Noncritical generation of nonclassical frequency combs via spontaneous rotational symmetry breaking

Synchronously pumped optical parametric oscillators (SPOPOs) are optical cavities containing a nonlinear crystal capable of down-converting a frequency comb to lower frequencies. These have received a lot of attention lately, because their intrinsic multimode nature makes them compact sources of quantum correlated light with promising applications in modern quantum information technologies. In this work we show that SPOPOs are also capable of accessing the challenging but interesting regime where spontaneous symmetry breaking plays a crucial role in the quantum properties of the emitted light, difficult to access with any other nonlinear optical cavity. Apart from opening the possibility of…

Arresting soliton collapse in two-dimensional nonlinear Schrödinger systems via spatiotemporal modulation of the external potential

We predict stable, collapse-free solitonslike structures in two-dimensional nonlinear Schr\"odinger systems in subdiffractive regimes, accomplished by a spatiotemporal modulation of the external potential. We investigate the scaling laws, the stability, and the dynamical properties of these subdiffractive solitons.

Electric quantum walks in two dimensions

We study electric quantum walks in two dimensions considering Grover, Alternate, Hadamard, and DFT quantum walks. In the Grover walk the behaviour under an electric field is easy to summarize: when the field direction coincides with the x or y axes, it produces a transient trapping of the probability distribution along the direction of the field, while when it is directed along the diagonals, a perfect 2D trapping is frustrated. The analysis of the alternate walk helps to understand the behaviour of the Grover walk as both walks are partially equivalent; in particular, it helps to understand the role played by the existence of conical intersections in the dispersion relations, as we show th…

Experimental approach to transverse wave-number selection in cavity nonlinear optics

Spontaneous transverse pattern formation is experimentally studied in a ${\text{BaTiO}}_{3}$ photorefractive oscillator under degenerate four-wave mixing conditions. A near self-imaging resonator of high Fresnel number and quasi-one-dimensional in the transverse plane is used. A fine control technique of the cavity detuning, $\ensuremath{\Omega}$, is described. It allows a precise study of the relation of $\ensuremath{\Omega}$ with the transverse wave number ${k}_{\ensuremath{\perp}}$ of the roll patterns selected by the system. The law ${k}_{\ensuremath{\perp}}^{2}=\ensuremath{-}\ensuremath{\Omega}∕a$ is verified, which evidences that wave-number selection is mainly dictated by the cavity …

Generalized complex Swift-Hohenberg equation for optical parametric oscillators

A generalized complex Swift-Hohenberg equation including diffraction and nonlinear resonance terms is derived for spatially extended nondegenerate optical parametric oscillators (OPOs) with flat end mirrors. For vanishing pump detuning this equation becomes the complex Swift-Hohenberg (SH) equation valid also for lasers. Nevertheless the similarities between OPOs and lasers are limited, since the diffractive character of OPOs is lost when the diffraction coefficients of signal and idler fields are equal. This manifests, e.g., in the absence of advection by traveling waves (TWs), a clear difference with lasers. When pump detuning is nonzero a nonlinear resonance develops, as it occurs in deg…

Quantum walk on a cylinder

We consider the 2D alternate quantum walk on a cylinder. We concentrate on the study of the motion along the open dimension, in the spirit of looking at the closed coordinate as a small or "hidden" extra dimension. If one starts from localized initial conditions on the lattice, the dynamics of the quantum walk that is obtained after tracing out the small dimension shows the contribution of several components, which can be understood from the study of the dispersion relations for this problem. In fact, these components originate from the contribution of the possible values of the quasi-momentum in the closed dimension. In the continuous space-time limit, the different components manifest as …

Hysteretic nonequilibrium Ising-Bloch transition

We show that a parametrically driven cubic-quintic complex Ginzburg-Landau equation exhibits a hysteretic nonequilibrium Ising-Bloch transition for large enough quintic nonlinearity. These results help to understand the recent experimental observation of this pheomenon [A. Esteban-Martin et al., Phys. Rev. Lett. 94, 223903 (2005)].

Rocking bidirectional lasers

Abstract We study the emission properties of a class A bidirectional laser under the action of an amplitude modulated injected signal, i.e. a rocked bidirectional laser. We derive two coupled autonomous amplitude equations valid close to the emission threshold and study their solutions. The most relevant result is that while in the absence of rocking the laser can only emit in either of the two unidirectional solutions, under suitable rocking conditions cw bidirectional emission appears and, moreover, it coexist bistably with unidirectional emission.

Interferometric Phase Retrieval in Optical Transient Detection

A transient detection imaging system (TDI), also known as optical novelty filter, is an adaptive interferometric device that detects temporal changes in a scene while suppressing its static parts. Removal of background improves contrast and helps visualizing and measuring intensity and phase. Following the first TDI proposal by Cudney et al. [1] , most TDI systems are based on photorefractive two-wave mixing [2] . Previous works rely on conventional intensity measurements, where partial information about input signal phase changes are obtained by previous calibration using an input phase-output intensity transfer function of the particular system.

