Abstract
We developed and implemented an intensity moments technique for measuring amplitude and initial phase spectra, the topological charge (TC) and orbital angular momentum (OAM) of the Laguerre-Gauss (LG) beams decomposed into the basis of Hermite-Gaussian (HG) modes. A rigorous theoretical justification is given for measuring the TC of unperturbed LG beams with different values of radial and azimuthal numbers by means of an astigmatic transformation on a cylindrical lens. We have shown that the measured amplitude and phase spectra of the HG modes make it possible to find the orbital OAM and TC, as well as digitally sorting the HG modes and then restoring the initial singular beam.
Highlights
We developed and implemented an intensity moments technique for measuring amplitude and initial phase spectra, the topological charge (TC) and orbital angular momentum (OAM) of the Laguerre-Gauss (LG) beams decomposed into the basis of Hermite-Gaussian (HG) modes
A rigorous theoretical justification is given for measuring the TC of unperturbed LG beams with different values of radial and azimuthal numbers by means of an astigmatic transformation on a cylindrical lens
We have shown that the measured amplitude and phase spectra of the HG modes make it possible to find the orbital OAM and TC, as well as digitally sorting the HG modes and restoring the initial singular beam
Summary
Где n 0, m 0, 0, r = (x, y) = (rcos , rsin ), r и φ – радиальная и азимутальная координаты, Hn() и L n ( ) – многочлены Эрмита и Лагерра соответственно. В нашем случае плоскость наблюдения совпадает с плоскостью двойного фокуса цилиндрической линзы, Z = 2f, поэтому z = 2f /z0 = 1 и x 2ei3 /4 , y 2ei /4 , r1. 2), Подставляя найденные параметры в (6) и, возвращаясь от ЭЛГ-мод к записи через ЛГ- и ЭГ-моды, получаем, что ЛГ-пучок в плоскости двойного фокуса цилиндрической линзы превращается в ЭГ-пучок: LG n,. В промежутке между исходной плоскостью Z = 0 и плоскостью двойного фокуса цилиндрической линзы. (8, 0) (в) и (25, –25) (д) до (а, в, д) и после (б, г, е) цилиндрической линзы с f = 18 см (инвертированные изображения)
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