Nonlinear Thin Films Research Articles

Development of the Banach contraction method for the solution of nonlinear thin film flows of non-Newtonian fluids

The aim of this study is to present a new implementation of an efficient iterative method proposed by Daftardar-Gejji and Bhalekar to solve a nonlinear initial value problem. We consider the thin film problem of a non-Newtonian fluid on a moving belt. The proposed method is based on using the Banach’s contraction principle. In order to determine the accuracy of the obtained approximate solutions, several comparisons were done against solutions obtained by other authors using the Runge–Kutta method as well as the Newton–Raphson–Euler-based solution. Comparisons with the variational iteration method and the homotopy perturbation method were also made. Several measures have been adopted to provide the error analysis for the derived approximate solution: the error remainder with the maximal error remainder, the second norm and the root mean squared norm. The application of the proposed technique shows the purpose of the obtained approximate solution where no additional assumptions are needed for the nonlinear terms. Calculations were performed using the computer algebra system MATHEMATICA®10.

Analytical solution of second-harmonic generation in a lithium-niobate-birefringence thin-film waveguide via modal phase matching

We present a systematic theoretical investigation of second-harmonic generation (SHG) in a subwavelength lithium niobate (LN) single-crystal thin-film waveguide with birefringence in permittivity and refractive index and strong anisotropy in the nonlinear susceptibility ${\ensuremath{\chi}}^{(2)}$. In a macroscopic birefringence LN crystal, the birefringence phase matching scheme that makes use of the refractive index management between the extraordinary light (EL) and ordinary light (OL) is dominantly used to ensure high-efficiency SHG. Yet, this scenario needs significant modification in a subwavelength LN thin film, where one should instead consider the waveguide modes of fundamental wave (FW) and second-harmonic wave (SHW) to participate in the SHG process. To this end, we first analytically solve and calculate the dispersion and modal profile of optical waveguide modes supported in the birefringence LN planar waveguide in a broad bandwidth ranging from ultraviolet to infrared regimes for TM (EL-like) and TE (OL-like) polarization states and at different waveguide thicknesses. Then we systematically examine the phase matching conditions that are necessary for high-efficiency energy conversion from FW waveguide mode to SHW waveguide mode via SHG. We find several modal phase matching schemes by exploiting the versatile freedoms of the FW and SHW waveguide mode number and polarization, and the waveguide thickness and symmetry. Yet modal phase matching only takes place at very limited discrete wavelengths of FW pump light. Under the modal phase matching condition, we derive the nonlinear coupled mode theory from Maxwell's equations and calculate the conversion efficiency of SHG, and find that the efficiency of SHG is determined by the nonlinear coupling coefficients that are closely associated with the modal profile overlap extent and mode transition strength between FW mode and SHW mode, and the involved nonlinear coefficient components of ${\ensuremath{\chi}}^{(2)}$. Finally, we have analytically derived the explicit formula that allows for direct calculation of the SHG efficiency as a function of the interaction length of FW mode and SHW mode, the nonlinear coupling coefficient, and the FW pump intensity, for both the small signal and general large signal situations. Our analytical theory and formulation can greatly facilitate the deep understanding of nonlinear optical interaction physics and provide a convenient tool for accurate quantitative evaluation of the SHG energy conversion efficiency of a pump laser in nanoscale LN single-crystal thin films. This analytical theory can also benefit for the design of nanoscale nonlinear optical devices based on the material platform of LN and other nonlinear crystal thin films.

Highly nonlinear varistors fabricated by hot-dipping tin oxide thin films in Ta2O5 powder at different temperatures

This work proposed a smart approach to fabricate highly nonlinear SnOx-Ta2O5 thin film varistors. During processing, tin oxide films in nanoscaled thickness were firstly deposited onto electrically conducting silicon wafers through radio frequency magnetron sputtering a sintered tin oxide ceramic target; and then, the obtained films were hot-dipped in Ta2O5 powder in a Muffle oven for 60min at different temperatures. With the hot-dipping temperature increased from 300 to 800°C, the nonlinear coefficient of the samples increased first and then decreased, reaching the maximum of 16.8 at 600°C, which is a record in all the reported SnO2-based varistors and comparable with those of the most extensively investigated and commonly commercially applied ZnO-based ceramic varistors. Correspondingly, the leakage current decreased first and then increased, obtaining the minimum of 4.1mA/cm2. Besides, the breakdown electric field increased first and then decreased, presenting the maximum of 0.0313V/nm. Such nanoscaled thin film varistors would be promising in electrical and electronic devices working in low-voltage.

