Expanding direction of the period doubling operator

We prove that the period doubling operator has an expanding direction at the fixed point. We use the induced operator, a Perron-Frobenius type operator, to study the linearization of the period doubling operator at its fixed point. We then use a sequence of linear operators with finite ranks to study this induced operator. The proof is constructive. One can calculate the expanding direction and the rate of expansion of the period doubling operator at the fixed point.     

Generation of tunable 7-fs ultraviolet pulses: achromatic phase matching and chirp management

Ultraviolet pulses with a duration of 7 fs are efficiently generated by frequency doubling the output of a noncollinear optical parametric amplifier. The ultraviolet pulses are tunable between 275 to 335 nm. The acceptance bandwidth of the doubling crystal is increased by a factor of 80 through high-order achromatic phase matching. The chirp of the visible pulses and the dispersion introduced along the beam path are compensated partially before and partially after the doubling crystal. For the design of the dispersion management, we investigate the second harmonic generation of pulses with mixed orders of chirp and explicitly discuss the transfer of the spectral phase in frequency doubling. A simple analytic theory is derived that correctly describes frequently observed spectral narrowing effects. We find that chirped SHG avoids spectral narrowing and allows for precompression of dispersion encountered in the ultraviolet beam path. We apply chirped SHG to generate 18.7 fs ultraviolet pulses in an extremely simple setup. PACS 42.65.Re; 42.65.Ky; 42.65.Yj     

Roughening and preroughening transitions in crystal surfaces with double-height steps

We investigate phase transitions in a solid-on-solid model where double-height steps as well as single-height steps are allowed. Without the double-height steps, repulsive interactions between up-up or down-down step pairs give rise to a disordered flat phase. When the double-height steps are allowed, two single-height steps can merge into a double-height step (step doubling). We find that the step doubling reduces repulsive interaction strength between single-height steps and that the disordered flat phase is suppressed. As a control parameter a step doubling energy is introduced, which is assigned to each step doubling vertex. From transfer matrix type finite-size-scaling studies of interface free energies, we obtain the phase diagram in the parameter space of the step energy, the interaction energy, and the step doubling energy.     

About the realization of chiral symmetry in QCD2

Two dimensional massless quantum chromodynamics presents many features which resemble those of the true theory. In particular the spectrum consists of mesons and baryons arranged in flavour multiplets without parity doubling. We analyze the implications of chiral symmetry, which is not spontaneously broken in two dimensions, in the spectrum and in the quark condensate. We study how parity doubling, an awaited consequence of Coleman's theorem, is avoided due to the dimensionality of space-time and confinement. We prove that a chiral phase transition is not possible in the theory.     

Efficient green generation by intracavity frequency doubling of an optically pumped semiconductor disk laser

We report the use of bismuth borate for efficient intracavity frequency doubling of an optically pumped semiconductor disk laser. An output power of 220 mW at 529 nm at room temperature has been demonstrated, corresponding to 52% conversion efficiency with respect to the fundamental power. The results are compared to frequency doubling with a potassium titanyl phosphate nonlinear crystal. PACS 42.55.Px; 42.70.Mp; 42.72.Bj     

A broad and tunable 250- to 430-nm source for microscopy and lifetime measurements by frequency doubling of a 78-MHz-picosecond white-light laser

Broadly tunable picosecond pulses in the UV for nonlinear microscopy and lifetime measurements are not yet readily available. Complex synchronously pumped optical parametric oscillators with subsequent frequency doubling are typically used. We show that direct second harmonic generation of a visible picosecond supercontinuum source at 78 MHz renders pulses easily tunable from 250 to 430 nm. We find that an unexpectedly large numerical aperture and the use of thick crystals increase the efficiency of the frequency doubling process dramatically. The observed spectral width and efficiency are nearly two orders of magnitude larger than predicted by conventional theory. With broadband achromatic doubling, a 130 nm wide spectrum is achieved. Pulse durations of 17–35 ps are found in the UV and an average power between 1 and 70 μW. This qualifies the setup for most UV-based microscopic investigations. As first application, the fluorescence lifetime of two differing conformations of 2-(2′-hydroxyphenyl) benzothiazole is measured.     

