Two-photon optical absorption in PbO-SiO2 glasses

Tanaka, Keiji; Yamada, Naohito; Oto, Masanori

doi:10.1063/1.1618929

Cited by 14 publications

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“…Note that this distribution is compatible with the experimental ␣͑ប͒ and also with an electronic band structure, in which optical absorption is assumed to occur from Pb 6s to Pb 6p states. 16,18 A calculated n͑ប͒ is shown in ͑b͒ by a solid line, which is in agreement with the experimental refractive index of ϳ1.9.…”

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confidence: 69%

“…However, if calculated n 2 ͑ប͒ is restricted to substantially lower energy region than ␤͑ប͒, applications of the nonlinear Kramers-Kronig relation to degenerate data may be reasonable. 19 We then insert a Gaussian spectrum of ␤͑ប͒ with A = 12 cm/ GW, E 0 = 2.65 eV, and = 0.36 eV, which is the best fit to the experimental data 16 as shown in Fig. 2͑a͒, into ⌬␣͑⍀͒. A numerical integration provides the smooth line shown in Fig.…”

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confidence: 99%

“…3 with those ͑squares͒ calculated from the two-photon absorption spectra. 16 Error bars attached to the experimental data arise from z-scan noises ͑see Fig. 1͒, inhomogeneous glass ingots, etc.…”

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confidence: 99%

“…The one-photon absorption spectrum ␣͑ប͒ shown by open circles in ͑a͒ is replotted from Ref. 16, and a refractive index n ͑Ϸ1.9͒ at ប = 1.17 eV in ͑b͒ is estimated from linear reflectance. As a preliminary check of numerical calculations, we first apply the conventional Kramers-Kronig relation: to these results, where the integration should be carried out from zero to infinite frequencies.…”

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confidence: 99%

“…16 The ingots were polished to thin flakes with thickness of 80-100 m. Nonlinear refractive indices n 2 at wavelength of 1.06 m ͑ប = 1.17 eV͒ were evaluated through the conventional z-scan method 17 using a pulsed Nd:YAG laser ͑ϳ5 ns͒, which was also previously employed, 16 an aberration-corrected focusing lens with a focal length of 10 cm, a fast-response photodiode, and a digital oscilloscope. Note that this lens had a diffraction length of 150 m, being greater than the sample thickness, which is needed for applying an approximated analysis assuming small wave-front distortion.…”

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Optical nonlinearity in PbO–SiO2 glass: Kramers–Kronig analyses

Tanaka¹,

Minamikawa²

2005

Applied Physics Letters

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Relationship between nonlinear refractivity and two-photon absorption has been studied for PbO -SiO 2 glasses using a nonlinear Kramers-Kronig relation. Nonlinear refractive indices, which are determined with z-scan measurements, are consistent with those which are calculated using the relation from two-photon absorption spectra. This consistency suggests that large intensity-dependent refractivity in this glass system arises from resonant two-photon electronic transitions from oxygen 2p to lead 6p states. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1891269͔With developments of optical fibers and devices, nonlinear properties in photonic glasses have attracted growing interests. This is because the optical nonlinearity in glasses, which may be smaller than that in crystals, appears in substantial magnitudes in fibers, 1,2 waveguides, [3][4][5] and microspheres 6 due to long propagation distances. In addition, the nonlinearity can be continuously changed by varying glass composition. [7][8][9] The nonlinearity can be induced at selected positions. 5 In some cases, the nonlinearity is responsible for photoinduced phenomena.10 Because of these features, several applications such as all-optical switches, optical limiters, and waveguide formation have been extensively explored. 4,11 However, the optical nonlinearity in glasses remains to be studied. Specifically, fundamental mechanisms of the intensity-dependent refractivity n 2 ͑n = n 0 + n 2 I + ...͒ in glasses have been less-well understood than those in simple systems such as two-level atoms 12 and crystalline semiconductors. 13 For glasses, only empirical or semiempirical relationships have been proposed, 14 most of which cannot provide spectral dependence. It seems to be very difficult to predict the magnitude of n 2 in glasses from an expectation value of polarization which is formulated quantum mechanically. 12 Here, another way to grasp the intensity-dependent refractivity is to relate it with nonlinear absorption. That is, we start with the absorption, which can be connected with photoelectronic transitions between some electronic energy levels. Then, using a nonlinear Kramers-Kronig relation, 15 we can derive the nonlinear refractivity explicitly. Such a procedure has provided satisfactory understanding for crystalline materials.13 It should also be noted that this procedure has an experimental advantage, since absorption spectra can be obtained more easily through transmittance measurements than refractivity spectra. To the authors' knowledge, however, such a procedure has not been applied to glasses.To obtain a unified insight into the optical nonlinearity in glasses, we explore the above method in the present work. As an example, a PbO system is taken, which is known to be a kind of heavy-metal oxide glasses. We measure the nonlinear refractivity n 2 using z-scan measurements, and compare the results with those derived by applying a nonlinear Kramers-Kronig relation to nonlinear absorption spectra. Since the absorption spectra can be directly ...

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confidence: 69%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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