Types I and II intermittencies in a cascade laser model

Abstract We report on types I and II intermittencies found in a cascade laser model. A continuous transition from one to another type of intermittency, which involves the coexistence of both types of laminar phases within the same time series, is found. Type II intermittency has special characteristics such as its origin at a frequency locked two-torus. When frequency unlocked this torus bifurcates to a three-torus, further giving rise to a type II intermittent like behaviour with new features during the laminar phases.

Closed Busse balloon for rolls and skew-varicose instability in a Swift-Hohenberg model with nonlinear resonance

Abstract A Swift-Hohenberg model incorporating a nonlinear resonance is shown to produce stable rolls only in a closed region of the parameter space. This Busse balloon is limited by zigzag and Eckhaus boundaries. A skew-varicose instability outside the balloon also exists. Implications with nonlinear optics and hydrodynamic convection are commented.

Class-B two-photon Fabry–Pérot laser

Abstract We study the stationary operation and stability properties of a class-B two-photon Fabry–Perot laser. We show that, differently from the one-photon laser, the intensity emitted by the two-photon laser is larger in a Fabry–Perot than in a ring cavity. The lasing solution loses stability through a subcritical Hopf bifurcation, as it occurs in the unidirectional ring laser. The stability domain in the parameter space is larger in the Fabry–Perot than in the ring cavity configuration.

Generation of multimode squeezing and entanglement in the space and frequency domains : A general “supermode” approach

Optical parametric oscillators (OPO) have been extensively used in the continuous variable quantum optics community as a resource to produce non-classical states of light, including squeezed states or entangled beams. They have been widely studied, theoretically and experimentally, in the single mode case, and have found many applications to quantum information protocols and high sensitivity optical measurements. However, as the complexity of quantum information protocols increases, the need for multiplexed quantum channels has emerged, which require the use of multimode non-classical states of light.

Multimode emission in inhomogeneously broadened ring lasers

The threshold for multilongitudinal-mode emission in inhomogeneously broadened ring lasers is analytically investigated. In the homogeneous limit the multimode instability corresponds to the classical Risken–Nummedal–Graham–Haken instability. It is found that by increasing the inhomogeneous linewidth, the instability threshold is decreased and the growth of high-frequency side modes is favored. In the limit where the population-inversion decay rate γ‖ is much smaller than the polarization decay rate γ⊥ (class B lasers), analytical expressions for the instability threshold are found, which are then generalized to three-level lasers for a comparison with experimental results obtained with erb…

Intermittent and quasiperiodic behavior in a Zeeman laser model with large cavity anisotropy

Type I optical parametric oscillators above threshold are perfect squeezers for empty gauss-hermite modes at any pumping level

A type I optical parametric oscillator pumped by a Gaussian beam above threshold and tuned to its first transverse mode family is shown to yield a perfectly squeezed, empty Gauss-Hermite mode at any pumping level.

Quantum coherence and fast-gain effects in laser modelocking: The coherent master equation

Modelocking embraces a variety of techniques leading to the periodic emission of ultrashort laser pulses, typically on the picosecond scale and below, whose impact in science and technology can be hardly exaggerated.

Observability of the Risken–Nummedal–Graham–Haken instability in Nd:YAG lasers

Multilongitudinal mode instability in ring Nd:YAG lasers is theoretically analyzed. After we review the way in which the standard two-level laser theory applies to this laser we extend the theoretical treatment to include transverse effects. We do this by taking into account the finite transverse section of the active medium and by assuming a Gaussian transverse distribution for the intracavity field. Finally we demonstrate that multimode emission develops whenever the intracavity field waist diameter is almost equal to the active rod diameter. We conclude that continuous-wave diode-pumped Nd:YAG lasers with low cavity losses are good candidates for the observation of the Risken–Nummedal–Gr…

Interferometric measurement of complex-field changes in transient detection imaging.

We report an experimental method that combines nonlinear-crystal-based transient detection imaging (TDI) with interferometric complex-field retrieval. The system allows measuring both phase and amplitude of a dynamic scene while suppressing stationary background. Theoretical and experimental results prove the linear relation existing between input and output phases, as well as the benefits of phase analysis for both detection and measurement with high resolutions of λ/30, even under noisy conditions. Additionally, we present experimental evidence of the remarkable ability of the technique to detect phase sign changes in the scene —what we call differential-phase TDI— showing great detection…

Understanding and controlling N-dimensional quantum walks via dispersion relations: application to the two-dimensional and three-dimensional Grover walks-diabolical points and more

The discrete quantum walk in N dimensions is analyzed from the perspective of its dispersion relations. This allows understanding known properties, as well as designing new ones when spatially extended initial conditions are considered. This is done by deriving wave equations in the continuum, which are generically of the Schrodinger type, and allows devising interesting behavior, such as ballistic propagation without deformation, or the generation of almost flat probability distributions, which is corroborated numerically. There are however special points where the energy surfaces display intersections and, near them, the dynamics is entirely different. Applications to the two- and three-d…

Modal expansions in lasers outside the uniform-field limit

We show that, in lasers characterized by a slow population dynamics, the expansion of the electric field on longitudinal modes is useful even beyond the uniform-field limit. The dynamical behavior of the laser above the second threshold can be well reproduced by a set of ordinary differential equations, whose integration is much faster than that of the complete Maxwell–Bloch equations. The conditions for the uniform-field limit are also clarified.