Pairs Of Counter-propagating Waves Research Articles

Multimode semiconductor laser gyroscope and factors determining its operation

We report the results of a study of a multimode semiconductor laser gyroscope (MSLG) with a long fibre-optic ring cavity (RC) and alternating frequency dithering formed by a lithium niobate phase modulator, and discuss the factors that determine the device operation. The fundamental limitations in MSLG operation are phase fluctuations and the multimode nature of radiation. Phase fluctuations caused by spontaneous emission of photons in a semiconductor optical amplifier (SOA) result in a slow drop in the beat amplitude. However, its complete decay does not occur due to the periodic and short-term lock-in phenomenon, which leads to the equalisation of the fluctuation levels in pairs of counterpropagating waves (PCPWs) that form the RC modes, and, thereby, to the restoration of the beat amplitude. The limitations associated with the multimode lasing regime are overcome due to the fact that the emission spectrum consists of a small number of narrow lines, and the positions of the antinodes and nodes of standing waves in the SOA field distribution coincide or are close. Both factors lead to the mode locking in spectral lines and, as a consequence, to synchronisation of PCPW beats at the device output. The mechanism of the formation of these factors is not yet clear.

Laser frequency upconversion in plasmas with finite ionization rates

Laser frequency can be upconverted in a plasma undergoing ionization. For finite ionization rates, the laser pulse energy is partitioned into a pair of counterpropagating waves and static transverse currents. The wave amplitudes are determined by the ionization rates and the input pulse duration. The strongest output waves can be obtained when the plasma is fully ionized in a time that is shorter than the pulse duration. The static transverse current can induce a static magnetic field with instant ionization, but it dissipates as heat if the ionization time is longer than a few laser periods. This picture comports with experimental data, providing a description of both laser frequency upconverters and other laser-plasma interaction with evolving plasma densities.

Coupled Klein–Gordon equations and energy exchange in two-component systems

A system of coupled Klein–Gordon equations is proposed as a model for one-dimensional nonlinear wave processes in two-component media (e.g., long longitudinal waves in elastic bi-layers, where nonlinearity comes only from the bonding material). We discuss general properties of the model (Lie group classification, conservation laws, invariant solutions) and special solutions exhibiting an energy exchange between the two physical components of the system. To study the latter, we consider the dynamics of weakly nonlinear multi-phase wavetrains within the framework of two pairs of counter-propagating waves in a system of two coupled Sine–Gordon equations, and obtain a hierarchy of asymptotically exact coupled evolution equations describing the amplitudes of the waves. We then discuss modulational instability of these weakly nonlinear solutions and its effect on the energy exchange.

Modulational instability of two pairs of counter-propagating waves and energy exchange in a two-component system

The modulational instability of two pairs of plane counter-propagating waves in a two-component system is considered within the framework of two coupled Sine-Gordon equations. The emphasis is on the generic case when the system is not integrable, and the group velocities of each pair of waves are arbitrary and usually different from each other. We consider the dynamics of weakly nonlinear wave packets, and using an asymptotic multiple-scales expansion we obtain several sets of evolution equations describing the two components of the system. Depending on the wave packet length scale vis-a-vis the wave amplitude scale, these evolution equations are either four non-dispersive and nonlinearly coupled envelope equations, or four non-locally coupled nonlinear Schrödinger equations. We also consider a set of fully coupled nonlinear Schrödinger equations, even though in general this system contains small dispersive terms which are strictly beyond the leading order of the asymptotic multiple-scales expansion procedure. Although each set of amplitude equations can be used to describe a range of dynamical phenomena, we focus here on stability of plane-wave solutions, and show that they may be modulationally unstable. We study these instabilities in the context of solutions exhibiting an energy exchange between the two physical components of the system. We also perform numerical simulations of the original unapproximated coupled Sine-Gordon equations to assess the accuracy of the instability predictions derived from the various asymptotic models, and consider the range of validity of each asymptotic model. We show that the instabilities can lead to the formation of localized structures, and to a modification of the linear energy exchange, which then continues for some time into the nonlinear regime as an energy exchange between these localized structures. When the system is close to being integrable, the time evolution is distinguished by a remarkable almost periodic sequence of energy exchange scenarios, with spatial patterns alternating between approximately uniform wavetrains and localized structures, which invites further theoretical study of this special case.

Doppler-free resonances of the second-order raman scattering

The possibility of the observation of Raman scattering resonances completely free from the influence of the Doppler effect has been examined for the first time. The phenomenon is based on the excitation of a Raman oscillation standing wave in a gas by two standing light waves, whose frequency difference is equal to half the Raman frequency. The complete compensation of Doppler shifts results from the simultaneous interactions between atomic particles and two pairs of counter-propagating waves. Doppler-free resonances of the second-order Raman light scattering appear in the number of particles excited to the upper Raman level and in the radiation at the Stokes and anti-Stokes frequencies. The amplitude estimate for the resonance in the number of particles is given for the example of neon.