Confocal fundamental

Flell S W and Stelzer E FI K 1992 Fundamental improvement of resolution with a four Pi-confocal... 

The natural way to increase the efficiency of such a frequency conversion process is to use a focused fundamental beam (or, alternatively, a waveguide structure). An established theory of SHG using focused cw beams " predicts, for negligible birefringence waUc-off, an optimal focusing condition which is expressed by the ratio L/b 2.83, where b is the confocal parameter (b = k wQ, where Wqi and ky are the focal spot radius and the wave vector of the fundamental wave respectively). However, this theory applies only to the long-pulse or cw case, where GVM is negligible... 

Three major advancements in resolution have occurred since Hookes s discovery of the optical microscope in 1665 [46]. In 1873, Ernst Abbe established fundamental criteria for the resolution limit in optical microscopy [47], which did not exceed the range of a couple of 100 nanometers even after the introduction of the confocal optical microscope [43,48]. The invention of the transmission electron microscope by Ernst Ruska in 1933 extended the resolution of microscopes to the nanometer scale [49]. Finally, scanning tunnelling microscopy introduced, by Binnig and Rohrer in 1981, made a breakthrough when atomic... 

Fig. 7. Depolarization by high-NA focusing, (a) Geometrical optics explanation of the depolarization due to the focusing of an annular beam leading to the three displayed characteristic patterns for the field components in x, y, and z direction, (b) Confocal imaging using a focused annular beam. Suitably oriented molecules recover the fundamental patterns as indicated by the white labels.

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. 

S. HeU, E.H.K. Stelzer, Fundamental improvement of resolution with a 4Pi-confocal Huorescence microscope using two-photon excitation. Opt. Commun. 93, 277-282 (1992)... 

Figure 1.45 Optical path in the confocal microscope. (Reproduced with permission from D.B. Murphy, Fundamentals of Light Microscopy and Electronic Imaging, Wiley-Liss. 2001 John Wiley Sons Inc.)...

For the fundamental or TEMooq mode, the Hermite polynomials are unity. X is the free-space radiation wavelength, d is the mirror separation, and q + 1 the number of half-wavelengths between the mirrors. The beam waist, Wg, is the distance from the center of the cavity to the 1/e points of the field strength. The beam waist is a maximum when d = R, the confocal arrangement, and falls to zero when d = 0 or d = 2R. Using the radius of curvature of one of our mirrors, 84 cm, and a mirror separation of 70 cm, the beam waist at 10 GHz is 12.6 cm. The k/>2/2R factor accounts for curvature of the wave front arising because of the curved mirrors. The phase front is... 

Confocal Laser Scanning Microscopy (CLSM). Prior to the invention of confo-cal microscopy, conventional wide-field microscopy has a fundamental limitation for providing three-dimensional imaging due to blurring of the image caused by... 

For very low-power laser radiation, e.g. from small diode lasers, SHG is still observed, but its efficiency is extremely low. In order to improve on the conversion requires placing the crystal into a confocal enhancement resonator, as shown in Figure 4.23c, where the NLO crystal is placed into the beam waist at the centre of the resonator. The mirrors are highly reflective for the fundamental wave, but they transmit the second-harmonic wave as fully as possible. With careful design, the fundamental wave can build up inside the resonator more than 100-fold with respect to the incident wave, and conversion for low- to medium-power CW lasers in the rage of a few per cent up to more than 50 per cent has been demonstrated (e.g. see... 

Fig. 5.10. Phase fronts and intensity profiles of the fundamental TEMqo rnode at several locations z in a confocal resonator with the mirrors at z = J/2...

The phase fronts of the fundamental modes inside a confocal resonator close to the resonator axis can be described as spherical surfaces with a z-dependent radius of curvature. For za) = R/2 R = R. This means that at the... 

At the center of the resonator z = 0-> o = 0 R = oc. The radius R becomes infinite. At the beam waist the constant phase surface becomes a plane z = 0. This is illustrated by Fig. 5.10, which depicts the phase fronts and intensity profiles of the fundamental mode at different locations inside a confocal resonator. 

---