Cooperative frequency locking and tristability in a class-B laser

The locking and unlocking phenomena of the modes of the transverse familyq=1 in a CO₂ laser are investigated. The experimental results show three characteristic regions: a bistability between two helical waves of opposite handedness, a tristability among the two helicities of opposite handedness and an unlocked state, and the unlocked state. Near the locking threshold, oscillations which can be interpreted as due to the oscillations of the modal amplitudes and relative phase are also observed. These results are found to be consistent with solutions of the two-mode Maxwell-Bloch equations for class-B lasers.     

The influence of misaligned holophote of the axisymmetric-fold-combination CO2 laser on phase locking

Under the condition of ideal phase locking, output beams with excellent coherence from improved axisymmetric-fold-combination (ASFC) CO₂ laser can be obtained. Unfortunately, misalignments are inevitable. The influence of the misalignment of holophote of fold cavity on phase locking is analyzed, and the light intensity distributions are given by numerical simulation. The conclusion is demonstrated that the method of phase locking of the CO₂ laser is fully feasible under the conditions of the ideal and the misaligned. The results have shown that the effect of phase locking is still excellent when the misalignment angle is in the range of tolerance.     

Offset frequency locking for nanosecond laser pulses

A method of multi-pulse discriminating frequency and high probability average value filtering is presented for offset frequency locking with ns laser pulses. In the experiment, the frequency locking for cavity-dumped CO₂ laser with 100 ns pulse width and the repetition rate of 10 kHz was studied. The precision was up to ±2 MHz at the heterodyne frequency 90 MHz. However, it is more than ±10 MHz for the single pulse discriminating frequency. This method can also be applied to laser offset frequency locking for many kinds of short pulse lasers.     

Active mode locking of a high pressure CW waveguide CO2 laser

In this paper, we report on a new concept for active mode locking of lasers. It has been successfully applied to a cw waveguide CO₂ laser and pulse widths as short as 2 ns have been obtained.     

Frequency-domain performance of a femtosecond laser with carrier-envelope phase stabilized by the direct locking method

We analyzed frequency-domain characteristics of a femtosecond laser whose carrier-envelope phase (CEP) was stabilized by the direct locking method (DLM). To evaluate the CEP-stabilized laser with zero carrier-envelope-offset frequency (f _ceo), as imposed by DLM, a self-referencing f-to-2f interferometer with a shifted frequency comb by an acousto-optic modulator was employed in an out-of-loop. The measurement of the square root of triangle variance confirmed that DLM is a phase-locking method. The tight locking was verified from a narrow bandwidth of f _ceo, measured using the out-of-loop interferometer, and from a small frequency jitter measured with a frequency counter referenced to a Rb-clock. The femtosecond laser with CEP stabilized by DLM is, thus, well suited for applications in the frequency domain as well as in the time domain.     

Mode competition and frequency locking

A theoretical study is presented of frequency locking to be observed in lasers with broad homogeneous emission lines, when the cavity losses are reduced, at a certain frequency ω₀, by placing inside the cavity a suitable element (e.g., a selectively reflecting “mirror”). Two kinds of locking effects are analyzed: i) When tuning the center frequency of the laser output ω_f towards ω₀, by means of a filter or a grating, the laser frequency becomes locked to ω₀, when |ω_f ? ω₀| reaches a critical value. ii) In the absence of frequency-selective elements, the laser oscillates only in a narrow spectral range centered at ω₀. Special emphasis is given to the role played by mode competition in these locking phenomena.     

Method to investigate the symmetry of saturated absorption signals by means of laser frequency locking techniques

It is shown that the line shape of a saturated absorption signal — especially its symmetry — can be investigated by combining laser frequency locking methods. The laser frequencyv, modulated with a frequencyf, is stabilized alternatively to the zero crossings of the synchronously detected 2f and 3f absorption signals. In addition, almost any other part of the profile can be tested by locking the laser frequency to neighboruing points of the zero crossings by using an offset technique. With two prestabilized Ar⁺ lasers atv=582 THz the symmetry of different¹²⁷ I ₂ hfs signals was investigated with an uncertainty of typically 2×10^–12 v or 10^–3 halfwidths.     

EIT locking of a semiconductor diode laser: significant improvement over Doppler locking

We report a precise frequency locking technique using electromagnetically induced transparency in an atomic vapour cell for a semiconductor diode laser. The sub natural line-width of EIT (Electromagnetically induced transparency) allows improvement in the stability of the laser diode under the locked condition. D₂ transition of ⁸⁵Rb atom is used for this experiment. Frequency stability of the laser under the locked condition is of the order of 426 kHz which provides nearly 80 times better stability than the Doppler locked condition.     

