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Unformatted text preview: Notes #6, ECE594I, Fall 2009, E.R. Brown 101 Gaussian-beam methodology A key assumption behind the predictions given from scalar diffraction theory is that the illumination across the aperture is uniform. This is a good assumption in some circumstances such as predicting the power collected by a receive antenna from a distance source whose pattern beam-width measured at the receive antenna is much larger than the lateral extent of the receive antenna. But there are other times when the uniform-intensity assumption is inaccurate, such as in describing the radiation coupled to a fundamental-mode feedhorn or planar antenna by a second feedhorn or antenna a short distance away. This situation arises in many THz transceivers and simple bench-top set-ups where the power is transferred in free space “quasi-optically” from component-to-component; i.e, using traditional optical components from the visible region of the spectrum, such as lenses, but at the much longer wavelengths of THz or even lower-frequencies. As a matter of fact, such “quasi-optical” techniques started early in the history of microwave and millimeter-wave systems, but have been gradually replaced by transmission-line or guided-wave coupling techniques as printed integrated circuits have become available. However, quasi-optical techniques persist in the THz region, largely because integrated circuits are much less prevalent, and the transmission lines and waveguides that interconnect them have much greater attenuation than at lower frquencies. One of the useful features of scalar-diffraction theory is its ability to predict what happens to the radiation once the uniform-illumination assumption is violated. For example, if the aperture is circular and if the illumination distribution is a Gaussian in the lateral plane with respect to the axis of symmetry, then the radiation pattern is also Gaussian, at least in the far-field limit. Intuitively, this makes sense since in this limit the Fresnel-Kirchoff integral reduces to a Fourier transform, and the Fourier transform of a Gaussian is always a Gaussian. It turns out that this result, commonly known as the Gaussian beam pattern, also applies to the near-field behavior with increasing accuracy as d/ λ increases far beyond unity. Although the Gaussian-beam result was known early in the history of electromagnetics, it was apparently not fully appreciated until the advent of the laser. The gain media in gas and solid-state lasers typically have very large values of d/ λ , and generally emit much greater intensity at the center than at the lateral edges. A useful way to develop the Gaussian behavior is to model the gain medium with a quadratic complex refractive-index lateral profile....
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- Spring '09
- Gaussian beam, Beam Waist, E.R. Brown