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Analytical solution for the Doppler broadening function using the Kaniadakis distribution
摘要： Several works have been done for the development of models that generalize the Maxwell-Boltzmann distribution, aimed at encompassing physical phenomena that lie outside the thermal equilibrium. Amongst these, there are distributions that result from the non-extensive statistics of Tsallis and Kaniadakis. Starting from these generalized distributions, a Doppler broadening function was proposed in recent papers, using the deformed Kaniadakis distribution, which was numerical, evaluated with the use of a Gauss-Legendre quadrature. From this perspective, this paper presents an analytical solution for the generalized Doppler broadening function through obtaining a partial differential equation, considering the Kaniadakis distribution. This equation is solved analytically using the methods of Frobenius and variation of parameters, in order to obtain a generalized solution for the Doppler broadening function, containing a deformation parameter j; that measures the deviation in relation to the Maxwell-Boltzmann distribution. Finally, the results were produced considering several values for j; with the intent of making a comparison with the reference values. For the validation of the deformed Doppler broadening function’s analytical solution, a numerical solution of the partial differential equation was generated. It was possible to use this numerical solution as a benchmark for the analytical solution that was derived. It was demonstrated that the analytical solution obtained is consistent, because when j tends to zero, the solution falls in the conventional form, when the Maxwell-Boltzmann distribution is considered. Apart from this, the results were shown to be good, especially when we consider the temperature and power ranges for practical applications, as the maximum error obtained was smaller than 1%.
关键词： Frobenius method,Quasi-Maxwellian distribution,Generalized Doppler broadening function,Kaniadakis distribution
更新于2025-09-23 15:23:52
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Accurate modeling of event-by-event backprojection for a germanium semiconductor Compton camera for system response evaluation in the LM-ML-EM image reconstruction method
摘要： We develop an image reconstruction method, considering the physical phenomenon in the measurement process of a Compton camera. The image quality is improved by applying an accurate error model of the Compton scattering angle. The angular error has two properties: an error distribution function specific to the detector material and the variation of its function parameters, depending on each measurement event. We incorporate these factors into the backprojection of the list-mode maximum-likelihood expectation-maximization method as the system response function. We apply our image reconstruction method to simulated data assumed to be measured by a Ge-semiconductor Compton camera GREI, and the imaging data of a tumor-bearing live mouse obtained using GREI. This method is evaluated by comparing an image with variable angular error with that having fixed angular error. The consideration of the variable angle estimation error improves the spatial resolution and reduces image roughness.
关键词： Ge-semiconductor,image reconstruction,Compton camera,LM-ML-EM method,Doppler broadening
更新于2025-09-23 15:19:57
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Effects of a chiral atomic medium on the manipulation of light birefringence and lateral Goos–H?nchen shifts via Kerr nonlinearity and local field effects
摘要： We present a new scheme to report on the effects of a five-level chiral atomic medium on the lateral Goos–H?nchen (GH) shift in Gaussian probe beams via Kerr nonlinearity (KNL) and local field effects. The physical realization of birefringence in absorption, dispersion, reflection and transmission beams is investigated, with special emphasis on the manipulation of absolute and fractional change in lateral GH shifts in birefringence transmission and reflection beams, via local fields and Kerr nonlinearity. We have employed a semiclassical atomic density-matrix formalism so as to obtain the expression for electric and magnetic susceptibilities of the chiral medium and the corresponding chirality coefficients in conjunction with Kerr and local fields, both separately and in combination. Stationary-phase theory is used to compute GH shift from the calculated birefringent reflection and transmission coefficients of probe beams. A negative and positive GH shift is observed in reflection and transmission beams, respectively, subjected to local field and Kerr effect. In contrast, a positive GH shift is observed in both reflection and transmission beams in the presence of both local field and Kerr effects. The local and Kerr fields also alter the divergence angle between left and right circularly polarized birefringence beams. GH shift depends on incident angle and probe detuning. The anisotropy of medium is lessened by switching ON the Kerr field in the medium. We observed a positive fractional change of ±30% in the GH shift in the birefringence reflection beam in the presence of a local field without KNL, while a 20% fractional GH shift was observed in the presence of both local field and KNL effects. Our results suggest promising applications in nonlinear optical, plasmonic and biophotonic devices for the manipulation of light propagation and optical signal processing.
关键词： stationary-phase theory,Kerr nonlinearity,birefringence chiral medium,Goos–H?nchen shift,density-matrix formalism,Doppler broadening medium
更新于2025-09-23 15:19:57
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Frequency Selected Coherent Optical Storage Based on Electromagnetically Induced Transparency in Rubidium Vapor
摘要： Storage capacity is a key requirement for multiplexed quantum memory in long-distance quantum communication and quantum calculation. The data exchange and processing of a quantum system would speed up, with the bene?t from the increasing storage capacity. In this paper, we demonstrate a frequency selected optical storage based on the electromagnetically induced transparency scheme in warm atomic vapor. Two probe pulses with di?erent frequencies could be stored and retrieved in di?erent memory cell individually, in which the memory cells are divided by the velocity of atomic motion in Doppler broadening atomic vapor. The theoretical predictions show that the frequency bandwidth of the proposed multiplexed optical storage is decided by the width of Doppler broadening and the frequency bandwidth of each memory cell is decided by the width of electromagnetically induced transparency window. The proposed frequency selected storage signi?cantly advances the pursuit of multiplexed optical memory and should have important applications in classical and quantum information processing.
关键词： electromagnetically induced transparency,storage,optical,Doppler broadening
更新于2025-09-09 09:28:46
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Implications of spectral-hole burning on the manipulation of spatial Goos–H?nchen shift in an atomic cell
摘要： We present a new scheme to report on Goos–H?nchen (GH) shift experienced by the Gaussian light beam incident at the plane optical interface filled with four-level sodium atomic medium in the spectral-hole burning region with and without Doppler broadening effect. Theoretical atomic density-matrix formalism is employed to obtain the susceptibility of atomic medium while the stationary-phase-theory is used to compute the GH shift in the reflected and transmitted probe beams subjected to control fields. A steep normal slope of dispersion is observed with a maximum and zero probability of transmission and reflection coefficients, respectively, at the regions of the spectral holes burning. In the normal dispersion spectrum at the region of spectral-hole burning, positive and negative GH shift is observed, respectively, in the transmitted and reflected light beams. However, at anomalous dispersive regions negative GH shift in the transmission beam and positive GH shift in the reflection beam is observed. The reflection and transmission coefficients as well as the spatial GH shift are the functions of probe detuning, collective phase of control fields and inverse Doppler broadening effect in the spectral-hole burning region. The study is expected to be useful for optoelectronic devices and optical-clocking applications.
关键词： Doppler broadening medium,Density-matrix formalism,Spectral hole burning,Spatial Goos–H?nchen shift,Stationary-phase-theory
更新于2025-09-09 09:28:46