Illumination Gaussian approximation

Fig. 20-4 (a) The fraction of total power in a uniform beam that excites modes of a step-profile fiber as a function of the tilt angle 0j, where P includes all modes with the same values of U in Fig. 14-4, and bm is the total excited power [2]. (b) Variation of the excitation efficiency with the fiber parameter for on-axis illumination, where solid curves denote the exact solution of Eq. (20-27c) and the dashed curve is the Gaussian approximation of Eq. (20-28a). (d) The corresponding curves for the fundamental mode for various ratios of beam to core radii calculated from Eqs. (20-27c) and (20-28b). (c) Plots of Pq/Pi for the fundamental mode and different ratios of beam to core radii. 

The expression in Eq. (20-30) for the fundamental-mode efficiency is also the result which we would obtain using the Gaussian approximation of Eq. (20-24) for an arbitrary profile. Thus we have a general expression for lens illumination. For example. Table 15-2, page 340, gives Tq = p/(21n for the step profile, and at K = 2.4 the error between Eq. (20-30) and an exact analysis is less than 1 % [10]. 

Fig. 20-7 (a) The fraction of power, calculated from Eq. (20-34X that enters the fundamental mode as a function of the angular spread 0 of a diffuse source for step (sX Gaussian (g) and infinite parabolic (p) profile fibers, (b) The percentage error in the geometric optics analysis of totally incoherent illumination of a multimode fiber as a function of the fiber parameter. The solid curve is the exact result calculated from Eq. (20-39) and the dashed curve is the approximation of Eq. (20-41) [11]. 

Many optical particle sizing instruments and particle characterization methods are based on scattering by particles illuminated with laser beams. A laser beam has a Gaussian intensity distribution and the often used appellation Gaussian beam appears justified. A mathematical description of a Gaussian beam relies on Davis approximations [45]. An nth Davis beam corresponds to the first n terms in the series expansion of the exact solution to the Maxwell equations in power of the beam parameter s,... 

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