Spontaneous emission is not inherent to an emitter, but rather depends on its electromagnetic environment. In a microcavity, the spontaneous emission rate can be greatly enhanced compared with that in free space. This T he spontaneous emission (SE) rate in a microcavity is enhanced by the Purcell factor 1 (F), proportional to the ratio of the cavity quality factor (Q) to mode volume (V mode ). Until now, the advantages of large SE rate enhancement have not been fully explored in lasers because of their large mode volumes. Thus, their SE properties have been dictated by the intrinsic radiative lifetime of the bulk material. With the recent advances in semiconductor fabrication and crystal growth, it has become possible to produce high-quality photonic crystals. These are structures of alternating refractive index 2,3 that provide unprecedented control over the electromagnetic environment. Cavities introduced into the photonic crystal can have extremely high Q/V mode ratios, and therefore can enable large Purcell factors. So far, such nanocavities have been used for cavity quantum electrodynamic (QED) experiments 4-12 such as SE rate enhancement 4,5,9-11 and suppression 4 , and also for single-photon sources 4,12 and lower-threshold lasers [13][14][15][16][17] . Here, we demonstrate extremely fast photonic crystal nanocavity lasers with response times below the 2 ps detection limit of our measurement apparatus. The turn-on delay times are measured as near 1 ps, more than an order of magnitude faster than previous measurements 18,19 .There are two important laser modulation schemes: smalland large-signal modulation. We analyse the laser dynamics by solving the laser rate equations 20 for photon and carrier densities. Communication systems use both small-and largesignal modulation [20][21][22] . In the small-signal regime, the laser is driven with an above-threshold d.c. pump power L in,0 and modulated with a small time-varying (a.c.) signal L in . The carrier and photon densities follow the pump with d.c. and a.c. components N 0 + N and P 0 + P, respectively. The modulation response is given by P/ N. At low d.c. driving power above threshold, the bandwidth of the laser is limited by the relaxation oscillation frequency: