Exact Solutions of the Bloch Equations of a Two-Level Atom Driven by the Generalized Double Exponential Quotient Pulses with Dephasing

Grira, Sofiane; Boutabba, N.; Eleuch, Hichem

doi:10.3390/math10122105

Cited by 4 publications

(2 citation statements)

References 43 publications

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“…In addition, the rate equations represent a dynamic equation for laser output derived from altering population inversion at the atomic level within the gain medium, which can be utilized to derive the characteristic output curve of the laser. Specific research teams have successfully solved the rate equations to a greater extent to simulate and control the pulse waveform of the laser output [20][21][22]. For similar purposes, by incorporating the spatial overlap efficiency into the rate equations, the laser's output performance can be more accurately simulated and calculated to reflect the resonator's actual oscillation.…”

Section: Introductionmentioning

confidence: 99%

Computation and Verification of Spatial Rate Equations for an Electro-Optically Q-Switched Laser-Diode Side-Pumped Nd:YAG Laser

Yan

2023

Applied Sciences

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In a side-pumped laser module, we simulate the pumping power distribution across the cross-section of Nd:YAG rods at varying diameters. The coupled rate equations with the spatial overlap efficiency for a four-level actively Q-switched side-pumped laser are considered complete. After a Q-switched pulse terminates, the expressions of laser output parameters are derived. We assess the single pulse energy, pulse width, and peak power using the analysis function. The 200 Hz Q-switched side-pumped Nd:YAG laser with a peak power of 103 kW and beam quality factors M2 = 1.67 is developed to the validity of theoretical models.

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Section: Introductionmentioning

confidence: 99%

Computation and Verification of Spatial Rate Equations for an Electro-Optically Q-Switched Laser-Diode Side-Pumped Nd:YAG Laser

Yan

2023

Applied Sciences

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“…The equations were reduced to the Demkov model, and the solution was expressed in terms of the generalized hypergeometric function. Exact solutions of a two-level atom pumped by generalized double exponential quotient pulses with dephasing were also obtained in [22]. Furthermore, Boutabba et al [23] studied the excitation of a multi-level atomic system using a fast laser pulse with a q-deformed hyperbolic waveform.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of the Bloch Equations to the Asymmetric Hyperbolic Cosine Pulse with Chirped Frequency

Grira

Boutabba²,

Eleuch

2023

Mathematics

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In this research study, we derive the exact solutions of the Bloch equations describing the dynamics of a two-level atom with dephasing. In the two-level atom, a strong laser pump couples a ground state to an upper excited state with a time-dependent Rabi-frequency. The exact solutions are given for the atomic population inversion and the real and imaginary parts of the coherence while the input pulse is an asymmetric hyperbolic cosine form. Additionally, the system is under a chirped detuning. The method of solving the Bloch equations analytically is a very tedious part of the research, and as far as we know, there are few exact solutions available in this field. Hence, our solutions might be of great interest to various research areas, including nuclear magnetic resonance, where analytical solutions to the Bloch equations play a major role in the study of the information on the state of the medium as determined by the NMR signals.

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Saturation Effect Produced by Laser Pulses: Karplus–Schwinger Approach versus Bloch Solution

Astapenko

Lisitsa

2022

Atoms

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The saturation effect during the excitation of a two-level system by laser pulses is investigated in the framework of two approaches: excitation probability based on Karplus–Schwinger spectral profile and exact solution of Bloch equations. Simple analytical expression for the excitation probability by exponential pulse is derived. The excitation spectra obtained using this expression were compared with the result of solving the Bloch equations for various values of the pulse duration and the Rabi frequency, which describes the strength of the electromagnetic interaction. It is shown that in the case of long pulses, there is a satisfactory correspondence between the two approaches, but in short-pulse limit and strong saturation, the probability description based on Karplus–Schwinger spectral profile and perturbation theory does not provide satisfactory results.

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Exact Solutions of the Bloch Equations of a Two-Level Atom Driven by the Generalized Double Exponential Quotient Pulses with Dephasing

Cited by 4 publications

References 43 publications

Computation and Verification of Spatial Rate Equations for an Electro-Optically Q-Switched Laser-Diode Side-Pumped Nd:YAG Laser

Computation and Verification of Spatial Rate Equations for an Electro-Optically Q-Switched Laser-Diode Side-Pumped Nd:YAG Laser

Exact Solutions of the Bloch Equations to the Asymmetric Hyperbolic Cosine Pulse with Chirped Frequency

Saturation Effect Produced by Laser Pulses: Karplus–Schwinger Approach versus Bloch Solution

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