Pairs Of Sidebands Research Articles

Hydrodynamic modulation instability triggered by a two-wave system.

The modulation instability (MI) is responsible for the disintegration of a regular nonlinear wave train and can lead to strong localizations in the form of rogue waves. This mechanism has been studied in a variety of nonlinear dispersive media, such as hydrodynamics, optics, plasma, mechanical systems, electric transmission lines, and Bose-Einstein condensates, while its impact on applied sciences is steadily growing. It is well-known that the classical MI dynamics can be triggered when a pair of small-amplitude sidebands are excited within a particular frequency range around the main peak frequency. That is, a three-wave system, consisting of the carrier wave together with a pair of unstable sidebands, is usually adopted to initiate the wave focusing process in a numerical or laboratory experiment. Breather solutions of the nonlinear Schrödinger equation (NLSE) revealed that MI can generate much more complex localized structures, beyond the three-wave system initialization approach or by means of a continuous spectrum. In this work, we report an experimental study for deep-water surface gravity waves asserting that a MI process can be triggered by a single unstable sideband only, and thus, initialized from a two-wave process when including the contribution of the peak frequency. The experimental data are validated against fully nonlinear hydrodynamic numerical wave tank simulations and show very good agreement. The long-term evolution of such unstable wave trains shows a distinct shift in the recurrent Fermi-Pasta-Ulam-Tsingou focusing cycles, which are captured by the NLSE and fully nonlinear hydrodynamic simulations with some distinctions.

Helical Gearbox Defect Detection with Machine Learning Using Regular Mesh Components and Sidebands.

The current paper presents helical gearbox defect detection models built from raw vibration signals measured using a triaxial accelerometer. Gear faults, such as localized pitting, localized wear on helical pinion tooth flanks, and low lubricant level, are under observation for three rotating velocities of the actuator and three load levels at the speed reducer output. The emphasis is on the strong connection between the gear faults and the fundamental meshing frequency GMF, its harmonics, and the sidebands found in the vibration spectrum as an effect of the amplitude modulation (AM) and phase modulation (PM). Several sets of features representing powers on selected frequency bands or/and associated peak amplitudes from the vibration spectrum, and also, for comparison, time-domain and frequency-domain statistical feature sets, are proposed as predictors in the defect detection task. The best performing detection model, with a testing accuracy of 99.73%, is based on SVM (Support Vector Machine) with a cubic kernel, and the features used are the band powers associated with six GMF harmonics and two sideband pairs for all three accelerometer axes, regardless of the rotation velocities and the load levels.

Higher-order modulation instability and multi-Akhmediev breathers of Manakov equations: Frequency jumps over the stable gaps between the instability bands

We study higher-order modulation instability phenomena in the frame of Manakov equations. Evolution that starts with a single pair of sidebands expands over several higher harmonics. The choice of initial pair of sidebands influences the structure of unstable frequency components and changes drastically the wave evolution, leading, in some cases, to jumps across spectral components within the discrete spectrum. This complex dynamics includes several growth-decay cycles of evolution. We show this using numerical simulations of the modulation instability process and confirm the results using the exact multi-Akhmediev breather solutions. Detailed explanations of the observed phenomena are given.

A new angle-domain cepstral method for generalised gear diagnostics under constant and variable speed operation

