Beam radius

Figure 3. The phase lag produced by the Gouy phase, calculated using the analytic model described in the text for 0)3 + 3t0i excitation, with two additional coi photons in one of the channels. The calculations are performed for various ratios of the molecular beam radius d to the Rayleigh range zr.

As the disc spins, a protein edge passes through a focused Gaussian beam that has a beam radius p0. At the moment when the optic axis coincides with the protein edge in the near field, there is a quadrature condition in the far field set by... 

Note that the translational diffusion time decreases when the beam radius is decreased but not the rotational correlation time. 

Here, ry is the backscatter coefficient for the substrate and the line input dose which is equal to i /x. The Gaussian beam radius in the resist at penetration z is... 

Fig. 24 Typical z-scan spectra of 2 for 4-ns pulse train with about 0.06 mW input power for (a) w0 = 7 am beam radius and 3 GW/cm2 on-focus intensity and (b) w0 = 20 im beam radius and 0.06GW/cm2 on-focus intensity (solid curves represent theoretical fit) [60]...

Fig. 25 Typical open-aperture z-scan spectra of 2 with normalized transmittance plotted as a function of sample position z for two different linear transmittance of w(j = 20 xm beam radius at the same input power (0.06 mW) [60]...

The beam radius w0, which was found to be almost constant for various input intensities I0, and the NL absorption coefficient /Jeff were used as free parameters in Fig. 26 [42],... 

Due to the high NLA of 10, the sample was placed at the focus where beam radius was 34.2 p,m. Input fluences vs. output fluences are plotted in Fig. 28. Compound 10 shows good OL behavior, since input fluences increase up to 60 J/cm2, and output fluences remain almost constant at about 1 J/cm2. 

The Gaussian beam of Eq. (8) has a radial amplitude dependence exp(-p /w (z)X where w z) is given by Eq. (20). The quantity w(z) is called the beam radius its minimum value—the beam waist Wq—occurs at z = 0. Conventionally, z = 0 is referred to the beam waist the context makes it clear whether Wq or z = 0 is being discussed. As z increases, w(z) increases monotonically. It is easy to show from Eq. (20) that lim w(z)/z = A/ttwo, the asymptote of a hyperbola. We call the quantity tan (A/ttwo) the asymptotic beam growth angle. 

In order to understand why this ratio is greater than unity, we must consider that the truncated beam contains higher order modes than the fundamental because of diffraction from the finite aperture. As the aperture is stopped down (made smaller), the diffraction fringes become better resolved. For aperture diameters that are not too small, however, the principal effect on the beam is an apparent broadening of the beam radius due to unresolved diffraction fringes with significant intensity away from the optical axis. 

For those samples that have a radius greater than twice the beam radius over the entire sample, the sample radius does not enter the filling factor calculation because it has no effect on the fields. 

The second term on the right-hand side of Eq. (93) may be expanded in terms of the Gaussian beam modes discussed in the Appendbc. The vector d in Eq. (93) represents a displacement of a fundamental Gaussian beam along the

output beam because the path difference A.5 beam waist, R and so we neglect a phase correction in Eq. (93) that is proportional to ik/2R. We include the phase correction in the subsequent analysis for completeness, although its effect is small. 

We will now derive explicit mathematical expressions from which the curves in Figs. 11 and 12 are derived. We consider first a two mirror system where the amplitudes of reflection and transmission are given by r, and f, respectively, where the subscript i indicates mirror 1 or mirror 2. For mirrors of high reflectivity, there will be many reflections within the interferometer that will cause the apparent beam radius to grow. This effect is shown in Fig. 12b, which demonstrates how the beam radius grows with each round trip in the interferometer. We will account for this effect quantitatively in the sequel. 

The signal decreases for a smaller laser beam radius because fewer scatterers are illuminated by a constant power density. 

Power output Pulse length Laser beam radius... 

Rl has been deduced for the case of the rotational axis being normal to the primary beam. The common Lorentz formulation is valid if a crystallite is rotated within the beam by co = 27i. For a certain number of crystallites with a rotational radius less than the beam radius this is true. Crystallites outside this radius experience a rotation coeff that is dependent upon their rotational radius and the width of the primary beam. It can be given as ... 

Figure 8. Beam radius of curvature as a function of temperature for 50 pm thick EPO-TEK 600.

Angle of incidence Gaussian beam radius Spatial coordinate Spatial coordinate Incubation parameter... 

For the indication of absolute laser fluence values, e.g., for ablation, modification, melting etc. of a material, the determination of the spot size is crucial. Fluence values allow the comparison of laser treatment with different types of lasers showing various spatial beam characteristics like a square (e.g., excimer laser) or a Gaussian beam profile (e.g., Tksapphire laser). In the following, the determination of the Gaussian beam radius is described. 

Fig. 7 Plot of transmitted energy t vs razor blade ( moving edge ) position x=l for the evaluation of the focus area. The solid line represents a fit according to Eq. 3 yielding a Gaussian beam radius of Wq=25 pm...

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