Hillion's proof of the nonexistence of certain solutions ofMaxwell's equations

The author notes that P. Hillion (see ibid., vol.33, no.2, p.144-5, 1991) has greatly simplified the author's proof that Maxwell's equations have generally no solution in the case of propagation of electromagnetic signals in lossy media. He clarifies some remarks on conservation of energy and causality law     

Comments on `Solutions of Maxwell''s equations for generalnonperiodic waves in lossy media by M.E. El-Shandwily

The commenter notes that the intention of M.E. El-Shandwily's paper (see ibid., vol.30, no.4, p.577-82, Nov. 1988) is to demonstrate that the linear Maxwell's equations can be applied to the case of a pulse or step-function field change. If this can be demonstrated, then, it is claimed, the Harmuth Ansatz (see ibid., vol.EMC-28, no.4, p.250-8, Nov. 1986) for solving Maxwell's equations to obtain the magnetic field for impulse excitation is unnecessary. The commenter seeks to show that El-Shandwily actually implements the Harmuth Ansatz, which explains the concurrence of Harmuth's and El-Shandwily's predictions     

A comparison of transient solutions of Maxwell's equations to thatof the modified Maxwell's equations

In 1986 H.F. Harmuth introduced a modification of Maxwell's equations to study the propagation of transient electric and magnetic field strengths in lossy media. Opponents of this modification of Maxwell's equations have claimed and attempted to demonstrate that Maxwell's equations in their known forms can correctly be solved, for example by the Laplace transformation method, to obtain solutions of transient electric and associated magnetic field strengths in lossy media without encountering any difficulties. This work presents detailed computer plots of Harmuth's transient solutions of the modified Maxwell's equations and that of Maxwell's equations solved by the Laplace transformation characteristic for the two solutions, which indicate that they are not the same. It is shown that Harmuth's procedure results in physically more plausible solutions     

On approximate analytical solutions of rate equations for studying transient spectra of injection lasers

We discuss the feasibility of constructing approximate, analytical solutions of the rate equations for an injection laser with several longitudinal modes. By adjusting a few empirical parameters it is possible to reproduce the principal features of the exact numerical solutions for the electron and photon densities and to provide explicit expressions for the frequency and time decay rates of the relaxation oscillations. The solutions show that the relative powers of the modes change continually during the transient period. Initially, many longitudinal modes begin to oscillate with nearly equal amplitudes which decay at different rates until they settle down to form a Lorentzian, steady-state distribution. In short lasers (<50 mum) this behavior permits a single mode to establish itself rapidly, leading to single wavelength operation. The decay rates of the longitudinal laser modes are found to be inversely proportional to their corresponding steady-state mode amplitudes.     

Comments on the self-focusing of short light pulses

A simple analysis of the self-focusing of a short pulse shows that the distance at which the focal region first appears exceeds the minimum focusing distance Zfby an amount dependent upon the initial pulsewidth. This focal region subsequently expands as it moves down the medium, the limiting width being the width of the portion of the pulse above the critical power.     

超短腔染料激光器时间特性的研究

超短腔染料激光器可产生窄脉冲，可调谐激光脉冲输出~[1～3]。输出激光的时间特性与泵浦激光强度有关，选择合适的泵浦强度则可获得单脉冲激光，而在较高的泵浦强度时，则产生     

Comments on “transient radiation of traveling-wave wireantennas”

Wu and Ruan (see ibid., vol.41, p.120-23, 1999), based on the formalism of Podosenov, Svckis and Sokolov (1995), tried to calculate the electromagnetic radiation field from the current of a traveling wave propagating along a thin curvilinear wire with free ends. In this article the author tries to prove that in the paper of Wu et al. one problem was substituted by another. In fact, another problem, but not that which was formulated by the authors, was solved. It is not the problem of radiation from a curvilinear antenna of finite length, but the problem of radiation from part of an infinite antenna and two external sources emerging under a forcible requirement of satisfying the Lorentz condition for a subsystem, where this condition does not operate a fortiri. The proof is based on the following easily verifiable facts: (1) a coincidence of the expressions for the magnetic field; and (2) a dissimilarity of the expression for the electric field from the formula to a forcible imposing of the Lorentz condition being invalid for subsystems. The author comments on the second point in more detail     

Comments on the solutions of dipoles in semi-infinite media

It is pointed out that Baños's formulas of the contribution from the pole in the evaluation of the Hertz vector for the radiation field of a dipole cannot be applied even when both the dipole and the observing point are in the lossy half-space due to the approximate method for the integration.     