This paper proposes a gear diagnostic method denoted as the angle cepstrum comb liftering (ACCL) method. It uses comb liftering in the cepstrum of the order tracked acceleration signal to select all rahmonics of the gearmesh quefrency of a particular meshing gear pair. When converted to the equivalent log spectrum, it thus contains only the harmonics of both gear speeds, and in particular the gearmesh harmonics. The spectrum could thus be adjusted to be periodic at the gearmesh frequency. This implies that the technique not only removes dynamic transfer function effects, independently of speed, but also the (purely static) “mesh transfer functions” (MTFs), defined in Mark’s classic papers on gear vibrations, to give a forcing function very closely related to the combined elemental transmission error (TE) components, both geometric and due to elastic deflections. The paper first develops the method, including the theoretical basis for the removal of the transfer functions, and important practical considerations. The method is then applied to several sets of data corresponding to a range of different faults in gear pairs, including tooth root cracks, and pitting due to surface failure. It was found that Mark’s ALR (average log ratio) method, applied to the cepstrally edited signal, was a natural and appropriate way to evaluate the results, and track fault development. By combining the modified amplitude spectrum with the response phase spectrum, the newly proposed method also allows extraction of angular-domain waveforms similar to the classic TSA (time synchronous average) for each gear, and also the residual signal obtained by removing gearmesh harmonics and one or two pairs of sidebands around them. These are however “closer to the source”, without resonant response effects, and thus not dependent on the operating conditions. The newly proposed approach was found to give similar results for different speeds, and even speed variations up to ±20%, making it a very powerful generalised diagnostic tool. When combined with the original ALR approach, the method is particularly effective for local faults, such as tooth root cracks and presumably large localised spalls, but also for uniformly distributed pitting. In the latter case, it was possible to find parameters that correlate well with indicators of pitting severity, as measured from direct observations of the tooth surface topography. One gear diagnostic technique excluded by this approach is that based on resonant responses to sharp impacts (similar to bearing fault diagnosis), which has been found in some cases to give earlier warning of incipient cracks, for which a different approach would be required. Another is uniform abrasive wear of profiles, but this can often be easily diagnosed by changes in gearmesh harmonics and close sidebands, for which the proposed approach might also be found useful.

Entangled sideband control scheme via frequency-comb-type seed beam.

We report a control scheme of entangled sideband modes without coherent amplitude by employing a frequency-comb-type seed beam. In this scheme, each tooth of the frequency comb serves as a control field for the corresponding downconversion mode. Consequently, all the degrees of freedom can be actively controlled, and the entanglement degrees are higher than 6.7 dB for two pairs of sidebands. We believe that this scheme provides a simple solution for the control of sideband modes, which could be further applied to achieve compact channel multiplexing quantum communications.

Dual-Wavelength Light Source Assisted Frequency Response Measurement Method of Photodetectors

Dual-wavelength light source assisted frequency response measurement of photodetectors based on double-sideband suppressed-carrier modulation is proposed in this letter. In this method, a directly modulated laser with a modulation frequency of f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> combined with an optical tunable filter is used to generate a dual-wavelength carrier, which can be highly stable since only one light source is introduced. The dual-wavelength carrier generates two pairs of first-order sidebands under double-sideband suppressed-carrier modulation of the Mach-Zehnder modulator at frequency f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> . Afterwards, the modulated signal is injected into the photodetector under test, and the frequency response of the photodetector can be extracted by recording the electric power at specific frequencies. Based on this method, we used a 35-GHz modulator to measure the frequency response of photodetectors with bandwidth of 15 GHz and 43.5 GHz respectively. Moreover, a comparison of the results is performed between our method, the swept frequency method, and electro-absorption modulator deduction method. The results show that the new method extends the frequency response measurement range from f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> to f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> +2f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> , and the influence of the modulator on the frequency response measurement results is reduced simultaneously.

Finesse and four-wave mixing in microresonators

We elaborate a comprehensive theory of the sharp variations of the four-wave-mixing (FWM) threshold happening with the tuning of the pump frequency along the dispersive tails of the nonlinear resonance in the driven Kerr microresonators with high finesses and high finesse dispersions. Our theory leads to the explicit estimates for the difference in the pump powers required for the excitation of one sideband pair with momenta $\pm\mu$, and for the simultaneous excitation of the two neighbouring pairs with momenta $\pm\mu$, $\pm(\mu+1)$. This power difference also measures the depth of the Arnold tongues in the pump-frequency and pump-power parameter space, associated with the aforementioned power variations. A set of select pump frequencies and powers, where the instabilities of the two sideband pairs come first, forms the threshold of complexity, which is followed by a sequence of conditions specifying critical powers for the simultaneous instabilities of three, four and so on pairs. We formally link finesse dispersion and the density of states notion borrowed from the condensed matter context and report a value of the finesse dispersion and a critical mode number signalling the transition from the low- to the high-contrast tongue structure. We also demonstrate that the large finesse dispersion makes possible a surprising for the multimode resonators regime of the bistability without FWM.

