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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.
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Spontaneous symmetry breaking is an important concept in many areas of physics. A fundamentally simple symmetry breaking mechanism in electrodynamics occurs between counter-propagating electromagnetic waves in ring resonators, mediated by the Kerr nonlinearity. The interaction of counter-propagating light in bi-directionally pumped microresonators finds application in the realisation of optical non-reciprocity (for optical diodes), studies of PT-symmetric systems, and the generation of counter-propagating solitons. Here, we present comprehensive analytical and dynamical models for the nonlinear Kerr-interaction of counter-propagating light in a dielectric ring resonator. In particular, we study discontinuous behaviour in the onset of spontaneous symmetry breaking, indicating divergent sensitivity to small external perturbations. These results can be applied to realise, for example, highly sensitive near-field or rotation sensors. We then generalise to a time-dependent model, which predicts new types of dynamical behaviour, including oscillatory regimes that could enable Kerr-nonlinearity-driven all-optical oscillators. The physics of our model can be applied to other systems featuring Kerr-type interaction between two distinct modes, such as for light of opposite circular polarisation in nonlinear resonators, which are commonly described by coupled Lugiato-Lefever equations.
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.
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.
Non-Hermitian systems, with symmetric or antisymmetric Hamiltonians under the parity-time ($mathcal{PT}$) operations, can have entirely real eigenvalues. This fact has led to surprising discoveries such as loss-induced lasing and topological energy transfer. A merit of anti-$mathcal{PT}$ systems is free of gain, but in recent efforts on making anti-$mathcal{PT}$ devices, nonlinearity is still required. Here, counterintuitively, we show how to achieve anti-$mathcal{PT}$ symmetry and its spontaneous breaking in a linear device by spinning a lossy resonator. Compared with a Hermitian spinning device, significantly enhanced optical isolation and ultrasensitive nanoparticle sensing are achievable in the anti-$mathcal{PT}$-broken phase. In a broader view, our work provides a new tool to study anti-$mathcal{PT}$ physics, with such a wide range of applications as anti-$mathcal{PT}$ lasers, anti-$mathcal{PT}$ gyroscopes, and anti-$mathcal{PT}$ topological photonics or optomechanics.
Dissipative solitons are self-localised structures that can persist indefinitely in open systems characterised by continual exchange of energy and/or matter with the environment. They play a key role in photonics, underpinning technologies from mode-locked lasers to microresonator optical frequency combs. Here we report on the first experimental observations of spontaneous symmetry breaking of dissipative optical solitons. Our experiments are performed in a passive, coherently driven nonlinear optical ring resonator, where dissipative solitons arise in the form of persisting pulses of light known as Kerr cavity solitons. We engineer balance between two orthogonal polarization modes of the resonator, and show that despite perfectly symmetric operating conditions, the solitons supported by the system can spontaneously break their symmetry, giving rise to two distinct but co-existing vectorial solitons with mirror-like, asymmetric polarization states. We also show that judiciously applied perturbations allow for deterministic switching between the two symmetry-broken dissipative soliton states, thus enabling all-optical manipulation of topological bit sequences. Our experimental observations are in excellent agreement with numerical simulations and theoretical analyses. Besides delivering fundamental insights at the intersection of multi-mode nonlinear optical resonators, dissipative structures, and spontaneous symmetry breaking, our work provides new avenues for the storage, coding, and manipulation of light.
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