By Y.T. Lo, S. W. Lee
Quantity 1: Antenna basics and Mathematical ideas opens with a dialogue of the basics and mathematical concepts for any type of paintings with antennas, together with simple ideas, theorems, and formulation, and methods. DLC: Antennas (Electronics)
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Additional info for Antenna Handbook - Fundamentals and Mathematical Techniques
New York, 1993), p. 33 26 2 Optical Properties and Optical Spectroscopy of Rare Earth Ions in Solids 15. C. Gorrller-Walrand, K. Binnemans, Handbook on the Physics and Chemistry of Rare Earths, vol. 25 (Elsevier Science, 1998), p. 167 16. E. McCumber, Theory of phonon-terminated optical lasers. Phys. Rev. 134(2A), A299– A306 (1964) 17. J. S. Quimby, General procedure for the analysis of Er3+ cross sections. Opt. Lett. 16(4), 258–260 (1991) 18. H. N. Sandoe, S. Parke, Variations of Nd3+ cross section for stimulated emission with glass composition.
On a practical note, for fiber laser development in which Yb3+ glass plays a central role, it is practically impossible to perform a calculation of the Judd-Ofelt parameters and therefore calculate cross-section values using Judd-Ofelt theory because there is only a 2 F5=2 ! , essentially a two-level transition) for Yb3+. Other theoretical methods (described later) are used in the case of Yb3+ to determine cross-section values of optical transitions. 2 McCumber Theory In a glass environment, rare earth ions demonstrate broad emission and absorption spectra; therefore, the previously introduced Einstein relationships need to be adjusted.
The theory gives the following expression for the oscillator strength of the electric dipole transition (f ed) : fijed ¼ 2 X 2 8p2 mm ð n2 þ 2Þ Â Â Xk f N J jUk jf N J 0 3hð2J þ 1Þ 9n k¼2;4;6 ð2:19Þ where i is the initial state of the transition, j is the final state of the transition, v is the transition frequency, n is the refractive index of the host material, m is the electron mass, and hf N J jjUk jjf N J 0 i are the reduced matrix elements, tabulated in . Within this theory, the strength of any transition f can be determined by a set of three parameters: Xi (i = 2, 4, 6; see Eq.
Antenna Handbook - Fundamentals and Mathematical Techniques by Y.T. Lo, S. W. Lee