Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities

TL;DR

This paper investigates soliton pulse compression using cascaded quadratic nonlinearities, deriving scaling laws and conditions for achieving sub-two-cycle pulses in bulk nonlinear media through extensive numerical simulations.

Contribution

It introduces a detailed model including higher-order nonlinear terms and defines an effective soliton number to predict pulse compression behavior.

Findings

Successful compression requires the effective soliton number to be greater than one.

Clean pulses below two optical cycles are achievable in BBO crystals with proper parameters.

Scaling laws similar to fiber soliton compressors are applicable in the stationary regime.

Abstract

We present a detailed study of soliton compression of ultra-short pulses based on phase-mismatched second-harmonic generation (\textit{i.e.}, the cascaded quadratic nonlinearity) in bulk quadratic nonlinear media. The single-cycle propagation equations in the temporal domain including higher-order nonlinear terms are presented. The balance between the quadratic (SHG) and the cubic (Kerr) nonlinearity plays a crucial role: we define an effective soliton number -- related to the difference between the SHG and the Kerr soliton numbers -- and show that it has to be larger than unity for successful pulse compression to take place. This requires that the phase mismatch be below a critical level, which is high in a material where the quadratic nonlinearity dominates over the cubic Kerr nonlinearity. Through extensive numerical simulations we find dimensionless scaling laws, expressed through the effective soliton number, which control the behaviour of the compressed pulses. These laws hold in the stationary regime, in which group-velocity mismatch effects are small, and they are similar to the ones observed for fiber soliton compressors. The numerical simulations indicate that clean compressed pulses below two optical cycles can be achieved in a $\beta$-barium borate crystal at appropriate wavelengths, even for picosecond input pulses.