Supercontinuum generation in a solid-state medium was investigated experimentally. A continuum covering 460 to 950 nm was obtained when 0.8 mJ/30 fs Ti:sapphire laser pulses were applied to seven thin fused silica plates at a 1 kHz repetition rate. The primary processes responsible for spectral broadening were self-phase modulation (SPM) and self-steepening, while SPM and self-focusing were balanced to optimize the spectral broadening and suppress the multiphoton process. The output was compressed to a 5.4 fs and a 0.68 mJ pulse, corresponding to two optical cycles and 0.13 TW of peak power.

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We study the exponential sum involving multiplicative function f under milder conditions on the range of f , which generalizes the work of Montgomery and Vaughan. As an application, we prove cancellation in the sum of additively twisted coefficients of automorphic L-function on GL m (m 4), uniformly in the additive character.

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