Ultrafast pulses Serrodyne nonlinear broadening and frequency shift in molecular alignment system

  Objective  The advancement in ultrafast optics has propelled research on light-matter interactions into extreme optical conditions characterized by strong fields and high energies. However, many innovations and applications demand specialized laser parameters, including wavelength, intensity, pulse duration, and repetition rate. Particularly, wavelength is a crucial yet less flexible parameter to control. This paper reports the Serrodyne nonlinear broadening and frequency conversion induced by the molecular alignment effect in ultrafast pulses, achieving precise wavelength shifting. By investigating the relationship between pulse shape and transient frequency, we elucidate the mechanism of the Serrodyne effect in triggering nonlinear dynamical processes. Unlike Kerr nonlinearity, in the molecular alignment system, the magnitude of spectral shift is influenced by both the molecular response time and pulse width, providing possibilities for introducing new degrees of freedom in the control of ultrafast light sources.

  Methods  In our study, we employ numerical simulations to introduce the Serrodyne effect into the Kerr system and achieve molecular alignment through the nonlinear Schrödinger propagation equation. Our objective is to establish the relationship between the shape and direction of the sawtooth pulse and the spectral frequency shift of the pulse. The nonlinear propagation dynamical induced by the Serrodyne effect are elucidated by mapping the transient frequency in relation to the pulse shape in the time domain. To comprehensively explore this effect, we adopt two approaches. Firstly, we maintain the steepness of the sawtooth-shaped pulse constant while adjusting the pulse width by varying t₁ and t₂ in equal proportions. This approach enables a systematic investigation into the effect of pulse width with a fixed shape pulse. Secondly, we vary the steepness of the pulse by adjusting the ratio of t₁ and t₂, denoted as Ri (Ri = t₂/t₁), allowing us to explore the impact of changes in steepness.

  Results and Discussions  Figure 1 reveals that the spectrum exhibits symmetrical redshift and blueshift as the direction of the sawtooth pulse changes. For Kerr nonlinearity, a more substantial shift is achieved by generating steeper sawtooth pulses, as depicted in Fig.1(a) and Fig.1(b) with Ri set at 3. A clear observation from Fig.2(a) and 2(b) reveal the symmetrical nature of the Kerr shift when the direction of the sawtooth pulses is reversed. Results obtained at Ri of 10, depicted in 2(c) and 2(d), show that when the ratio of Ri increases, there is no significant alteration in the nature of the frequency shift, only a reduction in the shift range. To gain a deeper understanding of Kerr's symmetrical frequency shift, the pulse shape is plotted against the transient frequency in Fig.3(a)-3(d). A comparison indicates that as the steepness decreases (i.e., the pulse width increases), there is minimal difference in the overlap of pulse energy with the transient frequency, maintaining the fundamental nature of the frequency shift. Figure 5-6 illustrate the frequency shift of molecular alignment with different sawtooth waveforms. In contrast to the Kerr effect, molecular alignment exhibits two significant differences. Firstly, when sawtooth pulses with the same degree of steepness and opposite directions are applied, the shifted results show asymmetry. Secondly, varying degrees of steepness in sawtooth pulses result in different properties of shifted frequency.

  Conclusions  In this study, we explore two distinct nonlinear effects arising from the introduction of sawtooth pulses generated by the Serrodyne effect based on both the Kerr nonlinearity and the molecular alignment nonlinearity. Comparative analysis reveals that the molecular alignment system exhibits more complex and nuanced nonlinear processes than the regular periodic Kerr nonlinearity. Within the molecular alignment regime, the transient frequency's magnitude is influenced by the molecular response time and pulse duration, introducing novel degrees of freedom for nonlinear frequency shifting of spectra. Our study provides a new perspective on our understanding of nonlinear effects in molecular alignment, thereby deepening our knowledge of designing ultrafast light sources. At the practical application level, precise tuning of parameters, such as the steepness and direction of the sawtooth pulse, enables directional control of the nonlinear Serrodyne effects. Optimizing these pulse parameters facilitates precise manipulation of nonlinear effects to induce frequency shifts, thereby opening up new possibilities for enhancing the performance and innovative applications of ultrafast light sources. Such new light source, applicable in strong field physics, precision spectroscopy, optical communication, and imaging, offers a large bandwidth, tunability, efficiency, and compactness, along with flexible and diverse regulatory mechanisms.