Daftardar-Jafari method for solving nonlinear thin film flow problem

The aim of this paper is to develop the Daftardar-Jafari iterative method (DJM) for a mathematical model that represents the nonlinear thin film flow of a non-Newtonian third-grade fluid on a moving belt with the aim to obtain an approximate solution of high accuracy. When applying the DJM there is no need to resort to any additional techniques such as evaluating Adomian’s polynomials as in the Adomian decomposition method (ADM) or such as using Lagrange multipliers in the variational iteration method (VIM). The accuracy of our results is numerically verified by evaluating the functions of the error remainder and the maximal error remainders. In addition, these results are analyzed by comparing the accuracy of the DJM solutions with those of the fourth order Runge-Kutta method (RKM), ADM and VIM at the same parameter values. All the evaluations have been successfully performed in an iterative way by using the symbolic manipulator Mathematica®.

Metal-insulator transition and nonlinear optical responseof sputter-deposited V3O5 thin films

The compound V3O5, a member of the vanadium oxide Magnéli series, exhibits a metal-insulator transition near 430 K, the highest known temperature value among all vanadium oxides. It has been studied before mainly in single-crystal form, and for the very few cases in which thin films have been fabricated before, the procedure has required extensive post-deposition annealing of other oxides or vanadium metal at high temperatures in tightly controlled atmospheres. For the present work, V3O5 films were deposited directly on SiO2 glass substrates, without subsequent annealing, by DC magnetron sputtering. X-ray diffraction study of the samples evidenced oxygen deficiency, accommodated by oxygen vacancies. Resistivity measurements from 300 to 500 K revealed the metal-insulator transition by Tc ∼ 430 K, with an associated resistivity change by a factor of 20, and no detectable hysteresis in heating-cooling cycles, in agreement with most single-crystal studies. Resistivity values obtained were, however, lower than published results for bulk crystal values, particularly at temperatures below Tc. This was attributed to conduction electrons generated by the oxygen vacancies. Gradual resistivity increase in a very thin sample, through heating in air at temperatures up to 500 K, lends support to this argument. Using a pump-probe scattering technique, the V3O5 films were also probed for ultrafast nonlinear optical response. A reduction in the transient relative scattered light signal was recorded, which reached –10% within ∼800 fs. This observed response, likely related to the photoinduced insulator-to-metal phase transition, should stimulate additional interest in this material.

Efficient Nonlinear Metasurface Based on Nonplanar Plasmonic Nanocavities

Since their discovery in the 1960s, nonlinear optical effects have revolutionized optical technologies and laser industry. Development of efficient nanoscale nonlinear sources will pave the way for new applications in photonic circuitry, quantum optics and biosensing. However, nonlinear signal generation at dimensions smaller than the wavelength of light brings new challenges. The fundamental difficulty of designing an efficient nonlinear source is that some of the contributing factors involved in nonlinear wave-mixing at the nanoscale are often hard to satisfy simultaneously. Here, we overcome these limitations by developing a new type of nonplanar plasmonic metasurfaces, which can greatly enhance the second harmonic generation (SHG) at visible frequencies and achieve conversion efficiency of ∼6 × 10–5 at a peak pump intensity of ∼0.5 GW/cm2. This is 4–5 orders of magnitude larger than the efficiencies observed for nonlinear thin films and doubly resonant plasmonic antennas. The proposed metasurface cons...

