Gaussian beam, radiation

We have now found a physical meaning for the complex origin shift Zpi it characterizes the 1 /e radius of the dipole radiation at z = 0. The Cornell FIR spectrometer uses Zp = 117 mm, which corresponds to Wp = 6.7 mm. Thus, even at z = 0, where z — izp has its smallest magnitude, the quantity (tVp/Zp) = 3.28 X 10 (which characterizes the paraxial approximation) is a small number. We may use the paraxial approximation with confidence to derive the properties of the fundamental Gaussian beam. 

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. 

At this point, we have quantified the domain of validity of the paraxial approximation and established when we may neglect the nontransverse components of the Gaussian beam. We still need to examine our solution in more detail, because we have not yet addressed diffraction effects. This analysis is necessary because the wavelength of FIR radiation is of the... 

Let us now trace the polarization evolution of a Gaussian beam as it traverses the optical system shown in Fig. 7. Polarizer P passes radiation linearly polarized at 45° (L450) with respect to the normal to the plane of the page. The polarization-transforming reflector (PTR) converts linearly... 

High-resolution CARS can be also performed with injection-seeded pulsed dye lasers [334, 351]. If the radiation of a single-mode cw dye laser with frequency o) is injected into the cavity of a pulsed dye laser that has been mode matched to the Gaussian beam of the cw laser (Vol. 1, Sect. 5.8), the amplification of the gain medium is enhanced considerably at the frequency co and the pulsed laser oscillates on a single cavity mode at the frequency co. Only some milliwatts of the cw laser are needed for injection, while the output of the single-mode pulsed laser reaches several kilowatts, which may be further amplified (Vol. 1, Sect. 5.5). Its bandwidth Av for pulses of duration At is only limited by the Fourier limit Av = 1 f(27tAt). 

So far, we have assumed that the wave fronts of the laser radiation field are planes and that the molecules move parallel to these planes. However, the phase surfaces of a focused Gaussian beam are curved except at the focus. As Fig. 3.20 illustrates, the spatial phase shift Acf) = x2n/X experienced by an atom moving along the r-direction perpendicular to the laser beam z-axis... 

High-resolution CARS can be also performed with injection-seeded pulsed dye lasers [8.43,8.60]. If the radiation of a single-mode cw dye laser with frequency co is injected into the cavity of a pulsed dye laser that has been mode matched to the Gaussian beam of the cw laser (Sect. 5.8), the amplification of the gain medium is enhanced considerably at the frequency co and... 

Fig. 5.5 (a) Radiation force of a Gaussian beam and (b) resonant interaction of laser light with a two-level atom. 

The theoretical model of CARS signal generation from an arbitrary Raman scatterer by tightly focused Gaussian beams in collinear configuration was described by Cheng et al. [4]. In the general formulation derived from the NLO wave equation, the coherent radiation field is calculated from a three-dimensional (3D) object. This provides a quantitative description of the contrast mechanisms of CARS. 

Intracavity absorption cells are particularly advantageous, if the absorption is monitored via the laser-induced fluorescence. Since the radiation field inside the active resonator or inside the mode-matched passive cavity is concentrated within the region of the Gaussian beam (Sect.5.11), the laser-excited fluorescence can be effectively imaged onto the entrance slit... 

A very important characteristic of laser radiation is the beam shape. So far most LA experiments have been performed with Gaussian laser beams. Lasers with uniform distribution of the beam cross-section have been used only recently to achieve high lateral and depth resolution. Specially designed beam homogenizers must be used for this purpose [4.226-4.228]. The Cetac LSX-200 system has a flat-top distribution of the laser beam. 

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