Stokes Wave Research Articles

2nd-order random lasing in a multimode diode-pumped graded-index fiber

Raman lasing in a graded-index fiber (GIF) attracts now great deal of attention due to the opportunity to convert high-power multimode laser diode radiation into the Stokes wave with beam quality improvement based on the Raman clean-up effect. Here we report on the cascaded Raman generation of the 2nd Stokes order in the 1.1-km long GIF with 100-μm core directly pumped by 915-nm diodes. In the studied all-fiber scheme, the 1st Stokes order is generated at 950–954 nm in a linear cavity formed at GIF ends by two fiber Bragg gratings (FBGs) securing beam quality improvement from M2 ≈ 30 to M2 ≈ 2.3 due to special transverse structure of FBGs. The 2nd Stokes wave is generated either in linear (two FBGs) or half-open (one FBG) cavity with random distributed feedback via Rayleigh backscattering. Their comparison shows that the random lasing provides better beam quality and higher slope efficiency. Nearly diffraction limited beam (M2 ≈ 1.6) with power up to 27 W at maximum gain (996 nm), and 17 W at the detuned wavelength of 978 nm has been obtained, thus demonstrating that the 2nd-order random lasing in diode-pumped GIF with FBGs provides high-efficiency high-quality beam generation in a broad wavelength range within the Raman gain spectral profile.

Characteristics of noise-like pulse with broad bandwidth based on cascaded Raman scattering.

A noise-like pulse (NLP) with broadband emission spectrum and superior beam quality from a dispersion managed mode-locked Yb-doped fiber laser has been demonstrated based on stimulated Raman scattering. After insertion of a 150 m long single mode fiber into the laser cavity, the second order stoke wave from 1.3 MHz repetition rate of NLP can be excited. With a 320 mW pump power, the highest pulse energy of NLP was about 35.1 nJ and the emission spectrum was extended from 1000 to 1160 nm. Through a multi-mode fiber laser, the broad bandwidth NLP can produce relatively low speckle noise imaging with contrast below 0.04. The generated NLPs can be used as a superior light source for the biomedical diagnosis and laser projection in the near future.

Enhanced flatness of 20 GHz channel spacing multiwavelength Brillouin-Raman fiber laser with sub-millimeter air gap.

We discover the technique of controlling the flatness in signal amplitude of a multiwavelength Brillouin-Raman fiber laser by employing an air-gap outside of the cavity. The structure that is adjustable within sub-millimeter length behaves as flexible optical feedback that provides modifiable portions of multiple Fresnel reflectivities. This is the main benchmark that allows the efficient management of gain competition between self-lasing modes and Brillouin Stokes waves that is vital for self-flattening initiation. When setting the Brillouin pump wavelength at 1529 nm and the air-gap distance to 0.4 mm, 296 Stokes lines are produced with a channel spacing of 0.158 nm. The lasing bandwidth is 46.60 nm that covers from 1529.16 to 1575.76 nm wavelength. In this case at Raman power of 950 mW, the intense Brillouin pump power of 2 dBm saturates the cascaded higher-orders lasing lines. As a result, the overall peak power discrepancy is maintained at just 1.8 dB where an average optical-signal-to-noise ratio of 20 dB is realized. To date, this is the widest bandwidth with the flattest spectrum attained in multiwavelength fiber lasers that incorporate a single Raman pump unit.

On the fully nonlinear water entry of a cone in Stokes wave

Motivated by the wave entry problems of the three-dimensional (3D) ship bow, the paper concentrates on the interaction between an incident wave and a falling cone. The nonlinear 5th order Stokes wave is used to model the undisturbed fluid field, and the wave disturbed by the falling cone satisfies the fully nonlinear boundary conditions. The numerical model is calculated by boundary element method. During the numerical procedure, stretched coordinated system and improved Eulerian method are adopted to trace the highly distorted wave surface. Water entry with different wave heights has been compared with calm water case, oblique entry has been simulated, and the flow behaviors on the up-wave, down-wave and lateral side of the body are investigated. The relative deadrise angle, the relative velocity between body and fluid particles, the propagation direction of the wave as well as the non-uniform distribution of flow velocity are considered together to investigate the 3D pressure field.

