Effective Nonlinear Parameter Research Articles

New probe of non-Gaussianities with primordial black hole induced gravitational waves

We propose a new probe of primordial non-Gaussianities (NGs) through the observation of gravitational waves (GWs) induced by ultra-light (MPBH<109g) primordial black holes (PBHs). Interestingly enough, the existence of primordial NG can leave imprints on the clustering properties of PBHs and the spectral shape of induced GW signals. Focusing on a scale-dependent local-type NG, we identify a distinct double-peaked GW energy spectrum that, contingent upon MPBH and the abundance of PBHs at the time of formation, denoted as ΩPBH,f, may fall into the frequency bands of upcoming GW observatories, including LISA, ET, SKA, and BBO. Thus, such a signal can serve as a novel portal for probing primordial NGs. Intriguingly, combining BBN bounds on the GW amplitude, we find for the first time the joint limit on the product of the effective non-linearity parameter for the primordial tri-spectrum, denoted by τ¯NL, and the primordial curvature perturbation power spectrum PR(k), which reads as τ¯NLPR(k)<4×10−20ΩPBH,f−17/9(MPBH104g)−17/9.

Characterization of optimal healing efficiency based on a new nonlinear ultrasonic method for the process of gradient heating healing in asphalt mixture

In this research, we proposed a new nonlinear ultrasonic method, second harmonic generation (SHG) technique, to investigate the gradient heating-healing properties and determine the optimal healing efficiency in asphalt mixture based on the principle of ultrasonic Rayleigh surface wave. The energy approach is used to characterize the released energy based on the laws of Newton's convection. The released energy can be used to determine the optimum healing period according to law of conservation of energy. Three healing indices, absorbed energy, effective healing depth and nonlinear ultrasonic parameter, are respectively defined to characterize the healing efficiency of asphalt mixture for different healing periods. The healing gradient direction is verified by the X-ray computed tomography (CT) scanning images and corresponding porosity calculation. The results indicate the existence of an optimal healing period and healing efficiency in the healing process of asphalt mixture, and the calculation method proposed here is suitable to predict the optimal healing efficiency. While the nonlinear parameter is considerably prominent due to its sensitivity and high resolution for each healing period. Finally, through the correlation analysis of three healing indices, it is found that the nonlinear ultrasonic parameter is an ideal alternative of two other healing indices in terms of characterizing the gradient heating-healing properties of asphalt mixture specimens.

An optical parametric Bragg amplifier on a CMOS chip

Abstract We demonstrate a complementary metal–oxide–semiconductor (CMOS)-compatible optical parametric Bragg amplifier on an ultra-silicon-rich nitride chip. The amplifier design incorporates advantageous group index properties in a nonlinear Bragg grating to circumvent phase matching limitations arising from the bulk material and waveguide dispersion. The grating structure further augments the effective nonlinear parameter of 800 W−1/m, considerably lowering the power required for the observation of strong parametric gain. On/off optical parametric gain of 20 dB is achieved using a low peak power of 1.6 W, in good agreement with numerical calculations. This represents a 7 dB improvement in the parametric gain compared to the absence of grating enhancement which is attributed to the Bragg grating induced superior phase matching.

Optimizing the Kerr Nonlinear Optical Performance of Silicon Waveguides Integrated With 2D Graphene Oxide Films

The Kerr nonlinear optical performance of silicon nanowire waveguides integrated with 2D layered graphene oxide (GO) films is theoretically studied and optimized based on experimentally measured linear and nonlinear optical parameters of the GO films. The strong mode overlap between the silicon nanowires and highly nonlinear GO films yields a significantly enhanced Kerr nonlinearity for the hybrid waveguides. A detailed analysis for the influence of waveguide geometry and GO film thickness on the propagation loss, nonlinear parameter, and nonlinear figure of merit (FOM) is performed. The results show that the effective nonlinear parameter and nonlinear FOM can be increased by up to 52 and 79 times relative to bare silicon nanowires, respectively. Self-phase modulation (SPM)-induced spectral broadening of optical pulses is used as a benchmark to evaluate the nonlinear performance, examining the tradeoff between enhancing Kerr nonlinearity and minimizing loss. By optimizing the device parameters to balance this, a high spectral broadening factor of 27.8 can be achieved, more than 6 times that achieved in previous experiments. Finally, the influence of pulse chirp, material anisotropy, and the interplay between saturable absorption and SPM is also discussed, together with the comparison between the spectral broadening after going through GO-coated and graphene-coated silicon waveguides. These results provide useful guidance for optimizing the Kerr nonlinear optical performance of silicon waveguides integrated with 2D layered GO films.

