Nonlinear Propagation Effects Research Articles

Experimental study of intramodal XPM reduction by intramodal dispersion in weakly coupled FMF.

The understanding of nonlinear propagation effects in low-crosstalk few-mode fiber is crucial for a weakly coupled mode-division multiplexed system. In this Letter, we report the first, to the best of our knowledge, experimental verification of the advantage of intramodal dispersion on mitigating intramodal cross-phase modulation in a weakly coupled few-mode fiber transmission. The experimental system is established over a 70-km multiple-ring-core few-mode fiber accommodating 6 linearly polarized modes, based on which the influences of intramodal cross-phase modulation on transmission performances of each linearly polarized mode are evaluated. Experimental results show that the intramodal cross-phase modulation of degenerate linearly polarized modes with much larger intramodal dispersion values are significantly weaker than those of non-degenerate linearly polarized modes, in which the maximum suppression of intramodal cross-phase modulation noise is up to 9.7 dB. We believe that this work would be beneficial to practical applications of weakly coupled mode-division multiplexing technologies.

Propagation Characteristics of Initial Compression Wave Induced by 400 km/h High-Speed Trains Passing through Very Long Tunnels

When high-speed trains enter tunnels, an initial compression wave is generated. As the compression wave propagates at the local speed of sound to the tunnel exit, it radiates into the surrounding environment, forming micro-pressure waves (MPWs). MPWs create sonic booms, resulting in significant environmental issues. The magnitude of the micro-pressure waves is directly proportional to the pressure gradient of the compression wave at the tunnel exit. The nonlinear effects of the initial compression wave during propagation lead to a significant increase in pressure gradient. Therefore, the propagation characteristics of the initial compression wave during the tunnel are the crucial factor affecting the amplitude of MPWs. Based on the one-dimensional compressible unsteady non-isentropic flow model and the improved generalized Riemann variable characteristic method, this paper researched the propagation and evolution characteristics of an initial compression wave generated when 400 km/h high-speed trains enter tunnels with three portal shapes: (no tunnel entrance hood (no hood), an oblique, enlarged tunnel entrance hood (type A), an enlarged equal-section non-uniform opening hole tunnel entrance hood (type B)). The results show that when the initial compression wave propagates inside very long tunnels, the pressure gradient of the compression wave exhibits a trend of initially increasing and then decreasing with the increase in propagation distance. When the pressure gradient of the compression wave reaches its maximum value, the corresponding propagation distance is the steepening critical distance. For no tunnel entrance hoods, type A tunnel entrance hoods, and type B tunnel entrance hoods, the steepening critical distances are 5 km, 6 km, and 16 km, respectively. The steepening critical distance shortens with increasing train speed. Steady friction and unsteady friction effects mainly affect the pressure amplitude and pressure gradient during compression wave propagation, respectively. At lower ambient temperatures, the nonlinear effects in compression wave propagation are significantly enhanced. The mitigation effects of type A tunnel entrance hoods and type B tunnel entrance hoods on pressure gradient reduction are mainly concentrated within 4 km and 12 km, respectively. It is necessary to determine the optimal matching relationship between the tunnel entrance hood and tunnel length based on the characteristics of compression wave propagation to ensure their mitigating performance is maximized.

Multiphoton-initiated laser writing of semiconductors using nanosecond mid-infrared pulses

