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3. NANOMEMS PHYSICS: Quantum Wave Phenomena                   147

             emission can be  forbidden, thus potentially  eliminating  non-radiative
             transitions.  This is so  because, in the band gap of  a  PBC,  the  density  of
             photons states,  ρ  =  0 . The first experimental demonstration of the use of
                            PBC
                 -
             three dimensional PBCs to control the dynamics of spontaneous  emission
             from quantum dots has been recently published [173]. In this case, Fig. 3-31,






































             Figure 3-31. (a) Scanning electron microscope image of the (111) face of a titania inverse
             opal with lattice parameter a=460 nm. Reprinted with permission from[170] Copyright 2004
             Nature. (b) Luminescence decay curves of quantum dots inside three different photonic
                                                      -1
                                                                           -1
             crystals. The data are recorded at frequencies 15,670 cm  (a= 370 nm) and 15,100 cm  (a
             =420 nm, and a=500 nm). The curves have been overlapped after 5 ns. The first part of the
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             decay curve is influenced by emission of titania (recorded at 15,400 cm ). After 5 ns this
             contribution is negligible. [173].
             the spectral distribution  and  time-dependent decay  of  light  emitted from
             excitons confined in the CdSe quantum dots are shown to be controlled by
             the  host PBC. In particular, the fact that  lifetimes of  .9 ±  1 . 0  ns  and
                                                                 6
             19  3 . ±  2 . 0  ns  for quantum  dots embedded in PBCs of lattice constants
             a=420 nm and a=500 nm, respectively, are obtained, demonstrate a factor of
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