INDEX spontaneous transition

He points out that the variation of lifetime with glass matrix is due to at least two causes, the first being the changes in refractive index. If the wave functions of the ion remain essentially the same from host to host, the spontaneous-transition probability will increase with increasing refractive index because of the increase in density of final states. The second cause is configuration mixing of 4/ and 5d states, which must reflect the size and symmetry of the crystal field produced at the ion by the surroundings. 

The excited-state wavepacket spontaneously emits photons while undergoing transitions to any of the electronically-ground vibrational wavefunctions t (where we have lumped the final state quantum numbers i>/, jf in a single index f). The rate of emission from a given 4% component of the excited wavepacket to a given ground state is given in terms of the Einstein A-coefficient [9],... 

The interest in quantum interference stems from the early 1970s when Agarwal [4] showed that the ordinary spontaneous decay of an excited degenerate V-type three-level atom can be modified due to interference between the two atomic transitions. The analysis of quantum interference has since been extended to other configurations of three- and multilevel atoms and many interesting effects have been predicted, which can be used to control optical properties of quantum systems, such as high-contrast resonances [5,6], electro-magnetically induced transparency [7], amplification without population inversion [8], and enhancement of the index of refraction without absorption [9]. 

Thin films have been prepared from relatively simple versions of the benzothiophene hexatriene structure decorated with ferf-butyl groups (the fcrf-butyl isomer of 4, for example), which can be used to photomodulate the refractive index [37]. However, photoactivity is reduced in this example and while irradiation of solutions produce as much as 45 % of the ring-closed isomer, only 10% can be generated in the spin-cast film. Another limitation with this example is the relatively low glass transition temperature (Eg), which was measured to be 47 °C. For practical applications, a Tg above 100 is desirable to avoid spontaneous crystallization. Compounds 18 [38], 19 and 20 [39] were prepared to address this limitation (Chart 21.3). 

---