The advent of more powerful mid-infrared nanosecond laser sources allows using them as attractive tools in material laser processing. For semiconductor bulk processing, laser intensities must remain modest to avoid detrimental nonlinear propagation and pre-focal plasma screening effects. Accordingly, nanosecond pulses are usually appropriate to locally initiate energy deposition by multiphoton absorption and subsequent modification, hardly achievable with ultrashort pulses. Employing a 2.8-μm 2.5-ns laser source, we explore the possibility to modify silicon and other semiconductors. With interactions initiated by three-photon absorption, we modify and determine the surface and bulk modification thresholds of Si, GaAs, and InP. For Si, compared to previous studies at telecom wavelengths, we report on a reduction of the energy threshold for volume modification with processing depth, and repeatable rear-surface modifications. Compared to Si, we find for GaAs and InP important fluctuations in the modification responses, which we attribute to an absorption mechanism initially triggered by a greater presence of defects. We also study germanium, as this narrower bandgap semiconductor very interesting for mid-infrared electro-optical applications is transparent at the newly introduced wavelength. Despite the ability to modify the surface, the bulk of Ge remains inaccessible in this two-photon regime, mainly attributed to beam aberrations and nonlinearities. Nonetheless, we demonstrate the ability to process Si chips integrating Ge layers. All these results showcase the potential of mid-infrared wavelengths to offer new degrees of flexibility for 3D laser processing technologies turned to silicon photonics and microelectronics packaging.

Rock Layer Classification and Identification in Ground-Penetrating Radar via Machine Learning

Ground-penetrating radar (GPR) faces complex challenges in identifying underground rock formations and lithological structures. The diversity, intricate shapes, and electromagnetic properties of subsurface rock formations make their accurate detection difficult. Additionally, the heterogeneity of subsurface media, signal scattering, and non-linear propagation effects contribute to the complexity of signal interpretation. To address these challenges, this study fully considers the unique advantages of convolutional neural networks (CNNs) in accurately identifying underground rock formations and lithological structures, particularly their powerful feature extraction capabilities. Deep learning models possess the ability to automatically extract complex signal features from radar data, while also demonstrating excellent generalization performance, enabling them to handle data from various geological conditions. Moreover, deep learning can efficiently process large-scale data, thereby improving the accuracy and efficiency of identification. In our research, we utilized deep neural networks to process GPR signals, using radar images as inputs and generating structure-related information associated with rock formations and lithological structures as outputs. Through training and learning, we successfully established an effective mapping relationship between radar images and lithological label signals. The results from synthetic data indicate a rock block identification success rate exceeding 88%, with a satisfactory continuity identification of lithological structures. Transferring the network to measured data, the trained model exhibits excellent performance in predicting data collected from the field, further enhancing the geological interpretation and analysis. Therefore, through the results obtained from synthetic and measured data, we can demonstrate the effectiveness and feasibility of this research method.

Improvement of contrast ratio between cavitation bubbles and tissue by frequency filtering in triplet pulse ultrasound imaging

Bubble-enhanced high-intensity focused ultrasound treatment requires selective imaging of cavitation bubbles to ensure their localization to the target tissue. Previous studies have proposed the ultrasound imaging of cavitation bubbles with a filtering method, which makes bubble extraction by a triplet pulse sequence more selective. The envelope component as well as harmonic components are generated during the nonlinear propagation of an ultrasonic imaging pulse, but the triplet pulse sequence can significantly reduce only the harmonic components, and its selectivity is degraded by the residual envelope component. In this study, the effects of nonlinear propagation at various intensities of imaging pulse and the frequency filtering to obtain better selectivity are investigated for the triplet pulse sequence with a filtering method. The result shows that the imaging pulse intensity is an important parameter that determines the strength of the effect of nonlinear propagation and that the optimal frequency filtering changes according to it.

Scenario-based tsunami hazard assessment for Northeastern Adriatic coasts

Significant tsunamis in the Northern Adriatic are rare, and only a few historical events have been reported in the literature, with sources mostly located along central and southern parts of the Adriatic coasts. Recently, a tsunami alert system has been established for the whole Mediterranean area; however, a detailed description of the potential impact of tsunami waves on coastal areas is still missing for several sites. This study aims to model the hazard associated with possible tsunamis generated by offshore earthquakes, with the purpose of contributing to tsunami risk assessment for selected urban areas along the Northeastern Adriatic coasts. Tsunami modelling is performed by the NAMI DANCE software, which allows accounting for seismic source properties, variable bathymetry, and nonlinear effects in wave propagation. Hazard scenarios at the shoreline are developed for the coastal areas of Northeastern Italy and at selected cities (namely, Trieste, Monfalcone, Lignano and Grado). An extensive set of potential tsunamigenic sources of tectonic origin located in three distance ranges (namely at Adriatic-wide, regional and local scales) are considered for the modelling. Sources are defined according to available literature, which includes catalogues of historical tsunamis and existing active faults databases. Accordingly, a set of tsunami-related parameters and maps are obtained (e.g. maximum run-up, arrival times, synthetic mareograms) that are relevant to planning mitigation actions at the selected sites.

