Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media
Spotlight summary: Strongly compressed few-cycle optical pulses enable monitoring of ultra-fast processes, such as chemical reactions, and can realize precisely controllable light-matter interactions with femtosecond precision.
An elegant approach to the generation of ultrashort pulses, which necessarily have ultra-broadband spectrum with the bandwidth inversely proportional to the pulse duration, is based on the concept of soliton pulse compression. With this scheme, the pulse propagates through a nonlinear medium, where its spectrum becomes broadened due to self-phase modulation, and simultaneously the pulse is compressed in time due to the interplay between linear dispersion and nonlinearity. Importantly, this process can be very robust, as it is based on the formation of solitons - self-localized waves, which are stable under appropriate conditions. The key requirement for this concept to work is that the types of nonlinearity and dispersion should be matched to support the soliton formation. At near-infrared wavelengths, the dispersion is predominantly normal and a self-defocusing nonlinearity is needed, however the instantaneous cubic or Kerr-type material nonlinearity is usually self-focusing.
This paper presents a detailed theoretical analysis of nonlinear pulse compression, which predicts that few-cycle pulses can be created by employing cascaded wave interactions based on ultrafast quadratic nonlinearity. Remarkably, it is shown that, under practical conditions, cascaded quadratic interactions can produce effective self-defocusing cubic nonlinearity, which can be stronger than the material self-focusing response, in a very broad spectral region. As a result, few-cycle soliton pulses can be generated from multi-cycle pump pulses within a short propagation distance of several millimetres in crystals with strong quadratic nonlinearity including BBO and MgOLN. Additionally, the cascaded interactions can be specially tuned to compensate for pulse distortions associated with the delayed Raman response, such as the spectral red-shift.
The theoretical analysis is based on the generalized nonlinear Schrödinger equation for the slowly-varying electric field envelope, which is derived in the paper taking into account self-phase modulation, cascading, and Raman effects. Since the slowly-varying envelope approximation may break down for few-cycle pulses, the authors additionally validate their simulation results by direct modelling of the dynamics of the electric field using nonlinear wave equations formulated for nonlinear birefringent media.
This article should stimulate further experimental advances towards the realization of efficient nonlinear pulse compression down to few-cycle durations.
Technical Division: Light–Matter Interactions
ToC Category: Nonlinear Optics
|OCIS Codes:||(190.2620) Nonlinear optics : Harmonic generation and mixing|
|(190.5650) Nonlinear optics : Raman effect|
|(190.7110) Nonlinear optics : Ultrafast nonlinear optics|
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