Thermal Nonlinearity Research Articles

Improved Z-scan adjustment to thermal nonlinearities by including nonlinear absorption

We propose a modified mathematical model of thermal optical nonlinearities which allow us to obtain the nonlinear refraction index and the nonlinear absorption coefficient with only one measurement. This modification is motivated by the influence that nonlinear absorption has on the measurement of the nonlinear refraction index at far field, when the material presents a large nonlinearity. This model, where nonlinear absorption is considered to adjust the curves of nonlinear refraction index obtained by Z-scan technique, has the best agreement with experimental data. The model is validated with two ionic liquids and the organic material: Eysenhardtia polystachya, in thin media. We present these results after comparing our proposed model to other reported models.

Evaluating the reliability of the cylinder liner of a low-speed marine engine subjected to high-cycle fatigue with high mean stress

Reliability evaluation was performed on the cylinder liner of a low-speed marine engine experiencing high-cycle fatigue with high mean stress. The stress distribution in the cylinder liner under operating condition was estimated through structural analysis, which included thermal boundary conditions and material nonlinearity. Results indicated that the highest stress concentration developed at the round part below the liner collar. Material tests revealed that the Goodman relation can predict the effect of mean stress on fatigue limit. As indicated by the combined results of the structural analysis and experiment, the cylinder liner is reliable under operating condition.

Lead sulfide colloidal nanocrystals with strong optical nonlinearity

Colloidal PbS nanocrystals have been synthesized by a developed procedure. UV–Vis absorption and Z-scan technique was also applied to study the nonlinear optical properties of prepared lead sulfide nanocrystals at 532 nm wavelength. The nonlinear refractive (n2) and absorption (β) were determined which are confirming the strong nonlinearity at 532 nm of colloidal PbS nanocrystals. The obtained results have not been reported before. In this study, only a weak thermal optical nonlinearity was observed and the dominating nonlinear response is resulted by the electronic origin. The nonlinear optical properties of prepared sample supported wide applications in nanophotonics.

Self-Inversion of the Image of a Small-Scale Opaque Object in the Process of Focusing of the Illuminating Beam in an Absorbing Medium

We describe the process of adaptive self-inversion of an image (nonlinear switching) of smallscale opaque object, when the amplitude-modulated laser beam, which illuminates it, is focused in a weakly absorbing medium. It is shown that, despite the nonlocal character of the process, which is due to thermal nonlinearity, the brightness-inverse image is characterized by acceptable quality and a high conversion coefficient. It is shown that the coefficient of conversion of the original image to the inverse one depends on the ratio of the object dimensions and the size of the illuminating beam, and decreases sharply for relatively large objects. The obtained experimental data agree with the numerical calculations. Inversion of the images of several model objects and microdefects in a nonlinear KDP crystal is demonstrated.

Role of mechanical and thermal nonlinearities in imaging by Atomic Force Microscope

In this paper, the effects of nonlinearities such as hysteresis, creep and thermal drift of piezoelectric elements on imaging by Atomic Force Microscope have been studied via a semi-analytical approach. The Generalized Differential Quadrature Method (GDQM) has been used to find the dynamic response of a system. Bouc-Wen and PI hysteresis models have been incorporated with the presented linear model to obtain the effects of nonlinearities; and thermal drift has been augmented in an offline scheme. All the sub-models have been validated by comparing their results with the findings of previously reported experiments. Finally, these nonlinear effects have been applied on AFM-based imaging operations, and the obtained results have been evaluated. In comparison with the linear case in which the hysteresis effects are not taken into consideration, in the nonlinear imaging model, depending on the scan direction, the asperities on a rough substrate are sensed at different locations. In the creep case, the high level of error obtained during scan at the ascending points of substrate profile is due to the delay in the time interval in which the input increases. According to the results, the imaging of a standard sample substrate while assuming a 2° temperature change during a 10min scan of the substrate has yielded a maximum thermal drift error of about 3.3nm. At the end, based on the presented comprehensive nonlinear imaging model, the coupled effects of creep-hysteresis-thermal drift on the final image have been reported and discussed.

Six-wave interaction with double wavefront reversal on thermal nonlinearity in a medium with a nonlinear absorption coefficient

The spatial selectivity of a six-wave radiation converter w1 + w1 + w2 – w1 – w1 = w2 on thermal nonlinearity with allowance for the nonlinear absorption coefficient was studied. Relationships for the half-bandwidths of the spatial frequencies of object waves that are related both directly to the thermal nonlinearity and to the nonlinear character of variation of the absorption coefficient with varying signal wave divergence, nonlinear medium thickness, and pump wave intensity were analyzed. It was shown that for a highly diverging signal wave, the half-bandwidths of the spatial frequencies of object waves with a double-reversed wavefront are several times different.