High harmonic generation in epitaxially grown zinc oxide films

High harmonic generation (HHG) in solids has been identified as a promising mechanism for light source generation and for spectroscopy of materials. HHG from bulk solids, however, often suffers from nonlinear propagation effects, resulting in a loss of spectral coherence and the skewing of spectroscopic measurements. Here, we study HHG in epitaxial ZnO thin films grown on Al2O3 substrates using atomic layer deposition. We find that the HHG emission consists of narrow spectral peaks, in contrast to those seen in bulk, and that the dependence of the harmonic yield on the film thickness differs for above-gap and below-gap harmonics, which can be understood from analytical models based on the linear and nonlinear response of the medium. The measured harmonic spectra depend qualitatively on the preparation of the films, with as-grown films generating even harmonic orders, which are absent in annealed films. The results are interpreted using transmission electron microscopy measurements, which indicate different morphologies for the as-grown and annealed films.

A global model of intensity autocorrelation to determine laser pulse duration

We present a new global model of collinear autocorrelation based on second harmonic generation nonlinearity. The model is rigorously derived from the nonlinear coupled wave equation specific to the autocorrelation measurement configuration, without requiring a specific form of the incident pulse function. A rigorous solution of the nonlinear coupled wave equation is obtained in the time domain and expressed in a general analytical form. The global model fully accounts for the nonlinear interaction and propagation effects within nonlinear crystals, which are not captured by the classical local model. To assess the performance of the global model compared to the classic local model, we investigate the autocorrelation signals obtained from both models for different incident pulse waveforms and different full-widthes at half-maximum (FWHMs). When the incident pulse waveform is Lorentzian with an FWHM of 200 fs, the global model predicts an autocorrelation signal FWHM of 399.9 fs, while the classic local model predicts an FWHM of 331.4 fs. The difference between the two models is 68.6 fs, corresponding to an error of 17.2%. Similarly, for a sech-type incident pulse with an FWHM of 200 fs, the global model predicts an autocorrelation signal FWHM of 343.9 fs, while the local model predicts an FWHM of 308.8 fs. The difference between the two models is 35.1 fs, with an error of 10.2%. We further examine the behavior of the models for Lorentzian pulses with FWHMs of 100 fs, 200 fs and 500 fs. The differences between the global and local models are 17.1 fs, 68.6 fs and 86.0 fs, respectively, with errors approximately around 17%. These comparative analyses clearly demonstrate the superior accuracy of the global model in intensity autocorrelation modeling.

Direct numerical simulations of long-range infrasound propagation: Implications for source spectra estimation.

The evolution of observed dominant frequencies from a high-intensity infrasonic pulse with receiver range and stratospheric temperature is investigated using direct numerical simulations of the two-dimensional unsteady compressible Navier-Stokes equations. There is a high level of uncertainty in estimating source dominant frequencies based on received signals at sparse points on the ground. Nonlinear propagation effects in the ground-level thermospheric arrivals are found to significantly alter dominant frequency measurements compared to stratospheric arrivals with smaller amplitude sources. With a larger amplitude source, variations in observations are minimized as a result of nonlinear effects being ubiquitous across all atmospheric components of received signals but have a greater offset to the source dominant frequency. An approach to determine the source dominant frequency and minimize atmospheric variability is presented by calculating a source-to-receiver spectral transfer function averaged across the atmospheric states. This method reduces atmospheric variability in source frequency estimates within the pseudo-linear propagation regime and the average error to the known source frequency with a large amplitude source. The reduction of errors in source frequency estimates demonstrates the feasibility of using remote infrasound measurements as an indicator of source frequency and, in turn, the explosive yield of clandestine nuclear weapon test explosions.