Vector modulation instability in birefringent graded-index multimode fibers

We study vectorial modulation instability occurring inside a birefringent graded-index (GRIN) fiber when the two polarization components of the optical field are coupled nonlinearly through cross-phase modulation. In the scalar case in which only modes of one polarization are excited, the geometric parametric instability is known to produce an infinite number of sidebands around the wavelength of the input optical beam. We show that the birefringence of a GRIN fiber splits each of these sidebands into a triplet, whose frequency spacing depends on the differential group delay between the orthogonally polarized components. We verify the predictions of the linear stability analysis numerically by solving two coupled nonlinear Schrödinger equations that include spatial self-imaging effects through an effective nonlinear parameter. We present results for both continuous and pulsed optical beams experiencing normal or anomalous group-velocity dispersion inside a GRIN fiber.

Enhanced Four‐Wave Mixing in Silicon Nitride Waveguides Integrated with 2D Layered Graphene Oxide Films

AbstractLayered 2D graphene oxide (GO) films are integrated with silicon nitride (SiN) waveguides to experimentally demonstrate an enhanced Kerr nonlinearity via four‐wave mixing (FWM). SiN waveguides with both uniformly coated and patterned GO films are fabricated based on a transfer‐free, layer‐by‐layer GO coating method along with standard photolithography and lift‐off processes, yielding precise control of the film thickness, placement, and coating length. Detailed FWM measurements are carried out for the fabricated devices with different numbers of GO layers and at different pump powers, achieving up to ≈7.3 dB improvement in the FWM conversion efficiency for an uniformly coated device with one layer of GO and ≈9.1 dB for a patterned device with five layers of GO. A detailed analysis of the influence of pattern length and position on the FWM performance is performed. The dependence of GO's third‐order nonlinearity on layer number and pump power is also extracted, revealing interesting physical insights about the layered 2D GO films. Finally, an enhancement is obtained in the effective nonlinear parameter of the hybrid waveguides by over a factor of 100 relative to bare SiN waveguide. These results demonstrate the high nonlinear optical performance of SiN waveguides integrated with layered 2D GO films.

Enhanced Kerr Nonlinearity and Nonlinear Figure of Merit in Silicon Nanowires Integrated with 2D Graphene Oxide Films.

Layered two-dimensional (2D) graphene oxide (GO) films are integrated with silicon-on-insulator (SOI) nanowire waveguides to experimentally demonstrate an enhanced Kerr nonlinearity, observed through self-phase modulation (SPM). The GO films are integrated with SOI nanowires using a large-area, transfer-free, layer-by-layer coating method that yields precise control of the film thickness. The film placement and coating length are controlled by opening windows in the silica cladding of the SOI nanowires. Owing to the strong mode overlap between the SOI nanowires and the highly nonlinear GO films, the Kerr nonlinearity of the hybrid waveguides is significantly enhanced. Detailed SPM measurements using picosecond optical pulses show significant spectral broadening enhancement for SOI nanowires coated with 2.2 mm long films of 1-3 layers of GO and 0.4 mm long films with 5-20 layers of GO. By fitting the experimental results with theory, the dependence of GO's Kerr nonlinearity on layer number and pulse energy is obtained, showing interesting physical insights and trends of the layered GO films from 2D monolayers to quasi bulk-like behavior. Finally, we show that by coating SOI nanowires with GO films, the effective nonlinear parameter of SOI nanowires is increased 16-fold, with the effective nonlinear figure of merit (FOM) increasing by about 20 times to FOM > 5. These results reveal the strong potential of using layered GO films to improve the Kerr nonlinear optical performance of silicon photonic devices.

