共查询到20条相似文献,搜索用时 187 毫秒
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本文通过菲涅耳-基尔霍夫衍射积分方法,推导了一般稳定和非稳定球面镜谐振腔中自再现模的解析表达式,揭示了从稳定腔变为非稳腔过程中自再现模的变化规律.进一步地,本文在几何光学近似条件下得到了非稳腔的自再现模,通过与衍射积分结果对比,发现基于几何光学近似得到的非稳腔最低阶偶对称模(即基模)和最低阶奇对称模的空间分布与衍射积分结果一致.而对于更高阶的自再现模,当非稳腔接近稳定腔时,几何光学近似得到的自再现模空间分布和衍射积分结果之间存在较大差异.本文的结果可以作为激光原理教学内容的重要补充. 相似文献
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The basic set of fluid equations can be reduced to the nonlinear Kortewege-de Vries (KdV) and nonlinear Schrödinger (NLS) equations. The rational solutions for the two equations has been obtained. The exact amplitude of the nonlinear ion-acoustic solitary wave can be obtained directly without resorting to any successive approximation techniques by a direct analysis of the given field equations. The Sagdeev's potential is obtained in terms of ion acoustic velocity by simply solving an algebraic equation. The soliton and double layer solutions are obtained as a small amplitude approximation. A comparison between the exact soliton solution and that obtained from the reductive perturbation theory are also discussed. 相似文献
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Yang Jing Wen Xiang Lin Yang 《International Journal of Infrared and Millimeter Waves》1998,19(7):963-975
The modified quantum nonlinear Schrodinger equation of ultra-short pulse propagating in fiber is derived using dispersion relation and the Hamiltonian of the transmission system. The derived equation is solved with linearization approximation, and modulation instability is analyzed. The equation is also solved with Hartree approximation. The results indicate that pulse power, loss and self-steeping effect change the critical frequency, the maximum gain and the gain spectrum range, but the third order dispersion has no effect on modulation instability. The expectation value of optical field is average of a set of modified classical solitons, and higher order terms change the amplitude, pulse position and phase of soliton. 相似文献
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The active mode-locking process of the multimode laser with an external pump modulation is theoretically investigated in the frequency domain within the framework of the continuous-mode approximation. Intermode interaction and mode-coupling effects, including both AM and FM modulations, are naturally considered in a hierarchical equation of the mode components derived from the multimode Maxwell-Bloch equations. It is reduced to a continuous-mode equation that can be solved analytically in a stationary case, and used to discuss the spectral line shape and the phase dynamics of mode-components as a function of modulation amplitude and detuning of the modulation frequency. We predict a novel oscillation existing below the threshold of the ordinary complete mode-locking: The intensity of the total electric field yields a stable pulse train but its phase varies irregularly in time. This semi-locked state is characterized by a nonlinear chirping, an asymmetric spectrum, and drifting phases of the field mode-components. 相似文献
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L. M. Kovachev L. I. Pavlov L. M. Ivanov D. Y. Dakova 《Journal of Russian Laser Research》2006,27(3):185-203
We have investigated the evolution of picosecond and femtosecond optical pulses governed by the amplitude vector equation
in the optical and UV domains. We have written this equation in different coordinate frames, namely, in the laboratory frame,
the Galilean frame, and the moving-in-time frame and have normalized it for the cases of different and equal transverse and
longitudinal sizes of optical pulses or modulated optical waves. For optical pulses with a small transverse size and a large
longitudinal size (optical filaments), we obtain the well-known paraxial approximation in all the coordinate frames, while
for optical pulses with relatively equal transverse and longitudinal sizes (so-called light bullets), we obtain new non-paraxial
nonlinear amplitude equations. In the case of optical fields with low intensity, we have reduced the nonlinear amplitude vector
equations governing the light-bullet evolution to the linear amplitude equations. We have solved the linear equations using
the method of Fourier transform. An unexpected new result is the relative stability of light bullets and the significant decrease
in the diffraction enlargement of light bullets with respect to the case of long pulses in the linear propagation regime. 相似文献
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B. V. Novozhilov Z. I. Kaganova A. A. Belyaev 《Russian Journal of Physical Chemistry B, Focus on Physics》2009,3(1):91-98
Various regimes of combustion in end-burning-grain solid-propellant rocket motors were examined within the framework of the phenomenological theory of unsteady combustion. A system of equations capable of describing the interaction between the process of burning and acoustic waves was derived. A specific feature of the problem is that its formulation involves two characteristic times: the acoustic time and oscillation amplitude variation time. These characteristic times differ by about three orders of magnitude, a circumstance that requires a high accuracy of calculations. Based on the quadratic approximation in oscillation amplitude, a simpler method for solving the problem was proposed, according to which only the effects associated with the oscillation amplitude variation time are taken into account. Numerical results were obtained for the simplest model of propellant burning, which contains the minimum number of parameters and disregards entropy waves in the combustion products. The steady and unsteady regimes of burning were identified. In the latter case, nonlinear effects may generate shock waves in the combustion chamber. 相似文献
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Fluorescence quenching of UVITEX‐OB [2,5‐thiophenediylbis(5‐tert‐butyl‐1,3‐benzoxazole)] by aniline in different polar and nonpolar solvents was examined at room temperature by steady‐state fluorescence measurements. Positive deviations from the nonlinear Stern–Volmer plots were observed in most of the solvents indicating the extent of quenching to be large. The quencher concentration dependence data were analyzed using ground‐state complex and sphere of action static quenching models in order to interpret the results. The magnitudes of the quenching rate parameters suggest that a sphere of action static quenching model is expected to describe the data most accurately. Also, the results are suggestive of both static and dynamic quenching processes being responsible for the observed positive deviation in the Stern–Volmer plot. Experimental results are described by an equation derived using the finite sink approximation model, which allows the evaluation of diffusion‐limited interaction and the estimation of encounter distance and mutual diffusion coefficient independently. 相似文献
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We study dynamical behaviors in coupled nonlinear oscillators and find that under certain conditions, a whole coupled oscillator
system can cease oscillation and transfer to a globally nonuniform stationary state [i.e., the so-called oscillation death
(OD) state], and this phenomenon can be generally observed. This OD state depends on coupling strengths and is clearly different
from previously studied amplitude death (AD) state, which refers to the phenomenon where the whole system is trapped into
homogeneously steady state of a fixed point, which already exists but is unstable in the absence of coupling. For larger systems,
very rich pattern structures of global death states are observed. These Turing-like patterns may share some essential features
with the classical Turing pattern.
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Quartz resonators in contact with metal-covered spheres have been used to study the tribology of micron-sized metal-metal contacts at high speed (1 m/sec and high frequency (12 MHz), while maintaining a shear amplitude in the nanometer range. The data aquisition is based on ring-down experiments, where the electrical excitation is periodically interrupted and the free decay of the oscillation is analyzed. At contact, an amplitude-dependent frequency and decay rate are found, indicative of an underlying nonlinear equation of motion. Using perturbation theory and the two-timing approximation, a nonlinear spring constant kappa(1)(x) and a nonlinear drag coefficient xi(1)(x) are explicitly derived. We find a local slip-to-stick-transition at a shear amplitude of 0.5 nm. Coating the gold sufaces with a self-assembled thiol monolayer removes the stick. 相似文献