitude. Although the contribution of domain wall motion to the real part of the permittivity is not preponderant (less than 10%), it represents more than 50% of the material's global dielectric losses. This illustrates the importance to consider domain wall motion even in the microwave frequency region and the necessity to take into account the applied AC field amplitude (and thus the incident power) when characterizing ferroelectric materials. The present study has been realized on BST thin films, elaborated by pulsed laser deposition on MgO/Ir substrates.

Optimizing third-harmonic generation at terahertz frequencies in graphene

We model third-harmonic generation in doped monolayer graphene at terahertz frequencies by employing a nearest-neighbor tight-binding model in the length gauge. We show that for a given incident-field amplitude there is an optimum Fermi level that maximizes the emitted third-harmonic field. The optimum Fermi level depends very strongly on the incident-field amplitude as well as on the scattering time and increasing either enhances the third-harmonic response. We consider the general case of Fermi-level-independent scattering as well as three different scattering mechanisms that are Fermi-level dependent: phonon, long-range impurity, and short-range impurity scattering. For each case, we determine the optimal Fermi level as well as the amplitude of the optimized third-harmonic response for single-cycle incident fields with central frequencies of 1 THz and amplitudes in the range of 25--75 kV/cm. We find that although nonlinear processes beyond third order suppress third-harmonic generation, we still obtain third-harmonic amplitudes as large as 1.6% of the fundamental of the transmitted field.

Measurements of electron avalanche formation time in W-band microwave air breakdown

We present measurements of formation times of electron avalanche ionization discharges induced by a focused 110 GHz millimeter-wave beam in atmospheric air. Discharges take place in a free volume of gas, with no nearby surfaces or objects. When the incident field amplitude is near the breakdown threshold for pulsed conditions, measured formation times are ∼0.1–2 μs over the pressure range 5–700 Torr. Combined with electric field breakdown threshold measurements, the formation time data shows the agreement of 110 GHz air breakdown with the similarity laws of gas discharges.

Tilt scanning interferometry: a numerical simulation benchmark for 3D metrology

Tilt scanning interferometry (TSI) is a novel experimental technique that allows the measurement of multicomponent displacement fields inside the volume of a sample. In this paper, we present a simulation model that allows for the evaluation of the speckle fields recorded in TSI when this technique is applied to the analysis of semitransparent scattering materials. The simulation is based on the convolution of the optical impulsive response of the optical system and the incident field amplitude. Different sections of the simulated imaging system are identified and the corresponding optical impulsive responses are determined. To evaluate the performance of the proposed model, a known internal displacement field as well as the illumination and detection strategies in a real TSI system are numerically simulated. Then, the corresponding depth-resolved out-of-plane and in-plane changes of phase are obtained by means of the data processing algorithm implemented in a TSI system.

Interplay between optical nonlinearity and localization in a finite disordered Fibonacci chain

Both the average transmission coefficients and dimensionless optical resistances of a nonlinear disordered Fibonacci chain are calculated as functions of the photon flux of an incident light field with various types of chains of scatters, numbers of embedded nonlinear-optical scatterers, and energies of incident photons. If the incident optical field is very weak, the nonlinear-optical scattering in the chain becomes negligible and the chain behaves just like a transparent dielectric slab. As for the interplay between the optical nonlinearity and localization effect in the finite disordered Fibonacci chain, it is found that the localization effect introduced in the disordered Fibonacci chain exhibits a reduction in the transmission only when the incident optical field is strong. The localization effect, which increases with the number of scatterers in the chain, is found to yield an enhanced optical nonlinearity of the system. The localization effect on the incident optical wave in the chain can be accelerated by an intense light illumination in the presence of a large number of nonlinear-optical scatterers. When energetic photons fly through the chain, they tend to ignore most of the deeply embedded optical scatterers. When the number of scatterers in the system is ${F}_{16}=1597$, a complete localization in the chain is reached for an incident field amplitude as low as $50\phantom{\rule{0.3em}{0ex}}\mathrm{kV}∕\mathrm{cm}$.

