Michael Krause

The recent demonstration of a continuous-wave silicon Raman laser (1) has been considered a major milestone in the expanding field of silicon photonics, which recently has witnessed significant progress in a lot of areas, including high-speed electro-optical modulators (2, 3) and sharp, low-loss waveguide bends (4). Such developments contribute to the continuing vision that a lot of optical functionality might one day be integrated tightly with electronic integrated circuits on silicon chips (5).			

Among the various existing approaches to achieving light amplification and emission in silicon (6), the Raman effect is particularly attractive because it does not require any structural modification or introduction of dopants. Furthermore, it is applicable in the entire transparency range of silicon, provided that appropriate pump laser sources are available. Thus, technological processes that are standard in the electronics industry today can be used to build optical Raman amplifiers and lasers on a silicon chip. Since the first observation of stimulated Raman scattering in a silicon waveguide in 2003 (7), many groups have exploited this phenomenon to build chip-scale amplifiers (8–10) and wavelength converters (11), as well as pulsed (12) and continuous-wave (1) lasers. 

The Raman lasers considered here essentially consist of a silicon waveguide and reflectors for the Stokes (lasing) wavelength at the two ends of the waveguide, forming the laser cavity (see Figure 1). In the silicon-on-insulator (SOI) technology, silicon, with its high refractive index of about 3.5, forms the core of the waveguide (as shown in Figure 2). It is surrounded by materials of lower refractive index, typically a silica buffer layer below (refractive index of about 1.5), and silica or air above. The cavity reflectors can be formed by polished waveguide end surfaces, by thin-film coatings on the end surfaces, or by waveguide Bragg gratings. The Raman laser is pumped optically by a pump laser whose light is injected into the waveguide. 

The operation principle of the laser is simple: when the pump laser at the wavelength λ

 is switched on, spontaneous Raman scattering will generate light at new wavelengths, the most intense peak being generated at the Stokes wavelength λ

 corresponding to an optical frequency downshifted by about 15.6 THz from the pump frequency. The spectral width of the Raman peak is about 100 GHz. Furthermore, any Stokes light in the cavity will be amplified through the effect of stimulated Raman scattering — it will experience Raman gain proportional to the amount of pump power. When reaching the ends of the waveguide, part of the Stokes light leaves the waveguide (forming the output beam), and part of it is reflected back into the waveguide. When the pump power is high enough, this feedback plus the amplification through stimulated Raman scattering leads to an increasing buildup of optical power at the Stokes wavelength. Eventually, a steady state is reached in which the laser continuously converts the pump radiation at λ

However, there are two nonlinear absorption mechanisms that compete with the Raman gain and limit the efficiency of Raman lasing in silicon or even prevent it completely. First, even though silicon is transparent in the wavelength range of interest (λ = 1.1 . . . 5 μm), the effect of two-photon absorption (TPA) becomes noticeable at the high optical powers necessary for Raman amplification. In TPA, two photons are absorbed simultaneously, generating an electron-hole pair. The absorption caused by this effect alone does not impair the Raman-amplification process significantly. However, the increased conductivity of the silicon waveguide due to TPA-generated charge carriers leads in turn to additional optical losses called free-carrier absorption (FCA), which can indeed be substantial. The strength of FCA depends upon how much the carriers accumulate in the waveguide core before recombining. This is quantified by an effective charge-carrier lifetime τ

, which is lower when carriers quickly recombine or diffuse out of the areas of high light intensity.  

 is a property of the waveguide determined by its geometry and the technological processes taken to manufacture it. If it is too high, it is impossible to make the waveguide lase. To reduce the lifetime and thus the impact of FCA, the authors in reference 1 applied a static electric field transversely across the waveguide. The field sucks the carriers out of the waveguide-core area after being generated by TPA before they can accumulate and cause significant FCA to the propagating light. The authors could indeed show that by increasing the applied electric field, the effective lifetime is decreased and lasing becomes more efficient. 

On the other hand, we have recently proposed another way of increasing the efficiency of Raman amplification and lasing in silicon waveguides. By tapering — that is, varying the waveguide width along the propagation direction (as illustrated in Figure 1) — the balance between FCA and Raman gain can be adjusted optimally at each waveguide position and the net gain can be increased (13, 14). Before explaining this concept in detail, however, we have a look at the model for a standard Raman laser. 

In our model for the steady-state characteristics of a silicon Raman laser, there are forward- (+) and backward-propagating (–) waves at the pump (

) of which change along the propagation direction ±

 according to the differential equations (15) (see Figure 1). 

, the right-hand sides of Equations 1 and 2 represent the local gain for the pump and Stokes waves, respectively, which is the sum of four terms. The first term represents the linear losses α present in every optical waveguide, for example, due to light scattering at the waveguide-sidewall roughness produced during etching. The second term describes the effect of stimulated Raman scattering (it appears as a loss to the pump waves and as a gain to the Stokes waves) with a Raman-gain coefficient 

. The third term describes TPA with the TPA coefficient β. Finally, the last term gives the loss due to FCA, which is proportional to an effective charge carrier density, 

 is the effective carrier lifetime explained in the previous section. The expression for 

 is of second order in the optical powers, because carrier generation takes place through TPA as opposed to one-photon absorption. Note that spontaneous Raman scattering does not appear in our differential equations, as its contribution is negligible once the laser has reached its steady state.  

An important constant appearing in Equations 1–3 is the effective area 

, which characterizes how strongly the waveguide confines the light. The efficiency of all nonlinear effects depends upon the intensity of light. Consequently, if the same optical power is confined to a smaller area 

, light intensity is higher and all nonlinear effects such as Raman scattering, TPA, and FCA are more effective (see Equations 1–3). Note in particular that the FCA term is inversely proportional to the square of 

Finally, the reflection of the Stokes (and, optionally, also the pump) waves at the two end faces of the SOI waveguide (at 

 and the input coupling of the pump power 

 are taken into account by the boundary conditions  

Articles

The authors review the operating principles of a silicon Raman laser and show that by introducing a longitudinal variation of the waveguide width in the cavity, the lasing efficiency can be increased significantly.

Michael Krause

Articles

Efficient Raman Lasing in Tapered Silicon Waveguides

Efficient Raman Lasing in Tapered Silicon Waveguides (PDF)