Threshold of complexity and Arnold tongues in Kerr-ring microresonators

We show that the threshold condition for two pump photons to convert into a pair of the sideband ones in Kerr microresonators with high-quality factors breaks the pump laser parameter space into a sequence of narrow in frequency and broad in power Arnold tongues. Instability tongues become a dominant feature in resonators with the finesse dispersion parameter close to and above one. As pump power is increased, the tongues expand and cross by forming a line of cusps, i.e., the threshold of complexity, where more sideband pairs become unstable. We elaborate theory for the tongues and threshold of complexity, and report the synchronisation and frequency-domain symmetry breaking effects inside the tongues.

Correlation between geometric parametric instability sidebands in graded-index multimode fibers.

The spectral analysis of the light propagating in normally dispersive graded-index multimode fibers is performed under initial noisy conditions. Based on the obtained spectra with multiple simulations in the presence of noise, we investigate the correlation in energy between the well-separated spectral sidebands through both the scattergrams and the frequency-dependent energy correlation map and find that conjugate couples are highly correlated while cross-combinations exhibit a very poor degree of correlation. These results reveal that the geometric parametric instability processes associated with each sideband pair occur independently from each other, which can provide significant insights into the fundamental dynamical effect of the geometric parametric instability and facilitate the future implementation of high-efficiency photon pair sources with reduced Raman decorrelations.

A Study on Asymmetry of Electromagnetic Force Modes of Permanent Magnet Synchronous Motors With Rotor Eccentricity

This article deals with electromagnetic forces of permanent magnet synchronous motors (PMSMs) with inclined and parallel rotor eccentricity. The electromagnetic forces have the spatial orders of the main components (multiples of pole numbers) and the sideband components when the rotor is eccentric. Although other studies have reported that each amplitude of an upper and a lower sideband is different, the causes of the asymmetry have not been fully investigated. The rotor eccentricity leads to changes in the gap permeance, the working point of the rotor magnets, and the distribution of gap magnetic flux density. By considering these effects in detail, we develop a new analytical expression of electromagnetic force, which expresses the asymmetry of a pairs of sidebands. The expression is compared with 3-D magnetic field analyses of PMSMs with inclined and parallel rotor eccentricity. As a result, it is found that upper sideband amplitudes are larger than lower sideband amplitudes, and the ratio of an upper sideband to the lower sideband of parallel eccentricity is larger than that of inclined eccentricity.

Modulation instability induced by cross-phase modulation of transient stimulated Raman scattering and self-phase modulation in calcite.

Pairs of sidebands about the transient stimulated Raman scattering (SRS) 1086cm-1 vibration mode peak are observed for calcite under 517 nm 390 fs pulse excitation. These pairs of side frequency lobes arise from modulation instability (MI) from the interaction of cross-phase modulation (XPM) from self-phase modulation (SPM) and SRS. The pairs of secondary frequencies are attributed to the daughter 1086cm-1 decay product modes from the multiphonon of 3, 4, and 5 decays. The main sideband peak from 1086cm-1 phonon at 546cm-1 suggests the operation of the Orbach effect.

Nonlinear evolution of bichromatic waves based on the fifth order solution of benjamin bona mahony equation

This research concerns on the influence of higher order solution to nonlinear evolution of bichromatic waves based on Benjamin Bona Mahony (BBM) equation. Asymptotic method was applied to determine the solution expanded to the fifth order. In previous researches, this method was applied on the same equation to find its solution up to the third order and it was obtained that the waves underwent deformation and amplitude amplification affected by the occurrence of a pair of side bands during their propagation. In this study, the effect of the higher order solution on the increasing amplitude was observed. A quantity called as Maximal Temporal Amplitude (MTA) was measured to find the maximum position where the highest amplitude occurred and the Amplitude Amplification Factor (AAF). MTA gives information about the waves’ highest elevation at every spatial position during the observation time. The analysis includes comparison between the third and fifth order solutions in their contribution to the rise of the amplitude and the maximum position.

