On the downhill method

An algorithm for the calculation of the propagation constant of integrated optics waveguides was developed. The waveguide may consist of any number of layers with complex refractive indexes due to gain and loss. It allows the additional determination of the field distribution. Thus, all parameters necessary for heterostructure laser development can be calculated. The resulting program was run on a personal computer; numerical results are presented.

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“…In order to find the roots of (19), we used an algorithm similar to the one described in [8]. This "downhill method" works in the following way.…”

Section: Algorithm Numerical Resultsmentioning

confidence: 99%

The complex propagation constant of multilayer waveguides: an algorithm for a personal computer

Schlereth

Tacke

1990

IEEE J. Quantum Electron.

149

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“…Let us consider an specific example, where ðx s ; z s Þ ¼ ð0;70Þ m, ðx r ; z r Þ ¼ ð80;0Þ m, z ¼ 40 m, and the properties in Table 1. We solve equation E-4 by stepwise iteration, using the downhill method (Bach, 1969). The function to be solved must be analytic in the region, where the root is being sought.…”

Section: Examplementioning

confidence: 99%

On Fermat’s principle and Snell’s law in lossy anisotropic media

Carcione

Ursin

2016

GEOPHYSICS

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Fermat's principle of least action is one of the methods used to trace rays in inhomogeneous media. Its form is the same in anisotropic elastic and anelastic media, with the difference that the velocity depends on frequency in the latter case. Moreover, the ray, envelope, and energy velocities replace the group velocity because this concept has no physical meaning in anelastic media. We have first considered a lossy (anelastic) anisotropic medium and established the equivalence between Fermat's principle and Snell's law in homogeneous media. Then, we found that the different ray velocities defined in the literature were the same for stationary rays in homogeneous media, with phase and inhomogeneity angles satisfying the principle and the law. We considered an example of a transversely isotropic medium with a vertical symmetry axis and wavelike and diffusionlike properties. In the first case, the differences were negligible, which was the case of real rocks having a quality factor greater than five. Strictly, ray tracing should be based on the so-called stationary complex slowness vector to obtain correct results, although the use of homogeneous viscoelastic waves (zero inhomogeneity angle) is acceptable as an approximation for earth materials. However, from a rigorous point of view, the three velocities introduced in the literature to define the rays present discrepancies in heterogeneous media, although the differences are too small to be measured in earth materials. The findings are also valid for electromagnetic waves by virtue of the acoustic-electromagnetic analogy.

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“…In the absence of the electron beam, the "hot" dispersion (18) reduces to (11). Once the complex transcendental equation for and in (18) is solved using the downhill method [8], the small signal gain of each period of the circuit is derived from the imaginary part of the solutions for , and indicate the growth of the signal as it propagates through the SWS.…”

Section: Linear Theory Of a Coaxial Ridged Disk-loaded Sws For Rmentioning

confidence: 99%

Analysis of Coaxial Ridged Disk-Loaded Slow-Wave Structures for Relativistic Traveling Wave Tubes

Yue

Wang

Gong

et al. 2004

IEEE Trans. Plasma Sci.

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The coaxial ridged disk-loaded structure which is a new disk-loaded periodic system is presented and analyzed in this paper. As an all-metal slow-wave circuit, it has properties that can be used in high-power traveling wave tubes (TWT) and relativistic TWTs. The dispersion equation and coupling impedance of the structure are investigated in the first part of this paper. The results of numerical calculations of the dispersion relation and coupling impedance with different structure dimensions indicate that the interaction impedance of the ridged disk-loaded structure is higher than that of the disk-loaded structure without ridges in most frequency ranges. In the second part, the "hot" dispersion equation of this circuit with an annular electron beam is obtained according to a self-consistent linear theory. The influence of physical dimensions and beam parameters on the small signal gain is discussed.Index Terms-Coaxial ridged disk-loaded slow-wave structure, coupling impedance, dispersion relation, relativistic travelingwave tube, small signal gain.

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On the downhill method

Cited by 33 publications

References 3 publications

The complex propagation constant of multilayer waveguides: an algorithm for a personal computer

The complex propagation constant of multilayer waveguides: an algorithm for a personal computer

On Fermat’s principle and Snell’s law in lossy anisotropic media

Analysis of Coaxial Ridged Disk-Loaded Slow-Wave Structures for Relativistic Traveling Wave Tubes

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