1980
DOI: 10.1070/qe1980v010n07abeh010486
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Electrooptic lithium tantalate switch

Abstract: We study the behaviour of truncated Rayleigh-Schrödinger series for the low-lying eigenvalues of the one-dimensional, time-independent Schrödinger equation, in the semiclassical limith → 0. Under certain hypotheses on the potential V (x), we prove that for any given smallh > 0 there is an optimal truncation of the series for the approximate eigenvalues, such that the difference between an approximate and exact eigenvalue is smaller than exp(−C/h) for some positive constant C. We also prove the analogous result… Show more

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Cited by 4 publications
(3 citation statements)
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“…We confirmed that the length of the induced structure was directly proportional to the square root of the average power of the laser beam. If we assume that the length of the induced structure is directly proportional to the length of the filament, the result is in a good agreement with the theory of Zverev et al25 Therefore, filamentation due to the balance of self‐focusing arose from increase in refractive index and self‐defocusing arose from plasma formation takes an important role in the oxidation of Mn 2+ to Mn 3+ . The trap levels of defect centers may be deep, thus resulting into the stable Mn 3+ at room temperature.…”
Section: Space‐selective Valence State Manipulation Of Transition Andsupporting
confidence: 86%
“…We confirmed that the length of the induced structure was directly proportional to the square root of the average power of the laser beam. If we assume that the length of the induced structure is directly proportional to the length of the filament, the result is in a good agreement with the theory of Zverev et al25 Therefore, filamentation due to the balance of self‐focusing arose from increase in refractive index and self‐defocusing arose from plasma formation takes an important role in the oxidation of Mn 2+ to Mn 3+ . The trap levels of defect centers may be deep, thus resulting into the stable Mn 3+ at room temperature.…”
Section: Space‐selective Valence State Manipulation Of Transition Andsupporting
confidence: 86%
“…We also confirmed that the length of the femtosecond laser induced structure was directly proportional to the square root of the average power of the laser beam. This result is in good agreement with the theory of Zverev et al, 25 if we assume that the length of the induced structure is directly proportional to the length of the filament, which is due to the balance between self-focusing arising from an increase in the refractive index and selfdefocusing arising from plasma formation. We have also confirmed that no change is observed in the absorption spectrum of the nanoparticle-precipitated glass sample after heat treatment at room temperature even for 6 months, indicating that the precipitated nanoparticles are stable at room temperature.…”
supporting
confidence: 91%
“…For these results, we assumed that the length of the induced structure varies with the depth of the focal spot, because the length is largely dependent on the linear and non-linear refractive index of the material. Zverev and Pashkov demonstrated that the filamentation length, L fil , generated by self-focusing of the laser radiation in solid dielectrics is expressed as follows [36]:…”
Section: Filamentation-dependent Induced Structurementioning
confidence: 99%