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Can light be spatially confined and transported in free space without angular spread? Although the wave nature of light precludes the existence of such an idealization, light can take | Fundamentals of Photonics Bahaa E. A. Saleh Malvin Carl Teich Copyright 1991 John Wiley Sons Inc. ISBNs 0-471-83965-5 Hardback 0-471-2-1374-8 Electronic CHAPTER 3 BEAM OPTICS THE GAUSSIAN BEAM A. Complex Amplitude B. Properties TRANSMISSION THROUGH OPTICAL COMPONENTS A. Transmission Through a Thin Lens B. Beam Shaping C. Reflection from a Spherical Mirror D. Transmission Through an Arbitrary Optical System HERMITE - GAUSSIAN BEAMS LAGUERRE - GAUSSIAN AND BESSEL BEAMS The Gaussian beam is named after the great mathematician Karl Friedrich Gauss 17771855 . Lord Rayleigh John W. Strutt 1842-1919 contributed to many areas of optics including scattering diffraction radiation and image formation. The depth of focus of the Gaussian beam is named after him. 80 Can light be spatially confined and transported in free space without angular spread Although the wave nature of light precludes the existence of such an idealization light can take the form of beams that come as close as possible to spatially localized and nondiverging waves. A plane wave and a spherical wave represent the two opposite extremes of angular and spatial confinement. The wavefront normals rays of a plane wave are parallel to the direction of the wave so that there is no angular spread but the energy extends spatially over the entire space. The spherical wave on the other hand originates from a single point but its wavefront normals rays diverge in all directions. Waves with wavefront normals making small angles with the z axis are called paraxial waves. They must satisfy the paraxial Helmholtz equation derived in Sec. . An important solution of this equation that exhibits the characteristics of an optical beam is a wave called the Gaussian beam. The beam power is principally concentrated within a small cylinder surrounding the beam axis. The intensity distribution in any transverse plane is a circularly symmetric Gaussian function centered about the beam axis. The width of this .