Comments on recent solutions to the inverse black body radiationproblem

It is shown that both the Boltzmann and the Gibbs maximum-entropy (ME) methods are appropriate for the underdetermined inverse black body radiation problem. The choice of either or an alternative method is subjective. With a minimum of assumptions they are attractive alternatives to other formally correct but impractical solutions. The ME solutions illustrate, by means of a synthetic data example, the strong dependence of a most probable coldness distribution on measured data     

Comments, on `Three-dimensional finite, boundary, and hybridelement solutions of the Maxwell equations for lossy dielectric media'[and reply]

For the original article see ibid., vol.36, no.4, p.682-93 (1988). The commenters point out a potential source of error with the finite-element analysis of the vector wave equation in the paper of K.D. Paulsen, et al. Specifically, this error source is connected with the finding that, if spurious modes exist in the finite-element solution of the eigenvalue problem, the corresponding solution to the externally driven problem may consist of some linear combination of the nonphysical spurious modes in addition to the physical modes. In replying, the author acknowledges the importance of the question of spurious modes     

Direct solutions of sparse network equations by optimally ordered triangular factorization

Matrix inversion is very inefficient for computing direct solutions of the large sparse systems of linear equations that arise in many network problems. Optimally ordered triangular factorization of sparse matrices is more efficient and offers other important computational advantages in some applications. With this method, direct solutions are computed from sparse matrix factors instead of from a full inverse matrix, thereby gaining a significant advantage in speed, computer memory requirements, and reduced round-off error. Improvements of tea to one or more in speed and problem size over present applications of the inverse can be achieved in many cases. Details of the method, numerical examples, and the results of a large problem are given.     

Effect of surface recombination on the transient decay of excess carriers produced by short wavelength laser pulses

Effect of surface recombination on the transient decay of excess carriers injected very near to the surface region has been analysed for a semi-infinite semiconductor sample. The one dimensional continuity equation for the excess minority carriers has been solved analytically assuming that the surface recombination is important only on the front surface from which the excess carriers are injected. The decay of total excess carrier charge as a function of time is calculated for various values of the surface recombination velocities. It is found that values of S lower than 10³ cm/sec. have little effect on the decay of total excess charge and the decay is exponential. For values of S larger than 10⁴ cm/sec. the initial decay of excess charge is much faster and is dominated by the surface recombination. However, if one waits long enough for the excess carrier to diffuse into the semiconductor the decay becomes exponential when the excess charge decays to about 5% of its initial value. This exponential decay can be used to determine the excess carrier lifetime fairly accurately. A source of error in such experiments may arise from the heating of the silicon sample by the laser pulse. This effect, however is negligible for short duration pulses of low average power.     

Comments on "Thermal transient effects in optically pumped repetitively pulsed lasers"

The expression for temperature transients for optically pumped cylindrical laser rods has been derived. The earlier derivation of Chun and Bischoff was dimensionally incorrect. This anomaly has been rectified. The heating of the laser rod has been approximated by considering instantaneous generation of heat on the cylindrical surface.     

考虑腔内光强高斯分布时调Q激光器的速率方程及其解

在主动调Ｑ激光器速率方程中考虑腔内光强的高斯分布,数值求解该速率方程得至归一化的脉冲能量、峰值功率和脉冲宽度与泵浦条件之间的关系,并做图表示,同时与采用平面波近似时所得结果进行比较,并对相关问题进行讨论。     

Theoretical solutions of transient radiation from traveling-wavelinear antennas

Analytic expressions based on time-domain integral equations for the electric and magnetic field intensities are developed for linear antennas of finite length. With the help of Fourier transformation and successive partial integrations, explicit closed-form expressions for the transient radiation are obtained. There are no restrictions on the waveform of the current along the antennas, the length of antennas, and the position of observations. The method can also be adopted to solve for the transient radiations due to reflected traveling-wave currents along the antennas, with similar results     

Reply to Comments on Maxwell's equations by J.E. Gray and S.P.Bowen

J.E. Gray and S.P. Bowen (see ibid., vol.30, no.4, p.586-9, Nov. 1988) use a modification of Maxwell's equations by substituting distributions for functions differentiable in the sense of Leibnitz and Newton. The commenter notes that the work of Gray and Bowen confirms what he has claimed previously, i.e. that Maxwell's equations must be modified. The commenter then considers which modification(s) can explain all the experimental results that the current theory cannot explain     

Comments on `Correction of Maxwell's equations for signals I andII' [by R.J. Mohr]

The commenter states that Harmuth's (see ibid., vol.28, no.4, p.250, 1986) characterization of Godel's (1931) work is incorrect, or, at the very best, extremely misleading. He also states that Godel did not show, as Harmuth claims, that every statement cannot be proven and that they can only be disproven using counterexample     

Generalized solutions of semistate equations and stability

In this paper, solvability and stability of nonlinear, time-varying semistate equations is discussed. It is shown that generalized solutions exist in a vicinity of an equilibrium. Moreover, results on a Liapunov-like (uniform, asymptotic) stability are given.