External optical feedback effects in a frequency locking dual frequency laser

We present a systematic study of external optical feedback effects on the output characteristics of the two orthogonally polarized modes in a frequency locking dual frequency laser. Accompanied by the change of the external cavity length, the length of the resonance cavity is changed very slowly to set the oscillating modes sweeping across the laser gain curve. Comprehensive results are obtained and a strong mode competition is observed. Particularly, when the laser runs in the middle region of the gain curve, which mode can oscillate is determined by the movement direction of the external feedback mirror. Based on the phenomenon, a displacement sensor with directional discrimination is proposed and its capability is also discussed.     

Applications of non-collinear second harmonic generation in one-dimensional periodically poled crystals

Whereas the commonly used collinear quasi-phase-matched interaction is usually suitable for phase matching only a single nonlinear process, non-collinear interactions offer rich variety of phase matching possibilities, employing different elements of the nonlinear tensor, and various orders of quasi phase matching. By studying the dependence of the second harmonic process on the angle and the phase matching order in a periodically poled LiNbO₃ crystal, we can non-destructively derive the duty cycle of the structure. The obtained duty cycle agrees well with surface scan measurements using an atomic force microscope. Furthermore, by proper selection of the non-collinear angle, we demonstrate simultaneous second harmonic generation of two cross polarized waves.     

Formation pathways of HO2 and OH changing as a function of temperature in photolytically initiated oxidation of dimethyl ether

The time resolved product formation in oxidation of dimethyl ether (DME) has been studied between 298-625 K and 20-90 torr total pressure. Near-infrared frequency modulation spectroscopy (FMS) with Herriott type multi pass optics and UV absorption spectroscopy (UV) were conducted in the same cell. The reaction was initiated by pulsed photolysis in a mixture of Cl₂, O₂, and DME via CH₃OCH₂ radical formation. The reaction process was investigated through FMS measurement of HO₂ and OH, and UV measurement of CH₃OCH₂O₂. The yields of HO₂ and OH are obtained by comparison with reference mixtures, Cl₂, O₂, and CH₃OH for HO₂, and Cl₂, O₂, CH₃OH, and NO for OH, which convert 100% of initial Cl to HO₂ and OH. The CH₃OCH₂O₂ yield is also obtained. It was found that the HO₂ yield increases sharply over 500 K mainly with a longer time constant than that of R + O₂ reaction, while a prompt component exists throughout the temperature range at a few percent yield. OH was found to be produced promptly at a yield considerably larger than that known for the simplest alkanes. The CH₃OCH₂O₂ profile has a prompt rise followed by a gradual decay whose rate is consistent with the slow HO₂ formation. The species profiles were successfully predicted with a model constructed by modifying the existing one to suit the reduced pressure condition. After modification, it was inferred that the HO₂ formation over 500 K is secondary from HCHO + OH and HCO + O₂ and a part of HCO is formed directly from the O₂ adduct, whereas the HO₂ formation below 500 K is governed by CH₃OCH₂O₂ chemistry. The HCO forming pathway via isomerization-decomposition of the O₂ adduct, which was not included in the former models, was supported by our quantum-chemical calculations.     

Wave propagation in thermo-chiral elastic medium

The propagation of time harmonic waves through an infinite thermo-chiral elastic material has been investigated. The elastic field of thermo-chiral medium has been described by extending the governing equations and constitutive relations of hemitropic micropolar material to include temperature field. Seven basic waves consisting of three coupled dilatational waves and four coupled shear waves traveling with distinct speeds may exist in the medium. All the waves are found to be dispersive, however the coupled dilatational waves are attenuating and temperature dependent, while the coupled shear waves are independent of temperature field. The phase speeds and corresponding attenuation quality factors of all the coupled dilatational waves have been computed numerically for a specific model. The effect of chirality and temperature field have been shown graphically.     