Reflection positivity and graviton doubling in Euclidean lattice gravity

Lattice Euclidean quantum gravity, formulated in analogy to the usual gauge theories, is considered. We prove that positivity is satisfied only for a special set of quantities which, however, in the continuum limit furnish the expectation values of the closed loops and correlation functions thereof. We work out the perturbative limit by expanding around a flat background in order to examine the particle content of the theory. A doubling phenomenon (analogous to the doubling of lattice chiral fermions) appears; such a phenomenon is shown to be of general nature for a class of lattice formulations of gravity.     

Compensating group-velocity mismatch in parametric frequency generation

We propose and numerically investigate a simple scheme based on frequency-selective mirrors for compensating group-velocity mismatch during harmonic generation. We address the case of frequency doubling and illustrate the effectiveness of the approach for multipass frequency doubling in LiNbO(3).     

Generation of a wide discrete visible spectrum in a frequency-doubling optical fiber

We describe some special features of frequency doubling in a Ge-doped SiO₂ optical fiber. The generation of a multi-frequency visible spectrum in a single short fiber pumped with 1.06 µm radiation is demonstrated. This effect is the result of an interplay between the processes of frequency doubling and third-order nonlinear frequency mixing. Most of the new components coincide with the characteristic stimulated four-wave-mixing spectrum of the fiber, although the power of the internally generated 0.532 µm pump was more than an order of magnitude below the respective thresholds.     

Universal Scalings in Homoclinic Doubling Cascades

Cascades of period doubling bifurcations are found in one parameter families of differential equations in ℝ³. When varying a second parameter, the periodic orbits in the period doubling cascade can disappear in homoclinic bifurcations. In one of the possible scenarios one finds cascades of homoclinic doubling bifurcations. Relevant aspects of this scenario can be understood from a study of interval maps close to x↦p+r(1 −x ^β)², β∈ (?,1). We study a renormalization operator for such maps. For values of β close to ?, we prove the existence of a fixed point of the renormalization operator, whose linearization at the fixed point has two unstable eigenvalues. This is in marked contrast to renormalization theory for period doubling cascades, where one unstable eigenvalue appears. From the renormalization theory we derive consequences for universal scalings in the bifurcation diagrams in the parameter plane. Received: 16 June 1999 / Accepted: 24 April 2001     

Spectroscopy, laser operation at 1.3 μm and self-frequency doubling in GdAl3(BO3)4: Nd

We report for the first time the spectroscopy and the laser operation of GdAl₃(BO₃)₄: Nd³⁺ (NGAB) near 1338 nm corresponding to the ⁴F_3/2→⁴I_13/2 channel. Their features have been found favorable for self-frequency doubling in order to generate a red radiation at 669 nm and more generally for self-frequency conversions. The emission cross-section in σ-polarization was estimated to be 5.5×10⁻²⁰ cm². We demonstrated self-frequency doubling despite of non-optimal experimental conditions.     

Gauge invariance and fermion doubling on the lattice

(1) We consider a possible chiral invariant solution of the lattice fermion doubling problem. This makes the unwanted states decouple in the continuum limit, at least in the non-interacting theory. The introduction of gauge interactions restores doubling. We examine how local gauge invariance makes all the species in a doubled spectrum act alike. (2) We generalise earlier results to show how gauge invariance forces a doubled spectrum on us even when other considerations do not.     

Subcritical period doubling in the Duffing equation-type 3 intermittency,attractor crisis

We study period doubling bifurcations, subcritical period doubling, and type 3 intermittency of the Duffing equation. The Floquet exponents of the linearization show a remarkably ordered structure and serve as a guidance of the solutions when control parameters are changed.     

