Gaussian beam defined

In order to relate the lateral dimensions of the laser-generated cavities to the laser spot size, a lateral extension parameter q can be defined. It is the ratio between the measured cross-sectional area of the ablation crater and the area illuminated by a Gaussian beam defined according to Eq. 1. When ablation is limited to the area with F(x,y)[Pg.266]

It is common to call tvp the beam-waist radius. In the literature one often finds the phrase at the beam waist, which refers to that value of z for which the function u has its minimum radial extent. For u defined by (8), this occurs at z = 0. The distance Zp is called the confocal distance. When z < Zp we say that the Gaussian beam is in the near field. When z > Zp, the Gaussian beam is in the far field. The majority of this chapter is concerned with the behavior of u in the range 0 < z < Zp, the near-field region. The phase and amplitude of m is a complicated function of position in the near field. When z Zp and p z or when we are in the far field and the paraxial approximation is valid, it is straightforward to show that the asymptotic behavior of u approaches a diverging spherical wave from a point source at z = 0. 

For a Gaussian beam, the fields of the radiating electric and magnetic multipoles satisfy the same boundary conditions (vanishing faster than 1/p as p oo) so that the fields in the plane(s) defined by the transverse E (H) field and the optical axis are symmetric. It is difficult to generate a balanced hybrid mode in conventional smooth-walled metallic waveguide instead, one may use a component called a scalar horn. 

We will test the consistency of our solution by evaluating the diffraction field of a Gaussian beam from a reference plane defined by 2 = 0. We will use the Huygens-Fresnel construction (Born and Wolf, 1980, pp. 370-386), where we treat each point on the wavefront in the reference plane as the source point for a secondary wavefront of the form exp(tk r)/r and sum over all source points. If the diffracted field has the same functional form as the incident field, then we will have demonstrated that our solution is useful even in the presence of diffraction. 

If the beam is not a pure Gaussian beam but contains admixtures of higher order modes, the beam quality can be defined by the parameter... 

Fig. 10-1 Electric field amplitude (r) and diffraction intensity pattern A (u) for (a) a Gaussian beam and (b) a uniform beam. The dashed curve is the Gaussian beam approximation of Eq. (10-1) for the uniform beam, and is defined by Eq. (10-2).

This profile is the simplest example for determining the physical attributes of Gaussian-beam illumination [5-7], and is defined by... 

The two most common methods used to correct resolved peak profiles for the broadening imposed by the finite width of the X-ray beam in the diffractometer, are due to Jones (15) and Stokes (16). Both are essentially unfolding or deconvolution methods, but the Jones method defines specific functions for both the uncorrected and the instrumental broadening profile. If the uncorrected profile is Gaussian, then... 

The two parallel incident laser beams with a Gaussian intensity profile are focused by a lens with / = 5 cm in a BOX CARS arrangement into the sample. Estimate the spatial resolution, defined by the halfwidth Sa(z) of the CARS signal, when the beam diameter of each beam at the lens is 3 mm and their separation is 20 mm. 

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