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Spontaneous phase symmetry breaking in a gas coupled-cavity ring laser
摘要： A theoretical model is proposed that describes the lasing dynamics in a gas ring laser (GRL) with coupled cavities. The conditions are found under which spontaneous phase symmetry of counterpropagating waves is broken in the GRL with an antiphase optical coupling of the cavities. It is shown that in the case of spontaneous phase symmetry breaking, two branches appear on the GRL frequency characteristic. In some region of frequency non-reciprocity of a ring cavity, both branches can exist under the same conditions. In this case, radiation bistability appears in the GRL, and hysteresis phenomena can be observed.
关键词： spontaneous symmetry breaking,phase non-reciprocity,beat mode,gas ring laser,coupled cavities
更新于2025-09-16 10:30:52
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[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Symmetry Breaking: Balancing Asymmetries
摘要： Spontaneous symmetry breaking (SSB) is a ubiquitous natural phenomenon where a system characterized by certain symmetries can evolve into a state that does not exhibit those symmetries. SSB underpins many fundamental phenomena, including phase transitions in meta-materials or Bose-Einstein condensates, the emergence of the Nambu-Goldstone and Higgs modes of crucial importance in particle physics, or bifurcations in lasers, and could have significant applications, especially in photonics. Physical systems however often exhibit deviations from perfect symmetry because of naturally occurring imperfections. How small asymmetries affect SSB-related dynamics is therefore an important problem. Surprisingly, this has barely been considered in experiments, and even then restricted to situations with only one asymmetry parameter [1]. Here, we report spontaneous breaking of a mirror symmetry in an optical experiment with two controllable asymmetry parameters. Specifically, we explore how controlled asymmetries affect the range of co-existence of two homogeneous states (HSs) with different polarizations in a driven Kerr resonator, and discover that different asymmetries can compensate for each other.
关键词： Kerr resonator,Symmetry breaking,asymmetries,optical experiment,polarization
更新于2025-09-12 10:27:22
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[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Electric-Dipole Based Chiral Sensitivity in High Harmonic Generation by Dynamical Symmetry Breaking Spectroscopy
摘要： Chirality is a fundamental asymmetry property that appears abundantly in nature [1]. A system is chiral if and only if it is distinct from its mirror image (its opposite handedness chiral-partner), e.g. circularly polarized light or chiral molecules. Such systems are unique in that their properties are completely independent of their handedness up until the moment they interact with another chiral object. For instance, partner chiral molecules have identical cross-sections for absorption of linearly-polarized light, but not for absorption of circularly polarized light, leading to circular dichroism (CD) [1]. Standardly, chirality is analyzed by chiroptical techniques that measure the medium’s response to elliptically polarized light. However, such techniques rely on magnetic-dipole or higher electric-moment transitions, because electric-dipole interactions average-out to zero in isotropic media (circularly polarized light has a helical pitch that is negligible in the dipole approximation) [1]. Consequently, standard chiroptical approaches lead to very weak signals, especially in the gas phase. In recent years, several seminal electric-dipole based methods were developed that lead to much larger chiral signals, including photoelectron CD [1–4], coulomb explosion imaging [5], and microwave three-wave mixing [6]. Importantly, high harmonic generation (HHG) was shown to be chirality-sensitive, leading to relatively large (up to 10%) femtosecond-resolved chiral signals [7,8]. Still, the chiral signal in HHG is based on magnetic-dipole interactions (same as in the standard techniques), and the signal is relatively large only due to the non-perturbative nature of the process. Extending HHG to produce an electric-dipole chiral response could open-up many possibilities for optically exploring ultrafast chirality and weakly-chiral systems. Here we propose and theoretically explore a novel HHG-based chiroptical approach