Gain-managed nonlinear amplification of ultra-long mode-locked fiber laser.

In this study, we explored the gain-managed nonlinear (GMN) amplification of ultra-low repetition rate pulses in the range of less than 1 MHz. By seeding the developed 1040 nm ultralong fiber modelocked laser to the GMN amplifier, we achieved high gain and boosted the nonlinear pulse propagation effects. We demonstrated that GMN amplification of low repetition rate pulses provided amplification exceeding 32 dB and spectral broadening up to 91 nm at relatively low pump power levels. Achieving broadband 57 fs pulses with energy exceeding 55 nJ suggests that ultralong fiber lasers paired with GMN amplifiers can be effectively utilized as powerful tools for generating femtosecond broadband pulses at ultra-low repetition rates, with controllable spectral characteristics.

Investigation of the effect of a multi-frequency ultrasound signal on the inertial cavitation threshold is various viscoelastic mediums

The objective of the present study is the numerical investigation of the inertial cavitation threshold in soft tissue under different multi-frequency signals of high intensity focused ultrasound (HIFU). For the modeling of bubble dynamics, the Gilmore-Akulichev-Zener model was used. The inertial cavitation threshold was calculated for different criteria, for different signal modes (single-, dual-, and triple-frequency), and for different viscoelastic mediums. Effect of nonlinear wave propagation and mechanical effects of acoustic caviation have been also studied. The obtaining results demonstrated that a criterion, based on bubble size, gives lower threshold values than a criterion using bubble collapse velocity. An increase in the values of viscosity and elasticity leads to a rise in the threshold amplitude. Analyzing threshold values for dual- and triple-frequency signal modes, it can be seen that the inertial cavitation threshold can be sufficiently reduced when a multi-frequency signal with the correct frequency combination is applied. However, the inertial cavitation threshold also depends on the initial bubble size. This dependency was also investigated in the current study.

Effect of the nature of uncertainty on the optimization of collision avoidance maneuvers

With the soaring number of space debris, collision avoidance maneuvers have become crucial to ensure the safety of any operating satellite. In real-world scenario, the problem gets a little more complicated due to the presence of uncertainty in the values of the states of the space objects. Also, the uncertainty distribution assigned to a given state variable evolves over time. This paper studies the effects of linear and nonlinear propagation of the uncertainty distributions on the collision avoidance maneuver optimization. These different methods for error propagation lead to differing shapes and sizes of the error distribution, resulting in differing regions to be avoided during the encounter, thus resulting in different optimal Δv requirements. In the method using nonlinear propagation of uncertainty distribution, the uncertainty of the passive object is propagated using Monte Carlo samples while that of the operating spacecraft is evolved using Unscented Transform. The sigma points from the Unscented Transform of the operating spacecraft are required to lie outside the stretch of most of the debris uncertainty while implementing cumulative density function. This also results in defining a new probabilistic measure which is like a modified Mahalanobis distance but for a non-Gaussian distribution. The other approach uses linearly propagating the error covariances and a combined error ellipsoid to ensure the maintenance of a desired Mahalanobis distance of the hard body from the uncertainty distribution to ascertain safety. Both the approaches consider nonlinear state dynamics while incorporating the perturbing forces to find the optimal thrust profile and the corresponding steer angles. The approach implementing nonlinear propagation of uncertainty and using cumulative density to ensure that the sigma points of the satellite avoid the debris’ uncertainty distribution is found to require lower Δv compared to the other method while also representing the error propagation better. However, the method implementing linear propagation of uncertainty and using Mahalanobis distance of the hard body from the combined error distribution to frame the avoidance constraint proves to be computationally much faster.

