Optics of Gaussian Beams

We note that the term quasioptics implies that it is not sufficient to borrow familiar optical concepts, such as point focus, the lensmaker s equation, etc. without modification. In fact, diffraction plays a crucial role in characterizing system behavior. Fortunately, the quasioptics formalism allows us to avoid the time-consuming computation of diffraction integrals that would otherwise be necessary for a complete system analysis. We will concentrate instead on those aspects of quasioptics that are readily amenable to calculation in the paraxial approximation (see subsequent text). In particular, we will study the propagation of Gaussian beams. 

In this chapter we will discuss the basic characteristics of Gaussian beams and their transformation by optical elements such as lenses, mirrors, prisms and optical gratings. The following presentation follows that of the recommendable review by Kogelnik and Li [314]. 

An MNF/microcylinder sensor exploits WGMs resonances in a cylinder (optical fiber), which are excited by an MNF. The arrangement of an MNF and a cylinder is shown in Fig. 13.li. As opposed to the WGM in a microsphere and microdisk considered in Sect. 13.3.1, the beam launched from the MNF into the cylinder spreads along the cylinder surface and eventually vanishes, even if there is no loss. The theory of resonant transmission of the MNF/microcylinder sensor was developed in Ref. 18. The resonant transmission power of this device can be modeled by a self-interference of a Gaussian beam that made n turns along the cylinder circumference ... 

M.I. Angelova and B. Pouligny Trapping and Levitation of a Dielectric Sphere with off-Centered Gaussian Beams I Experimental. Pure Appl. Optics 2,261 (1993). 

Although paraxial approximation becomes imsuitable for higher-WA optics and for non-Gaussian beams, the above insights should remain qualitatively valid in these cases as well. Since only the above-the-threshold intensity part of the spatio-temporal envelope of the beam is important for photomodification, usually this part can be reasonably well approximated by a Gaussian. 

E. Torrontegui, X. Chen, M. Modugno, A. Ruschhaupt, D. Guery-OdeUn, and I. G. Muga. Fast transitionless expansion of cold atoms in optical Gaussian-beam traps. Phys. Rev. A, 85(3) 033605-033613(2012). 

Fig. 3.20. Signals of fluorescence kinetics representing fly-through relaxation of an optically depopulated initial level (a) rectangular profile of the beam (b) limited Gaussian profile (c) unlimited Gaussian profile (d) experimentally registered signal. Values of the non-linearity parameter Bwpvp/ro are shown in brackets.

Silicon films that were electron beam evaporated at a rate of 5 nm sec-1 on silica substrates at 440°C were subsequently irradiated with an Ar+ laser. The rapidly scanned Gaussian beam formed a smooth lateral temperature gradient in the film hence it provided a simple means to study the crystallization mechanism. The laser-heated track reveals two easily discernible areas. A 1 -//m-thick film showed color changes from black to deep red at the margins of the track to light yellow in the middle of the track. Despite the smooth fall of the laser intensity, the different boundaries are abrupt. Optical absorption measurements of the respective areas are also displayed in Fig. 1. The curve E440 represents the as grown evaporated film and is in... 

A Gaussian beam is a modified plane wave whose amplitude decreases, not necessarily monotonically, as one moves radially away from the optical axis. The simplest, or fundamental, Gaussian beam has an exp(—p /w ) radial dependence, where p is the radial distance from the optical axis and w is the 1/e radius of the electromagnetic field. The phase of a Gaussian beam also differs from that of a plane wave due to diffraction effects, as we will show subsequently. 

The paraxial approximation is essentially a Taylor series expansion of an exact solution of the wave equation in powers of p/w, terminated at ( p/tv), that allows us to exploit the rapid decay of a Gaussian beam away from the optical axis. We will develop a more precise criterion in the sequel. We will also show that the phase and amplitude modulation of the underlying plane wave structure of the electromagnetic field is a slowly varying function of distance from the point where the beam is launched. 

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