Swept-source lasers are versatile light sources for spectroscopy, imaging, and microscopy. Swept-source-powered multiphoton microscopy can achieve high-speed, inertia-free point scanning with MHz line-scan rates. The recently introduced spectro-temporal laser imaging by diffractive excitation (SLIDE) technique employs swept-source lasers to achieve kilohertz imaging rates by using a swept-source laser in combination with a diffraction grating for point scanning. Multiphoton microscopy at a longer wavelength, especially in the shortwave infrared (SWIR) region, can have advantages in deep tissue penetration or applications in light detection and ranging (LiDAR). Here we present a swept-source laser around 1550 nm providing high-speed wavelength agility and high peak power pulses for nonlinear excitation. The swept-source laser is a Fourier-domain mode-locked (FDML) laser operating at 326 kHz sweep rate. For high peak powers, the continuous wave (cw) output is pulse modulated to short picosecond pulses and amplified using erbium-doped fiber amplifiers (EDFAs) to peak powers of several kilowatts. This FDML-master oscillator power amplifier (FDML-MOPA) setup uses reliable, low-cost fiber components. As proof-of-principle measurement, we show third-harmonic generation (THG) using harmonic nanoparticles at the 10 MHz pulse excitation rate. This new, to the best of our knowledge, laser source provides unique performance parameters for applications in nonlinear microscopy, spectroscopy, and ranging.