The strong confinement of light in silicon-on-insulator (SOI) materials enables silicon light guides to be scaled down to ultra-small cross-sections that are less than 0.1μm^{2}. These tiny guides are termed Si photonic wires (SPW). The materials system for SPWs is compatible with commercial Si "fab" lines, so guided-wave devices can be patterned with high precision across the full area of a photonic chip to form an ultra-low-loss Si light circuit. Because SOI has a high refractive index contrast, light paths can be folded using sharp bends, making the circuits very compact.

Our collaborating group at Columbia and IBM has begun exploring using these small waveguides as miniature chip-scale “optical fibers” for transmitting data signals at very high bit rates (greater than 1Tbs) for communication among on-chip electronic systems, such as microprocessors (see Figure. 1).^{1} In fact, by using wavelength-division multiplexing (WDM) techniques in conjunction with high bit rates at each wavelength, our group has shown that high bandwidth data streams can be transmitted and received with state-of-the-art bit-error rates.

**Figure 1.** (a) Input spectrum for the aggregate 1.28Tb/s data stream, composed of 32 40Gb/s wavelength channels propagating through a 5cm Si photonic wire; (b) input (top) and output (bottom) eye diagrams for channels (from left to right) C23, C28, C46, and C51 with 10ps/div.

Two concerns motivate the study of nonlinear optical phase physics in Si wires. First, as in conventional optical-fiber data communications, it is essential to understand the conditions under which nonlinear impairments will limit the Si-wire link performance. Second, and conversely, if nonlinear phase control is possible, it is of equal interest to understand whether nonlinear effects can be harnessed to allow all-optical control, signal direction, or signal grooming.

Nonlinear phenomena are important in Si wires because of the extremely large third-order nonlinear optical susceptibility of single-crystal Si, which is about two to three orders of magnitude larger than that of silica. This large cubic nonlinearity in Si, in connection with the strong SPW optical confinement, leads to further enhancement of the effective optical nonlinearity. This enhancement results in a relatively low optical power or threshold for achieving strong nonlinear optical effects.

In addition, because of the submicron dimensions of Si photonic wires, their dispersion properties are markedly different from those of standard optical fibers or even of silicon waveguides that have a few microns in cross-sectional dimension. In particular, due to their ultrasmall dimensions, their dispersion is controlled by the exact geometry of their cross-sectional area. This property leads to the possibility of tailoring their basic dispersion characteristics by techniques such as the group-velocity dispersion (see Figure 2).^{2,3} This ability to engineer the optical dispersion is important for the control of Si nonlinear optical functionalities because it affects signal interaction time and phase matching.

**Figure 2.** Demonstration of dispersion engineering in silicon photonic wires. The graphs show calculated dispersion coefficients. Inset: Transmission electron microscope image of a typical Si photonic wire waveguide and calculated *E*_{11}^{x} mode.

Our team's research on nonlinear propagation in Si wires has explored and demonstrated the basic scaling physics of ultrafast pulses in Si wire links. We have developed a complete theoretical model for nonlinear pulse propagation in Si wires, including the effects of optically generated free carriers and the effects of crystalline anisotropy. In this model, we have used a rigorous approach based on a system of nonlinear coupled equations describing the pump and probe field envelopes and the carrier density to interpret accurately the various nonlinear processes.

In addition to our rigorous theoretical model, we have thoroughly investigated these effects experimentally. Thus we have observed self-phase modulation, cross-phase modulation, and supercontinuum in Si wires by comparing results from long pulse and short pulse sources.^{4} In our experiments, the interaction length between the pump and the probe pulses is less than the waveguide length. Furthermore, the use of ultra-short-pulse lasers of duration ∼200fs allows us to investigate an interesting regime where the nonlinear and various dispersion lengths are all comparable. Such a system yields complex but rich information on pulse propagation and pulse distortion in Si wires.

Our experimental observations agree well with theory and show clearly that SPWs have the potential to form a fiber-on-a-chip system allowing for nonlinear optical control of on-chip functions or integrated photonic circuits. In fact, we have recently carried out basic systems link performance measurements of multiwavelength data streams transmitted onto a single Si link, as is shown in Figure 1.

Richard Osgood

Electrical Engineering

Columbia University

New York, NY