Symmetry breaking and self-oscillations in intracavity vectorial second-harmonic generation

We show that, in vectorial intracavity second-harmonic generation, symmetry breaking occurs if the input amplitude exceeds a critical value. The resulting asymmetric stationary solutions are characterized by a second harmonic that is independent of the input amplitude. The solutions can destabilize through Hopf bifurcations, leading to self-oscillations with pronounced antiphase dynamics. We demonstrate that symmetry breaking can be exploited for flip-flop operation.     

All-optical image processing with cavity type II second-harmonic generation

The possibilities offered by type II intracavity second-harmonic generation for all-optical parallel processing of images are investigated. By injecting an image in a linearly polarized pump beam and a homogeneous field with orthogonal polarization, we obtain, according to the value of the latter, either frequency and polarization transfer or contrast enhancement and contour recognition. Noise-filtering effects are also predicted.     

Observation of spatial modulation instability in intracavity second-harmonic generation

We report the observation of spatial instabilities in singly resonant intracavity second-harmonic generation. Self-focusing as well as spatially ordered near- and far-field structures are observed. Experimental results are compared with mean-field analysis as well as three-dimensional numerical simulations.     

Vacuum instabilities in models with spontaneous symmetry breaking

Adopting as a reference a simple model with spontaneously broken symmetry we show that the extra massless field present in the three approximation in addition to the true Goldstone bosons may induce, through the radiative corrections to its vacuum expectation value, infrared effects which are not compensable without spoiling the symmetry itself. We further extend the analysis to generic lagrangian field models with spontaneous symmetry breaking and prove that the only constraint to their renormalizability arises from the radiative corrections to the vacuum expectation value of the massless fields, except for the true Goldstone bosons which never induce such pathologies.     

Solitons in models with dynamical spontaneous symmetry breaking

An approximate quasi-classical method for the investigation of solitons appearing at quantum level is described. The existence of the soliton in the model with Yukawa coupling in two-dimensional space-time is established with the help of this method. The existence of solitons in the Georgi-Glashow type model with dynamical spontaneous symmetry breaking is shown.     

Self-suppression of axial mode hopping by intracavity second-harmonic generation

Intracavity second-harmonic generation (SHG) in a single-frequency laser has an associated loss for adjacent nonlasing modes, from sum-frequency generation, that is greater than the loss from SHG for the lasing mode. Mode hopping is thereby suppressed, as the lasing mode dominates neighboring modes. We have investigated this behavior in a Nd:YAG laser with LBO intracavity frequency doubler, obtaining frequency tuning over more than 80 axial mode spacings, without mode hopping.     

The geometry of spontaneous symmetry breaking

The problem of classifying the theoretically allowed patterns of spontaneous symmetry breading, in theories where the ground state is determined as a minimum of a G-invariant potential (G a compact group of transformations), is analyzed. A detailed, complete, and rigorous justification of a recently proposed approach to the determination of the minima of G-invariant potentials [10.] is presented. The results are obtained through an analysis of the geometry of the finite-dimensional representations of G, which leads to a complete characterization of the structure of orbit space and its partition in subsets (strata) formed by orbits with the same symmetry under G-transformations (orbit type), and to a new theorem stating that the gradients of complex analytic G-invariant functions annihilate on one-dimensional strata. Polynomial potentials in particular are studied. Conditions for instability of the residual symmetry (second-order phase transitions) are determined.     

Group theory of spontaneous symmetry breaking

The connection between the minimality of the Higgs field potential and the maximal little groups of its representation obtained by spontaneous symmetry breaking is analyzed. It is shown that for several representations the lowest minimum of the potential is related to the maximal little group of those representations. Furthermore, a practical necessity criterion is given for the representation of the Higgs field needed for spontaneous symmetry breaking.     

Spatial solitary waves and patterns in type II second-harmonic generation

The existence of Turing patterns and of spatial solitary waves that arise from a polarization instability of the fundamental field is predicted in type II second-harmonic generation in a quadratically nonlinear optical cavity. The analogy between these dissipative structures and those studied in absorptive optical bistability is pointed out.     

内腔二次谐波过程中光场强度自脉冲振荡的增强

本文利用宏观非线性极化模型,分析了相干驱动内腔二次谐波过程中光场的动力学演化行为.发现了光场的一种新的动力学不稳定性.在此基础上,提出了一个增强光场强度自脉冲振荡的可能途径.     