A semi-analytical iterative method for solving nonlinear thin film flow problems

This paper presents a new implementation of a reliable iterative method proposed by Temimi and Ansari namely (TAM) for approximate solutions of a nonlinear problem that arises in the thin film flow of a third grade fluid on a moving belt. The solution is obtained in the form of a series that converges to the exact solution with easily computed components, without any restrictive assumptions for nonlinear terms. The results are bench-marked against a numerical solution based on the classical Runge–Kutta method (RK4) and an excellent agreement is observed. Error analysis of the approximate solution is performed using the error remainder and the maximal error remainder. An exponential rate for the convergence is achieved. A symbolic manipulator Mathematica ®10 was used to evaluate terms in the iterative process.

On the determination of \u03c7(2) in thin films: a comparison of one-beam second-harmonic generation measurement methodologies

The determination of the second-order susceptibility (χ(2)) of thin film samples can be a delicate matter since well-established χ(2) measurement methodologies such as the Maker fringe technique are best suited for nonlinear materials with large thicknesses typically ranging from tens of microns to several millimeters. Here we compare two different second-harmonic generation setups and the corresponding measurement methodologies that are especially advantageous for thin film χ(2) characterization. This exercise allows for cross-checking the χ(2) obtained for identical samples and identifying the main sources of error for the respective techniques. The development of photonic integrated circuits makes nonlinear thin films of particular interest, since they can be processed into long waveguides to create efficient nonlinear devices. The investigated samples are ABC-type nanolaminates, which were reported recently by two different research groups. However, the subsequent analysis can be useful for all researchers active in the field of thin film χ(2) characterization.

Matrix formalism for radiating polarization sheets in multilayer structures of arbitrary composition

In optical studies on layered structures, quantitative analysis of radiating interfaces is often challenging due to multiple interferences. We present here a general and analytical method for computing the radiation from two-dimensional polarization sheets in multilayer structures of arbitrary compositions. It is based on the standard characteristic matrix formalism of thin films, and incorporates boundary conditions of interfacial polarization sheets. We use the method to evaluate the second harmonic generation from a nonlinear thin film, and the sum-frequency generation from a water/oxide interface, showing that the signal of interest can be strongly enhanced with optimal structural parameters.

An Investigation into the Role of Capping on Second Harmonic Generation from Nonlinear Organic Polymer and Guest-Host Thin Films by In-Situ Poling

In attempts to fabricate thermally stable second-order nonlinear polymer thin films, we have investigated the second harmonic generation (SHG) from both nonlinear polymer and guest-host thin films. We have also investigated the role of capping on the SHG, temporal stability and relaxation of dipole alignment. Corona poling techniques were employed to orient the dopants into the noncentrosymmetric structure required to obtain the SHG. The effect of capping with a polymeric encapsulant below the glass transition temperature of the polymers on the unpoled and corona poled thin films was studied. Capping of the nonlinear polymer and guest host thin films have resulted in high SHG with good temporal stability. SHG signal falls drastically during the first 8 days after poling while no further significant decay in SHG signal was observed after about 33 days. Our investigations have identified the characteristics required for a good encapsulant on a non-con-ductive surface.

The physical understanding on dynamic readout/detection of super-resolution pits with nonlinear reverse saturation absorption thin films

The physical mechanism and understanding behind dynamic readout/detection of super-resolution pits with a nonlinear reverse-saturation absorption active layer, such as an InSb active layer, is presented on the basis of experimental results of open-aperture z-scan measurements and pump–probe transient time response analysis. The super-resolution of an InSb active layer is a result of the formation of a sub-wavelength scatterer region at the center of the focused spot. The frequency response function also verifies that the cutoff frequency with an InSb active layer is clearly extended compared to when an InSb active layer is not used. The findings are useful for understanding the physical process of the far-field super-resolution effect with nonlinear reverse-saturation absorption characteristics.

Direct detection of the transient superresolution effect of nonlinear saturation absorption thin films

Using a strong nonlinear saturation absorption effect is one technique for breaking through the diffraction limit. In this technique, formation of a dynamic and reversible optical pinhole channel and transient superresolution is critical. In this work, a pump–probe transient detection and observation–experimental setup is constructed to explore the formation process directly. A Ge2Sb2Te5 thin film with strong nonlinear saturation absorption is investigated. The dynamic evolution of the optical pinhole channel is detected and imaged, and the transient superresolution spot is directly captured experimentally. Results verify that the superresolution effect originates from the generation of an optical pinhole channel and that the formation of the optical pinhole channel is dynamic and reversible. A good method is provided for direct detection and observation of the transient process of the superresolution effect of nonlinear thin films.

