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High gain free electron laser with waveguide
Published in R A Cairns, A D R Phelps, P Osborne, Generation and Application of High Power Microwaves, 2020
Now, in the slowly-varying envelope approximation (SVEA) ∂a∂z≪|ka| and ∂a∂z|≪|ωa∣ second-order derivatives can be neglected and ∂2∂z2−1c2∂2∂t2aei(kz−ωt)≈2ik∂∂z+1c∂∂taei(kz−ωt)
Reflection and transmission on the boundary of a resonant medium
Published in M. G. Benedict, A. M. Ermolaev, V. A. Malyshev, I. V. Sokolov, E. D. Trifonov, Super-radiance, 2018
M. G. Benedict, A. M. Ermolaev, V. A. Malyshev, I. V. Sokolov, E. D. Trifonov
In the following we shall use the slowly varying envelope approximation in time (SVEAT), but an important point is that the same (slowly varying envelope) approximation in space (SVEAS) will not be exploited. Accordingly we seek the averaged macroscopic field and the polarization inside the medium, in the form () E(x,t)=12E(x,t)e−iωt+c.c. () P(x,t)=12P(x,t)e−iωt+c.c.
Full Coupled-Mode Theory
Published in Le Nguyen Binh, Guided Wave Photonics, 2016
Firstly, a slowly varying envelope approximation is assumed, that is |a˜″0|≪2βf0|a˜′0||b˜″m|≪2βsm|b˜′m|
Reconstruction of the high-fidelity vortex wavefront via double dark resonances in a four-level atomic medium
Published in Waves in Random and Complex Media, 2023
Under the slowly varying envelope approximation, the propagation equation of the probe field is governed by the Maxwell equation where is the coupling constant with N being the atomic density, is the wave number of the probe field. is the electric dipole matrix element associated with the transition from to . The first term on the right-hand side of Equation (11) accounts for the transverse variation of the probe field, which is responsible for the diffraction either in the medium or in vacuum. Here, we choose the incident field at the entrance of the atomic medium as an LG mode where is the initial Rabi frequency and is the beam waist. r is the transverse radius and ϕ is the azimuthal angle. is a generalized Laguerre polynomial. The radial index and azimuthal index are defined by p (zero or positive integers) and l (any integers), respectively.
Solvent randomness and intramolecular considerations of optical responses in four-wave mixing
Published in Journal of Modern Optics, 2021
J. L. Paz, Patricio Espinoza-Montero, Marcos Loroño, Lenin A. González-Paz, Edgar Marquez, Joan Vera-Villalobos, José R. Mora, Ysaias J. Alvarado
Using the slowly varying envelope approximation in the Maxwell’s equation, the FWM signal evolution in the z-propagation optical length, we obtain: where corresponds to the third-order absorption coefficient evaluated at frequency , given by , and where is the refraction index. In this treatment . It is important to note that the nonlinear optical properties obtained, corresponding to the electromagnetic field responses associated with the generated FWM signal beam along the optical path. A dependence on both, the molecular structure aspect referred to the vibronic coupling and the presence of the solvent, with solute-solvent dissipation mechanism, which is identified by the intensity of the stochastic noise, is presented.
Aberrated moving soliton in nonlinear photonic crystal
Published in Journal of Modern Optics, 2020
Dimensionless variables are related to the physical ones in the following way: Equations (1) and (2) were derived in [65], following the paper [71], for the pulses with duration no less than 100 fs, taking into account the beam diffraction along all space coordinates, neglecting the second-order dispersion but taking into account the dependence of the group velocity on the photonic structure element indexes. It means that we do not use a slowly varying envelope approximation along the pulse propagation coordinate [72,73]. However, we use a slowly varying envelope approximation in the time coordinate. Let us note that, opposite to our approach, in paper [71] the electric field strength is represented in the form and the second-order dispersion on the coordinate z is taken into account.