that relies solely on electric-dipole interactions. The method is implemented through bi-chromatic non-collinear HHG, where the beams’ properties are chosen from group theory symmetry-based considerations to exhibit reflection or inversion dynamical symmetries (DSs) [9]. This scheme leads to forbidden harmonic selection rules from isotropic achiral media which are broken in chiral media, because it does not exhibit reflection and inversion symmetries. As a result, ‘forbidden’ harmonics are emitted only if the medium is chiral, and their intensity is correlated to the enantiomeric excess (ee), providing a single-shot background free signal. We analytically derive the general conditions that allow an electric-dipole based chiral response, and numerically demonstrate several feasible geometries [10]. For instance, using DS group theory considerations [9], we numerically demonstrate that the bi-chromatic non-collinear chiral HHG scheme presented in Fig. 1(a) – two intense non-collinear bi-chromatic (3:5 carrier frequency ratios), counter rotating, elliptically polarized beams propagate with a relative opening angle of 2α – leads to an electric-dipole based ‘forbidden harmonic’ signal. When this field interacts with an achiral medium (e.g. a non-oriented racemic mixture of chiral molecules), even harmonic emission is forbidden due to a dynamical inversion symmetry selection rule (the pump is invariant under the DS: (cid:1870)?→-(cid:1870)?, t→t+T/2) [9]. However, when this field interacts with a chiral medium, even harmonics are emitted in all polarizations, and the electric-dipole response does not average-out to zero [10]. This results from the medium breaking the pump’s inversion DS; hence, the intensity of the even harmonics is correlated to the ee, while the odd harmonics are chirality-independent and can be used as a reference (see Fig. 1(c)). This scheme leads to a nearly background free chiral/achiral signal, reaching as high as 97% for the normalized harmonic response from chiral media compared to achiral media (Fig. 1(d)).
关键词： Electric-Dipole,Dynamical Symmetry Breaking Spectroscopy,Chirality,High Harmonic Generation
更新于2025-09-11 14:15:04
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[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Spontaneous Symmetry Breaking, Oscillations, and Chaotic Regimes in Bidirectionally-Pumped Ring Resonators
摘要： Spontaneous symmetry breaking has been recently demonstrated experimentally in bidirectionally-pumped dielectric microresonators [1,2]. This process is mediated by cross-phase modulation due to the Kerr nonlinearity. We present comprehensive analytical and dynamical models for this symmetry breaking, with novel results in both time-dependent and time-independent cases, including chaos. The time-dependent system is described by the following pair of dimensionless coupled equations: ˙e1,2 = ?e1,2 ? [1 + i(|e1,2|2 + 2|e2,1|2 ? Δ)]e1,2, wherein ?e1,2 are the (clockwise or counterclockwise) electric ?eld amplitudes sent to the cavity, e1,2 are the (clockwise or counterclockwise) electric ?eld amplitudes coupled into the cavity, and Δ is the normalised detuning of the laser with respect to the non-Kerr-shifted cavity resonant frequency. Above a symmetry-breaking threshold, in which the stationary amplitudes of the two ?elds are different from each other, the system is strongly susceptible to oscillations [3], implying periodic energy exchange between the two modes. Above a theoretically-determined value of input power, oscillations develop with observable amplitudes (see Fig. 1 for typical ranges of instability). At still higher values of input power, we observe more complicated time-dependent behaviour: the onset of period-doubling, whereby much more complicated waveforms, and ?nally chaos, emerge [3]. Numerical integration of Eqs. (1) con?rms the ranges of instability and frequencies of oscillation [3]. In addition to being of fundamental interest, this theory is relevant for many applications, such as optical diodes and logic gates, as well as opening up the possibility of constructing an all-optical oscillator. The rich time-dependent behaviour exhibited by this system suggests applicability to other devices, such as scramblers and random number generators, all within a compact form factor, such as a microresonator. Note that many of the results presented here are general with respect to changes in the coef?cients of self- and cross-phase modulation in Eqs. (1).
