Abstract
We demonstrate that stimulated supercontinuum generation alleviates restrictions on spectral broadening in silicon waveguides. At telecommunications wavelengths, two-photon and free-carrier absorption typically deplete the pump before large broadening factors can be achieved. However, broadening via modulation instability (MI) can be enhanced by seeding, which also substantially improves the energy efficiency of spectral broadening in media with nonlinear loss. Coherent seeding also generates a stable output spectrum, in contrast to conventional approaches where broadening starts from noise. The combination of self-phase modulation and stimulated modulation instability generates broadening factors in excess of 40-fold at moderate intensity levels, with >15-times better energy efficiency.
Broadband “white” light known as supercontinuum (SC) radiation1,2 finds diverse applications in frequency metrology,3 spectroscopy,4,5 biophotonics,6,7 and wavelength-division multiplexing (WDM) communication.8–10 While nonlinear optical fiber is typically employed to produce this radiation, the generation of broadband light in silicon waveguides has been experimentally and theoretically investigated,11–14 and is of interest for, e.g., chip-scale sensing applications and future optical interconnects based on WDM.8,15 Rapid spectral broadening requires an intense pump and a strong optical nonlinearity. Silicon has a strong Kerr nonlinearity, but two-photon absorption (TPA) and free-carrier absorption (FCA)—phenomena that are absent in optical fiber—restrict the broadening factor.14,16 Furthermore, Raman scattering in silicon has a relatively narrow gain bandwidth and an appreciable frequency shift and, thus, does not play a significant role in broadening the spectrum. Consequently, the broadening factors found in silicon are much smaller than those in optical fiber.
A high-intensity pump pulse in a silicon waveguide modulates the medium’s refractive index, leading to self-phase modulation (SPM) of the pulse and, thus, spectral broadening. Both the Kerr nonlinearity and refraction caused by free carriers (FCR) contribute to SPM. The carriers are generated by TPA and tend to accumulate due to their relatively long lifetime. The Kerr effect produces blueshifted frequencies on the pulse’s trailing edge and redshifted components on its leading edge, while FCR induces a blueshift throughout the pulse. The net effect is a blueshifted continuum with new frequencies residing predominantly in the pulse’s trailing side.14,17 However, the accumulating carriers substantially attenuate these components. Together with TPA, this process leads to self-limited broadening in the normal dispersion regime.14
Broader bandwidths can be realized (but with similar broadening factors) by driving the nonlinear process with ultrashort pump pulses, which also produce fewer free carriers for a fixed power level.13,18 Anomalous and higher-order dispersion also create the possibility of achieving large bandwidths through modulation instability (MI) (Ref. 19 ) and soliton fission.13 However, TPA and FCA tend to dampen MI and inhibit broadening, except in the mid-infrared regime where nonlinear absorption is nearly eliminated.20
In this paper, we realize large spectral broadening factors in a silicon waveguide despite the presence of TPA and free-carrier effects. In our simulations, previous spectral broadening limitations are overcome by stimulating MI with a weak seed that jumpstarts the nonlinear interaction. In addition, we show that coherent seeding produces a low noise SC, in contrast to that resulting from noise-driven MI. To motivate further discussion, we show the impact of a weak seed on pulse propagation in a silicon waveguide with anomalous dispersion (cf. Fig. 1). An understanding of this result is facilitated by a brief examination of spectral broadening effects in fiber.