Stochastic numerical treatment for thin film flow of third grade fluid using unsupervised neural networks

In the present study, novel soft computing techniques are developed for numerical treatment of non-linear thin film flow (TFF) problem of third grade fluids using artificial neural networks (ANNs), particle swarm optimization (PSO), sequential quadratic programming (SQP), and their hybrid combinations. The strength of universal function approximation capabilities of ANNs is exploited in formulation of mathematical model of the problem based on an unsupervised error. The training of the design parameter of the networks is performed with PSO, SQP, and hybrid approach PSO–SQP. The proposed schemes are evaluated on four variants of the two cases of TFF problems by taking different values of material parameter and Stokes number. The reliability and effectiveness of the proposed approaches are validated through the results of statistical analyses based on sufficient large number of independent runs.

Strong nonlinear saturation absorption-induced optical pinhole channel and super-resolution effects: a multi-layer system model.

This work focuses on the strong nonlinear saturation absorption (NSA)-induced optical super-resolution effect. A multi-layer system model is proposed to understand the strong NSA-induced formation of an optical pinhole channel and the generation of a super-resolution spot. Taking a Sb2Te3 thin film as an example, numerical simulations were conducted. The results illustrate that an optical pinhole channel is clearly formed by the NSA characteristics. This pinhole channel is similar to a near-field light probe. Light travels through the pinhole channel, and a super-resolution spot is generated at its apex. The near-field spot scanning experimental results show that the reduction ratio of the spot is approximately 44.8%, which is basically consistent with the numerical simulation result of 43%. This work is helpful for understanding optical nonlinear super-resolution effects and developing nanolithography, nanodata storage, high-resolution optical imaging technologies with nonlinear thin films.

Symmetry-selective third-harmonic generation from plasmonic metacrystals.

Nonlinear processes are often governed by selection rules imposed by the symmetries of the molecular configurations. The most well-known examples include the role of centrosymmetry breaking for the generation of even harmonics, and the selection rule related to the rotational symmetry in harmonic generation for fundamental beams with circular polarizations. While the role of centrosymmetry breaking in second harmonic generation has been extensively studied in plasmonic systems, the investigation of selection rules pertaining to circular polarization states of harmonic generation is limited to crystals, i.e., symmetries at the atomic level. In this Letter we demonstrate the rotational symmetry dependent third harmonic generation from nonlinear plasmonic metacrystals. We show that the selection rule can be imposed by the rotational symmetry of metacrystals embedded into an isotropic organic nonlinear thin film. The results presented here may open new avenues for designing symmetry-dependent nonlinear optical responses with tailored plasmonic nanostructures.

Formation of super-resolution spot through nonlinear Fabry–Perot cavity structures: theory and simulation

This study explores how interference manipulation breaks through the diffraction limit and induces super-resolution nano-optical hot spots through the nonlinear Fabry-Perot cavity structure. The theoretical analytical model is established, and the numerical simulation results show that when the thickness of the nonlinear thin film inside the nonlinear Fabry-Perot cavity structure is adjusted to centain value, the constructive interference effect can be formed in the central point of the spot, which causes the nanoscale optical hot spot in the central region to be produced. The simulation results also tell us that the hot spot size is sensitive to nonlinear thin film thickness, and the accuracy is required to be up to nanometer or even subnanometer scale, which is very large challenging for thin film deposition technique, however, slightly changing the incident laser power can compensate for drawbacks of low thickness accuracy of nonlinear thin films. Taking As(2)S(3) as the nonlinear thin film, the central hot spot with a size of 40nm is obtained at suitable nonlinear thin film thickness and incident laser power. The central hot spot size is only about λ/16, which is very useful in super-high density optical recording, nanolithography, and high-resolving optical surface imaging.

