No Arabic abstract
Both the group velocity and phase velocity of two solitons can be synchronized by a Kerr-effect mediated interaction, causing what is known as soliton trapping. Trapping can occur when solitons travel through single-pass optical fibers or when circulating in optical resonators. Here, we demonstrate and theoretically explain a new manifestation of soliton trapping that occurs between counter-propagating solitons in microresonators. When counter-pumping a microresonator using slightly detuned pump frequencies and in the presence of backscattering, the group velocities of clockwise and counter-clockwise solitons undergo periodic modulation instead of being locked to a constant velocity. Upon emission from the microcavity, the solitons feature a relative oscillatory motion having an amplitude that can be larger than the soliton pulse width. This relative motion introduces a sideband fine structure into the optical spectrum of the counter-propagating solitons. Our results highlight the significance of coherent pumping in determining soliton dynamics within microresonators and add a new dimension to the physics of soliton trapping.
We solve the (2+1)D nonlinear Helmholtz equation (NLH) for input beams that collapse in the simpler NLS model. Thereby, we provide the first ever numerical evidence that nonparaxiality and backscattering can arrest the collapse. We also solve the (1+1)D NLH and show that solitons with radius of only half the wavelength can propagate over forty diffraction lengths with no distortions. In both cases we calculate the backscattered field, which has not been done previously. Finally, we compute the dynamics of counter-propagating solitons using the NLH model, which is more comprehensive than the previously used coupled NLS model.
We present a pump-probe technique for monitoring ultrafast polarizability changes. In particular, we use it to measure the plasma density created at the temporal focus of a self-compressing higher-order pump soliton in gas-filled hollow-core photonic crystal fiber. This is done by monitoring the wavelength of the dispersive wave emission from a counter-propagating probe soliton. By varying the relative delay between pump and probe, the plasma density distribution along the fiber can be mapped out. Compared to the recently introduced interferometric side-probing for monitoring the plasma density, our new technique is relatively immune to instabilities caused by air turbulence and mechanical vibration. The results of two experiments on argon- and krypton-filled fiber are presented, and compared to numerical simulations. The technique provides an important new tool for probing photoionization in many different gases and gas mixtures as well as ultrafast changes in dispersion in many other contexts.
We report the experimental observation of oscillatory antiphase switching between counter-propagating light beams in Kerr ring microresonators, including the emergence of periodic behaviour from a chaotic regime. Self-switching occurs in balanced regimes of operation and is well captured by a simple coupled dynamical system featuring only the self- and cross-phase Kerr nonlinearities. Switching phenomena are due to temporal instabilities of symmetry-broken states combined with attractor merging that restores the broken symmetry on average. Self-switching of counter-propagating light is robust for realising controllable, all-optical generation of waveforms, signal encoding and chaotic cryptography.
Light is generally expected to travel through isotropic media independent of its direction. This makes it challenging to develop non-reciprocal optical elements like optical diodes or circulators, which currently rely on magneto-optical effects and birefringent materials. Here we present measurements of non-reciprocal transmission and spontaneous symmetry breaking between counter-propagating light in dielectric microresonators. The symmetry breaking corresponds to a resonance frequency splitting that allows only one of two counter-propagating (but otherwise identical) light waves to circulate in the resonator. Equivalently, the symmetry breaking can be seen as the collapse of standing waves and transition to travelling waves within the resonator. We present theoretical calculations to show that the symmetry breaking is induced by Kerr-nonlinearity-mediated interaction between the counter-propagating light. This effect is expected to take place in any dielectric ring-resonator and might constitute one of the most fundamental ways to induce optical non-reciprocity. Our findings pave the way for a variety of applications including all optical switching, nonlinear-enhanced rotation sensing, optically controllable circulators and isolators, optical flip-flops for photonic memories as well as exceptionally sensitive power and refractive index sensors.
The method of Doppler - free comb - spectroscopy for dipole transitions was proposed. The calculations for susceptibility spectrum for moving two-level atoms driving by strong counter propagating combs have been done. The used theoretical method based on the Fourier expansion of the components of density matrix on two rows on kv (v-velocity of group of atoms, k-projection of wave vector) and {Omega} (frequency between comb components). For testing of validity of this method the direct numerical integration was done. The narrow peaks with homogeneous width arise on the background of Doppler counter. The contrast of these peaks is large for largest amplitudes of comb-components. Power broadening is increasing with increase of field amplitudes. The spectral range of absorption spectrum is determined by the spectral range of comb generator and all homogeneous lines arise simultaneously. The spectral resolution is determined by the width of homogeneously-broadening lines. The physical nature of narrow peaks is in the existence of multi-photon transitions between manifolds of quasi-energy levels arising for different groups of atoms moving with velocities that satisfy to the resonant conditions 2kv= (n+l){Omega}, where n, l - are integers and {Omega} - frequency difference between comb teeth.