Investigation on four-wave mixing toward mid-infrared waveband in tellurite photonic crystal fiber

The evolution characteristics of the degenerate four-wave mixing (DFWM) effect in the proposed tellurite photonic crystal fiber (PCF) are investigated systematically. The influence of the pitch distance and diameter-to-pitch ratio on the phase-matching condition is analyzed numerically. The effects of fiber length, signal wavelength, idler wavelength, initial pump power and initial signal power on the signal gain and idler conversion efficiency are investigated. Based on the DFWM occurring in the proposed tellurite PCF, the signal (anti-Stokes) wave is efficiently amplified and the idler (Stokes) wave is efficiently generated at the mid-infrared (mid-IR) waveband with the pump wavelength of 1.553 μm. The signal gain can be increased by increasing the initial pump power. The idler conversion efficiency can reach ~ 26%. The simulated results will be instructive for the experimental FWM process to generate mid-IR optical parametric oscillators.

Stokes 파 중의 바지형 부유체의 굽힘강성변화에 따른 유탄성 응답 해석

Stokes waves representing the deep sea waves are expressed as superposition of several linear waves. To evaluate the motions of floating bodies in the deep seas, it is necessary to evaluate the motions of the bodies in the Stokes waves. The fifth-order Stokes waves are expressed as superposition of five linear waves. Therefore, the motion responses of the bodies in the Stokes waves would be expressed as superposition of the motion responses of the bodies in each linear wave. In this research, the experimental results were compared with the numerical results in linear waves and Stokes waves.

Energy scaling and extended tunability of a ring cavity terahertz parametric oscillator based on KTiOPO4 crystal**Project supported by the National Basic Research Program of China (Grant Nos. 2015CB755403 and 2014CB339802), the National Key Research and Development Program of China (Grant No. 2016YFC0101001), the National Natural Science Foundation of China (Grant Nos. 61775160, 61771332, and 61471257), China Postdoctoral Science Foundation (Grant

A wide terahertz tuning range from 0.96 THz to 7.01 THz has been demonstrated based on ring-cavity THz wave parametric oscillator with a KTiOPO4 (KTP) crystal. The tuning range was observed intermittently from 0.96 THz to 1.87 THz, from 3.04 THz to 3.33 THz, from 4.17 THz to 4.48 THz, from 4.78 THz to 4.97 THz, from 5.125 THz to 5.168 THz, from 5.44 THz to 5.97 THz, and from 6.74 THz to 7.01 THz. The dual-Stokes wavelengths resonance phenomena were observed in some certain tuning angle ranges. Through the theoretical analysis of the dispersion curve of the KTP crystal, the intermittent THz wave tuning range and dual-wavelength Stokes waves operation during angle tuning process were explained. The theoretical analysis was in good agreement with the experiment results. The maximum THz output voltage detected by Golay cell was 1.7 V at 5.7 THz under the pump energy of 210 mJ, corresponding to the THz wave output energy of 5.47 μJ and conversion efficiency of 2.6 × 10−5.

Modulational instability in a full‐dispersion shallow water model

AbstractWe propose a shallow water model that combines the dispersion relation of water waves and Boussinesq equations, and that extends the Whitham equation to permit bidirectional propagation. We show that its sufficiently small and periodic traveling wave is spectrally unstable to long wavelength perturbations if the wave number is greater than a critical value, like the Benjamin‐Feir instability of a Stokes wave. We verify that the associated linear operator possesses infinitely many collisions of purely imaginary eigenvalues, but they do not contribute to instability to the leading order in the amplitude parameter. We discuss the effects of surface tension. The results agree with those from a formal asymptotic expansion and a numerical computation for the physical problem.

