Trajectory and smooth attractors for Cahn-Hilliard equations with inertial term

The paper is devoted to a modification of the classical Cahn-Hilliard equation proposed by some physicists. This modification is obtained by adding the second time derivative of the order parameter multiplied by an inertial coefficient which is usually small in comparison to the other physical constants. The main feature of this equation is the fact that even a globally bounded nonlinearity is "supercritical" in the case of two and three space dimensions. Thus the standard methods used for studying semilinear hyperbolic equations are not very effective in the present case. Nevertheless, we have recently proven the global existence and dissipativity of strong solutions in the 2D case (with a cubic controlled growth nonlinearity) and for the 3D case with small inertial coefficient and arbitrary growth rate of the nonlinearity. The present contribution studies the long-time behavior of rather weak (energy) solutions of that equation and it is a natural complement of the results of our previous papers. Namely, we prove here that the attractors for energy and strong solutions coincide for both the cases mentioned above. Thus, the energy solutions are asymptotically smooth. In addition, we show that the non-smooth part of any energy solution decays exponentially in time and deduce that the (smooth) exponential attractor for the strong solutions constructed previously is simultaneously the exponential attractor for the energy solutions as well

High-efficiency generation in a short random fiber laser

We demonstrate a high-efficiency random lasing in a 850 m span of a phosphosilicate fiber. Random distributed feedback owing to the Rayleigh backscattering in the fiber enables narrowband generation with output power of up to 7.3 W at the Stokes wavelength λS = 1308 nm from 11 Wof the pump power at λP = 1115 nm. The laser demonstrates unique generation efficiency. Near the generation threshold, more than 2 W of output power is generated from only 0.5 W of pump power excess over the generation threshold. At high pump power, the quantum conversion efficiency defined as a ratio of generated and pump photons at the laser output exceeds 100%. Itis explained by the fact that every pump photon is converted into the Stokes photon far from the output fiber end, while the Stokes photons have lower attenuation than the pump photons

Comparative numerical study of efficiency of energy deposition in femtosecond microfabrication with fundamental and second harmonics of Yb-doped fiber laser

We present the results of comparative numerical study of energy deposition in single shot femtosecond laser inscription for fundamental and second harmonic of Yb-doped fiber laser. We have found that second harmonic is more efficient in absorbing energy which leads to lower inscription threshold. Hence this regime is more attractive for applications in femtosecond laser microfabrication

Broadly tunable high-power random fibre laser

As shown recently, a long telecommunication fibre may be treated as a natural one-dimensional random system, where lasing is possible due to a combination of random distributed feedback via Rayleigh scattering by natural refractive index inhomogeneities and distributed amplification through the Raman effect. Here we present a new type of a random fibre laser with a narrow (∼1 nm) spectrum tunable over a broad wavelength range (1535-1570 nm) with a uniquely flat (∼0.1 dB) and high (>2 W) output power and prominent (>40 %) differential efficiency, which outperforms traditional fibre lasers of the same category, e.g. a conventional Raman laser with a linear cavity formed in the same fibre by adding point reflectors. Analytical model is proposed that explains quantitatively the higher efficiency and the flatter tuning curve of the random fiber laser compared to conventional one. The other important features of the random fibre laser like "modeless" spectrum of specific shape and corresponding intensity fluctuations as well as the techniques of controlling its output characteristics are discussed. Outstanding characteristics defined by new underlying physics and the simplicity of the scheme implemented in standard telecom fibre make the demonstrated tunable random fibre laser a very attractive light source both for fundamental science and practical applications such as optical communication, sensing and secure transmission

Mode decomposition of Kerr self-cleaned beams by phase only SLM

Graded-index multimode optical bers have recently attracted a renewed attention, thanks to the discovery of new nonlinear eects, such as Kerr beam self-cleaning. In essence, Kerr self-cleaning involves a ow of the propagating beam energy into the fundamental mode of the ber, accompanied by a redistribution of the remaining energy among high-order modes. Increasing the fundamental mode energy leads to a signicant improvement of the output beam quality. A standard method to determine beam quality is to measure the M2 parameter. However, since self-cleaning involves the nonlinear redistribution of energy among a large number of ber modes, measuring a single beam quality parameter is not sucient to characterize the eect. A properly informative approach requires performing the mode decomposition of the output beam. Mode decomposition permits to evaluate the energy distribution among all of the excited ber modes, which enables investigations of nonlinear mode coupling processes at a qualitatively new level. In this work, we demonstrate an eciency mode decomposition method based on holography, which is suitable for analyzing the self-cleaning eect. In a theoretical study, we describe the solution of the mode decomposition problem for the modes of the gradedindex multimode ber. In an experimental investigation, we demonstrate the decomposition of both low-power (speckled) and self-cleaned beams, involving more than 80 modes

Holographic planar lightwave circuit for on-chip spectroscopy

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Multicolour nonlinearly bound chirped dissipative solitons

The dissipative soliton regime is one of the most advanced ways to generate high-energy femtosecond pulses in mode-locked lasers. On the other hand, the stimulated Raman scattering in a fibre laser may convert the excess energy out of the coherent dissipative soliton to a noisy Raman pulse, thus limiting its energy. Here we demonstrate that intracavity feedback provided by re-injection of a Raman pulse into the laser cavity leads to formation of a coherent Raman dissipative soliton. Together, a dissipative soliton and a Raman dissipative soliton (of the first and second orders) form a two (three)-colour stable complex with higher total energy and broader spectrum than those of the dissipative soliton alone. Numerous applications can benefit from this approach, including frequency comb spectroscopy, transmission lines, seeding femtosecond parametric amplifiers, enhancement cavities and multiphoton fluorescence microscopy