**Figure 2.**

*Nonlinear Optics - Novel Results in Theory and Applications*

*from vibrationally excited molecules that interfere coherently.*

Due to its Raman-shifted output, SRS is a workable method for generating coherent radiation at new frequencies. SRS permits, in principle, the amplification in a wide interval of wavelengths, from the ultraviolet to the infrared. Since the Raman frequency of a medium is usually fixed, the tunability can be achieved by using a tunable pump laser. Raman lasing occurs when the Raman-active gain medium is placed between mirrors, reflecting the first Stokes wavelength. This is analogous to lasers, where the gain medium must be placed inside a cavity to achieve laser threshold. Raman lasers and traditional lasers differ in the wavelength of light required for pumping. In the case of Raman laser, it does not depend on the electronic structure of the medium, so the wavelength of pump laser can be chosen

*(a) Spontaneous Raman scattering: incident photons inelastically scatter off spontaneously from vibrationally excited molecules, behaving independently. (b) Stimulated Raman scattering: two incident lights, a pump and a Stokes laser beams, whose energy difference matches a particular vibrational energy, drive the molecule at ων = ω<sup>S</sup> − ωP, producing coherent Raman signals at ωS = ωP + ων. SRS modalities are: SRG, stimulated Raman gain; SRL, stimulated Raman loss. (c) Stimulated Raman scattering: inelastic scattering of probe photons off* 

In order to tailor Raman laser characteristics and performances, there are two main basic configurations. The first one, external-resonator Raman laser, the Raman crystal is placed inside a cavity, resonating the Stokes field (**Figure 2(a)**). This configuration is used for pump pulses that are longer than the transit time through the Raman crystal. The second one, the intracavity Raman laser (**Figure 2(b)**) combines both a Raman medium and the laser medium inside a single cavity, so that

Raman amplification, demonstrated in the early 1970s, is a feasible approach for fiber optics amplification, being only restricted by the pump wavelength and Raman active modes of the gain medium [4]. In this case, optical fiber is used as Raman gain medium and both pump and signal waves are launched into it (**Figure 2(c)**). In the past century, fused silica has been the main material used for transmission of optical signals, because of its good optical properties and attractive trade-off between Raman gain and losses. The main disadvantage of the current silica fiber amplifiers is the limited usable bandwidth for Raman

munications was achieved opening the communication range to span from 1270 to 1650 nm, corresponding to about 50 THz bandwidth [5]. For future amplification requirements, due to this significant increase in bandwidth, the use of existing Er-doped fiber amplifiers is kept out, while Raman gain becomes the key

). A development in fiber optics com-

the fundamental and Stokes fields are both resonating within the cavity [3].

**128**

mechanism.

to minimize absorption.

**Figure 1.**

amplification (5 THz, approx. 150 cm<sup>−</sup><sup>1</sup>

*Basic configurations of Raman laser: (a) external-resonator Raman laser; (b) intracavity Raman laser; (c) fiber Raman amplifiers; and (d) silicon on insulator waveguide Raman laser.*

Silicon photonics is an important player in the low-cost optical interconnect technology, as silicon-based optical components could be manufactured using the existing silicon fabrication techniques [6]. Silicon on insulator (SOI) waveguides allows to limit the optical field into an area 100 times smaller than the modal area of a typical single-mode optical fiber. In addition, the Raman gain in silicon is much stronger than in glass (≈10,000 times), therefore allowing to reduce the length required from kilometers of fiber to centimeters of silicon waveguides [2]. The waveguide approach, schematically reported in **Figure 2(d)**, led to the demonstration of pulsed Raman silicon laser [7] and continuous-wave (CW) lasing [8]. The merit of this approach is the ability to use pure silicon without the need for Er doping; i.e. it is fully compatible with silicon microelectronics manufacturing. On the other hand, there are three main limitations. The first, Raman laser cannot be electrically excited and it requires an off-chip pump. The second, the narrowband (105 GHz) of stimulated Raman gain makes it unsuitable for its use in WDM applications, unless expensive multi-pump schemes are implemented. The third,

Raman gain in Si at the wavelength of interest for telecommunications is reduced by two-photon absorption (TPA).

We note that as a general rule, in all laser gain bulk materials there is a tradeoff between gain and bandwidth: linewidth may be increased at the expense of peak gain. In nature, we have material with high Raman gain and small bandwidth (for example, silicon), and others with a large bandwidth but with small Raman gain (for example, silica). This trade-off is a fundamental limitation toward the realization of sources with high efficiency and large emission spectra. In this book chapter, a review of the most significant accomplishments in the field of SRS in micro- and nanophotonics is reported. From a theoretical point of view, the difference between micro- and nanostructures is significant. In microstructures, the measured SRS enhancement can be related to photons confinements effect and it can be quantified by a corresponding gain (*gmicro*), given by: *gmicro* = *f*\**gbulk*, where *f* is the optical field enhancement due to the presence of microstructures and *gbulk* is the gain of bulk material, making up the microstructures [2]. According to this formula, photonics microstructures allow an enhancement of Raman gain, but the bandwidth does not change, therefore the fundamental trade-off between gain and bandwidth of bulk materials cannot be overcome using microstructures. Concerning SRS in nanostructures, although a general theory on the relation between nanostructuring and Raman gain is not established, we expect that the Raman gain of nanomaterials *gnano* should be related to the intrinsic properties of materials and for this reason different from bulk. Therefore, the fundamental trade-off between gain and bandwidth should be overcome, too.

The chapter is organized as follows. In Section 2, some the most successful applications areas of SRS in microstructures are described. In Section 3, a number of investigations concerning SRS in nanostructures are described. Finally, in the appendix, for the sake of completeness, the basic theory of SRS and experimental methods for measuring Raman gain are reported.