Nonlinear interactions and scattering of space charge waves in sillenites

For the first time the effects of overall doubling, spatial doubling, and overall rectification of space charge waves in a photorefractive crystal (Bi₁₂GeO₂₀, BGO) have been detected and theoretically studied. The effects of overall doubling and overall rectification resemble second-harmonic generation and rectification of light in nonlinear optics. A good agreement between theory and experiment is found for the effect of spatial doubling, while for overall doubling and overall rectification effects only a qualitative agreement between theory and experiment has been established until now. Received: 13 July 2001 / Published online: 10 October 2001     

The quasi-periodic doubling cascade in the transition to weak turbulence

The quasi-periodic doubling cascade is shown to occur in the transition from regular to weakly turbulent behaviour in simulations of incompressible Navier–Stokes flow on a three-periodic domain. Special symmetries are imposed on the flow field in order to reduce the computational effort. Thus we can apply tools from dynamical systems theory such as continuation of periodic orbits and computation of Lyapunov exponents. We propose a model ODE for the quasi-period doubling cascade which, in a limit of a perturbation parameter to zero, avoids resonance related problems. The cascade we observe in the simulations is then compared to the perturbed case, in which resonances complicate the bifurcation scenario. In particular, we compare the frequency spectrum and the Lyapunov exponents. The perturbed model ODE is shown to be in good agreement with the simulations of weak turbulence. The scaling of the observed cascade is shown to resemble the unperturbed case, which is directly related to the well known doubling cascade of periodic orbits.     

Red, yellow, green and blue – four-color light from a single, aperiodically poled LiTaO3 crystal

We demonstrate simultaneous quasi-continuous wave generation of red, yellow, green and blue coherent radiation based on quadruple quasi-phase matching (QPM) frequency upconversion from a single, aperiodically poled LiTaO₃ (APPLT) crystal with a diode-pumped Nd:YVO₄ dual-wavelength laser oscillating at 1342 and 1064 nm. We designed and prepared an APPLT crystal, which can provide four pertinent reciprocals for simultaneous quadruple QPM processes. Namely, frequency doubling of 1342 nm generates red light at 671 nm, sum-frequency mixing of 1342 nm and 1064 nm produces yellow light at 593 nm, frequency doubling of 1064 nm achieves green light at 532 nm and sum-frequency mixing of 1342 nm and 671 nm obtains blue light at 447 nm. PACS 42.65.Ky; 42.79.Nv; 42.55.Xi; 42.72.Bj     

Finite-size effects on a lattice calculation

We study in this Letter the finite-size effects of a non-periodic lattice on a lattice calculation. To this end we use a finite lattice equipped with a central difference derivative with homogeneous boundary conditions to calculate the bosonic mass associated to the Schwinger model. We found that the homogeneous boundary conditions produce absence of fermion doubling and chiral invariance, but we also found that in the continuum limit this lattice model does not yield the correct value of the boson mass as other models do. We discuss the reasons for this and, as a result, the matrix which cause the fermion doubling problem is identified.     

Turnable Second Harmonic Generation from an Organic Dye Laser

Abstract

Ultraviolet light has been generated from a Rhodamine 60 organic dye laser by frequency doubling with a KDP crystal. The second harmonic was tuned from 2900Å to 3000Å with peak powers of 40 watts.

Organic dye lasers have now been reported with output wave-lengths extending throughout the visible and near infrared^1-12. The tunability^4,6,13 and output energies now available in the visible protion of the spectrum suggest frequency doubling as a means of obtaining a tunable source of ultraviolet light. We wish to report the observation of tunable second harmonic radiation centered at 2950Å generated from the laser output of a 10^?4 molar solution of Rhodamine 6G dissolved in ethyl alcohol.     

An all-solid-state laser source at 671 nm for cold-atom experiments with lithium

We present an all-solid-state narrow-linewidth laser source emitting 670 mW output power at 671 nm delivered in a diffraction-limited beam. The source is based on a frequency-doubled diode-end-pumped ring laser operating on the ⁴ F _3/2→⁴ I _13/2 transition in Nd:YVO₄. By using periodically poled potassium titanyl phosphate (ppKTP) in an external buildup cavity, doubling efficiencies of up to 86% are obtained. Tunability of the source over 100 GHz is accomplished. We demonstrate the suitability of this robust frequency-stabilized light source for laser cooling of lithium atoms. Finally, a simplified design based on intra-cavity doubling is described and first results are presented.     

外腔谐振技术及其应用

本文叙述了连续单模染料激光在外腔谐振中增强的原理,外腔的构成,介绍了外谐振腔在无多普勒光谱测量中的应用,特别在单模连续染料激光倍频中,应用这种外谐振腔使倍频转换效率提高百余倍。