Resonators and Mode Structure

As for a microwave cavity, several types of transverse electromagnetic oscillations or modes are possible for a laser cavity. Generally, one tries to 

As a consequence of the coherence, the laser light can be transmitted as an almost parallel bundle. The small divergence is a consequence of the unavoidable influence of diffraction. For radiation in phase and with the same amplitude over a circular aperture of diameter d, the angle 6 between the centre of the diffraction pattern and the first dark interference ring is given by 

A visible diffraction-limited laser with an emerging beam of diameter 1 mm will have a divergence of about 0.5 mrad. Many practical systems have a divergence that is limited only by diffraction. For such a laser the spot at a distance of 1 km has a diameter of about 0.5 m. By first expanding 

A very high degree of linear polarization can be obtained for a laser with low losses in one direction of oscillation and high losses in the perpendicular direction. For a laser with a gas as the active medium this is accomplished by placing the windows of the gas container at Brewster s angle to the optical axis of the laser (Fig.8.5). For other lasers some other type of polarizer can be placed inside the cavity. 

We have now discussed different characteristics of laser light without dealing with its frequency distribution in detail. It is evident that a stable oscillation mode can be achieved in the resonator only if there is constant constructive interference, i.e. standing waves. This occurs when an integer number of half wavelengths fit into the cavity of (optical) pathlength t By considering two adjacent modes we obtain the mode separation Au 

A fiuther useful quantity, related to focused laser beams, is the confocal parameter defined as the distance between the two locations at each side of the focus at which the intensity has fallen to 50% of the maximum value  

We have now discussed different characteristics of laser light without dealing with its frequency distribution in detail. It is evident that a stable oscillation mode can be achieved in the resonator only if there is constant 

Generation of polarized laser light using intracavity Brewster angle dows 

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The geometrical shape of the cavity and the specific mode selected will of course govern the Q and these considerations are always present in any resonator problem. In the superconducting cavity, however, the geometry and mode structure nave an important bearing on the fabrication methods that may be used. For example, suppose we wish to make a cylindrical resonator. In order that the active surface area be in a reasonably good physical state, we would probably make it in two separate halves, so that the inside surfaces could be reached for subsequent electropolishing. However the cavity has to be split in such a... 

One period of such a structure can be considered as a finite periodic grating with a defect layer in its middle and that is why a very narrow resonance (defect mode) appears inside of the band gap. 

An interesting aspect of many structural phase transitions is the coupling of the primary order parameter to a secondary order parameter. In transitions of molecular crystals, the order parameter is coupled with reorientational or libration modes. In Jahn-Teller as well as ferroelastic transitions, an optical phonon or an electronic excitation is coupled with strain (acoustic phonon). In antiferrodistortive transitions, a zone-boundary phonon (primary order parameter) can induce spontaneous polarization (secondary order parameter). Magnetic resonance and vibrational spectroscopic methods provide valuable information on static as well as dynamic processes occurring during a transition (Owens et ai, 1979 Iqbal Owens, 1984 Rao, 1993). Complementary information is provided by diffraction methods. 

It must be remembered that one of the conditions for resonance of molecules among several electronic structures is that the configuration of the molecule (the arrangement of the nuclei) remain constant during the electronic resonance it is the composite electronic structure that provides a single potential function determining the equilibrium configuration and modes of oscillation for the molecule. It is not possible for an amide to resonate between the structures... 

Moreover, in recent years broad band lasers have appeared which lack any frequency modal structure, at the same time retaining such common properties of lasers as directivity and spatial coherence of the light beam at sufficiently high spectral power density. The advantages of such a laser consist of fairly well defined statistical properties and a low noise level. In particular, the authors of [245] report on a tunable modeless direct current laser with a generation contour width of 12 GHz, and with a spectral power density of 50 /xW/MHz. The constructive interference which produces mode structure in a Fabry-Perot-type resonator is eliminated by phase shift, introduced by an acoustic modulator inserted into the resonator. 

Figure 12-2. IR-UV double resonant and R2PI spectra of three guanine-cytosine cluster structures. Stick spectra show calculated frequencies for modes, indicated in line types according to the key in the top panel. The relevant numbering is indicated in the structure (c). Structure (a) is corresponds to the Watson-Crick structure and is not observed for the unmethylated bases...

Resonance Raman (RR) spectroscopy is a powerfiil and versatile technique for the study of both vibrational and electronic structures of chromophoric molecular systems. RR spectra are obtained by irradiation of the sample with a monochromatic light source whose energy is close to that of an electric-dipole-allowed electronic absorption band. Most of the Raman bands are attenuated by the absorption, but some bands may be greatly enhanced. This effect arises from a coupling of the electronic and vibrational transitions, and the vibrational modes that do show enhancement are localized on the chromophore, that is, on the group of atoms that give rise to the electronic transition. 

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