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43216-G10
Strong Localization of Light in Photonic Crystals Without Bandgap

Vadym Apalkov, Georgia State University

The random resonators in disordered media manifest themselves as the bright spots in the speckled pattern of disordered dielectric films. Such random resonators have large quality factor and can trap light for a very long time. In disordered media with amplification the random resonators can result in coherent random lasing. Although random resonators are sparse, the intensity of the light within such resonators are very large due to their large quality factors. The resonators have a ring-shape structure with small enhancement of dielectric constant within the ring. The ring resonators can be also considered as a waveguide with whispering-gallery type modes. The areal density of random resonators has crucial dependence on the correlation radius of the disorder, i.e. on the size of the scatterers. We show that random resonators can be not only the source of coherent random lasing but also enhance the generation of second harmonic mode in nonlinear disordered media. Namely, we have studied the distribution of the intensity of second harmonic mode within nonlinear disordered system with the emphasis on very large intensities. The large intensity of the second harmonic mode is realized within a finite regions - spots. Therefore we can reformulate the problem in terms of the density of spots with a given very large intensity of SHM. The requirements for such spots are that they should trap both the fundamental mode and the second harmonic mode and the modes should satisfy the phase matching condition within the spot. We have shown that the most efficient way of trapping the light is within random resonators of a ring shape. Therefore to characterize the generation of the second harmonic mode of large intensity in a disordered media we need to find the density of random resonators which produce a given intensity of the second harmonic mode. The phase matching condition for random resonators becomes the condition that the angular momentum of the second harmonic mode is twice of the angular momentum of the fundamental mode. When the matching conditions are satisfied the intensity of the second harmonic mode is determined by a quality factor of resonator, i.e. by a trapping time.

We have shown that within some range of parameters of random media all random resonators, which can trap the fundamental mode of the light, satisfy the double resonant condition, i.e. they can trap both the fundamental and the second harmonic mode simultaneously. Such resonators can efficiently generate the second harmonic mode in random media. We have found the density of such random resonators or the spatial distribution of the intensity of the second harmonic mode. The random resonators are rare so there is no interaction between different random resonators within dielectric film. One of the manifestations of such random resonators in nonlinear disordered media would be the bright spots in the speckle pattern of the second harmonic mode in dielectric film. We have also found that the main parameter, which control the rear event in nonlinear disordered dielectric media is the correlation radius of disorder (or the radius of the scatterers).

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