The ‘ideal’ material for Raman amplification should have flat and high Raman gain across a broad wavelength range. However, a tradeoff for Raman amplification is typical: materials with relatively high Raman gain have small bandwidth (for example, silicon), whereas materials with large bandwidth have very small gain (for example, silica). This tradeoff is a serious limitation for the realization of micro- and nano-sources with broad and intense emission spectra.
In our previous paper43
, experimental results on spontaneous Raman scattering in Si-nc at the wavelength of interest for telecommunications (1.54
μm) were reported. We pointed out two significant improvements of silicon quantum dots with respect to crystalline silicon: the broadening of the spontaneous Raman spectra and the tuning of the Stokes shift. Our previous results combined with the present observation of enhanced Raman gain lead us to the conclusion that the traditional tradeoff between gain and bandwidth can be overcome in low-dimensional materials.
Most importantly, the present results show an impressive enhancement of the Raman gain in Si-nc compared with bulk silicon, by three–four orders of magnitude depending on the Si concentration (see ). It should be remembered that the volume of Si-nc does not exceed 10% of the volume of the sample, which makes the difference between the gain properties of Si-nc and bulk silicon even greater. It is also interesting to note that the gain coefficient is not simply proportional to the concentration of Si-nc. The difference of the amount of elemental Si constituting Si-nc increases from coordinate 5
cm to coordinate 0
cm by a factor of about 2, whereas the gain changes by a factor of 6.5.
Now, we briefly discuss possible reasons for the giant Raman gain observed from Si-nc. In SRS phenomenon, matter interacts with two light waves at different frequencies (the pump and Stokes waves), where the frequency difference corresponds to the vibrational energy. The origin of SRS can be understood in terms of a two-step process: first, the pump causes the molecular vibrations and thereby produces frequency sidebands (Stokes and anti-Stokes); and next, the Stokes wave beats with the pump wave leading to modulation of the total intensity that coherently excites the molecular vibrations. These two steps reinforce each other in the sense that the pump effect leads to a stronger Stokes wave, which in turn leads to stronger molecular vibrations14
The third-order nonlinear susceptibility is described by χ(3)
. The first term, χ(3)nr
, represents the non-resonant electronic contribution to the total third-order nonlinear susceptibility, which is a real quantity, and thus is independent of the Raman shift14
. This term is related to the nonlinear refractive index (or optical Kerr index) n2
and two-photon absorption coefficient β
. The nonlinear optical properties of Si-nc are affected by their structural parameters (size, distribution, density and crystallinity), and a large variation of the n2
values has been reported, which complicates the comparison of experimental and theoretical results44
. Recent studies45
on nonlinear refractive indices n2
films containing Si-nc and/or Si nanoclusters have demonstrated that both the defect states and the quantized electronic states should be taken into account to explain the origin of large values of n2
of Si clusters, up to two orders of magnitude with respect to crystalline silicon.
The second term, the complex quantity χ(3)r, represents the nuclear response of the molecules and provides the intrinsic vibrational mechanism of SRS. It is worth noting that χ(3)r exists only near the vibrational resonance, whereas at the exact Raman resonance χ(3)nr=0 and the Raman susceptibility χ(3)r is negative imaginary, therefore SRS is inherently insensitive to any non-resonant background contributions.
Large Raman gain is expected for materials with a large value of Im(χ(3)r
) (refs 14, 15
). It has been demonstrated that when the mean-free path of an electron is larger than that of a phonon, the electron can collide with the phonon many times, therefore a strong emission of optical phonons, that is, phonon amplification, can be obtained27
. From the point of view of energy transfer, the energy of the laser field is first absorbed by the electrons, and then transferred to the phonons through the electron–phonon interaction. We suggest that a similar mechanism may occur in Si-nc. If a resonance condition is obtained, for example, due to the interface levels, and the movement of electrons is strictly restricted due to the confinement effect, all light-generated electrons are expected to be involved in the electron–phonon interaction, resulting in significant amplification of phonons. Therefore, the efficiency of electron–phonon interaction in a nanocrystal may be much higher than in a bulk crystal. Moreover, the structure of interfaces, stoichiometric material disorder, stress and cluster shape may also influence Raman amplification. To better understand our results, a theoretical model of SRS in Si-nc has to be developed, which is outside the scope of our experimental work.
In conclusion, a giant Raman gain is obtained from Si-nc in silica, up to four orders of magnitude higher than that from crystalline silicon. From the fundamental point of view, these results will hopefully stimulate theoretical work required to develop a quantitative model of SRS in Si-nc. Concerning applications, we note that the basic idea behind the invention of silicon Raman laser was that the SRS effect in silicon was about 104 times larger than that in the glass fibre; therefore, an active device with typical dimensions of a few centimeters instead of several kilometres could be realized. Analogously, according to our results, a Raman laser with a length of a few microns can be developed based on Si-nc. This achievement would lead to all the advantages of combining optical and electronic functions on a single chip.