Optical analogues of the Newton-Schrödinger equation and boson star evolution.

Many gravitational phenomena that lie at the core of our understanding of the Universe have not yet been directly observed. An example in this sense is the boson star that has been proposed as an alternative to some compact objects currently interpreted as being black holes. In the weak field limit, these stars are governed by the Newton–Schrodinger equation. Here we present an optical system that, under appropriate conditions, identically reproduces such equation in two dimensions. A rotating boson star is experimentally and numerically modelled by an optical beam propagating through a medium with a positive thermal nonlinearity and is shown to oscillate in time while also stable up to relatively high densities. For higher densities, instabilities lead to an apparent breakup of the star, yet coherence across the whole structure is maintained. These results show that optical analogues can be used to shed new light on inaccessible gravitational objects.

3D finite element analysis of the whole-building behavior of tall building in fire

In this paper, a methodology to simulate the whole-building behaviour of the tall building under fire is developed by the author using a 3-D nonlinear finite element method. The mechanical and thermal material nonlinearities of the structural members, such as the structural steel members, concrete slabs and reinforcing bars were included in the model. In order to closely simulate the real condition under the conventional fire incident, in the simulation, the fire temperature was applied on level 9, 10 and 11. Then, a numerical investigation on the whole-building response of the building in fire was made. The temperature distribution of the floor slabs, steel beams and columns were predicted. In addition, the behaviours of the structural members under fire such as beam force, column force and deflections were also investigated.

Nonlinear plasmonics at high temperatures

Abstract We solve the Maxwell and heat equations self-consistently for metal nanoparticles under intense continuous wave (CW) illumination. Unlike previous studies, we rely on experimentally-measured data for metal permittivity for increasing temperature and for the visible spectral range. We show that the thermal nonlinearity of the metal can lead to substantial deviations from the predictions of the linear model for the temperature and field distribution and, thus, can explain qualitatively the strong nonlinear scattering from such configurations observed experimentally. We also show that the incompleteness of existing data of the temperature dependence of the thermal properties of the system prevents reaching a quantitative agreement between the measured and calculated scattering data. This modeling approach is essential for the identification of the underlying physical mechanism responsible for the thermo-optical nonlinearity of the metal and should be adopted in all applications of high-temperature nonlinear plasmonics, especially for refractory metals, for both CW and pulsed illumination.

Laboratory modeling of ionospheric heating experiments

AbstractTurbulent plasma processes, such as those which occur in the Earth's ionosphere during ionospheric heating by powerful radio waves, were studied under laboratory conditions, and new physical models of small‐scale ionospheric turbulence are proposed as a result of these studies. It is shown here that the mechanism of small‐scale plasma filamentation can be connected with the thermal self‐channeling of Langmuir waves. During this process, Langmuir waves are guided by a plasma channel, which in turn is formed by the guided waves through a thermal plasma nonlinearity. The spectrum of the self‐guided Langmuir waves exhibits sidebands whose features are similar to stimulated electromagnetic emission. We present two mechanisms of sideband generation. The first mechanism can be observed during the formation of the plasma channel and is connected with the parametric shift in the frequency of the self‐channeling wave. The second mechanism is connected with the scattering of the self‐channeling wave on the low‐frequency eigenmodes of the plasma irregularity.

Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators

Dissipative temporal Kerr solitons in optical microresonators enable to convert a continuous wave laser into a train of femtosecond pulses. Of particular interest are single soliton states, whose $\mathrm{sech}^{2}$ spectral envelope provides a spectrally smooth and low noise optical frequency comb, and that recently have been generated in crystalline, silica, and silicon-nitride resonators. Here, we study the dynamics of multiple soliton states containing ${N}$ solitons and report the discovery of a novel, yet simple mechanism which makes it possible to reduce deterministically the number of solitons, one by one, i.e. ${N\! \to\! N\!-\!1\! \to\! \dots \!\to\! 1}$. By applying weak phase modulation, we directly characterize the soliton state via a double-resonance response. The dynamical probing demonstrates that transitions occur in a predictable way, and thereby enables us to map experimentally the underlying multi-stability diagram of dissipative Kerr solitons. These measurements reveal the "lifted" degeneracy of soliton states as a result of the power-dependent thermal shift of the cavity resonance (i.e. the thermal nonlinearity). The experimental results are in agreement with theoretical and numerical analysis that incorporate the thermal nonlinearity. By studying two different microresonator platforms (integrated $\mathrm{Si_{3}N_{4}}$ microresonators and crystalline $\mathrm{MgF_{2}}$ resonators) we confirm that these effects have a universal nature. Beyond elucidating the fundamental dynamical properties of dissipative Kerr solitons the observed phenomena are also of practical relevance, providing a manipulation toolbox which enables to sequentially reduce, monitor and stabilize the number ${N}$ of solitons, preventing it from decay. Achieving reliable single soliton operation and stabilization in this manner in optical resonators is imperative to applications.

Influence of electron beam irradiation on nonlinear optical properties of Al doped ZnO thin films for optoelectronic device applications in the cw laser regime

We present the studies on third-order nonlinear optical properties of Al doped ZnO thin films irradiated with electron beam at different dose rate. Al doped ZnO thin films were deposited on a glass substrate by spray pyrolysis deposition technique. The thin films were irradiated using the 8 MeV electron beam from microtron ranging from 1 kG y to 5 kG y. Nonlinear optical studies were carried out by employing the single beam Z-scan technique to determine the sign and magnitude of absorptive and refractive nonlinearities of the irradiated thin films. Continuous wave He–Ne laser operating at 633 nm was used as source of excitation. The open aperture Z-scan measurements indicated the sample displays reverse saturable absorption (RSA) process. The negative sign of the nonlinear refractive index n2 was noted from the closed aperture Z-scan measurements indicates, the films exhibit self-defocusing property due to thermal nonlinearity. The third-order nonlinear optical susceptibility χ(3) varies from 8.17 × 10−5 esu to 1.39 × 10−3 esu with increase in electron beam irradiation. The present study reveals that the irradiation of electron beam leads to significant changes in the third-order optical nonlinearity. Al doped ZnO displays good optical power handling capability with optical clamping of about ∼5 mW. The irradiation study endorses that the Al doped ZnO under investigation is a promising candidate photonic device applications such as all-optical power limiting.

Nonlinear processes upon two-photon interband picosecond excitation of crystal

A new experimental method is proposed to study the dynamics of nonlinear processes occurring upon two-photon interband picosecond excitation of a lead tungstate crystal and upon its excitation by cw probe radiation in a temporal range from several nanoseconds to several seconds. The method is applied to the case of crystal excitation by a sequence of 25 high-power picosecond pulses with a wavelength of and cw probe radiation. Measuring the probe beam transmittance during crystal excitation, one can investigate the influence of two-photon interband absorption and the thermal nonlinearity of the refractive index on the dynamics of nonlinear processes in a wide range of times (from several nanoseconds to several seconds). The time resolution of the measuring system makes it possible to distinguish fast and slow nonlinear processes of electronic or thermal nature, including the generation of a thermal lens and thermal diffusion. An alternative method is proposed to study the dynamics of induced absorption transformation and, therefore, the dynamics of the development of nonlinear rocesses upon degenerate two-photon excitation of the crystal in the absence of external probe radiation.

Circuit-Based Electrothermal Simulation of Power Devices by an Ultrafast Nonlinear MOR Approach

This paper presents an efficient circuit-based approach for the nonlinear dynamic electrothermal simulation of power devices and systems subject to radical self-heating. The strategy relies on the synthesis of a nonlinear compact thermal network extracted from a finite-element model by a novel model-order reduction method requiring a computational time orders of magnitude lower than conventional techniques. Unlike commonly employed approaches, the proposed network allows reconstructing the whole time evolution of the temperature field in all the points of the domain with high accuracy. Electrothermal simulations are enabled in a commercial SPICE-like simulator by coupling such a network with subcircuits that describe the electrical device behavior by accounting for the temperature dependence of the key physical parameters. As a case study, the dynamic electrothermal analysis of a packaged silicon carbide power MOSFET undergoing a short-circuit test is performed, showcasing the performance of the approach and highlighting the need of including the thermal nonlinearities to achieve reliable results.

