Filamentation-assisted fourth-order nonlinear process in KTP crystal

We present an experimental investigation of a filamentation-assisted fourth-order nonlinear optical process in KTP crystals pumped by intense 1.53 eV (807 nm) femtosecond laser pulses. Femtosecond light pulses at 2.58 eV (480 nm) are generated by the fourth-order nonlinear polarization (P^(4)(\omega_2))=\chi^(4)(\omega_2, \omega, \omega, \omega, -\omega_1)E^3(\omega)E^*(\omega_1), where E(\omega) corresponds to the pump frequency and E(\omega_1) to the supercontinuum generated through filamentation). If the system is seeded by a laser beam at \omega_1 or \omega_2 and there are spatial and temporal overlaps with the pump beam, E(\omega_1) and E(\omega_2) are simultaneously amplified. When the intensity of the seed laser beam exceeds a certain intensity threshold, the contribution of P^(4)(\omega)=\chi^(4)(\omega, \omega_1,\omega_2, -\omega, -\omega)E(\omega_1)E(\omega_2)(E^*(\omega))^2 becomes non-negligible, and the amplification weakens. The conversion efficiency from the pump to the signal at 2.58 eV (480 nm) attains to 0.1%.