RETRACTED ARTICLE:Experimental Study on Crescent Waves Diffracted by A Circular Cylinder

Crescent waves often observed on the sea surface are unusual wave pattern induced by the instability of Stokes wave. The paper presents the experimental results of the wave field around a circular cylinder generated by the diffraction of crescent wave in order to examine the difference of diffracted crescent waves from the commonly-used diffracted Stokes waves. The results show that with the existence of the cylinder, the crescent wave pattern can still get fully developed, and with the presence of this type of wave pattern, the symmetry breaking of the wave amplitude distribution occurs and there are extra wave components at the frequencies of 0.5ω0, 1.5ω0 and 2.5ω0 (ω0 is the frequency of Stokes waves) appearing in the wave amplitude spectrum.

Efficient mid-infrared cascade Raman source in methane-filled hollow-core fibers operating at 2.8 μm.

We report here for the first time, to the best of our knowledge, a novel and efficient cascade Raman laser source operating at 2.8μm by two stages of methane-filled hollow-core fibers (HCFs). In the first stage, a commercial 1064.6nm laser is used as the pump source, and an efficient first-order Stokes wave of 1543.9nm is obtained with a quantum conversion efficiency of ∼87% in 2m ice-cream HCF filled with 2bar methane gas. In the second stage, efficient 2.8μm laser emission is also generated by the first-order stimulated Raman scattering of methane, while the pump source is the Stokes wave at 1543.9nm. A maximum quantum conversion efficiency of ∼75% is obtained with 2.2m node-less HCF filled with 11bar methane gas, resulting in a record total quantum efficiency of ∼65%, which is 1.6 times the previous similar result. This work provides a significant efficient method to obtain a wide wavelength range of mid-infrared, even far-infrared fiber laser sources from conveniently available 1μm band lasers with proper HCFs and different active gases.

Compact passively Q-switched RbTiOPO4 cascaded Raman operation.

Compact passively Q-switched RbTiOPO4 cascaded Raman laser operation has been investigated for the first time, to our knowledge. A Nd:YAG/Cr4+:YAG composite crystal was adopted for passively Q-switched fundamental laser generation. 440mW multi-Stokes laser output with X(ZZ)X configuration according to the Porto notations was achieved under the incident pump power of 10W. The measured spectra contained three wavelengths of 1149, 1165, and 1185nm based on the Raman shift of 271 and 687 cm-1. Different from actively Q-switch cascaded Raman laser with Stokes wave from low order to high order oscillating in sequence, three intensity lines were output for the whole experiment in this passively Q-switched multi-Stokes laser. The output spectra could be varied and optimized based on the output coupler coating design. Output spectra not sensitive to incident pump power for passively Q-switched cascaded Raman laser have advantages in multiwavelength laser applications.

Simultaneous Generation of Two Pairs of Stokes and Terahertz Waves from Coupled Optical Parametric Oscillations with Quasi-Phase-Matching

We present a theoretical investigation on simultaneous generation of two pairs of Stokes and terahertz (THz) waves from coupled optical parametric oscillations (OPOs) with a quasi-phase-matching (QPM) scheme. The two pairs of Stokes and THz waves are generated by stimulated polariton scattering (SPS) from periodically-inverted GaP. By analyzing the QPM conditions of coupled OPOs we find that the two THz waves with any frequency below the transverse optical (TO) mode frequency of GaP can be simultaneously generated with a suitable pump wavelength. We calculate the photon flux densities of the two THz waves by solving the coupled wave equations. The calculation results indicate that the two THz waves can be efficiently generated with high pump intensities, particularly in lower THz frequency band.

Dispersive shock waves governed by the Whitham equation and their stability

Dispersive shock waves (DSWs), also termed undular bores in fluid mechanics, governed by the non-local Whitham equation are studied in order to investigate short wavelength effects that lead to peaked and cusped waves within the DSW. This is done by combining the weak nonlinearity of the Korteweg–de Vries equation with full linear dispersion relations. The dispersion relations considered are those for surface gravity waves, the intermediate long wave equation and a model dispersion relation introduced by Whitham to investigate the 120° peaked Stokes wave of highest amplitude. A dispersive shock fitting method is used to find the leading (solitary wave) and trailing (linear wave) edges of the DSW. This method is found to produce results in excellent agreement with numerical solutions up until the lead solitary wave of the DSW reaches its highest amplitude. Numerical solutions show that the DSWs for the water wave and Whitham peaking kernels become modulationally unstable and evolve into multi-phase wavetrains after a critical amplitude which is just below the DSW of maximum amplitude.

