Rayleigh length

Figure 1.3 Field distributions along the Ag-tip surface and corresponding Ag-tip geometry. z = 0 corresponds to the Au-substrate. r/R is the normalized radius from the pointdirectly beneath the tip (R is the Rayleigh length R = /2n). Reprinted with permission from S. Klein, Electrochemistry, 71, 114 (2003). Copyright 2003, The Electrochemical Society of Japan.

The propagation of a laser pulse focused in a plasma at high intensity is affected by several linear and nonlinear phenomena, which can modify its amplitude and therefore its possibility to travel in the medium maintaining its original interaction conditions. The main limitation arises from optical diffraction that enables the propagation at the maximum intensity only over the Rayleigh length Z i. 

Fig. 14.2. Principle of filamentation. The beam first self-focuses and collapses due to the Kerr effect. Ionization at the non-linear focus then defocuses the beam. A dynamical balance establishes between both processes over distances much over the Rayleigh length...

The kind of information provided by reflectance-based optical data depends on whether the measurement is specular or nonspecu-lar and on the spectral range involved. Nonspecular (scattered light) data carry Information about macroscopic, spatially resolvable extrinsic features such as pits, scratches, or particulate contamination. The characteristic dimensions of these features must be of the order of or larger than the Rayleigh length 1 - 0.6IX, where X is the wavelength of light. 

To obtain a maximum lensing effect the sample should be located one Rayleigh length behind the focus [18]. After opening the shutter S at time t = 0 the intensity I(t) at the detector D is expected to obey the expression [18]... 

Fig. 2.35 Beam waist wq and Rayleigh length L for optimum focusing in two-photon spectroscopy...

Assume the laser beam in the z-direction is focused into a sample of N diffusing particles in the observation volume Vq = w Az, where w is the laser beam waist and Az the Rayleigh length of the focal region. In this case, the intensity correlation function... 

Fig. 5.130. Beam waist region and Rayleigh length of a Gaussian beam...

Fig. 5.131. Full Rayleigh lengths 2zr as a function of the beam waist wq for two different wavelengths 632.8 nm (HeNe laser) and 2 = 10.6 xm (CO2 laser)...

The output beam from an HeNe laser with a confocal resonator (R = L = 30 cm) is focused by a lens of / = 30 cm, 50 cm away from the output mirror. Calculate the location of the focus, the Rayleigh length, and the beam waist in the focal plane. 

The second term in (7.10) is called the Gouy-phase. It describes the fact, that a Gaussian beam acquires an additional phase (besides the normal Phase exp(i/ z)) when it passes through a focus (beam waist wq). It can be written as = arctan(z/zR) where zr = JtwlfX is the Rayleigh length (see below (7.26)). 

---