Maskless direct laser writing with visible light: Breaking through the optical resolving limit with cooperative manipulations of nonlinear reverse saturation absorption and thermal diffusion

In this work, the resolving limit of maskless direct laser writing is overcome by cooperative manipulation from nonlinear reverse saturation absorption and thermal diffusion, where the nonlinear reverse saturation absorption can induce the formation of below diffraction-limited energy absorption spot, and the thermal diffusion manipulation can make the heat quantity at the central region of energy absorption spot propagate along the thin film thickness direction. The temperature at the central region of energy absorption spot transiently reaches up to melting point and realizes nanolithography. The sample “glass substrate/AgInSbTe” is prepared, where AgInSbTe is taken as nonlinear reverse saturation absorption thin film. The below diffraction-limited energy absorption spot is simulated theoretically and verified experimentally by near-field spot scanning method. The “glass substrate/Al/AgInSbTe” sample is prepared, where the Al is used as thermal conductive layer to manipulate the thermal diffusion channel because the thermal diffusivity coefficient of Al is much larger than that of AgInSbTe. The direct laser writing is conducted by a setup with a laser wavelength of 650 nm and a converging lens of NA=0.85, the lithographic marks with a size of about 100 nm are obtained, and the size is only about 1/10 the incident focused spot. The experimental results indicate that the cooperative manipulation from nonlinear reverse saturation absorption and thermal diffusion is a good method to realize nanolithography in maskless direct laser writing with visible light.

Variational iteration and Adomian decomposition methods for the nonlinear thin film flow of a Jeffrey-six constant fluid on a vertically moving belt

In this paper, we investigate a thin film flow problem that arises in the lifting of a Jeffrey-six constant fluid on a vertically moving belt. The governing nonlinear differential equation is first integrated analytically and then solved by applying both He's variational iteration method (VIM) and Adomian's decomposition method (ADM). The numerical results obtained by these methods are compared through graphs and no visible difference is observed. This study highlights the significant features of the proposed methods and their ability for solving nonlinear problems arising in non-Newtonian fluid mechanics.

Parabolic approximation analytical model of super-resolution spot generation using nonlinear thin films: Theory and simulation

In this work, we present a theoretical analytical model called the parabolic approximation analytical model that considers the absorption coefficient and refractive index in a parabolic approximation profile along the radial direction. By using this model the generation of a super-resolution spot is analyzed in detail, and a numerical simulation subsequently conducted to verify the analytical model. This work is helpful in understanding the super-resolution effect of nonlinear thin films.

Performance improvement of super-resolving pupil filters via combination with nonlinear saturable absorption films

With the continuous development of the field of information technology, there has been a demand for recording mark size of optical data storage, optical imaging resolving power, and characteristic linewidth of photolithography to reach nanoscale. However, it is very difficult to realize the goal due to the optical diffraction limit restrictions. Much interest has focused on the study of optical far-field super-resolution spot by using pupil filters. However, common concerns have continued to plague super-resolving pupil filters based on either scalar diffraction theory or vector diffraction theory. These concerns include the fact that the side lobe becomes non-negligible when the central lobe is squeezed to a certain extent. Moreover, it is difficult to reduce the super-resolving spot to nanoscale. In this work, we proposed a novel method to combine the super-resolving pupil filters with nonlinear saturable absorption thin films to reduce the central spot size to nanoscale, lower the intensity ratio of side lobe to central lobe, and elongate the depth of focus or tunable tolerance distance between the super-resolving spot and sample. The simulated results indicate that by using the three-zone annular binary phase filter as the super-resolving pupil filter and Sb2Te3 as the nonlinear saturable absorption thin films, the central spot size can be reduced to nanoscale, the side lobe intensity is squeezed to about 10% of the central lobe intensity, and the tunable tolerance distance between the super-resolving spot and the sample is about two times that of the depth of focus of the diffraction limited spot at the incident laser wavelength of 405nm and the numerical aperture of focusing lens of 0.95. The combination of the super-resolving pupil filters with the nonlinear saturable absorption thin films is very useful for nano-optical data storage, maskless nanolithography, and nano-optical imaging. It is also easy to use in actual applications because of the operation in the far-field range.