关键词： Spontaneous symmetry breaking,bidirectionally-pumped ring resonators,chaotic regimes,oscillations
更新于2025-09-11 14:15:04
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Symmetry and asymmetry nonlinear modes in dual cylinder waveguide shells coupled by a rotating double-well connection
摘要： We study the fundamental nonlinear modes in a dual-cylinder waveguide shell, which features a self-focusing Kerr e?ect, coupled by a double-well connection. This double-well connection is twisted by a pitch rate and creates a spatial dependent linear mixing, which plays the role of an e?ective rotating double-well potential. Symmetry transition between the waveform and the power distribution of the fundamental nonlinear modes in this system can be induced both by the total power and by the rotation speed of the connection. Four types of modes (cid:1)(cid:1)(cid:1) wave symmetry and power symmetry (WSPS), wave symmetry and power asymmetry (WSPA), wave asymmetry and power symmetry (WAPS) and wave asymmetry and power asymmetry (WAPA) (cid:1)(cid:1)(cid:1) are found from the system. The dependence of these modes on the total power of the light ˉeld, the rotation speed and the coupling strength of the connection are systematically studied through the paper. The ˉnding of this paper may o?er potential applications in fabrication of new types of nonlinear all-optical devices.
关键词： self-focusing,Symmetry breaking,rotating systems,double-well coupling
更新于2025-09-11 14:15:04
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[IEEE 2019 21st International Conference on Transparent Optical Networks (ICTON) - Angers, France (2019.7.9-2019.7.13)] 2019 21st International Conference on Transparent Optical Networks (ICTON) - Microcavity-Enhanced Surface Nonlinear Optics
摘要： Confinement and manipulation of photons using microcavities have triggered intense research interest in both fundamental and applied photonics for decades. As a prominent example, whispering-gallery microcavities have ultrahigh Q factors and small mode volumes, making them promising candidates for enhancing light-matter interactions, especially for nonlinear optics. In this work, we report the second-order nonlinear optics induced by symmetry breaking at the surface of an ultrahigh-Q silica microcavity under a sub-milliwatt continuous-wave pump. By dynamically coordinating the double-resonance phase matching, a second harmonic is achieved with a co(cid:81)(cid:89)(cid:72)(cid:85)(cid:86)(cid:76)(cid:82)(cid:81)(cid:3)(cid:72)(cid:73)(cid:73)(cid:76)(cid:70)(cid:76)(cid:72)(cid:81)(cid:70)(cid:92)(cid:3)(cid:82)(cid:73)(cid:3)(cid:19)(cid:17)(cid:19)(cid:23)(cid:28)(cid:8)(cid:3031)(cid:58)-1, 14 orders of magnitude higher than that of the non-enhancement case.
关键词： nonlinear optics,symmetry breaking,microcavity,second harmonic generation,surface
更新于2025-09-11 14:15:04
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Surface Nonlinear Optics on Centrosymmetric Dirac Nodal‐Line Semimetal ZrSiS
摘要： Gapless surface states (SSs) are features of topological semimetals and are extensively observed. Nowadays, the emerging question is whether the SSs possess exotic and applicable properties. Here, associated with the symmetrical selection rule for nonlinear optical materials, the surface nonlinear optics on a centrosymmetric Dirac nodal-line semimetal ZrSiS crystal is studied and it is found that the SSs bring record nonlinear susceptibilities. The unprecedented conversion efficiencies for second and third harmonic generations are 0.11‰ and 0.43‰, respectively, more than ten orders of magnitude larger than the typical surface second harmonic generation. This work discovers a new route toward studying the SSs for applications in nonlinear photonics.
