Abstract
We derive approximate analytic expressions for the effective susceptibility tensor of a nonlinear composite, consisting of silicon nanocrystals embedded in fused silica. Two types of composites are considered: by assuming that (i) the crystallographic axes of different crystallites are the same, or (ii) crystallites are oriented randomly. In the first case, the tensor properties of the effective third-order susceptibility are shown to coincide with those of the bulk silicon. In the second case, however, the tensor properties of the susceptibility of the composite material are found to be quite different due to drastic modification of light interaction with optical phonons inside the composite. The newly derived expressions should be useful for modeling nonlinear optical phenomena in silica fibers and waveguides doped with silicon nanocrystals.
Highlights
Even though silicon was recognized as an important material for photonics technology more than 25 years ago [1], the relevant theoretical concepts have begun to be put into practice only recently [2, 3]
It was found that the ultrafast Kerr effect in silicon nanocrystals (Si NCs) may be, respectively, 10 000 and 100 times stronger than that in fused silica (SiO2) and bulk silicon
Much like silicon-on-insulator waveguides, silica glass doped with Si NCs (Si-NCs/SiO2 composite) enables tight confinement of optical fields, while its refractive index may be tuned to any value between 1.45 and 2.2 by changing the density of the Si NCs [11,12,13]
Summary
Even though silicon was recognized as an important material for photonics technology more than 25 years ago [1], the relevant theoretical concepts have begun to be put into practice only recently [2, 3]. Received 1 Oct 2012; revised 27 Oct 2012; accepted 27 Oct 2012; published 6 Nov 2012 19 November 2012 / Vol 20, No 24 / OPTICS EXPRESS 26276 possible the development of a variety of functional nonlinear devices, with both active and passive silicon elements These devices can generate and amplify optical signals [4, 5] but can modulate and switch them—either all-optically or electro-optically—at speeds approaching hundreds of gigabits per second [6, 7]. We extend our analysis and calculate the effective susceptibility for a situation in which NCs are randomly orientated in space with a uniform distribution In this case, the anisotropy of the nonlinear optical response of the whole composite is different from that of bulk silicon. The Raman response resulting from the vibrational subsystem of the NCs is modified the most
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