Download Applied optics and optical engineering,Vol.X by Robert R. Shannon and James C. Wynant PDF

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By Robert R. Shannon and James C. Wynant

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E. E(ρ, ψ, 0) = iφˆ J1 (αρ) exp −ρ 2 /w02 . 31) They derived analytical expressions for the propagation of this azimuthally polarized Bessel–Gauss beam in free space by solving the Fresnel diffraction integral. They also considered the linearly polarized fundamental Bessel–Gauss beam and found that, apart from the polarization vector and a phase factor, the far-field distributions of the two are similar. A more detailed study of the subject was conducted by Greene and Hall (1996); see also Seshadri (2008).


Figure 7a, where we have taken c = 0, illustrates the electric energy density and shows that the axial intensity is zero. Because of the incoherent superposition of a continuum of coherent single-ring contributions, the other minima are largely smoothed out. 25) Wφφ (x1 , 0, z, x1 , 0, z)Wφφ (x2 , 0, z, x2 , 0, z) are illustrated in Figure 7b and 7c, respectively, for c = 0. 24). The absolute value of the complex degree of azimuthal spatial coherence is shown in (b) and its phase in (c). 5. POLYCHROMATIC AND PULSED LOCALIZED WAVES Thus far we have assumed that the propagation-invariant field is either fully monochromatic or (in the case of partial coherence) we have considered a statistically stationary field at a single angular frequency ω.

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