Tissue characterization using R1rho dispersion imaging at low locking fields

Measurements of the variations of spin-locking relaxation rates (R_1ρ) with locking field amplitude allow the derivation of quantitative parameters that describe different dynamic processes, such as slow molecular motions, chemical exchange and diffusion. In some samples, changes in R_1ρ values between locking frequency 0 and 200 Hz may be dominated mainly by diffusion of water in intrinsic field gradients, while those at higher locking fields are due to exchange processes. The exchange and diffusion effects act independently of each other, as confirmed by simulation and experimentally. In tissues, the relevant intrinsic field gradients may arise from the magnetic inhomogeneities caused by microvascular blood so that R_1ρ dispersion over weak locking field amplitudes (≤ 200 Hz) is affected by changes in capillary density and geometry. Here we first review the theoretical and experimental background to the interpretation of R_1ρ dispersions caused by intrinsic magnetic susceptibility variations within the tissue. We then provide new empirical results of R_1ρ dispersion imaging of the human brain and skeletal muscle at low locking field amplitudes for the first time and identify potential applications of R_1ρ dispersion imaging in clinical studies.     

基于KTP键合晶体的Hansch-Couillaud双波长外腔频率锁定机理

基于KTP键合晶体采用Hansch-Couillaud频率锁定技术实现了双波长外腔同时共振,理论和实验上分别研究了基于键合KTP晶体的HC频率锁定方案. 研究表明,与采用单KTP晶体的结果相比,采用键合KTP晶体进行HC锁频时,能将激光频率分别锁定到e₁光或e₂光的共振峰值. 实验中将环形腔腔模频率锁定到938nm激光器的输出频率上,1583nm激光器的输出频率锁定到环形腔腔模频率上,从而实现了三者之间的相位关联锁定. 关键词： 键合KTP晶体 Hansch-Couillaud锁频 双波长外腔共振     

Flame locking of dye lasers to atom lines

Frequency locking of N₂-laser-pumped, flash-pumped and continuous-wave dye lasers near the non-inverted 3S-3P Na atom transitions is obtained by placing sodium vapor produced in a flame inside the untuned dye laser cavity. Several possible causes for the spectral condensation of the dye emission are suggested.     

Phase locking and bandwidth in a gyrotron oscillator

For imaging radar and for satelitte and space communication (e.g. NASA's deep space network), it is important that the bandwidth be as large as possible. Here we derive a formalism for computing the phase locking bandwidth that can be achieved in a gyrotron oscillator while varying the beam voltage. As an example, a second harmonic TE_02/03 gyrotron is considered. For this device, the effective bandwidth can be increased by a factor of about 3 compared with the fixed voltage case by allowing the beam voltage to change together with the input locking signal.     

Limits in CW injection-locking of stable resonator CO2 TEA lasers

The performances of CW injection-locking of CO₂ TEA lasers at line center and at ～600 MHz off line center are compared experimentally. Heterodyning of the injection frequency permits one to measure accurately the locking bandwidth as a function of the injected intensity. The minimum intensities needed to obtain reproducible frequency-looking were found to be 0.5 μW/cm² and 0.2 mW/cm² respectively. An analytical approach is described for predicting the tunability of injection-locked stable resonator CO₂ TEA lasers.     

Additive-pulse mode locking of a diode-pumped Nd:KGd(WO4)2 laser

Self-starting additive-pulse mode locking of a diode-pumped Nd:KGd(WO₄)₂ laser is demonstrated for the first time. An output power of 0.85 W is achieved with 2.3-ps pulses at a repetition frequency of 76.5 MHz. The shortest pulse generated had a duration of 1.9 ps. Received: 2 May 2002 / Published online: 25 October 2002 RID="*" ID="*"Corresponding author. Fax: +44-141/5482891, E-mail: a.major@phys.strath.ac.uk     

The effect of CO2 on the speciation of bromine in low‐temperature geological solutions: an XANES study

CO₂‐rich solutions are common in geological environments. An XANES (X‐ray absorption near‐edge structure) study of Br in CO₂‐bearing synthetic fluid inclusions has revealed that Br exhibits a strong pre‐edge feature at temperatures from 298 to 423 K. Br in CO₂‐free solutions does not show such a feature. The feature becomes smaller and disappears as temperature increases, but reappears when temperature is reduced. The size of the feature increases with increasing X(CO₂) in the fluid inclusion, where X(CO₂) is the mole fraction of CO₂ in the solution [n_CO2/(n_CO2 + n_H2O + n_RbBr); n indicates the number of moles]. The pre‐edge feature is similar to that shown by covalently bonded Br, but observed and calculated concentrations of plausible Br‐bearing covalent compounds (Br₂, CH₃Br and HBr) are vanishingly small. An alternative possibility is that CO₂ affects the hydration of Br sufficiently that the charge density changes to favour the 1s–p level transitions that are thought to cause the pre‐edge peak. The distance between the first two post‐edge maxima in the XANES also decreases with increasing X(CO₂). This is attributed to a CO₂‐related decrease in the polarity of the solvent. The proposed causes of the observed features are not integrated into existing geochemical models; thus CO₂‐bearing solutions could be predicted poorly by such models, with significant consequences for models of geological processes such as ore‐formation and metamorphism.     