Role of geometry in the superfluid flow of nonlocal photon fluids

Recent work has unveiled a new class of optical systems that can exhibit the characteristic features of superfluidity. One such system relies on the repulsive photon-photon interaction that is mediated by a thermal optical nonlinearity and is therefore inherently nonlocal due to thermal diffusion. Here we investigate how such a nonlocal interaction, which at a first inspection would not be expected to lead to superfluid behavior, may be tailored by acting upon the geometry of the photon fluid itself. Our models and measurements show that restricting the laser profile and hence the photon fluid to a strongly elliptical geometry modifies thermal diffusion along the major beam axis and reduces the effective nonlocal interaction length by two orders of magnitude. This in turn enables the system to display a characteristic trait of superfluid flow: the nucleation of quantized vortices in the flow past an extended physical obstacle. These results are general and apply to other nonlocal fluids, such as dipolar Bose-Einstein condensates, and show that "thermal" photon superfluids provide an exciting and novel experimental environment for probing the nature of superfluidity, with applications to the study of quantum turbulence and analogue gravity.

Optothermal nonlinearity of silica aerogel

We report on the characterization of silica aerogel thermal optical nonlinearity, obtained by z-scan technique. The results show that typical silica aerogels have nonlinear optical coefficient similar to that of glass (≃10−12 m2/W), with negligible optical nonlinear absorption. The nonlinear coefficient can be increased to values in the range of 10−10 m2/W by embedding an absorbing dye in the aerogel. This value is one order of magnitude higher than that observed in the pure dye and in typical highly nonlinear materials like liquid crystals.

Influence of annealing on the linear and nonlinear optical properties of Mn doped ZnO thin films examined by z-scan technique in CW regime

We present the studies on the influence of annealing on the third-order nonlinear optical properties of RF magnetron sputtered manganese doped zinc oxide (MZO) thin films with different doping concentration. It is revealed that the incorporation of Mn into ZnO and annealing lead to prominent changes in the third order nonlinearity. Nonlinear optical measurements were carried out by employing the z-scan technique using a continuous wave (CW) HeNe laser of 633 nm. The z-scan results reveal that the films exhibit self-defocusing thermal nonlinearity. The third-order nonlinear optical susceptibility χ(3) was found to be of the order of 10−3 esu and 10−2 esu for annealed MZO thin films at 200 °C and 400 °C respectively. The dependence of grain size on the observed nonlinearity was revealed by atomic force microscopy analysis. Optical limiting studies were carried out for a range of input power levels and an optical limiting of about ∼8 mW was observed indicating the possible application for photonic devices.

Temperature control for a vehicle climate chamber using chilled water system

The effective temperature control of a vehicle climate chamber was investigated. The temperature was regulated by electrical heater power and valve opening in the chilled water system. Cooling load and water flow rate through the adjusting valve were studied based on the distributed parameter model developed in a previous article. In order to ensure the flow capacity and increase linearity between the cooling side control output and the air temperature, two equal percentage valves were applied. The climate chamber has characteristics of large thermal inertia and non-linearity. Performance of a proportional–integral–derivative (PID) controller used in the existing system was not satisfactory, so a fuzzy self-tuning PID controller was designed. The PID gains were tuned online according to temperature error, error change rate, and air velocity using fuzzy logic. Model predictions showed that the fuzzy PID control stabilized the air temperature in a shorter time and with smaller overshoot and undershoot. The time averaged temperature error was reduced from 0.37°C to 0.09°C in the high temperature test, and that of the low temperature test was reduced from 0.42°C to 0.18°C.

Singular Dynamic Holography

Basic patterns of interaction of Gaussian and singular light beams (optical vortices) in media with resonant and thermal nonlinearity are experimentally investigated. It is demonstrated that interference of the Gaussian and singular beams in a nonlinear medium leads to the formation of dynamic volume holograms characterized by a singular structure. Under conditions of nonlinear holographic recording and Bragg diffraction on singular volume holograms, multiplexing of a topological charge and frequency conversion of optical vortices (transition from the IR to the visible range of the spectrum) is observed. Polarization recording of singular holograms that allows dynamic control to be performed over polarization of singular light beams including rotation of the polarization plane and conversion of linearly polarized radiation into circularly or elliptically polarized radiation.

Propagation of surface plasmon–polaritons at the boundary of a metal–dielectric with thermal optical nonlinearity

Media with thermal defocusing nonlinearity and bordering material with high thermal conductivity are investigated. The problem of creating a fixed optical waveguide at the boundary of a metal–dielectric with thermal nonlinearity is solved. The possibility of different types of waves propagating in such a wave guide is considered.