Nonlinear absorption in media with composite gold nanoparticles

We consider nonlinear absorption in a system consisting of a dilute mixture of identical metallic nanoparticles in a dielectric background. The nanoparticles consist of a core and a shell, one of which is gold and the other is a dielectric. By determining the effective nonlinear parameters of the nanoparticles, we find that the nonlinear absorption can be positive or negative, depending on the filling fraction of the gold. This shows that the magnitude and sign of the effective parameters depend not only on the constituent materials, but also on the details of the geometry.

Solid-core bismuth–tellurite glass fiber with low propagation loss and high nonlinearity

We have fabricated a single-mode bismuth-doped tellurite solid-core glass fiber using a multi-stage fiber fabrication method. Owing to the optimization of the glass composition and rod-in-tube fiber drawing technology, this fiber features a small mode area of 24.63 μm2 and low propagation loss of 0.9 dB/m at 1550 nm. By using the continuous-wave self-phase modulation method, the effective nonlinear parameter γ of this bismuth-doped tellurite glass fiber is estimated to be 417 W−1 km−1 at 1550 nm, which is the highest to date among all known solid-core tellurite glass fibers. Thus, we have developed an unprecedented high nonlinearity and low loss tellurite glass fiber. © 2019 Elsevier B.V. All rights reserved.

Damage prediction via nonlinear ultrasound: A micro-mechanical approach

Nonlinear constitutive mechanical parameters, predominantly governed by micro-damage, interact with ultrasound to generate harmonics that are not present in the excitation. In principle, this phenomenon therefore permits early stage damage identification if these higher harmonics can be measured. To understand the underlying mechanism of harmonic generation, a nonlinear micro-mechanical approach is proposed here, that relates a distribution of clapping micro-cracks to the measurable macroscopic acoustic nonlinearity by representing the crack as an effective inclusion with Landau type nonlinearity at small strain. The clapping mechanism inside each micro-crack is represented by a Taylor expansion of the stress-strain constitutive law, whereby nonlinear terms arise. The micro-cracks are considered distributed in a macroscopic medium and the effective nonlinearity parameter associated with compression is determined via a nonlinear Mori-Tanaka homogenization theory. Relationships are thus obtained between the measurable acoustic nonlinearity and the Landau-type nonlinearity. The framework developed therefore yields links with nonlinear ultrasound, where the dependency of measurable acoustic nonlinearity is, under certain hypotheses, formally related to the density of micro-cracks and the bulk material properties.

Doppler term in the galaxy two-point correlation function: Wide-angle, velocity, Doppler lensing and cosmic acceleration effects

We study the parity-odd part (that we shall call Doppler term) of the linear galaxy two-point correlation function that arises from wide-angle, velocity, Doppler lensing and cosmic acceleration effects. As it is important at low redshift and at large angular separations, the Doppler term is usually neglected in the current generation of galaxy surveys. For future wide-angle galaxy surveys, however, we show that the Doppler term must be included. The effect of these terms is dominated by the magnification due to relativistic aberration effects and the slope of the galaxy redshift distribution and it generally mimics the effect of the local type primordial non-Gaussianity with the effective nonlinearity parameter fNLeff of a few; we show that this would affect forecasts on measurements of fNL at low-redshift. Our results show that a survey at low redshift with large number density over a wide area of the sky could detect the Doppler term with a signal-to-noise ratio of ∼1−20, depending on survey specifications.

