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Register a new userTheory of the Chromatic Dispersion, Revisited
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Added by
Dimitar Popmintchev
Publication date
2020
fields
Physics
and research's language is
English
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We derive general analytic expressions for the chromatic dispersion orders valid to infinity, due to the k vector or phase {phi} dependence on the wavelength. Additionally, we identify polynomials and recursion relations associated with the chromatic dispersion orders and draw analogy to the generalized Lah and Laguerre transformations. Further, we give explicitly the dispersion terms to the 10th order and visualize the chromatic dispersion for material, grating and prism-pair compressors and hollow-core photonic anti-resonant fiber. These simple formulas are applicable for material dispersion, compressors, stretchers, waveguides, and any other type of known frequency-dependent phase.
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More and more applications require semiconductor lasers distinguished not only by large modulation bandwidths or high output powers, but also by small spectral linewidths. The theoretical understanding of the root causes limiting the linewidth is therefore of great practical relevance. In this paper, we derive a general expression for the calculation of the spectral linewidth step by step in a self-contained manner. We build on the linewidth theory developed in the 1980s and 1990s but look from a modern perspective, in the sense that we choose as our starting points the time-dependent coupled-wave equations for the forward and backward propagating fields and an expansion of the fields in terms of the stationary longitudinal modes of the open cavity. As a result, we obtain rather general expressions for the longitudinal excess factor of spontaneous emission ($K$-factor) and the effective $alpha$-factor including the effects of nonlinear gain (gain compression) and refractive index (Kerr effect), gain dispersion and longitudinal spatial hole burning in multi-section cavity structures. The effect of linewidth narrowing due to feedback from an external cavity often described by the so-called chirp reduction factor is also automatically included. We propose a new analytical formula for the dependence of the spontaneous emission on the carrier density avoiding the use of the population inversion factor. The presented theoretical framework is applied to a numerical study of a two-section distributed Bragg reflector laser.
Since its first demonstration in the sixties, coherent anti-Stokes Raman scattering (CARS) has become a powerful spectroscopic sensing tool with broad applications in biology and chemistry. However, it is a complex nonlinear optical process that often leads to the lacks of quantitative data outputs. In this letter, we observe how CARS signal builds up gradually and demonstrate how to control its deferral with laser-pulse shaping. A time-resolved three-color CARS that involves a pair of driving broadband femtosecond pulses and delayed shaped probe pulse is realized experimentally. Driving pulses are tuned to the Raman-resonance onto the vibrational ring modes of pyridine and benzene molecules. As a result, CARS-buildup is deferred in picoseconds as delayed probe pulse width varies from 50 down to 10 cm-1. With off-resonant driving of water molecules this effect, in contrary, does not occur. Laser control predicting deferred resonant processes can serve as a novel and important species-specific indicator in, e.g., machine learning applications for future nonlinear optical spectroscopy.
Three-color coherent anti-Stokes Raman scattering represents non-degenerate four wave mixing process that includes both a non-resonant and resonant processes, the contributions of which depend on how the molecular vibrational modes are being excited by the input laser pulses. Non-degenerate four wave mixing processes are complex and understanding these processes requires rigorous data analytical tools, which still lack in this research field. In this work, we introduce one- and two-dimensional intensity-intensity correlation functions in terms of a new variable (e.g., probe pulse delay) and new perturbation parameter (e.g., probe pulse linewidth). In particular, diagonal projections are defined here as a tool to reduce both synchronous and asynchronous two-dimensional correlation spectroscopy analyses down to one-dimensional analysis, revealing valuable analytical information. Detailed analyses using the all Gaussian coherent Raman scattering closed-form solutions and the representative experimental data for resonant and non-resonant processes are presented and compared. This intensity-intensity correlation analytical tool holds a promising potential in resolving and visualizing resonant versus non-resonant four wave mixing processes for quantitative label-free species-specific nonlinear spectroscopy and microscopy.
Using numerical simulations of an extended Lugiato-Lefever equation, we analyze the stability and nonlinear dynamics of Kerr frequency combs generated in microresonators and fiber resonators taking into account third-order dispersion effects. We show that cavity solitons underlying Kerr frequency combs, normally sensitive to oscillatory and chaotic instabilities, are stabilized in a wide range of parameter space by third-order dispersion. Moreover, we demonstrate how the snaking structure organizing compound states of multiple cavity solitons is qualitatively changed by third-order dispersion, promoting an increased stability of Kerr combs underlined by a single cavity soliton.
We propose and demonstrate a Terahertz (THz) oscilloscope for recording time information of an ultrashort electron beam. By injecting a laser-driven THz pulse with circular polarization into a dielectric tube, the electron beam is swept helically such that the time information is uniformly encoded into the angular distribution that allows one to characterize both the temporal profile and timing jitter of an electron beam. The dynamic range of the measurement in such a configuration is significantly increased compared to deflection with a linearly polarized THz pulse. With this THz oscilloscope, nearly 50-fold longitudinal compression of a relativistic electron beam to about 15 fs (rms) is directly visualized with its arrival time determined with 3 fs accuracy. This technique bridges the gap between streaking of photoelectrons with optical lasers and deflection of relativistic electron beams with radio-frequency deflectors, and should have wide applications in many ultrashort electron beam based facilities.
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