High-Resolution Range and Velocity Measurement Based on Photonic LFM Microwave Signal Generation and Detection

A microwave photonic approach is proposed to achieve a high resolution enhanced by a factor of 2 for the range and velocity measurement. In the transmitter, a V-shaped linear-frequency-modulated (LFM) microwave signal is generated through the frequency doubling enabled by photonics, with large time-bandwidth product for improving the range resolution, whereas in the receiver, the round-trip duration and Doppler frequency shift (DFS) between the transmitted LFM signal and the received echo signal are mapped into two doubled frequency spacings between two pairs of target sidebands by incorporating two cascaded electrooptic modulators. Thus, the distance and velocity of the moving target can be measured from the beat note of the target sidebands, showing a high resolution improved by a factor of 2. Experiments have been implemented and demonstrated in X-band with a bandwidth of 2 GHz. The distance measurement indicates an absolute error less than 3 mm. In addition, the performance of the proposed system in terms of low power level is discussed.

Fibre multi-wave mixing combs reveal the broken symmetry of Fermi–Pasta–Ulam recurrence

In optical fibres, weak modulations can grow at the expense of a strong pump to form a triangular comb of sideband pairs, until the process is reversed. Repeated cycles of such conversion and back-conversion constitute a manifestation of the universal nonlinear phenomenon known as Fermi–Pasta–Ulam recurrence. However, it remains a major challenge to observe the coexistence of different types of recurrences owing to the spontaneous symmetry-breaking nature of such a phenomenon. Here, we implement a novel non-destructive technique that allows the evolution in amplitude and phase of frequency modes to be reconstructed via post-processing of the fibre backscattered light. We clearly observe how control of the input modulation seed results in different recursive behaviours emerging from the phase-space structure dictated by the spontaneously broken symmetry. The proposed technique is an important tool to characterize other mixing processes and new regimes of rogue-wave formation and wave turbulence in fibre optics.

Modulation instability in dispersion oscillating fibers

In this review we present recent theoretical and experimental progress on modulation instability and parametric amplification processes in dispersion oscillating fibers. These optical fibers are characterized by longitudinal periodic variations of their outer diameter engineered over the meter-long scale, which provides an additional degree of freedom to the system and leads to the generation of multiple MI sideband pairs. The main results published in single-pass configurations and in passive cavities are summarized in this review.

The SuperWASP catalogue of 4963 RR Lyr stars: identification of 983 Blazhko effect candidates

We set out to compile a catalogue of RRab pulsating variables in the SuperWASP archive and identify candidate Blazhko effect objects within this catalogue. We analysed their light curves and power spectra for correlations in their common characteristics to further our understanding of the phenomenon. Pulsation periods were found for each SWASP RRab object using PDM techniques. Low frequency periodic signals detected in the CLEAN power spectra of RRab stars were matched with modulation sidebands and combined with pairs of sidebands to produce a list of candidate Blazhko periods. A novel technique was used in an attempt to identify Blazhko effect stars by comparing scatter at different parts of the folded light curve. Pulsation amplitudes were calculated based on phase folded light curves. The SuperWASP RRab catalogue consists of 4963 objects of which 3397 are previously unknown. We discovered 983 distinct candidates for Blazhko effect objects, 613 of these being previously unknown in the literature as RR Lyrae stars, and 894 are previously unknown to be Blazhko effect stars. Correlations were investigated between the scatter of points on the light curve, the periods and amplitudes of the objects' pulsations, and those of the Blazhko effect. A statistical analysis has been performed on a large population of Blazhko effect stars from the wide-field SuperWASP survey. No correlations were found between the Blazhko period and other parameters including the Blazhko amplitude, although we confirmed a lower rate of occurrence of the Blazhko effect in long pulsation period objects.