Homogenized description and retrieval method of nonlinear metasurfaces

A patterned, plasmonic metasurface can strongly scatter incident light, functioning as an extremely low-profile lens, filter, reflector or other optical device. When the metasurface is patterned uniformly, its linear optical properties can be expressed using effective surface electric and magnetic polarizabilities obtained through a homogenization procedure. The homogenized description of a nonlinear metasurface, however, presents challenges both because of the inherent anisotropy of the medium as well as the much larger set of potential wave interactions available, making it challenging to assign effective nonlinear parameters to the otherwise inhomogeneous layer of metamaterial elements. Here we show that a homogenization procedure can be developed to describe nonlinear metasurfaces, which derive their nonlinear response from the enhanced local fields arising within the structured plasmonic elements. With the proposed homogenization procedure, we are able to assign effective nonlinear surface polarization densities to a nonlinear metasurface, and link these densities to the effective nonlinear surface susceptibilities and averaged macroscopic pumping fields across the metasurface. These effective nonlinear surface polarization densities are further linked to macroscopic nonlinear fields through the generalized sheet transition conditions (GSTCs). By inverting the GSTCs, the effective nonlinear surface susceptibilities of the metasurfaces can be solved for, leading to a generalized retrieval method for nonlinear metasurfaces. The application of the homogenization procedure and the GSTCs are demonstrated by retrieving the nonlinear susceptibilities of a SiO2 nonlinear slab. As an example, we investigate a nonlinear metasurface which presents nonlinear magnetoelectric coupling in near infrared regime. The method is expected to apply to any patterned metasurface whose thickness is much smaller than the wavelengths of operation, with inclusions of arbitrary geometry and material composition, across the electromagnetic spectrum.

Enhanced optical nonlinearities in CMOS-compatible ultra-silicon-rich nitride photonic crystal waveguides

We present the design, fabrication, and characterization of photonic crystal waveguides (PhCWs) on an ultra-silicon-rich nitride (USRN) platform, with the goal of augmenting the optical nonlinearities. The design goals are to achieve an optimized group index curve on the PhCW band edge with a non-membrane PhCW with symmetric SiO2 undercladding and overcladding, so as to maintain back-end CMOS compatibility and better structural robustness. Linear optical characterization, as well as nonlinear optical characterization of PhCWs on ultra-silicon-rich nitride is performed at the telecommunication wavelengths. USRN's negligible two-photon absorption and free carrier losses at the telecommunication wavelengths ensure that there is no scaling of two-photon related losses with the group index, thus maintaining a high nonlinear efficiency. Self-phase modulation experiments are performed using a 96.6 μm PhCW. A 1.5π phase shift is achieved with an input peak power of 2.5 W implying an effective nonlinear parameter of 1.97 × 104 (W m)−1. This nonlinear parameter represents a 49× enhancement in the nonlinear parameter from the slow light effect, in good agreement with expected scaling from the measured group index.

Single-mode fluorotellurite glass fiber

By multi-stage rod-in-tube fiber drawing process, a single-mode fluorotellurite glass fiber was fabricated and reported for the first time. Benefiting from chemical–physical dehydration process to remove water and OH− groups, the propagation loss was decreased to 1.9dB/m at 1550nm and the infrared window is extended from 2.8μm to 4.2μm, i.e. a new kind of mid-infrared glass fiber. The fiber is with a small core of 3.52μm in diameter to meet single-mode condition, and the effective nonlinear parameter γ was estimated to be 236.7W−1km−1 at 1550nm by using continuous-wave self-phase modulation method. © 2015 Elsevier B.V. All rights reserved.

Polarization Effects on the Non-Linearity of a Highly Non-Linear Fiber

The effective non-linear parameter of a highly non-linear optical fiber was measured using the four-wave mixing effect. A value of γ = 10.6 W–1/km was obtained for a small wavelength separation between pump and signal waves, whereas for a large wavelength separation, a value of = 8γ/9 = 9.4 W–1/km was found. This value corresponds to an average of the Kerr non-linearity over the Poincaré sphere, since the polarization of both the pump and signal waves become uncorrelated in the last case. A theoretical model is proposed to describe the variation of the effective non-linear parameter with the wavelength separation between pump and signal waves, which is in good agreement with the experimental data.

Effect of l-cysteine on optical, thermal and mechanical properties of ADP crystal for NLO application

Abstract The ammonium dihydrogen phosphate (ADP) crystal doped with amino acid l -cysteine (LC) was grown by a slow evaporation technique. The grown crystal was transparent in the entire visible region, which is an essential requirement for a nonlinear crystal. The LC doping enhances the optical band gap of ADP (5.35 eV). The TG/DTA analysis of LC doped ADP crystal confirms the optimum thermal stability of grown crystal. The enhancement in the mechanical stability after LC doping was confirmed by Vicker׳s microhardness test. The LC doping showed significant impact on dielectric properties (dielectric constant and dielectric loss) of grown crystal. The third order nonlinear behavior of LC doped ADP crystal was investigated using a Z-scan technique at 632.8 nm and effective nonlinear optical parameters were evaluated.

