An efficient method for evaluation of the complex probability function: The Voigt function and its derivatives

Humlíček, Josef

doi:10.1016/0022-4073(79)90062-1

Cited by 284 publications

(112 citation statements)

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“…The Voigt function is not available in an analytic form; however, many useful approximations are available [2 11-[25]. The algorithm provided in [24] uses a 12 term rational approximation to calculate the Voigt profile for any combination of Lorentzian and Gaussian linewidths. The relative error of this algorithm is less than 2 *…”

Section: Frequency Noise Modelmentioning

confidence: 99%

“…Convergence is fairly rapid because the 20-dB linewidth is dominated more by the Lorentzian contribution while the 3-dB linewidth is strongly affected by the Gaussian component. The Voigt approximation used here is the one found in [24]. To test its accuracy over a wide range of inputs, this Voigt lineshape fitting procedure was applied to self-heterodyne lineshapes computed numerically.…”

Section: Effects Of L / F On Linewidth Measurementsmentioning

confidence: 99%

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1/f frequency noise effects on self-heterodyne linewidth measurements

Mercer

1991

J. Lightwave Technol.

320

125

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Abstract-The effects of 1 /f frequency noise on self-heterodyne detection are described and the results are applied to the problem of laser diode linewidth measurement. Laser diode linewidths determined by self-heterodyne methods are not adequate predictors of coherent communication system performance because these measurements often include significant broadening due to l / f frequency noise. In this paper the self-heterodyne autocorrelation function and power spectrum are evaluated for both the white and the l / f components of the frequency noise. From numerical analysis, the power spectrum resulting from the l / f frequency noise is shown to be approximately Gaussian and an empirical expression is given for its linewidth. These results are applied to the problem of self-heterodyne linewidth measurements for coherent optical communications and the amount of broadening due to l / f frequency noise is predicted. Two methods are then provided for estimating the portion of the measured self-heterodyne linewidth due to the white and l / f components of the frequency noise spectrum.

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Section: Frequency Noise Modelmentioning

confidence: 99%

Section: Effects Of L / F On Linewidth Measurementsmentioning

confidence: 99%

1/f frequency noise effects on self-heterodyne linewidth measurements

Mercer

1991

J. Lightwave Technol.

320

125

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“…Figures 13 and 14 show that tie linewidths determined from the width 20 dB down are much Good estimates of the Lorentzian and Gaussian components can be obtained by fitting a Voigt profile to the measured self-heterodyne lineshape. Efficient and accurate algorithms are available for estimating the Voigt lineshape for an) combination of Lorentzian and Gaussian contributions [22][23][24][25][26]. Some of the approximations for the Voigt profile also provide derivatives with respect to all of the parameters allowing application of nonlinear least-squares fitting procedures.…”

Section: Effects Of 1/f On Linewidth Measurementsmentioning

confidence: 99%

1/F Frequency Noise Effects on Self-Heterodyne Linewidth Measurements for Coherent Communications

Mercer¹

1990

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Prepared for Jie tfportzfent of die Air Force andt-,r GmCenime F L')h2fl-90,C.0092, ABSTRACTThe effects of l/f frequenc) noise on self-heterodyne detection are described and the results are applied to the problem of laser-diode-linew idth measurement. Laser diode line%%idths determined by sef-heterod)ne methods are not adequate predictors of coherent communications system performance because these measurements often include significant broadening due to I/f frequenc) noise. In this report, the autocorrelation functIor. and power spectrum of the detected belf-heterodyne photoLurrent are de eloped in terms of an arbitrary frequency noise spectrum and then e aluated for both the white and the 1/f components of the frequenc) noise. From numerical analysis, the power spectrum resulting from the l/f frequency noise is sho%%n to be approximately Gaussian and an empirical expression is gi-en for its lineNidth. These results are applied to the problem of self-heterodyne linexxidth measurements for c-oherent optical communication. and the amount of broadening due to l/f frequency noise is predicted. Two methods are then prox ided for estimating the portion of the measured self-heterod) ne line idth due to the white component of the frequency noise and the portion due to 1/f frequency noise.

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“…(36) with Eqs. (17), (22), and (23), and employing the normalization convention of Refs. [5,6], the orthonormality relation satisfied by the eigenvectors c n of the nonlinear eigenvalue problem in Eq.…”

Section: Mathematical Considerationsmentioning

confidence: 99%

“…(66) can be expressed utilizing the Faddeeva function [20,21,22,23,24,25,26] [ 39,40] for an alternative view).…”

Section: Mathematical Considerationsmentioning

confidence: 99%

Siegert pseudostates: Completeness and time evolution

2005

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Within the theory of Siegert pseudostates, it is possible to accurately calculate bound states and resonances. The energy continuum is replaced by a discrete set of states. Many questions of interest in scattering theory can be addressed within the framework of this formalism, thereby avoiding the need to treat the energy continuum. For practical calculations it is important to know whether a certain subset of Siegert pseudostates comprises a basis. This is a nontrivial issue, because of the unusual orthogonality and overcompleteness properties of Siegert pseudostates.Using analytical and numerical arguments, it is shown that the subset of bound states and outgoing Siegert pseudostates forms a basis. Time evolution in the context of Siegert pseudostates is also investigated. From the Mittag-Leffler expansion of the outgoing-wave Green's function, the timedependent expansion of a wave packet in terms of Siegert pseudostates is derived. In this expression, all Siegert pseudostates-bound, antibound, outgoing, and incoming-are employed. Each of these evolves in time in a nonexponential fashion. Numerical tests underline the accuracy of the method.

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An efficient method for evaluation of the complex probability function: The Voigt function and its derivatives

Cited by 284 publications

References 1 publication

1/f frequency noise effects on self-heterodyne linewidth measurements

1/f frequency noise effects on self-heterodyne linewidth measurements

1/F Frequency Noise Effects on Self-Heterodyne Linewidth Measurements for Coherent Communications

Siegert pseudostates: Completeness and time evolution

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