Effective index of refraction

Spontaneous emission and radiative lifetime of lanthanide excited state in condensed phases is determined by the electromagnetic field and the index of refraction as shown in eq. (3). In nanocrystals, spontaneous emission of photons is influenced by two mechanisms (1) the non-solid medium surrounding the nanoparticles that changes the effective index of refraction thus influences the radiative lifetime (Meltzer et al., 1999 Schniepp and Sandoghdar, 2002), (2) size-dependent spontaneous emission rate due to interferences (Schniepp and Sandoghdar, 2002). 

The dependence of radiative lifetime on the index of refraction, n, arises from the change in the density of states for photons in the medium of reduced light velocity and the modification of the polarizability of the surrounding medium. Since the nanoparticles occupy only a small fraction of the total volume, in order to compare the experimental results with eq. (3) it is necessary to introduce an effective index of refraction for the medium, eff, which consists of... 

The longer lifetime (1.84 ms) of 5Do in Eu Cb/ZnO is most possibly due to the non-solid medium surrounding the nanoparticles that changes the effective index of refraction. The filling factor is estimated to be approximately 58%, smaller than that of Eu Y203/Al2C>3 (72%). The much shorter 5Di lifetime (27 ps at RT) compared to the bulk counterpart (90-120 ps) is most possibly related to the enhanced nonradiative multiphonon relaxation induced by surface effects of nanocrystals. 

In order to describe the microdisk modes, the product of nR needs be known to several decimal places. An accurate value of nR may come directly from the FT of the emission spectrum [122]. Figure 22.38b is the FT of the emission spectrum in Figure 22.39a. If the units of the emission spectrum are measured in wavevector (fc = 2ir/A) then the unit of the FT is length [214]. In Figure 22.38b a single series of well-spaced peaks can be observed. The FT gives peaks at nR of 50.7 p,m. The physical disk diameter, D = 2R is 55 p,m and from the measured value of nR it gave 1.84 as the effective index of refraction. This value indicates that the fields of these modes are entirely contained within the polymer disk since the index of refraction of the DOO-PPV polymer is 1.8, which was measured by elipsometry on an unetched polymer film. 

Another type of photonic crystal fiber (PCF) is the 2-D structure shown in Figure 11. There are two types of PCF. The first is a real PCF (fig. 11 a), while the other (fig. lib) is said to have an effective index of refraction and its principle of operation is similar to a core-clad fiber. Fibers for the visible and NIR regions have been made of silica with air holes (Figure 12) by Russel et al. [85]. Fibers for the IR region have been made of silver halide by Katzir et al. [86]. 

The electron density in the path of a microwave adsorbs energy and attenuates the transmitted signal. This microwave attenuation can be used to analyze the plasma density. A plasma has an effective index of refraction for microwave radiation. By measuring the phase shift of transmitted/received microwave radiation as it passes through the plasma, the charge density can be determined. Generally the phase shift is determined by interferometric techniques. 

This quantitative theory fails for a monolayer or submonolayer of adsorbed molecules, because it is impossible to define a complex dielectric constant 2 for a film of molecular thickness since the layer is not a continuum. However, it is possible, in a first approximation, to treat the monolayer like the film and to define an effective index of refraction (or dielectric constant) for a submonolayer and an effective thickness d = ddo, where do is the thickness of a full monolayer and 0 is the degree of coverage of the surface by adsorbed species. It turns out that if d in Eq. (15) is replaced by 6do, the normalized reflectivity change Al /R will be, in a first approximation, proportional to the degree of coverage 0. 

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