Linear and Nonlinear Optics of Broad-Band Laser Pulses: Diffraction

The typical spectrally limited laser pulse in the near-infrared region is narrow-band up to 40-50 fs. Its spectral width Δk is much smaller than the carrying wavenumber k₀ (Δk ≪ k₀) . For such kinds of pulses, on distances of a few diffraction lengths, the diffraction is of a Fresnel's type and their evolution can be described correctly in the frame of the well-known paraxial evolution equation. The technology established in 1985 of amplification through chirping of laser pulses triggered remarkable progress in laser optics along with the construction of femtosecond (fs) laser facilities producing high intensity fields of the order of 10¹⁵-10²¹ W/cm². However, the duration of the pulse was quickly shortened from picoseconds down to 5-6 fs, which have a broad-band nature (Δk ∼ k₀). The linear and nonlinear propagation dynamics of broad-band pulses is quite different form their narrow-band counterparts. Here, we review the appropriate theoretical approach to study the evolution of the pulse. Moreover, we shed light on the different diffraction regimes inherent to both narrow-band and broad-band laser pulses and compare them to unveil the main differences. Using this very method, in subsequent papers, we will investigate the influence of the dispersion and nonlinearity on the laser pulse propagation in isotropic media.