We report on the evolution of the thickness-dependent electronic band structure of the two-dimensional layered-dichalcogenide molybdenum disulfide (MoS2). Micrometer-scale angle-resolved photoemission spectroscopy of mechanically exfoliated and chemical-vapor-deposition-grown crystals provides direct evidence for the shifting of the valence band maximum from Γ to K, for the case of MoS2 having more than one layer, to the case of single-layer MoS2, as predicted by density functional theory. This evolution of the electronic structure from bulk to few-layer to monolayer MoS2 had earlier been predicted to arise from quantum confinement. Furthermore, one of the consequences of this progression in the electronic structure is the dramatic increase in the hole effective mass, in going from bulk to monolayer MoS2 at its Brillouin zone center, which is known as the cause for the decreased carrier mobility of the monolayer form compared to that of bulk MoS2.

We report strong third-harmonic generation in monolayer graphene grown by chemical vapor deposition and transferred to an amorphous silica (glass) substrate; the photon energy is in threephoton resonance with the exciton-shifted van Hove singularity at the M point of graphene. The polarization selection rules are derived and experimentally verified. In addition, our polarization-and azimuthal-rotation-dependent third-harmonic-generation measurements reveal in-plane isotropy as well as anisotropy between the in-plane and out-of-plane nonlinear optical responses of graphene. Since the third-harmonic signal exceeds that from bulk glass by more than 2 orders of magnitude, the signal contrast permits background-free scanning of graphene and provides insight into the structural properties of graphene.

All-optical signal processing is envisioned as an approach to dramatically decrease power consumption and speed up performance of next-generation optical telecommunications networks 1-3 . Nonlinear optical effects, such as four-wave mixing (FWM) and parametric gain, have long been explored to realize all-optical functions in glass fibers 4 . An alternative approach is to employ nanoscale engineering of silicon waveguides to enhance the optical nonlinearities by up to five orders of magnitude 5 , enabling integrated chip-scale all-optical signal processing.FWM within silicon nanophotonic waveguides has recently been used to demonstrate several telecom-band (λ~1550nm) all-optical functions, including wavelength conversion 6-9 , signal regeneration 10 , and tunable optical delay 11 . Despite these important advances, strong two-photon absorption 12 (TPA) of the telecom-band pump has been a fundamental and unavoidable obstacle, limiting parametric gain to values on the order of a few dB 13 . Here we demonstrate a silicon nanophotonic optical parametric amplifier exhibiting gain as large as 25.4 dB, by operating the pump in the mid-IR near one-half the band-gap energy (E~0.55eV, λ~2200nm), at which parasitic TPA-related absorption vanishes 12,14 . This gain is high enough to compensate all insertion losses, resulting in 13 dB net off-chip amplification. Furthermore, dispersion engineering 15 dramatically increases the gain bandwidth to more than 220 nm, all realized using an ultra-compact 4 mm silicon chip. Beyond its significant relevance to all-optical signal processing, the broadband parametric gain also facilitates the simultaneous generation of