Two-pattern strings II—frequency of occurrence and substring complexity

The previous paper in this series introduced a class of infinite binary strings, called two-pattern strings, that constitute a significant generalization of, and include, the much-studied Sturmian strings. The class of two-pattern strings is a union of a sequence of increasing (with respect to inclusion) subclasses T_λ of two-pattern strings of scope λ, λ=1,2,…. Prefixes of two-pattern strings are interesting from the algorithmic point of view (their recognition, generation, and computation of repetitions and near-repetitions) and since they include prefixes of the Fibonacci and the Sturmian strings, they merit investigation of how many finite two-pattern strings of a given size there are among all binary strings of the same length. In this paper we first consider the frequency f_λ(n) of occurrence of two-pattern strings of length n and scope λ among all strings of length n on {a,b}: we show that lim_n→∞f_λ(n)=0, but that for strings of lengths n2λ, two-pattern strings of scope λ constitute more than one-quarter of all strings. Since the class of Sturmian strings is a subset of two-pattern strings of scope 1, it was natural to focus the study of the substring complexity of two-pattern strings to those of scope 1. Though preserving the aperiodicity of the Sturmian strings, the generalization to two-pattern strings greatly relaxes the constrained substring complexity (the number of distinct substrings of the same length) of the Sturmian strings. We derive upper and lower bounds on C₁(k) (the number of distinct substring of length k) of two-pattern strings of scope 1, and we show that it can be considerably greater than that of a Sturmian string. In fact, we describe circumstances in which lim_k→∞(C₁(k)−k)=∞.     

A frequency response study of thiophene adsorption in zeolite catalysts

The frequency response (FR) technique has been applied to study adsorption processes of thiophene (TP) on NaY zeolite and CeY zeolite. The FR spectra of TP on NaY and CeY were recorded at temperatures between 335 and 473 K and in the pressure range of 0.1-4.0 Torr. On NaY and CeY, adsorption of thiophene (TP) in the supercage is found to be the rate-controlling step and diffusion of benzene in the supercage is the rate-controlling step, respectively. On NaY, the adsorption process by π-electronic interaction of TP and adsorption via pore-filling mechanism were caught. Adsorption by π-electronic interaction is not the main sorption process but its effect is significant. While on Ce³⁺Y, the adsorption processes relating to the π-complexation and the direct forming of SM bond were observed, the adsorption by forming π-complexation is the main process. The relaxation time of the strong sorption interaction coming from the FR spectrum is two orders magnitude shorter than that of the weak adsorption process and the number of sites available for adsorption of TP in each process is calculated. The value of relaxation time reflects the ability of different processes and concentration of adsorption site. Combining the FR spectra and other methods such as isotherms and Langmuir model, thoroughly understanding of the thiophene adsorption process in zeolites can be got.     

Gaussian wavelet based dynamic filtering (GWDF) method for medical ultrasound systems

In this paper, a novel dynamic filtering method using Gaussian wavelet filters is proposed to remove noise from ultrasound echo signal. In the proposed method, a mother wavelet is first selected with its central frequency (CF) and frequency bandwidth (FB) equal to those of the transmitted signal. The actual frequency of the received signal at a given depth is estimated through the autocorrelation technique. Then the mother wavelet is dilated using the ratio between the transmitted central frequency and the actual frequency as the scale factor. The generated daughter wavelet is finally used as the dynamic filter at this depth. Frequency-demodulated Gaussian wavelet is chosen in this paper because its power spectrum is well-matched with that of the transmitted ultrasound signal. The proposed method is evaluated by simulations using Field II program. Experiments are also conducted out on a standard ultrasound phantom using a 192-element transducer with the center frequency of 5 MHz. The phantom contains five point targets, five circular high scattering regions with diameters of 2, 3, 4, 5, 6 mm respectively, and five cysts with diameters of 6, 5, 4, 3, 2 mm respectively. Both simulation and experimental results show that optimal signal-to-noise ratio (SNR) can be obtained and useful information can be extracted along the depth direction irrespective of the diagnostic objects.     

Boundary feedback stabilization of the undamped Timoshenko beam with both ends free

In this paper, we study a boundary feedback system of a class of nonuniform undamped Timoshenko beam with both ends free. We give some sufficient conditions and some necessary conditions for the system to have exponential stability. Our method is based on the operator semigroup technique, the multiplier technique, and the contradiction argument of the frequency domain method.     

Exponentially fitted methods applied to fourth-order boundary value problems

Fourth-order boundary value problems are solved by means of exponentially fitted methods of different orders. These methods, which depend on a parameter, can be constructed following a six-step flow chart of Ixaru and Vanden Berghe. Special attention is paid to the expression for the error term and to the choice of the parameter in order to make the error as small as possible. Some numerical examples are given to illustrate the practical implementation issues of these methods.