Simultaneous transmission of wired and wireless signals based on double sideband carrier suppression

Abstract In this paper, we proposed and experimentally demonstrated simultaneous transmission of wired and wireless signals based on double sideband optical carrier suppression. By properly adjusting the bias point of the dual-output mach-zehnder modulator (MZM), a central carrier in one output port and a pair of first-order sidebands in another output port are generated. The pair of first-order sidebands are fed into a second MZM to generate second-order order sidebands. A wired signal is embedded on the central carrier while a wireless signal is embedded on the second-order sidebands. Unlike other schemes, we did not use optical filter to separate the carrier from the optical sidebands. The measured bit error rate (BER) and eye-diagrams after a 25 km single-mode-fiber (SMF) transmission proved that the proposed scheme is successful for both wired and wireless signals transmission. Moreover, the power penalty at the BER of 10−9 is 0.3 and 0.7 dB for wired and wireless signals, respectively.

Experiments on higher-order and degenerate Akhmediev breather-type rogue water waves

A possible mechanism that is responsible for the occurrence of rogue waves in the ocean is the Benjamin–Feir instability or modulation instability. The deterministic framework that describes this latter instability of Stokes waves in deep water is provided by the family of Akhmediev breather (AB) solutions of the nonlinear Schrödinger equation (NLS). It is indeed very convenient to use these exact pulsating envelopes particularly for laboratory experiments, since they allow to generate extreme waves at any location in space at any instant of time. As such, using this framework is more advantageous compared to the classical initialization of the unstable wave dynamics from a three wave system (main wave frequency and one pair of unstable sidebands). In this work, we report an experimental study on higher-order AB hydrodynamics that describe a higher-order stage of modulation instability, namely, starting from five wave systems (main wave frequency and two pairs of unstable sidebands). The corresponding laboratory experiments, that have been conducted in a large water wave facility, confirm the NLS wave dynamics forecast while boundary element method-based numerical wave tank simulations show a very good agreement with the experimental data.

Nonconservative higher-order hydrodynamic modulation instability.

The modulation instability (MI) is a universal mechanism that is responsible for the disintegration of weakly nonlinear narrow-banded wave fields and the emergence of localized extreme events in dispersive media. The instability dynamics is naturally triggered, when unstable energy sidebands located around the main energy peak are excited and then follow an exponential growth law. As a consequence of four wave mixing effect, these primary sidebands generate an infinite number of additional sidebands, forming a triangular sideband cascade. After saturation, it is expected that the system experiences a return to initial conditions followed by a spectral recurrence dynamics. Much complex nonlinear wave field motion is expected, when the secondary or successive sideband pair that is created is also located in the finite instability gain range around the main carrier frequency peak. This latter process is referred to as higher-order MI. We report a numerical and experimental study that confirms observation of higher-order MI dynamics in water waves. Furthermore, we show that the presence of weak dissipation may counterintuitively enhance wave focusing in the second recurrent cycle of wave amplification. The interdisciplinary weakly nonlinear approach in addressing the evolution of unstable nonlinear waves dynamics may find significant resonance in other nonlinear dispersive media in physics, such as optics, solids, superfluids, and plasma.

Broadband optical parametric amplifier formed by two pairs of adjacent four-wave mixing sidebands in a tellurite microstructured optical fibre

A broadband fibre-optical parametric amplifier (FOPA) operating at a novel wavelength region that is far from the pump wavelength has been demonstrated by exploiting two pairs of adjacent four-wave mixing (FWM) sidebands generated simultaneously in a tellurite microstructured optical fibre (TMOF). Owing to the large nonlinearity of the TMOF and the high pump peak power provided by a picosecond laser, a maximal average gain of 65.1 dB has been obtained. When the FOPA is operated in a saturated state, a flat-gain amplification from 1424 nm to 1459 nm can be achieved. This broadband and high-gain FOPA operating at new wavelength regions far from the pump offers the prospect of all-optical signal processing.