A broadband light source device for creating broadband light pulses includes a hollow-core fiber and a pump laser source device. The hollow-core fiber is configured to create the broadband light pulses by an optical non-linear broadening of pump laser pulses. The hollow-core fiber includes a filling gas, an axial hollow light guiding fiber core configured to support core modes of a guided light field, and an inner fiber structure surrounding the fiber core and configured to support transverse wall modes of the guided light field. The pump laser source device is configured to create and provide the pump laser pulses at an input side of the hollow-core fiber. The transverse wall modes include a fundamental transverse wall mode and second and higher order transverse wall modes.