Laboratory and numerical experiments on stem waves due to monochromatic waves along a vertical wall

Abstract. In this study, both laboratory and numerical experiments are conducted to investigate stem waves propagating along a vertical wall developed by the incidence of monochromatic waves. The results show the following features: for small-amplitude waves, the wave heights along the wall show a slowly varying undulation. Normalized wave heights perpendicular to the wall show a standing wave pattern. The overall wave pattern in the case of small-amplitude waves shows a typical diffraction pattern around a semi-infinite thin breakwater. As the amplitude of incident waves increases, both the undulation intensity and the asymptotic normalized wave height decrease along the wall. For larger-amplitude waves with smaller angle of incidence, the measured data clearly show stem waves. Numerical simulation results are in good agreement with the results of laboratory experiments. The results of present experiments favorably support the existence and the properties of stem waves found by other researchers using numerical simulations. The characteristics of the stem waves generated by the incidence of monochromatic Stokes waves are compared with those of the Mach stem of solitary waves.

High-Efficiency, High Peak-Power, Narrow Linewidth 1.9 μm Fiber Gas Raman Amplifier

We reported here a high-efficiency, high peak-power, narrow linewidth 1.9 μ m fiber gas Raman amplifier based on stimulated Raman scattering (SRS) in an H2-filled antiresonance hollow-core fiber. A CW seed fiber laser near 1908 nm is amplified by the first vibrational Stokes wave of hydrogen molecules while pumping with a pulsed 1064 nm microchip laser. The seed laser significantly enhances the vibrational SRS and suppresses the rotational SRS, resulting in a record optical-to-optical conversion efficiency of ∼41% (quantum efficiency ∼73.5%) for such H2 vibrational Raman experiments in hollow-core fibers, with 1.4 m fiber and only 3 bar H2, which is more preferable in applications. The maximum average Stokes power of 74.2 mW and the peak power of ∼150 kW with the linewidth about 1 GHz (∼12 pm) are obtained. The linewidth characteristics of such fiber gas Raman laser sources are systematically studied for the first time by experimental methods. This paper provides an effective method to obtain efficient 1.9 μ m fiber sources of both high peak power and narrow linewidth.

Analysis of Different Methods for Wave Generation and Absorption in a CFD-Based Numerical Wave Tank

In this paper, the performance of different wave generation and absorption methods in computational fluid dynamics (CFD)-based numerical wave tanks (NWTs) is analyzed. The open-source CFD code REEF3D is used, which solves the Reynolds-averaged Navier–Stokes (RANS) equations to simulate two-phase flow problems. The water surface is computed with the level set method (LSM), and turbulence is modeled with the k-ω model. The NWT includes different methods to generate and absorb waves: the relaxation method, the Dirichlet-type method and active wave absorption. A sensitivity analysis has been conducted in order to quantify and compare the differences in terms of absorption quality between these methods. A reflection analysis based on an arbitrary number of wave gauges has been adopted to conduct the study. Tests include reflection analysis of linear, second- and fifth-order Stokes waves, solitary waves, cnoidal waves and irregular waves generated in an NWT. Wave breaking over a sloping bed and wave forces on a vertical cylinder are calculated, and the influence of the reflections on the wave breaking location and the wave forces on the cylinder is investigated. In addition, a comparison with another open-source CFD code, OpenFOAM, has been carried out based on published results. Some differences in the calculated quantities depending on the wave generation and absorption method have been observed. The active wave absorption method is seen to be more efficient for long waves, whereas the relaxation method performs better for shorter waves. The relaxation method-based numerical beach generally results in lower reflected waves in the wave tank for most of the cases simulated in this study. The comparably better performance of the relaxation method comes at the cost of larger computational requirements due to the relaxation zones that have to be included in the domain. The reflections in the NWT in REEF3D are generally lower than the published results for reflections using the active wave absorption method in the NWT based on OpenFOAM.

