B-Integral Calculator
Calculate cumulative B-integral and self-focusing critical power for ultrafast beam paths through optical elements.
The B-integral quantifies accumulated nonlinear phase in an optical beam propagating through a material: B = (2π/λ) ∫ n₂ I(z) dz. It is the standard figure of merit for self-phase modulation (SPM) in ultrafast laser systems — values above roughly π signal significant spectral broadening or beam quality degradation. This tool accepts pulse energy, beam radius, pulse duration (fs or ps), pulse temporal profile (Gaussian or sech²), and a list of optical elements — each defined by material and thickness. Supported materials include fused silica, BK7, SF11, sapphire, CaF₂, and YAG, with a custom n₂ entry. Outputs include peak intensity, per-element B-integral, cumulative B-integral across the full element stack, and the critical power for self-focusing in each material.