Gaussian beam waist radius

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. 

A given mesh reflectivity imposes a lower bound for the beam-waist radius, below which appreciable coupling losses can occur. The basic problem is that a Gaussian beam will continue to diverge upon repeated reflection within a planar interferometer as shown in Fig. 12b. If the spherical mirror of the cavity is designed to match the original (input) beam waist, beam divergence will cause a mismatch at the output, which... 

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. 

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

beam radius w [cf. Eq. (20)] and radius of curvature R [cf. Eq. (21)] at the output of the PTR are nearly identical for the two components of 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. 

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.

Wo is the radius at the centre of the cavity zo, and is often called the beam waist. It appears as a central bright region in the image of a laser beam, and as an axis-symmetric elevation in the grey-scale intensity plot (Figure 3.7). Gaussian beams are usually the... 

The fundamental modes have a Gaussian profile. For r = w z) the intensity decreases to 1/e of its maximum value io = C on the axis r = 0). The value r = w z) is called the beam radius or mode radius. The smallest beam radius wo within the confocal resonator is the beam waist, which is located at the center z = 0. From (5.31) we obtain with d = R... 

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