Cavities angular

In polarization modulated ENDOR spectroscopy (PM-ENDOR)45, discussed in Sect. 4.7, the linearly polarized rf field B2 rotates in the laboratory xy-plane at a frequency fr fm, where fm denotes the modulation frequency of the rf carrier. In a PM-ENDOR experiment the same type of cavity, with two rf fields perpendicular to each other, and the same rf level and phase control units used in CP-ENDOR can be utilized. To obtain a rotating, linearly polarized rf field with a constant magnitude B2 and a constant angular velocity Q = 2 fr (fr typically 30-100 Hz), double sideband modulation with a suppressed carrier is applied to both rf signals. With this kind of modulation the phase of the carrier in each channel is switched by 180° for sinQt = 0. In addition, the phases of the two low-frequency envelopes have to be shifted by 90° with respect to each other. The coding of the two rf signals is shown in Fig. 8. 

In any low angular momentum state the radiative decay rate is usually dominated by the high frequency transitions to low lying states, and as a result it is impossible to control completely the decay rate using a millimeter wave cavity. In a circular i = m = n - 1 state the only decay is the far infrared transition to the n — 1 level, and Hulet et al. have observed the suppression of the decay of this level.26 They produced a beam of Cs atoms in the circular n = 22, = m = 21 state by pulsed laser excitation and an adiabatic rapid passage technique.27 The beam of circular state atoms then passed between a pair of plates 6.4 cm wide, 12.7 cm long, spaced by 230.1 jum, and held at 6 K. The 0 K radiative lifetime is 460ps, and... 

The cavities are assumed to be spherically symmetric, which enables the elimination of the two angular portions of the triple integral, resulting in 47t. Substitution of the resulting equation into Equation 5.21 yields the final expression for the Langmuir constant in terms of the particle potential within the cavity. 

A pseudo potential approach was adopted by Hickman et al. [259] to calculate the excited metastable states of a He atom under liquid He. The density functional approach developed by Dupont-Roc et al. [260] was applied subsequently [261] for the description of the nature of the cavity formed around an alkali atom in the excited state of non-zero angular momentum. The resulting form of the cavity differs very much from the spherical shape. A similar approach was adopted by De Toffol et al. [262] to find qualitatively the first excited states of Na and Cs in liquid He. Earlier work in this direction was given in detail in Ref. [263]. 

Planck s radiation law determines the power emitted by a small aperture in a cavity, which is at a given equilibrium temperature. The spectral flux emitted by an isotropic blackbody source into a solid angle 2 = 2rr sin 0r (where 9r is the angular radius of the first optical element of the spectrometer) is ... 

The highest stability of the sensor-analyte complex is achieved when the substrate fits perfectly in the hole within the receptor. The analyte does not have to fit the receptor cavity perfectly efficient binding can be achieved by careful design of the receptor. In the case of metal ion sensors the receptor must contain a proper type and number of donor atoms angular orientation and directionality of lone electron pairs are also of crucial importance [5]. 

The value of / is derived via comparison with model calculations. Model calculations can be carried out with Monte Carlo methods The particles start at random positions outside the cavity with a randomly chosen direction. The angular distribution of the particle directions does, however, not necessarily have to be uniform. Each particle is followed if it enters the slit and as long as it is inside the cavity. Upon each wall collision a fraction s of the particle sticks to the wall and a fraction r = 1 — / is re-emitted with a cosine distribution with respect to the surface normal. When only a negligible part of the particle is left, e. g. 10-3, the next particle is started outside the cavity. In general, the trajectories of more than 106 particles have to be calculated to reach good statistics. For convenience, s = / is chosen in the calculation (this is equivalent to 7 = 0). As said before, the normalized profiles depend on the surface loss probability (3 only, so that this choice has no influence on the profile. 

The second kind of cavity which has been used is Fabry-Perot cavity [10]. These cavities are completely tunable and have the advantage that they are open, allowing far better access to the atoms than the closed cavity shown in Fig. 1. The improved access was critical for measurements of angular distributions of the electrons ejected in microwave ionization [11]. Their cylindrical symmetry is useful for measurements involving circularly polarized microwaves, but a closed cylindrically symmetric cavity is equally good [12]. 

We have indicated how a modest (1.3) enhancement in angular intensity can be obtained in cavity devices with Alq emissive layers. Further enhancements in angular intensity are possible by choosing emissive layers with narrower free-space emission spectra than Alq. Alq doped with small quantities of the laser dye pyrromethene 580 (PM) results in the emission spectrum of the system becoming narrower than that of Alq. This is result of resonance energy transfer33 from the excited states of Alq to the excited states of PM580. The full width at half-maximum of the luminescence drops from 100 nm to 45 nm. The spectra are shown in Fig. 4.12. The external quantum efficiency of noncavity devices is enhanced in comparison with devices with an undoped Alq emissive layer. For a device with a ITO/TAD/Alq+0.5%PM (20 nm)/Alq/Li (1 nm)/Al(200 m) structure, an external quantum efficiency of 1.8-2% photons/electron was measured. For comparison, equivalent LEDs without the pyromethene dye had an external quantum efficiency (with Li/Al cathodes) of 0.8%. 

TABLE 4.1. Angular and Integrated Enhancements of Cavity Devices with Alq+0.5% PM Emissive Layers Relative to Noncavity Devices with the Same Emissive Material. 

Cavity Resonance Integrated Enhancement Angular Enhancement (max 0)... 

Note The maximum 0 is the angle with respect to the cavity axis at which the maximum angular intensity is attained. 

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