Hybrid pulse propagation model and quasi-phase-matched four-wave mixing in multipass cells

Abstract

We describe a nonlinear propagation model based on a generalized Schrödinger equation in the time domain coupled to Gaussian beam evolution through ABCD matrices that account for Kerr lensing in the spatial domain. This model is well suited to simulate propagation in mildly nonlinear systems such as multipass cells for temporal compression. It is validated against both a full (x,y,z,t) numerical model and recently reported experimental results in multipass cells, with excellent agreement. It also allows us to identify the physical mechanism for the recently reported parasitic appearance of spectral content in the 700-950 nm range in argon-filled multipass cells that are used to compress pulses at 1030 nm. We think this is due to a quasi-phase matched degenerate four-wave mixing process. This process could be used in the future to perform wavelength conversion as is already done in fibers and capillaries.

Factor 30 pulse compression by hybrid multi-pass multi-plate spectral broadening

“…4(c). The generation of spectral side-bands was previously observed in gas-filled MPC experiments [13,32] and was studied explicitly in a simulation paper [33]. First signatures could be detected approximately 50 dB below the maximal power spectral density for 30 µJ output pulse energy.…”

Nonlinear Optics in Multipass Cells

“…[ 44,70 ] This generation appears at high nonlinearity level, and was interpreted as a four‐wave mixing process that satisfies a quasi‐phase matching relationship. [ 48 ] Although it was observed as a parasitic effect in pulse compression experiments, the periodic nature of the nonlinearity in MPCs offers phase matching opportunities that might be exploited to perform wavelength conversion through four‐wave mixing, as was reported in gas‐filled capillaries. [ 81 ]…”

“…[23] It continues to be an essential tool to test the potential of MPCs to be used in different contexts, such as with more exotic beams, [45,46] to generate supercontinua, [47] or to understand the appearance of parasitic nonlinear effects such as four-wave mixing. [48] Depending on the problem parameters, a number of approaches with a wide range of computational complexity have been undertaken.…”

“…However, if spatio-temporal couplings can be neglected, even simpler models that describe the field in the time domain E(t), in a fashion similar to what is done in optical fibers, have been shown to be useful. [48,41] In this case, the magnitude of the nonlinearity can be inferred from a Gaussian beam parameter that is propagated over the same infinitesimal step dz as the field. [48] This allows to retain to first order the influence of Kerr lensing over the beam size and radius of curvature upon propagation in the MPC.…”

“…[48,41] In this case, the magnitude of the nonlinearity can be inferred from a Gaussian beam parameter that is propagated over the same infinitesimal step dz as the field. [48] This allows to retain to first order the influence of Kerr lensing over the beam size and radius of curvature upon propagation in the MPC. Even simpler, the nonlinear parameter can be considered constant by averaging the beam size along the linear or nonlinear caustic described in Equations ( 1) or ( 6), [41] thereby obtaining an effective area.…”