关键词： density functional theory calculations,ZrSiS,surface states,nonlinear optics,symmetry breaking
更新于2025-09-11 14:15:04
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[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - All-Optical Background-Free Detection of Ring Currents by Dynamical Symmetry Breaking High Harmonic Spectroscopy
摘要： Excited atoms and molecules can carry long-lived currents that circulate in the microscopic media. From a quantum mechanical perspective, these currents can be understood as a coherent wave-packet comprising a superposition of bound- states that oscillates in time [1–3]. When the wave-packet has a non-zero angular momentum expectation value, ring-currents circulate in the medium. For instance, a hydrogen atom excited to a 2p-state with non-zero magnetic quantum number m (e.g. by interaction with circularly polarized light) carries a steady-state ring current [2]. More complex systems can also carry persistent ring currents, e.g. spin-orbit wave-packets in Xenon [4], or multi-electron wave-packets in larger molecules [1]. This phenomenon is general to any quantum system and is especially interesting because it occurs on the natural time-scale of electronic motion – attoseconds to femtoseconds. Understanding ring currents is thus fundamentally important for manipulating and controlling ultrafast processes on the nanoscale, including chemical bond formation and topologically protected surface currents [5], as well as for the generation of intense attosecond-duration magnetic fields [1,6]. However, ring currents are very difficult to detect, particularly in a time-resolved manner. Only very recently were ring currents directly experimentally resolved in Argon through pump-probe angularly-resolved incidence photoelectron spectrum measurements [3]. Here we propose and theoretically explore an all-optical technique for ultrafast time-resolved detection of ring currents in atoms, molecules and solids, based on high harmonic generation (HHG). In this technique a microscopic medium interacts with a bi-chromatic (ω-2ω) bi-elliptical laser pulse, generating high harmonic photons. We show that the harmonic spectra emitted from current-carrying media differs from that of current-free media. We use dynamical symmetry (DS) considerations [7] to derive conditions for a maximal (background-free) signal in the harmonic ellipticity, which occurs when the pump beams are cross-linearly polarized [8]. In this configuration the bi-chromatic laser field exhibits a dynamical reflection symmetry that leads to linearly polarized harmonic selection rules [7]; however, this selection rule is broken when the medium carries a current, because ring-currents are not reflection-symmetric (similar to chiral systems [9], but where the current can be described in 2D). Thus, current-carrying media emit elliptically polarized harmonics, where the harmonic ellipticity is correlated to the intensity and sign of the current in the system. We numerically demonstrate the approach by pump-probe HHG calculations from Neon noble gas atoms, and from both aligned and un-oriented aromatic molecules (benzene and furan), using a non-interacting electron quantum model, and time-dependent density functional theory calculations. The presented work could be useful for ultrafast spectroscopy of current-carrying processes (chemical reactions, topological currents, etc.), as well as for manipulation and control of ring currents, paving the way for their table-top all- optical detection.
关键词： high harmonic generation,ultrafast spectroscopy,ring currents,dynamical symmetry breaking
更新于2025-09-11 14:15:04
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Fabry-Perot interferometry in Weyl semi-metals
摘要： We show that the electrical transport across a minimal model for a time-reversal symmetry(TRS) breaking Weyl semi-metal (WSM) involving two Weyl nodes can be interpreted as an interferometer in momentum space. The interference phase depends on the distance between the Weyl nodes ( (cid:126)δk) and is anisotropic. It is further shown that a minimal inversion symmetry broken model for a WSM with four Weyl nodes effectively mimics a situation corresponding to having two copies of the interferometer due to the presence of an orbital pseudo-spin domain wall in momentum space. We point out that the value of the δk and consequently the interference phase can be tuned by driving the WSMs resulting in oscillations in the two terminal conductance measured in the direction of splitting of the Weyl nodes.
关键词： Weyl semi-metals,Fabry-Perot interferometry,inversion symmetry breaking,orbital pseudo-spin,time-reversal symmetry breaking
更新于2025-09-10 09:29:36
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[Springer Tracts in Modern Physics] Parity-time Symmetry and Its Applications Volume 280 || Nonlinear Beam Propagation in a Class of Complex Non- P T $$\mathcal {PT}$$ -Symmetric Potentials
摘要： The subject of PT -symmetry and its areas of application have been blossoming over the past decade. Here, we consider a nonlinear Schr?dinger model with a complex potential that can be tuned controllably away from being PT -symmetric, as it might be the case in realistic applications. We utilize two parameters: the ?rst one breaks PT -symmetry but retains a proportionality between the imaginary and the derivative of the real part of the potential; the second one, detunes from this latter proportionality. It is shown that the departure of the potential from the PT -symmetric form does not allow for the numerical identi?cation of exact stationary solutions. Nevertheless, it is of crucial importance to consider the dynamical evolution of initial beam pro?les. In that light, we de?ne a suitable notion of optimization and ?nd that even for non PT -symmetric cases, the beam dynamics, both in 1D and 2D – although prone to weak growth or decay– suggests that the optimized pro?les do not change signi?cantly under propagation for speci?c parameter regimes.
关键词： Solitons,PT -symmetry,Unbalanced gain and loss,Stability,Nonlinear Schr?dinger equation,Symmetry breaking
更新于2025-09-10 09:29:36