In modern short‐pulse fiber lasers, there is significant pulse breathing over each round trip of the laser loop. Consequently, averaged models cannot be used for quantitative modeling and design. Instead, lumped models, which are obtained by concatenating models for the various components of the laser, are required. As the pulses in lumped models are periodic rather than stationary, their linear stability is evaluated with the aid of the monodromy operator obtained by linearizing the round‐trip operator about the periodic pulse. Conditions are given on the smoothness and decay of the periodic pulse that ensure that the monodromy operator exists on an appropriate Lebesgue function space. A formula for the essential spectrum of the monodromy operator is given, which can be used to quantify the growth rate of continuous wave perturbations. This formula is established by showing that the essential spectrum of the monodromy operator equals that of an associated asymptotic operator. Since the asymptotic monodromy operator acts as a multiplication operator in the Fourier domain, it is possible to derive a formula for its spectrum. Although the main results are stated for a particular experimental stretched pulse laser, the analysis shows that they can be readily adapted to a wide range of lumped laser models.
- Award ID(s):
- 1807272
- NSF-PAR ID:
- 10326042
- Date Published:
- Journal Name:
- Twelfth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
Abstract -
The high power and variable repetition-rate of Yb femtosecond lasers makes them very attractive for ultrafast science. However, for capturing sub-200 fs dynamics, efficient, high-fidelity and high-stability pulse compression techniques are essential. Spectral broadening using an all-solid-state free-space geometry is particularly attractive, as it is simple, robust and low-cost. However, spatial and temporal losses caused by spatio-spectral inhomogeneities have been a major challenge to date, due to coupled space-time dynamics associated with unguided nonlinear propagation. In this work, we use all-solid-state free-space compressors to demonstrate compression of 170 fs pulses at a wavelength of 1030nm from a Yb:KGW laser to ∼9.2 fs, with a highly spatially homogeneous mode. This is achieved by ensuring that the nonlinear beam propagation in periodic layered Kerr media occurs in spatial soliton modes, and by confining the nonlinear phase through each material layer to less than 1.0 rad. A remarkable spatio-spectral homogeneity of ∼0.87 can be realized, which yields a high efficiency of >50% for few-cycle compression. The universality of the method is demonstrated by implementing high-quality pulse compression under a wide range of laser conditions. The high spatiotemporal quality and the exceptional stability of the compressed pulses are further verified by high-harmonic generation. Our predictive method offers a compact and cost-effective solution for high-quality few-cycle-pulse generation from Yb femtosecond lasers, and will enable broad applications in ultrafast science and extreme nonlinear optics.more » « less
-
more » « less
A monochromatic wave that circulates in a nonlinear and dispersive optical cavity can become unstable and form a structured waveform. This phenomenon, known as modulation instability, was encountered in fiber lasers, optically pumped Kerr microresonators and, most recently, in monolithic ring quantum cascade lasers (QCLs). In ring QCLs, the instability led to generation of fundamental frequency combs—optical fields that repeat themselves once per cavity round trip. Here we show that the same instability may also result in self-starting harmonic frequency combs—waveforms that repeat themselves multiple times per round trip, akin to perfect soliton crystals in ring Kerr microresonators. We can tailor the intermode spacing of harmonic frequency combs by placing two minute defects with a well-defined separation between them along the ring waveguide. On-demand excitation of frequency comb states with few powerful modes spaced by hundreds of gigahertz may find their use in future sub-terahertz generators.
-
more » « less
Characterization of ultrashort vacuum and deep ultraviolet pulses is important in view of applications of those pulses for spectroscopic and dynamical imaging of atoms, molecules, and materials. We present an extension of the autocorrelation technique, applied for measurement of the pulse duration via a single Gaussian function. Analytic solutions for two-photon ionization of atoms by Gaussian pulses are used along with an expansion of the pulse to be characterized using multiple Gaussians at multi-color central frequencies. This approach allows one to use two-photon autocorrelation signals to characterize isolated ultrashort pulses and pulse trains, i.e., the time-dependent amplitude and phase variation of the electric field. The potential of the method is demonstrated using vacuum and deep ultraviolet pulses and pulse trains obtained from numerical simulations of macroscopic high harmonic spectra.
-
While dq admittance models have shown to be very useful for stability analysis, extracting admittance models of inverter-based resources (IBRs) from the electromagnetic transient (EMT) simulation environment using frequency scans takes time. In this letter, a new perturbation method based on Gaussian pulses in combination with the system identification algorithms shows great promise for parametric dq admittance model extraction. We present the dq admittance model extracting method for a type-4 wind turbine. Challenges in implementing Gaussian pulse excitation are also pointed out. The extracted dq admittance model via the new method shows to have a high matching degree with the measurements obtained from frequency scans.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
