Empirical relationships for predicting nonlinear refractive index changes in optical solids

Boling, N. L.; Glass, Alexander J.; Owyoung, A.

doi:10.1109/jqe.1978.1069847

Cited by 350 publications

(137 citation statements)

References 21 publications

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“…On the other hand, the increase of the NL response of the samples due to the increase in the WO 3 amount is attributed to the high polarizability associated with the W-O bonds. [12][13][14] The values of n 2 were calculated using the semiempirical method due to Boling, Glass and Owyung ͑BGO-model͒ 25 which assumes that the NL polarizability is proportional to the linear polarizability squared and the optical dispersion of the material is determined by a single resonance at ប 0 . The laser frequency, , is considered to be off-resonance ͑ Ͻ 0 ͒ and n 2 is given by…”

Section: Resultsmentioning

confidence: 99%

“…The value of gS = 4.6 was determined through the best data fitting and is close to previous values measured for oxide glasses. 25,26 The values of n 2 calculated via the BGO model are summarized in Table III. The agreement with the experimental values for samples A, B, and C is very good but the theoretical result for sample D is larger than the experimental value probably because the assumption of Ͻ 0 is violated and the relevant two-photon absorption process is not considered in the BGO model.…”

Section: Resultsmentioning

confidence: 99%

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Near-infrared Kerr nonlinearity of Pb(PO3)2–WO3 glasses

Oliveira

Fedus

Manzani

et al. 2010

Journal of Applied Physics

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We report measurements of the nonlinear refractive index, n 2 , and the nonlinear absorption coefficient, ␣ 2 , of Pb͑PO 3 ͒ 2 -WO 3 glasses. The measurements were performed using 100 fs ͑17 ps͒ laser pulses at 800 nm ͑1064 nm͒. Positive values of n 2 ϳ 10 −19 m 2 / W and negligible ␣ 2 were measured. The results show that the nonlinearity is faster than 100 fs and it is observed an increase of n 2 with the increasing of the WO 3 amount in the samples. The Boling, Glass, and Owyoung model, based on the semiclassical harmonic oscillator model, was used to predict the values of n 2 , with basis on the values of the linear refractive index of the samples.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Near-infrared Kerr nonlinearity of Pb(PO3)2–WO3 glasses

Oliveira

Fedus

Manzani

et al. 2010

Journal of Applied Physics

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“…Based on easily accessible physical parameters, the BGO model allows a estimation of n 2 that is correct within less than one order of magnitude in the case of multicomponent glasses. 4 In the low frequency limit (x(x 0 ) the BGO model leads to an expression of n 2 given by: 2,19,35 …”

Section: A Evaluation Of the Nonlinear Response In The Frame Of Bgo mentioning

confidence: 99%

“…The factor gs has been found to be 3 in the case of materials with small nonlinear optical coefficients, while gs values in the range 1-2 provide a better agreement with experimental results in glasses presenting large nonlinear refractive indices. 4,19,36 In the present case we have considered the values of n at 550 nm and 1480 nm and a value of gs ¼ 1.5 6 0.5 to evaluate first Ns and x 0 and then n 2BGO at 800 nm. The theoretical values are included in Table IV Table IV) we observe that the model allows an accurate estimation in the case of bulk glasses but not for the films.…”

Section: A Evaluation Of the Nonlinear Response In The Frame Of Bgo mentioning

confidence: 99%

Structural origin of the nonlinear optical properties of lead niobium germanate film glasses

Muñoz-Martín¹,

Cruz²,

Fernández-Navarro³

et al. 2011

Journal of Applied Physics

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Linear and nonlinear optical susceptibilities and hyperpolarizability of borate LiNaB4O7 single crystals: Theory and experiment J. Appl. Phys. 112, 053526 (2012) Effect of Lorentz local field for optical second order nonlinear susceptibility in ZnO nanorod J. Appl. Phys. 111, 103112 (2012) Size dependent optical properties of the CdSe-CdS core-shell quantum dots in the strong confinement regime J. Appl. Phys. 111, 074312 (2012) Methyl groups at dielectric and metal surfaces studied by sum-frequency generation in co-and counterpropagating configurations J. Chem. Phys. 135, 044704 (2011) The third-order nonlinear optical coefficients of Si, Ge, and Si1−xGex in the midwave and longwave infrared J. Appl. Phys. 110, 011301 (2011) Additional information on J. Appl. Phys. The structural origin of the nonlinear optical susceptibility (/v (3) /) of lead-niobium-germanate film glasses with large Nb 2 O 5 contents has been investigated. /v (3) / shows a strong enhancement with the Nb content in the films with /v (3) / values close to 2 Â 10 À11 esu at 800 nm for a Nb content as high as 0.71. Boling-Glass-Owyoung and Lines' semiempirical models predict accurately the values of /v (3) / for transparent bulk glasses but not for film glasses. This discrepancy is related to the remarkable structural differences between them. Raman spectroscopy suggests the formation of a three-dimensional (3D) structure of [NbO 6 ] octahedra in the case of film glasses having large Nb contents, while X-ray photoelectron spectroscopy shows that a significant fraction of these units contain Nb 4þ ions. The combination of a 3D structure of [NbO 6 ] with the presence of Nb 4þ polarons and their migration through electron intervalence transfer is proposed as the origin of the observed enhancement of /v (3) / in the film glasses.

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“…Boling et al (2003) had estimated γ or n 2 by suggesting an experimental formula as an approximation method as follows: …”

Section: Introductionmentioning

confidence: 99%

Accurate Determination of Nonlinear Refractive Index for Some Binary Glass Systems

Moustafa¹

2011

American Journal of Applied Sciences

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Problem statement:This study investigates the relation between the nonlinear optical susceptibility (χ (3) ) and the ratio (α 1 /α o-2 ), then the nonlinear index determination for some binary glass systems. Recently suitable relationship between the oxidation polarizability and the nonlinear optical properties was established for simple oxides glasses. So in this study more attention and investigation is paid to the trend of that relation quantitatively as possible. Approach: The idea of the present research is how to obtain the non linear refractive index as function of ratio (α 1 /α o-2 ), as we know the cation polarizability α l can be determined easy and α o-2 also can be obtained according the energy gap or the real refractive index. Consequently a proposed scale has been established between the nonlinear optical susceptibility (χ (3) ) and the ratio (α 1 /α o-2 ) for some binary glass systems. Results: A comparison between our obtained results and the empirical method of Boling shows that there is a good agreement between them. Conclusion: The advantages of the suggested method fix on the expectation of the value (χ (3) ) without the complex and sensitivity experimental set-up.

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Empirical relationships for predicting nonlinear refractive index changes in optical solids

Cited by 350 publications

References 21 publications

Near-infrared Kerr nonlinearity of Pb(PO3)2–WO3 glasses

Near-infrared Kerr nonlinearity of Pb(PO3)2–WO3 glasses

Structural origin of the nonlinear optical properties of lead niobium germanate film glasses

Accurate Determination of Nonlinear Refractive Index for Some Binary Glass Systems

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