**1. Introduction**

Optical phenomena in materials with a space modulation of dielectric constant at distances close to the light wavelengths (so called photonic band-gap structures or photonic crystals) are of a great interest now because of the existence of band gaps in their photonic band structure (Bykov, 1972; Yablonovitch, 1987; John, 1987). These band gaps represent frequency regions where electromagnetic waves are forbidden, irrespective of the spatial propagation directions. Inside the band gaps, the photon density of states is equal to zero and so the emission of light sources embedded in these crystals should be inhibited in these spectral regions (Vats et al., 2002). Since the time the effect is predicted, many experiments have been devoted to studies of spontaneous emission of molecules embedded in photonic crystals (Gaponenko et al., 1999; Gorelik, 2007). Typical structures of photonic crystals and calculations of corresponding photonic band structures are presented in a book by Prof. Joannopoulos (Joannopoulos et al., 2008). Besides the emission inhibition effect, a number of new optical phenomena in 3D photonic crystals, interesting from the applied point of view, are under intensive study now. The main research directions are the following:


As a good prototype of 3D photonic crystals, synthetic opals made of α-SiO2 globules have been widely used (Gorelik, 2007). Diameter *D* of globules can be varied from 200 nm to 700 nm. Between globules there are tetrahedral and octahedral hollows (or pores) with a mean size of about 0.26*D*. Synthetic opals are characterized by a stop-band or a pseudogap (i.e., a band gap actual for one direction) in the [111] direction and a singular behaviour of photon density of states near by the stop-band edges. The existence of pores in the opal structure

Quantum Optics Phenomena in Synthetic Opal Photonic Crystals 89

The spontaneous emission spectrum *S*(*ω*) is completely determined by the spectral distribution of transitions frequencies *ωnm* and the density of optical states *g*(*ω*) within a

When frequencies *ωnm* are in photonic band gap, where *g*(*ω*) = 0, spontaneous emission must be completely inhibited. In general case, a dip in spontaneous emission spectrum should appear. The spectral position of this dip is correspondent to positions of reflection spectrum maximum and transmission spectrum minimum (Gaponenko et al., 1999). As a result of spontaneous emission inhibition the localisation of photon near by irradiative atom inside photonic crystal becomes possible if the transition frequency is within a band gap region or in the vicinity of band gap edges (John, 1987). In this case, bonded atom-photon state is coming into being. The photon emitted returns to the atom due to Bragg reflection and is reabsorbed by this atom. The existence of a group of such atoms may result in forming narrow photonic impurity band like an impurity band in semiconductor at sufficient concentrations of impurity atoms. Kinetics of luminescence in the vicinity of band gap edges demonstrates

Consider an elementary Stokes Raman scattering process as a disintegration of exciting

The Stokes process probability *W*(*ω*') is determined by the density of optical states *g*(*ω*') in

2

, (2)

int <sup>2</sup> <sup>ˆ</sup> *W mH g* ( ) 0 ()

ˆ *m H* 0 is the modulus of the matrix element of the Hamiltonian of the radiation-

photon (*ћωex*, *kex*) into scattered photon (*ћω*', *k*') and optical phonon (*ћΩ*, *Κ*) (Fig. 2).

region of these frequencies (Vats et al., 2002).

non-exponential behaviour (John, 1987).

Fig. 2. Elementary Stokes Raman scattering process

where int

substance interaction.

the region of scattered light frequencies (Poulet & Mathieu, 1970)

**2.2 Enhanced Raman scattering** 

allows modifying optical properties of such systems by filling the pores with various substances.

Synthetic opal photonic crystals containing nonlinear optical substances give a good chance to observe quantum optics phenomena in spatially nonuniform media where the photon mean free path is close to the light wavelength. Moreover, in this case the input optical power that is necessary to observe phenomena may be lower than the power required usually for observing the same phenomena in uniform nonlinear substances. The reason for it is the existence of diffuse transfer of photons that can result in photon accumulating inside photonic crystals and, consequently, in local optical power increasing. In particular, the possibility of experimental manifestation of Raman scattering and spontaneous parametric down-conversion in synthetic opals is discussed (Gorelik, 2007). The latter phenomenon is of special interest as it is convenient method to obtain bi-photon fields consisting of correlated photon pairs (Kitaeva & Penin, 2005). In the recent years, crystals with chirped structure of quadratic susceptibility (Kitaeva & Penin, 2004), and materials with spatially regular and stochastic distribution of quadratic optical susceptibility (Kalashnikov et al., 2009), are considered as sources of bi-photons. It is quite possible synthetic opal photonic crystals will be ranked with these sources.
