Gaussian beam propagation

Alda J (2003) Laser and gaussian beams propagation and transformation. In Encyclopedia of optical engineering. Marcel Dekker, New York... 

The most simple optical trap for cold atoms consists of a single focused beam formed by the TEMqo Gaussian mode. For a Gaussian beam propagating along the z-axis and with its focus at the origin of coordinates (x,y,z = 0), the beam intensity varies as /(r) = I 0) wo/w) exp( —(a 2 + y )fw ), where wp is the beam radius, which depends... 

Fig. 2 Relative excitation rates for the IPA and 2PA process along the beam propagation direction. (Solid line) On-axis intensity for a Gaussian beam with waist coq and wavelength k (dotted line) on-axis square of the intensity a Gaussian beam with waist coq and wavelength k (dashed line) on-axis square of the intensity a Gaussian beam with waist cjOq and wavelength 2k. In all cases, the ordinate is normalized to the value at the focus...

Self-focusing occurs when power, Pq, exceeds the critical self-focusing power Per- A Gaussian beam experiences self-focusing after propagating distance, isf [46] ... 

In contrast to the pulsed experiments, the main problem for many years in cw experiments was to observe any signal at all. However, this is not apparent from simple feasibility estimates, as we now show. We assume for simplicity that one excites the atoms using two counter-propagating plane-polarized gaussian beams each with the... 

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. 

Figure 7 Spatial dependence of optical force on an absorbing particle The radial and axial variation of the optical force is shown for both a TEMoo Gaussian beam and an LG03 Laguerre-Gaussian beam. Both beams have the same power (1 mW), spot size (2 urn) and wavenumber (free space wavelength 632.8 nm). The particle has a circular cross-section of radius 1 pm. Due to the cylindrical symmetry, there is no azimuthal variation of the force. The beam is propagating in the +z direction, with the beam waist at z = 0.

This reveals that in a homogeneous field (for example, an extended plane wave) V/ = 0 and the dipole force becomes zero. For a Gaussian beam with the beam waist w propagating in the z-direction, the intensity I (r) in the x-y-plane is, according to Vol. 1, (5.32)... 

Transverse electric field mode indicates that the electric field of the laser beam is perpendicular to its direction of propagation. TEMqo imphes a Gaussian beam profile. 

The Fresnel-Kirchhoff (FK) integral for transformation of a light beam through free space and a GI medium is discussed. Here we shall describe how a Gaussian beam changes when propagating in free space and in a GI medium. 

The focusing of an atomic beam by means of the gradient force was demonstrated first at Bell Laboratories (Bjorkholm et al. 1978, 1980). In the scheme used there, the atomic lens was created by a CW dye laser, which was focused to 200 pm and superimposed upon an atomic beam of sodium. The laser power was 50 mW and the frequency detuning A was —2 GHz. The atomic beam propagated along and inside a narrow Gaussian laser beam. The laser frequency was tuned below the atomic transition frequency, so that the gradient force was directed toward the laser beam axis. The radial potential here is determined by eqn (6.1), with the saturation parameter... 

The deviations of the measured values from the specification are caused by the geometry of the measurement beams of the two sensors. An essential difference between the sensor concepts is the course of the intensity profile of the measurement beam perpendicular to the beam propagation direction. For the sensors with pinhole, the intensity in the entire measurement beam cross section is almost constant. The size of this measurement beam cross sections is equal to the cross section of the pinhole. Hence, the beam cross section, that is used to determine a particle size from (12.4) and (12.5), is exactly known. The SE-F321 and the SE-C980-Sensor define measurement beams with Gaussian intensity profiles. The beam cross sections are theoretically infinite in size, so that the measurement beam cross section, which is used to determine mean particle sizes, is not exactly defined. To determine the particle sizes shown in Fig. 12.21, the 1/e diameter of the light beams is used. 

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