High Harmonic Generation near the Low-Frequency Edge of a Plateau under Nonlinear Propagation of 1.24-μm Near-Infrared Femtosecond Laser Radiation in a Dense Argon Jet

High (15–25) harmonic generation in the vacuum ultraviolet spectral range (83–50 nm) has been realized by focused (NA = 0.033) near-infrared femtosecond laser radiation (wavelength λ = 1.24 μm) with a vacuum intensity of ~7.5 × 1014 W/cm2 irradiating a dense gas jet. It has been shown experimentally that the use of such a high-numerical aperture focusing requires high (up to 10 bar) gas jet pressures to optimize phase matching. The use of the dense gas jet results in a noticeable manifestation of nonlinear propagation effects for generating radiation, which affect the generation process through the change in the phase matching conditions. Furthermore, it has been shown that the prechirping of the generating pulse makes it possible to compensate a chirp appearing due to self-phase modulation and to increase the harmonic generation efficiency because of the nonlinear compression of the generating pulse. This approach has allowed 17th (73 nm) harmonic generation with an energy of 2 pJ in a pulse and a generation efficiency of 5.4 × 10–9. The estimates obtained have shown that this radiation can be used for single-pulse maskless photolithography in the extreme ultraviolet range.

Numerical verification of the existence of shock waves in trombones

The brassy timbre associated with loudly played trombone notes is due to the accumulated effects of nonlinear wave propagation. Hirschberg et al. experimentally showed in [J. Acoust. Soc. Am. 99, 1754–1758] that wave steepening of such tones can be strong enough to produce shock waves. In this paper, pressure measurements collected along the trombone bore are presented and then numerically simulated using a three-dimensional time-domain model. The numerical solutions reveal that shock waves do form within the computational instrument within the vicinity of the approximated shock distance.

Ultrasonic needle hydrophone calibration in air by a parabolic off-axis mirror focused beam using three-transducer reciprocity

An acoustic field distribution investigation in air requires a small receiving sensor. Needle hydrophones seem to be an attractive solution, and it has previously been demonstrated that needle hydrophones designed for use in water can be used in air. The metrology problem is that an absolute sensitivity calibration is needed, because needle hydrophones are not characterized in air, especially for frequencies below 1 MHz, which is of interest for air-coupled ultrasound. Conventional, three-transducer/microphone reciprocity calibration requires measurements to be done in the far field. However, when transducer diameter is large and the frequency is high, the required measurement distance becomes very large: 3 m for a 20 mm source, transmitting at 1 MHz. Large propagation distance leads to high attenuation and nonlinear effects in air propagation, and distortion and losses accumulate. Small needle hydrophones have low sensitivity, so that high excitation amplitudes would be required, which can lead to transducer heating and increase nonlinearity effects. A derivative of the three-transducer reciprocity calibration method is proposed, where a large aperture transducer is focused onto a hydrophone, using hybrid of plane wave and spherical wave reciprocity. Use of a focused source minimizes the frequency-dependent diffraction effects, and the spherical wave approximation is valid at the focal distance, and low level excitation signals can be used. Focusing is accomplished using a parabolic off-axis mirror. Calibration is in transmission, which reduces the complexity of the electrical measurements. The corresponding equations have been derived for this setup. Calibration of the transducer and needle hydrophone absolute sensitivity is obtained.

Tailoring nonlinear ultrasound beams using acoustic lenses

Acoustic holographic lenses, i.e., acoustic holograms, can tailor ultrasound beams to precisely construct elaborate focal patterns. Due to their valuable capabilities, acoustic holograms are being rapidly investigated for a wide range of applications in physical acoustics and biomedical ultrasound. Modeling and demonstrating acoustic holograms in linear regimes is well documented in the literature. However, Acoustic holograms have the potential to improve the precision and affordability of therapeutic high-intensity focused ultrasound (HIFU). In this work, we will show the effects of nonlinear propagation on ultrasound fields tailored by acoustic holograms. The intensity-dependent effects of harmonic generation, diffraction, and nonlinear gain on the constructed pressure pattern are discussed. In addition, an accelerated method for simulating high-intensity 3D holographic ultrasound is introduced. We will show how the proposed algorithm greatly reduces the computational load for designing and predicting high-intensity holographic ultrasound patterns. This expedites the procedure of designing the acoustic lens, which allows for a more rapid and seamless implementation, especially in medical settings.