Nonlinear characterization on mid-infrared fluorotellurite glass fiber

By physical and chemical dehydration technique to remove OH group from raw materials and via built-in casting method to make glass fiber preform, mid-infrared fluorotellurite glass fibers with low loss of 3.61dB/m at 1550nm were fabricated recently. With the addition of fluoride components, fluorotellurite glass fiber cane presents a ‘water-free’ state with a broadband transparency in the range of 0.38–4.2µm. By the continuous-wave self-phase modulation method, the nonlinear refractive index n2 and the effective nonlinear parameter γ of the made fluorotellurite glass fiber were estimated to be 1.4×10−18m2/W and 20.9/W/km at 1550nm, respectively. © 2013 Elsevier B.V. All rights reserved.

Nonlinear mixing of ultrasonic coda waves with lower frequency-swept pump waves for a global detection of defects in multiple scattering media

An ultrasonic method providing for an efficient global detection of defects in complex media (multiple scattering or reverberating media) is reported herein; this method is based on the nonlinear acoustic mixing of coda waves (stemming from multiple scattering) with lower frequency-swept pump waves. Such a nonlinear mixing step is made possible by the presence of nonlinear scatterers, such as cracks and delamination, yet remains absent when the waves are scattered only by linear scatterers, as is the case in a complex but defect-free medium. A global inspection is achieved thanks to the use of wide-band coda and pump signals, which ensure the excitation of many resonances along with a homogeneous acoustic energy distribution in the medium. We introduce the existing sensitivity tools developed for Coda Wave Interferometry in extracting the pump amplitude-dependent parameters of the coda waves associated with effective nonlinear parameters of the medium. By comparing results at two damage levels, these effective nonlinear parameters are shown to be correlated with crack presence in glass samples. The mechanisms potentially responsible for the observed amplitude dependence on the tested elastic parameters and waveform modification are discussed.

Physics issues in diffraction limited storage ring design

Diffraction limited electron storage ring is considered a promising candidate for future light sources, whose main characteristics are higher brilliance, better transverse coherence and better stability. The challenge of diffraction limited storage ring design is how to achieve the ultra low beam emittance with acceptable nonlinear performance. Effective linear and nonlinear parameter optimization methods based on Artificial Intelligence were developed for the storage ring physical design. As an example of application, partial physical design of HALS (Hefei Advanced Light Source), which is a diffraction limited VUV and soft X-ray light source, was introduced. Severe emittance growth due to the Intra Beam Scattering effect, which is the main obstacle to achieve ultra low emittance, was estimated quantitatively and possible cures were discussed. It is inspiring that better performance of diffraction limited storage ring can be achieved in principle with careful parameter optimization.

Fatigue assessment of multi-loading suspension bridges using continuum damage model

Long-span steel suspension bridges carrying both highway and railway have been built in wind-prone regions. The fatigue assessment of such bridges under the combined action of railway, highway, and wind loading represents a challenging task in consideration of uncertainties in both fatigue loading and fatigue resistance. This paper presents a framework for fatigue assessment of a long-span suspension bridge under combined highway, railway, and wind loadings using a continuum damage model. The continuum damage model (CDM) is first established based on continuum damage mechanics with an effective stress range and an effective nonlinear accumulative parameter to represent all of the stress ranges within a daily block of stress time history of the bridge. The CDM is then applied to estimate damage accumulation of the Tsing Ma suspension bridge at fatigue-critical locations, and the results are compared with those estimated by the linear Miner’s model. A limit state function for fatigue reliability analysis based on CDM is also defined by introducing proper random variables into CDM. The Monte Carlo simulation (MCS) is then adopted to generate the random variables and to calculate failure probability. Finally, the failure probabilities of the Tsing Ma Bridge at the end of 120years are estimated for different loading scenarios. The results demonstrate that the fatigue condition of the Tsing Ma Bridge at the end of its design life depends on loading scenarios.