Higher-order Stokes Lines Research Articles

Three-dimensional capillary waves due to a submerged source with small surface tension

Steady and unsteady linearised flow past a submerged source are studied in the small-surface-tension limit, in the absence of gravitational effects. The free-surface capillary waves generated are exponentially small in the surface tension, and are determined using the theory of exponential asymptotics. In the steady problem, capillary waves are found to extend upstream from the source, switching on across curves on the free surface known as Stokes lines. Asymptotic predictions are compared with computational solutions for the position of the free surface. In the unsteady problem, transient effects cause the solution to display more complicated asymptotic behaviour, such as higher-order Stokes lines. The theory of exponential asymptotics is applied to show how the capillary waves evolve over time, and eventually tend to the steady solution.

Self-Seeded Multiwavelength Dual-Cavity Brillouin-Erbium Fiber Laser

A self-seeded multiwavelength Brillouin-erbium fiber laser (BEFL) is demonstrated in dual-cavity system. The BEFL comprised of two matching ring-cavities of erbium-doped fiber (EDF) lasers combined through sharing of a 25-km-long single-mode fiber (SMF). The self-seeded signal in BEFL is initiated by the oscillating waves generated from EDFs which cause spontaneous scattering and backscattered Stokes wave in the fiber. Stimulated Brillouin scattering (SBS) is established by resonance interaction between backscattered Stokes wave and induced acoustic wave which will then act as Brillouin-pump to excite higher order Stokes lines. The forward propagating lasing signal in one cavity seeds backward Stokes wave in the other cavity and avalanched several higher order Stokes alternately through cooperative SBS and Rayleigh backscattering process in the SMF. High stability and repeatable of more than 67 Stoke lines with 0.088 nm line spacing was produced from 100 mW 980 nm-pump powers. The superimposed free-running oscillating frequencies from the EDF resonators produce stable gain bandwidth of 5.64 nm and it is vital in assisting the generation of multi-Stoke signals.

Experimental and numerical study of high order Stokes lines in Brillouin-erbium fiber laser

We experimentally study the dependences of high-order Stokes lines on the erbium-doped fiber (EDF) pump power PEDF, the Brillouin pump (BP) power PBP, and its working wavelength in a multiwavelength Brillouin erbium-doped fiber laser (MBEFL). By using the rate and propagation equations, and the coupled wave equations of stimulated Brillouin scattering, we establish a lumped model to describe the MBEFL. Numerical simulations show that the number of Stokes lines can be increased by decreasing the spacing between the BP wavelength and the EDF peak gain or PBP as long as it is larger than a critical value PBP(cr)=1.7 mW, or by increasing PEDF without reaching a saturation value PEDF(cr)=250 mW. However, when PBP and PEDF are varied beyond PBP(cr) and PEDF(cr), respectively, the number of Stokes lines is reduced, accompanied by some self-lasing cavity modes. These results by numerical simulation are consistent with experimental observations from the MBEFL.

Enhancing stimulated Raman scattering of benzene high-order Stokes lines by fluorescence of 4-sulfphenyl porphyin in liquid-core optical fiber

Stimulated Raman scattering of benzene is studied in liquid-core fiber. Owing to fluorescence and third-order nonlinear 4-sulfphenyl porphyin, the high-order stimulated Raman scattering, such as sixth-order Stokes line of benzene, can be observed at a relatively low input-laser power. The threshold of high Stokes line is lowered with the addition of the 4-sulfphenyl porphyin when the concentration of solution is within 10-6 and 10-9 mol/L. At the same time, the Stokes line width becomes narrow with Stokes line order increasing. These results are expected to be applied to tunable laser, seeding laser, biological molecular structures and biological molecule used in none biological area.

Stimulated supercontinuum–radiation generation of carbon disulfide by all-trans-β-carotene fluorescence enhancement effect in liquid core optical fibre

We demonstrate stimulated supercontinuum-radiation of carbon disulfide (CS2) influenced by biological molecules all-trans-β-carotene in liquid core optical fibre (LCOF). By virtue of the broad fluorescence characteristics and large third-order optical nonlinearities of all-trans-β-carotene, the high-order Stokes lines of stimulated Raman scattering (SRS) and the multi-order Stokes lines of stimulated Brillouin scattering (SBS) excitated by SRS are observed at low input-laser energies. The results indicate that the fluorescence not only enhances the SRS, but also the SBS. These Stokes lines generate the SRS-SBS supercontinuum radiation (RBSR). A flat-amplitude bandwidth of 110 nm from 515 nm to 625 nm is observed when a frequency-doubled Nd:YAG laser at 532 nm with an energy of 0.86 mJ is used. This result is expected to be useful for the multi-wavelength fibre laser.

Influence of amplified spontaneous emission and fluorescence of β-carotene on stimulated Raman scattering of carbon disulfide

β-carotene with double fluorescence characteristics and large third-order optical nonlinearities, which is dissolved in the carbon disulfide (CS2) as the core medium of a liquid core optical fiber (LCOF), is applied in the study of the CS2 stimulated Raman scattering (SRS). The results of this study show that when the concentrations of solution are more than 3.72×10−7 mol/L, the amplified spontaneous emission (ASE) of β-carotene is the main factor influencing the threshold and intensity of Stokes lines; when the concentrations of solution are lower than 3.72×10−7 mol/L, the ASE disappears and the fluorescence plays the key role: The high-order Stokes lines may be observed at very low input-laser power, and the Stokes thresholds decrease as the solution concentration increases. The result may be widely used in the study of broadband stimulated radiation laser and seeding laser.

Stimulated Raman Stokes scattering influenced by all-trans-β -carotene in liquid-core optical fiber

We demonstrate stimulated Raman Stokes (SRS) scattering of carbon disulfide (CS2) influenced by a natural dye named all-trans-β-carotene in a liquid-core optical fiber (LCOF). These Stokes emissions can acquire the extra effects of seeding or suppression, both of which result from the optical properties of the carotenoids. Then, the efficient control of the selective developments of the Stokes lines by the natural dyes is available in LCOFs. Especially, the low threshold of the high-order Stokes lines, such as the 2nd Stokes line of CS2, can be more easily obtained through the seeding effect. The saturation intensity of the 1st Stokes line can be suppressed more when the concentration of all-trans-β-carotene in CS2 becomes high. Simultaneously, the threshold of the 1st Stokes line increases with the addition of the carotenoids. This result is expected to be worthy of new SRS-based fiber light sources for bio-medicine applications such as photodynamic therapy.

Exponential asymptotics of a fifth-order partial differential equation

We construct an asymptotic representation for the solution plane. The particular equation that we study is chosen in part to highlight the complexities that arise in high-order examples, resulting in particular from the non-existence of a suitable (steady-state) heteroclinic connection. Key points of this calculation are the identification, location and evolution of the active (in the sense that non-zero, though exponentially-small, terms are switched on across them) Stokes lines, and of the higher-order Stokes lines across which these can be activated or inactivated. In doing so, we need in particular to analyse two ‘levels’ of higher-order Stokes lines and to present the associated mechanisms by which they can themselves be activated or inactivated. By piecing together the information concerning which Stokes lines (both ordinary and higher-order) are active, we are able to deduce systematically which of the competing exponentials that can potentially arise within the asymptotic solution are actually present in each region of the complex plane.