Radial mode number

Fig. 8.33 Calculated sensitivity in bulk index sensing for different radial mode numbers with the same azimuthal number m 700...

Fig. 17.1 Illustrations of whispering gallery modes (WGM) in a spherical optical resonator. The WGM modes are classified in terms of their radial quantum number p as well as by their angular momentum quantum number / and the azimuthal quantum number m that can have (21+ 1) values, meaning that the resonance frequency ( ,/ has a (2/ + 1) degeneracy...

Fig. 4 Left panel Binary phase diagram. There is phase separation for pF > 2. Simulation results for pAB obtained from concentration histograms are shown as filled circles. The dashed line is a plot of the leading singular behavior, pab = /3(pF —2)/2, of the order parameter at the critical point. The inset shows a configuration 50,000 time steps after a quench along pab = 0 to pF = 3.62 (arrow). The dark (blue) and light (white) spheres are A and B particles, respectively. Parameters L/a = 6A,M =Mb = 5,k T = 0.0004, At = l,anda= 1. From [45]. Right panel Dimensionless radial fluctuations, ( u ), as a function of the mode number 1 for A = 0.45 (filled circles) andA = 0.60 (open circles) withAiBF = 0.0004. The average droplet radii are ro = 11.95u and ro = 15.21a, respectively. The solid lines are fits to (71). The inset shows a typical droplet configuration for Pab = —0.6, pF = 3.62 (A = 0.60 and k T = 0.0004). Parameters L/a = 64, Ma = 2, Mb = 8, At = 1, and a = 1. From [45]...

Fig. 8.34 Surface sensing sensitivity of different radial order modes are simulated by using the perturbation method with the same azimuthal number m 700.The adsorbed polymer layer is assumed to have a refractive index of 1.46...

These branches are now discussed for propagating modes depending on z and t as exp [/(-cot + fe)]. In fact, there are a number of choices with respect to the form (70) as represented by cosa and sina, and that satisfy the condition C2 = c2 of Eq. (8), thereby corresponding to the two directions along z and (p. From now on we also introduce the normalized radial coordinate p = r/ro, where ro stands for a characteristic radial dimension. 

Fig. 12.2. Schematic illustration of the absorption of an IR photon by the van der Waals complex Ar H2 and the subsequent dissociation into Ar+H2(n = 0). Voo(R) and Vn(i ) are the diagonal elements of the potential coupling matrix defined in Equation (3.6) which serve to define the zero-order radial wavefunc-tions employed in the Golden Rule expression for the dissociation rate. The assignment of the bound levels is (m,n), where m and n denote the number of quanta of excitation in the dissociation mode R and the vibrational mode of H2, respectively.

The radial charge redistribution caused by MLCT excitation outside the central atom can be effective in its oxidation and reduction of the ligand or even an external solvent molecule. These reaction modes are observed in complexes of metals at their low oxidation numbers (eg Cu1, Au1, Fe11, Ru11, MoIV) with relatively good 7r-acceptor ligands, eg CN, NCS, NO+, 0, pyridine, bipyridine, 1,10-phenanthroline, methylene blue) [48,53,79]. Often the final product is really not the oxidized, but only the substituted complex, eg ... 

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