Confocal cavity

The novel aspect of this experiment was that the confocal cavity was locked to continuous-wave radiation which was frequency shifted by an acousto-optic modulator such as to centre the filtering cavity onto the chirped amplified radiation. This reduced the residual amplifier shift to -2(1 MHz. The dominant contribution to this shift resulted from the cw light being injected off-axis into the cavity. Because the filter cavity had a high finesse we used a phase modulation scheme for locking. Indeed, we normally locked the dye laser to the filtering cavity and scanned the spectrum by scanning the filter cavity. 

Frequency stabilisation and scanning is accomplished by use of a confocal cavity of free spectral range matched to the dye laser repetition rate. Phase modulated sidebands are put on to the mode spectrum of the mode-locked pulse train and used to lock the laser to the reference cavity. The frequency modulation technique is also used to lock the ultra-violet enhancement cavity to the mode-locked pulse train. 

The first stage was the production of a pulsed free-jet molecular beam of helium containing 20% CO, which was then crossed with an electron beam to produce ionisation. The ions were produced close enough to the beam nozzle for cooling to occur downstream. Some 4 cm from the nozzle the beam entered a confocal Fabry-Perot cavity where it was exposed to millimetre wave radiation close to 120 GHz in frequency. Following microwave excitation, when on resonance, the beam was probed with a Nd YAG pumped dye laser beam with the frequency chosen to drive rovibronic components of the A 2 U-X 2 + band system. Figure 11.54 shows two recordings of a spin component of the lowest rotational transition the line shown in (a) is... 

Fig. 4.25. Increase of the density of Rh-dUTP in the oscillating field (4 kV cm at 4 Hz) observed in the confocal element between the tips and decay of the concentration as the field is switched off [50]. (a) Concept of the quadruple trap with a seven-element detector projected into the cavity (diameter 6 pm) surrounded by four electrodes (metal tips or microcapillaries). The observed particle undergoing diffusion will be repositioned by the electric field whose magnitude and direction is computed from the optical feedback (b) [51]...

N.D. Rezgui, J. Allen, J.G. Baker, J.F. Alder, Quantitative millimetre wave spectrometry. Part I design and implementation of a tracked millimetre wave confocal Fabry-Perot cavity spectrometer for gas analysis,. dwa/. Chim. Acta., 311, 99-108 (1995). 

Let us consider a many-electron atom of nuclear charge Z confined by a hard prolate spheroidal cavity. In this study the nuclear position will correspond to one of the foci as shown in Figure 4. In terms of prolate spheroidal coordinates, the nuclear position then corresponds to one of the foci for a family of confocal orthogonal prolate spheroids and hyperboloids defined, respectively, by the variables f and rj as [73] ... 

FIGURE 3.2 (Continued) (c) strip in elliptical cylinder (d) pipe in eccentric circular cylinder (e) confocal elliptical cylinders (/) sphere embedded in a half-space (g) circular pipe embedded in a half-space (h) hemispherical cavity in a half-space. 

A common alternative configuration is the optically equivalent combination of a spherical with a plane mirror, a semi-confocal cavity. This is more convenient in that the length of the cavity is reduced by a factor of two, but it does mean doubling the number of reflections and therefore the transmission loss for a given transit path of the radiation through the sample. 

Figure 2.4 Configurations for a Fabry-Perot optical cavity. The radii indicate the focal point of the mirrors. In (c) the hatched area indicates the beam shape in the confocal configuration (see text)...

For a confocal cavity the arccos term takes on the value nil and so the lateral... 

J.G. Baker, N.D. Rezgui and J.F. Alder, Quantitative MMW Spectrometry (III) Theory of Spectral Detection and Quantitative Analysis in a MMW Confocal Fabry-Perot Cavity Spectrometer, Anal. Chim. Acta, 1996, 319, 277-290. 

This glitch is caused by interaction between the cavity and the sample resonance profiles. It may be converted into an apparent frequency shift of the cavity resonance that is directly related to the absolute absorption coefficient. The linewidth can be determined fi-om the distance between the peaks of the glitch. This phenomenon became even more marked with the Mark II confocal Fabry-Perot cavity (Section 5.3), when it could be observed as a glitch in the correction voltage applied by the servo amplifier to the piezoelectric actuator of the moveable cavity mirror. Figure 4.7 shows a spectrum for the water line obtained in this manner. 

Bourges et al. studied the kinetics of polylactide (PLA) nanoparticle (NP) localization within the intraocular tissues and to evaluate their potential to release encapsulated material. Environmental scanning electron microscopy (ESEM) showed the flow of the NPs from the site of injection into the vitreous cavity and their rapid settling on the internal limiting membrane. Histology demonstrated the anatomic integrity of the injected eyes and showed no toxic effects. A mild inflammatory cell infiltrate was observed in the ciliary body 6 h after the injection and in the posterior vitreous and retina at 18-24 h. The intensity of inflammation decreased markedly by 48 h. Confocal and fluorescence microscopy and immunohistochemistry showed that a transretinal movement of the NPs was... 

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... 

The results of such an analysis are indeed in good agreement with observations using a non-confocal cavity. 

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