PT symmetry and spontaneous symmetry breaking in a microwave billiard

We demonstrate the presence of parity-time (PT) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the billiard depends on two parameters. The Hamiltonian is determined from the measured resonance spectrum on a fine grid in the parameter plane. After applying a purely imaginary diagonal shift to the Hamiltonian, its eigenvalues are either real or complex conjugate on a curve, which passes through the EP. An appropriate basis choice reveals its PT symmetry. Spontaneous symmetry breaking occurs at the EP.     

Efficient intracavity second-harmonic generation at 1063 nm in a GdCOB crystal

We report an efficient intracavity second-harmonic generation (SHG) at 1063 nm in a non-linear optical crystal, GdCa₄O(BO₃)₃ (GdCOB), performed with a diode end pumped continuous-wave (CW) Nd:GdVO₄ laser. In the case of a laser with an a-cut 0.4 at % Nd:GdVO₄ crystal frequency-doubled with a GdCOB crystal cut for Type I frequency doubling. A CW SHG output power of 2.25 W has been obtained using a 15 mm long GCOB crystal. The optical conversion efficiency with respect to the incident pump power was 12.4%.     

Vector solitary optical beam control with mixed type I–type II second-harmonic generation

The four vector equations, appropriate to a mixed type I–type II second-harmonic generation, in a thin planar waveguide, made from a second-order non-linear material, are solved, both approximately and exactly. The solutions are then used to generate possible applications. In this investigation, both the fundamental and the second-harmonic waves have two transverse field components. It is shown that, by controlling the ratio of the components of the fundamental wave, one component of the second-harmonic wave can be rigorously controlled, and even switched off. The ratio of the harmonic field components depends strongly upon the polarization angle of the fundamental wave, with the extinction angle depending strongly upon the phase mismatch parameter. In a second application, an aperture is placed at the output and it is shown that if approximate stationary states are used as an input to a quadratically non-linear medium, then varying the angle of incidence of two input beams produces an excellent output control. A numerical demonstration is given in which a switch from 80% of the input energy arriving at the output port to less than 3% is readily achievable.     

Confinement from spontaneous breaking of scale symmetry

We show that one can obtain naturally the confinement of static charges from the spontaneous symmetry breaking of scale invariance in a gauge theory. At the classical level a confining force is obtained and at the quantum level, using a gauge invariant but path-dependent variables formalism, the Cornell confining potential is explicitly obtained. Our procedure answers completely to the requirements by 't Hooft for “perturbative confinement”.     

Covariance of spontaneous symmetry breaking in non-inertial frames

It is pointed out that contrary to a recent claim the process of symmetry breaking is covariant in a non-inertial frame.     

Dynamical electroweak symmetry breaking with a heavy fourth generation

A heavy fourth generation with a mass of the order of 400 GeV or more could trigger dynamical electroweak symmetry breaking by forming condensates through the exchange of a fundamental Higgs scalar doublet. The dynamics leading to these condensates is studied within the framework of the Schwinger–Dyson equation. This scenario leads to the presence of three (two composite and one fundamental) Higgs doublets, with interesting phenomenological implications. In addition, this dynamical phenomenon occurs in the vicinity of the energy scale where the restoration of scale symmetry might happen.     

On the spontaneous breaking of chiral symmetry in QCD

We calculate the vacuum polarization functions of the vector and axial current for massless quarks in second-order perturbation theory. We find that, contrary to previous speculations, there is no indication, at this level, of spontaneous breaking of chiral symmetry in QCD.     

Possible spontaneous breaking of lorentz and CPT symmetry

One possible ramification of unified theories of nature such as string theory that may underlie the conventional standard model is the possible spontaneous breakdown of Lorentz and CPT symmetry. In this talk, the formalism for inclusion of such effects into a low-energy effective field theory is presented. An extension of the standard model that includes Lorentz-and CPT-breaking terms is developed. The restriction of the standard model extension to the QED sector is then discussed.     

Electromagnetic field and spontaneous symmetry breaking in biological matter

Dynamical effects of electromagnetic interaction among electric dipoles in biological systems are studied. On the basis of a previous analysis in terms of spontaneous breakdown of symmetry we show that the Anderson-Higgs-Kibble mechanism occurs, which manifests itself in a self-focusing mechanism of propagation for the electromagnetic field inside the biological systems. Phenomenological consequences, such as the formation of filamentary structures of the type occurring in cell cytoskeleton, are analyzed. The appearance of nonzero temperature due to the finite size and polarization of the system, and the relation with dissipativity are also discussed.