Analysis of Subaerial Landslide Data Using Nonlinear Fourier Transform Based on Korteweg-deVries Equation (KdV-NLFT)

Subaerial and underwater landslides, rock falls and glacier calvings can generate impulse waves in lakes, fjords and the open sea. Experiments with subaerial landslides have shown that, depending on the slide characteristics, different wave types (Stokes, cnoidal or bore-like waves) are generated. Each of these wave types shows different wave height decay with increasing distance from the impact position. Furthermore, in very shallow water, the first impulse wave shows characteristic properties of a solitary wave. The nonlinear Fourier transform based on the Korteweg–deVries equation (KdV-NLFT) is a frequency-domain analysis method that decomposes shallow-water free-surface data into nonlinear cnoidal waves instead of linear sinusoidal waves. This method explicitly identifies solitons as spectral components within the given data. In this study, we apply the KdV-NLFT for the very first time to available 2D and 3D landslide-test data. The objective of the nonlinear decomposition is to identify the hidden nonlinear spectral structure of the impulse waves, including solitons. Furthermore, we analyze the determined solitons at different downstream positions from the impact point with respect to soliton propagation and modification. Finally, we draw conclusions for the prediction of the expected landslide-generated downstream solitons in the far-field.

Modulational Instability and Rogue Waves in Crossing Sea States

AbstractWave statistical properties and occurrence of extreme and rogue waves in crossing sea states are investigated. Compared to previous studies a more extensive set of crossing sea states are investigated, both with respect to spectral shape of the individual wave systems and with respect to the crossing angle and separation in peak frequency of the two wave systems. It is shown that, because of the effects described by Piterbarg, for a linear sea state the expected maximum crest elevation over a given surface area depends on the crossing angle so that the expected maximum crest elevation is largest when two wave systems propagate with a crossing angle close to 90°. It is further shown by nonlinear phase-resolving numerical simulations that nonlinear effects have an opposite effect, such that maximum sea surface kurtosis is expected for relatively large and small crossing angles, with a minimum around 90°, and that the expected maximum crest height is almost independent of the crossing angle. The numerical results are accompanied by analysis of the modulational instability of two crossing Stokes waves, which is studied using the Zakharov equation so that, different from previous studies, results are valid for arbitrary-bandwidth perturbations. It is shown that there is a positive correlation between the value of kurtosis in the numerical simulations and the maximum unstable growth rate of two crossing Stokes waves, even for realistic broadband crossing sea states.

On the incomplete recurrence of modulationally unstable deep-water surface gravity waves

The issue of a recurrence of modulationally unstable water wave trains within the framework of the fully nonlinear potential Euler equations is addressed. It is examined, in particular, if a modulation, which appears from nowhere (i.e., is infinitesimal initially) and generates a rogue wave, can disappear with no trace. If so, this wave solution would be a breather solution of the primitive hydrodynamic equations. It is shown with the help of the fully nonlinear numerical simulation that when a rogue wave emerges from a uniform Stokes wave train, it excites other waves which have different lengths. This process prevents the complete recurrence and, eventually, results in a quasi-periodic breathing of the wave envelope. Meanwhile the discovered effects are rather small in magnitude, and the period of the modulation breathing may be thousands of the dominant wave periods. Thus, the obtained solution may be called a quasi-breather of the Euler equations.

0.83 W, single-pass, 1.54 μm gas Raman source generated in a CH4-filled hollow-core fiber operating at atmospheric pressure.

We report here the first watt-level efficient single-pass 1.54 μm fiber gas Raman source by methane-filled hollow-core fiber operating at atmospheric pressure. Pumped with a high-power MOPA (master oscillator power amplifier) structure Q-switched 1.06 μm pulsed solid-state laser, efficient 1.54 μm Stokes wave is generated in a single-pass configuration by vibrational stimulated Raman scattering of methane molecules. With an experimentally optimized fiber length of 3.2 m, we get a 1543.9 nm Stokes wave operating at atmospheric pressure with a record average power of ~0.83 W, which is about 12 times higher than the similar experiment previously reported, and the corresponding power conversion efficiency is about 45%. Operating at atmospheric pressure makes it more convenient in future applications.