On the non-linear behaviour of ultrasonic air-borne phased arrays

Air-coupled phased arrays are an increasing area of academic and industrial interest. Their application to acoustic levitation and mid-air haptics relies on high amplitude focussed fields capable of generating very high acoustic pressures (e.g. >150 dB SPL). At these elevated pressures non-linear propagation effects can become significant, for example: the generation of harmonic frequencies, waveform asymmetry and acoustic saturation. In this work the basics of non-linear acoustics are presented with emphasis on energy loss mechanisms. Experimental work shows non-linearities as a function of focussing distance and driving amplitude. Large 2D microphone scans normal and tangential to the acoustic axis are carried out. Comparisons to linear models are made as well as modification to saturation equations developed for water-coupled fields. It is shown that saturation losses can become significant at elevated transducer amplitudes and focal distances. Metrics such as the waveform asymmetry, total harmonic distortion and energy loss are used to show the onset and magnitude of non-linearities. The volumetric experimental data shows how the fundamental and harmonic fields can differ in amplitude sufficiently such that harmonic amplitudes can exceed the fundamental. Suggestions are made on how to identify non-linearities and their general effect on air-coupled arrays and their applications.

Ultrafast Laser Welding of Silicon

While ultrafast laser welding is an appealing technique for bonding transparent workpieces, it is not applicable for joining silicon samples due to nonlinear propagation effects which dramatically diminish the possible energy deposition at the interface. It is demonstrated that these limitations can be circumvented by local absorption enhancement at the interface thanks to metallic nanolayer deposition. By combining the resulting exalted absorption with filament relocation during ultrafast laser irradiation, silicon samples can be efficiently joined. Shear joining strengths >4 MPa are obtained for 21 nm gold nanolayers without laser‐induced alteration of the transmittance. Such remarkable strength values hold promise for applications in microelectronics, optics, and astronomy.

Simulation of nonlinear propagation of femtosecond laser pulses in air for quantitative prediction of the ablation crater shape.

The utilization of sub-100 fs pulses has attracted attention as an approach to further improve the quality and precision of femtosecond laser microfabrication. However, when using such lasers at pulse energies typical for laser processing, nonlinear propagation effects in air are known to distort the beam's temporal and spatial intensity profile. Due to this distortion, it has been difficult to quantitatively predict the final processed crater shape of materials ablated by such lasers. In this study, we developed a method to quantitatively predict the ablation crater shape, utilizing nonlinear propagation simulations. Investigations revealed that the ablation crater diameters derived by our method were in excellent quantitative agreement with experimental results for several metals over a two-orders-of-magnitude range in the pulse energy. We also found a good quantitative correlation between the simulated central fluence and the ablation depth. Such methods should improve the controllability of laser processing with sub-100 fs pulses and contribute to furthering their practical application to processes over a wide pulse-energy range, including conditions with nonlinear-propagating pulses.

Non-linear propagation effects of intense femtosecond pulses on below bandgap harmonics in solids

The non-linear propagation of the intense near-infrared (NIR) driving field in crystals poses a challenge and can offer an opportunity to control the spectral properties of harmonics in solids. Here, we have investigated the non-linear propagation effects in wide bandgap dielectrics such as Magnesium Oxide (MgO), Chromium (Cr) doped MgO (Cr: MgO), Sapphire (Sa) crystals, and fused silica (FS). Furthermore, we have generated second and third harmonics (TH) and measured the linear polarization dependence of harmonics in these thin solids to explore the non-linear response at a strong field. We observe spectral shifts and broadening of the driving field spectrum which is imprinted on the harmonics. We attribute these effects to the strong photoionization, generation of free-carrier density, and self-phase modulation effects. This work shows the sensitivity to control the spectral profile of harmonics by manipulating the driving field, showing the possibility of new tailored solid-state ultraviolet sources for optical diagnostics.