High-power high beam-quality multi-waveguide CO<Subscript>2</Subscript> amplifiers

The results from modeling the energy characteristics of a multi-waveguide power amplifier are presented. The optical schemes and calculations for the most promising circuits of multichannel waveguide CO₂ amplifiers are given. The amplifying system itself removes the problem of phase locking in individual channels of multichannel systems. The experimental results from the synchronization of arrays of multichannel waveguide CO₂ lasers allow the production of high-power (up to 15 kW) high beam-quality multibeam lasers. Technological lasers with such properties have yet to be produced anywhere in the world.     

Harmonic mode locking with reduced carrier-envelope phase noise in ytterbium-doped fiber laser

We experimentally explored the influence of passive harmonic mode locking on the temporal and spectral features of a ytterbium-doped fiber laser. Similar dependences of free-running linewidth of the laser carrier-envelope offset frequency (f₀) on the intracavity net dispersion were observed for the fundamental-, second-, and third-order mode-locking states. Due to the reduction of nonlinear effects and supermode phase locking that balanced the third-order dispersion in the fiber cavity, the third-order harmonic mode-locking exhibited the narrowest free-running f₀linewidth of ～120 kHz in the near-zero net dispersion regime.     

Theory of laser noise in the phase locking region

We start from quantum mechanical laser equations which were derived in a previous paper for an inhomogeneously broadened laser and which contain in particular the noise sources due to cavity losses, vacuum fluctuations, interaction with phonons and nonlasing photons and the pump. For the example of frequency locking caused by the nonlinear polarization we derive a quantum mechanical Langevin equation for the relative phase angleψ=2ψ ₂ —ψ ₁-ψ ₃, whereψ ₁,ψ ₂,ψ ₃, are the total phases of three axial modes which would be equally spaced in the unloaded cavity. In the resulting equation

$$\dot \psi = \delta - \beta \sin \psi + f(t)$$     

Mesh locking effects in the finite volume solution of 2-D anisotropic diffusion equations

Strongly anisotropic diffusion equations require special techniques to overcome or reduce the mesh locking phenomenon. We present a finite volume scheme that tries to approximate with the best possible accuracy the quantities that are of importance in discretizing anisotropic fluxes. In particular, we discuss the crucial role of accurate evaluations of the tangential components of the gradient acting tangentially to the control volume boundaries, that are called into play by anisotropic diffusion tensors. To obtain the sought characteristics from the proposed finite volume method, we employ a second-order accurate reconstruction scheme which is used to evaluate both normal and tangential cell-interface gradients. The experimental results on a number of different meshes show that the scheme maintains optimal convergence rates in both L² and H¹ norms except for the benchmark test considering full Neumann boundary conditions on non-uniform grids. In such a case, a severe locking effect is experienced and documented. However, within the range of practical values of the anisotropy ratio, the scheme is robust and efficient. We postulate and verify experimentally the existence of a quadratic relationship between the anisotropy ratio and the mesh size parameter that guarantees optimal and sub-optimal convergence rates.     

Calculation on the CO2 influences on the structure,stability of (MgO)m (m = 1–6) clusters

ABSTRACT

The concentration of carbon dioxide (CO₂) has a significant influence on the morphology of thermal decomposition products of magnesite. So, structures, stabilities and adsorption mechanisms of (MgO)_m (m?=?1–6) clusters by one or two CO₂ molecules were calculated by the GGA-PW91 method. The results show that the stability of the considered clusters is (MgO)_m(CO₂)₂ clusters > (MgO)_m(CO₂) clusters > (MgO)_m clusters by the average binding energy. Certain low-lying isomers of (MgO)_m(CO₂) and (MgO)_m(CO₂)₂ clusters which have an isolated O atom are deviating from the cluster center which possess higher kinetic activity. (MgO)_m clusters prefer to adsorb a CO₂ molecule, while (MgO)₃(CO₂) clusters prefer to adsorb a CO₂ molecule rather than the neighbors. Magnesite is difficult to transit to (MgCO₃)₂ clusters at room temperature. However, magnesite will spontaneously transit to (MgO)₂ clusters and further transit to MgO crystal which need to adsorb more energy at 700?K.