Optical bistability in thin molecular films

Within the framework of a developed model of a medium consisting of molecular J aggregates and placed in an external resonant light field, it is shown how exciton self-localization and the dependence of the dipole moment components on molecule deformation affect optical bistability. Deformation of the molecules substantially facilitates the observation of a bistable dependence of the state of the medium and of the transmitted field amplitude on the incident field amplitude. The evolution of the system to a quasi-stationary, nonground state after the passage of an electromagnetic field pulse under the conditions of self-localization of excitons is studied.

The long string as a field probe

We show how a long string can be used to probe the incident field across the target zone of a radar cross section (RCS) test range. The string may be stretched horizontally from wall to wall, or vertically from floor to ceiling. One end of the string is fixed and the other end is moved by an actuator mounted in the wall or ceiling. The resulting motion changes the angle of the string with respect to the incident-field direction, during which time the coherent radar echo is recorded as a function of the string angle. The coherent signal-as-a-function-of-angle data are then transformed to the cross-range domain using the fast Fourier transform (FFT), whence we obtain a chart of the incident field amplitude as a function of cross-range distance. Numerical examples are presented that show how variations in the incident field influence the string echo. A sample of experimental data shows that the processed data are readily interpreted

Effect of photon-assisted absorption on the thermodynamics of hot electrons interacting with an intense optical field in bulk GaAs

The use of a Boltzmann transport equation with a drift term is physically incorrect for optical-field frequencies. Also, the use of a simple energy-balance equation is found to lead to an inaccurate estimation of electron temperature. Therefore, we have established a Boltzmann-scattering equation for the accurate description of the relative scattering motion of electrons interacting with an incident optical field by including impurity- and phonon-assisted photon absorption as well as Coulomb scattering between two electrons. Multiple peaks on the high-energy tail of a Fermi-Dirac distribution are predicted and the effect of pair scattering is analyzed. Moreover, the effective electron temperature is calculated as a function of both the incident-field amplitude and the photon energy so that the thermodynamics of hot electrons may be investigated.

Dramatic localized electromagnetic enhancement in plasmon resonant nanowires

We investigate numerically the plasmon resonances of 10–50 nm nanowires with a non-elliptical section. Such wires have a much more complex behavior than elliptical wires and their resonances span a larger frequency range. The field distribution at the surface of these wires exhibits a dramatic enhancement, up to several hundred times the incident field amplitude. These strongly localized fields can provide an important mechanism for surface enhanced Raman scattering (SERS).

Intrinsic optical bistablility of an ultrathin film consisting of oriented linear aggregates

A theoretical study of transmittivity of an ultrathin film (of thickness smaller than an optical wavelength) consisting of oriented linear aggregates is carried out. We show that within a certain domain of the incident field amplitude, optical transitions of a single disordered aggregate, the eigenstates of which are represented by the Frenkel exciton states, can be treated in the framework of a two-level approximation. This allows us to claim that an ensemble of linear aggregates is analogous to that comprised of inhomogeneously broadened two-level systems. Based on this analogy, we show that the transmittivity of the film can manifest a bistable behavior originating from the coupling of the aggregates via the emission (far-zone) field. This mechanism of bistability differs from that occurring in a single perfect aggregate. In the latter case, bistability results from the population-dependent resonance frequency shift of an individual aggregate, originating from the coupling of the molecules via the dipole–dipole (near-zone) field. Estimates of the driving parameters show that real candidates, to realize the type of behavior we found, are such well-studied objects as J-aggregates of polymethine dyes or thin films of thiophene oligomers.

Intrinsic optical bistability in a thin layer of nonlinear optical material by means of local field effects

We show that a single thin layer (thickness much less than an optical wavelength) of nonlinear optical material can display optical bistability solely as a consequence of local field effects. Optical bistability is predicted when the phase of the complex third-order susceptibility χ (3) is nearly opposite that of the linear dielectric constant ϵ and when the incident field amplitude is adjusted so that | χ (3)|| E 0| 2 is approximately equal to 10 −3| ϵ| 3.