white_1984#
W. T. White III, W. L. Smith and D. Milam, “Direct measurement of the nonlinear refractive-index coefficient gamma at 355 nm in fused silica and in BK-10 glass”, Opt. Lett. 9, 10-12 (1984)
Source record · Catalogue · Review register
DOI: 10.1364/ol.9.000010
Source kind: measurement
Recorded technique: Two-beam time-resolved interferometry at 355 nm (p. 10): a collimated intense beam (2.5-mm diameter) passes twice through the sample and is combined with a weak reference beam; the fringe pattern is imaged on the slit of a streak camera and the maximum fringe shift Delta m is read at the peak intensity. Peak intensity from the peak fluence (0.1-0.3 J/cm^2) and the FWHM pulse width (typically 0.15-0.20 ns) of nominally Gaussian pulses, I0 = 2 (ln 2/pi)^(1/2) Gamma0/tau (Eq. 5). Samples: fused silica, Suprasil II (31.0 cm) and Dynasil 4000 (15.4 cm) plus Suprasil II (10 cm) end to end; BK-10, two 10.0-cm pieces end to end (p. 11). A check by time-integrated interferometry (television camera) on Suprasil II (p. 11).
Materials in structured entries: BK-10, SiO2
Dataset quantities: absorption_coefficient, nonlinear_index, two_photon_absorption_coefficient
Contents: 7 datasets; 0 formulas.
Curation notes#
Journal pages 10-12 = pdf pages 1-3. Identity checked against the first page.
DEFINITION. ‘Delta phi = 2 pi (gamma I/lambda0) Delta z, where gamma is the nonlinear refractive-index coefficient’ (Eq. 1, p. 10), i.e. n = n0 + gamma I; gamma is optmat’s n2, the self coefficient. Table 1, footnote a (p. 11): ‘Units of gamma: 10^-16 cm^2/W. To convert to electrostatic units, use n2(cm^3/erg)/gamma(cm^2/W) = cn/4pi 10^-7, where c is vacuum speed of light (cm/sec), n is the refractive index, and gamma I in Eq. (1) is replaced by n2 <E^2>. <E^2> denotes the square of the macroscopic electric-field amplitude averaged over many optical cycles.’ Double-pass reduction (Eqs. 2-4, p. 10-11): gamma = Delta m lambda0 / [int I1 dz + int I2 dz], and without absorption gamma = Delta m lambda0 / T(1 + T^2) I0 L (Eq. 4). Eq. (3) as printed has lost its left side and its absorption equation is printed ‘dI/dz = alpha + beta I(z)’ (sign and the factor I of the linear term lost); only Eq. (4) matters for silica (alpha << 0.001 cm^-1). The polarization is not stated.
PART. The pulses are 0.15-0.20 ns (150-200 ps); the paper does not discuss the Raman or electrostrictive contributions. By the rule for picosecond pulses the values include the whole Raman response: part ‘total’ (electrostriction, whose response time is set by the acoustic transit across the 2.5-mm beam, is not discussed).
UNCERTAINTY (p. 11): ‘The uncertainty of our measurements cited in Table 1, +-45%, is the square root of the sum of the squares of several individual experimental uncertainties ... the largest single source of uncertainty is in determining Delta m ... +-40%. By comparison, other sources of uncertainty ... are much less (typically +-10%). The actual rms scatter in our data varies between +-30% for time-integrated measurements and +-45% for time-resolved measurements.’ Level not stated.
TABLE 1 (p. 11). The 355-nm column is this work; the 1064-nm column is ‘Previous Work’: fused silica ‘measured previously’ (footnote b, Ref. 2: Weber, Milam and Smith 1978), BK-10 ‘predicted from Eq. (38) of Ref. 10 and is believed to be accurate to about 20%’ (text, p. 11; Ref. 10 is Boling, Glass and Owyoung 1978, boling_1978, whose Eq. (38) is the Abbe-number formula), but footnote c of the table names Ref. 11 (C. C. Wang 1970). The text and the footnote disagree; the text is specific (an equation number), so the prediction is taken to be Boling et al.’s formula (to be checked). The table image matches the extracted cells.
OTHER VALUES. Time-integrated interferometry on Suprasil II: gamma = (2.7 +- 0.8) x 10^-16 cm^2/W at 355 nm (p. 11), entered inline. Linear absorption at 355 nm: alpha << 0.001 cm^-1 (fused silica), alpha = 0.0107 cm^-1 (BK-10) (p. 11, measured). Two-photon absorption ‘obtained from published values’: fused silica beta < 1.25 x 10^-3 cm/GW (Refs. 8 and 9, an upper bound, not recorded), BK-10 beta = 0.0055 cm/GW (Ref. 9). Surface transmittances at 355 nm: T = 0.96 (fused silica), 0.95 (BK-10) (no quantity). Predictions for silica at 355 nm (p. 11): gamma(355)/gamma(1064) about 1.3-2.2 (from Hellwarth’s modified theory, Ref. 6, Eq. 13.4, for an effective resonance of 13-8 eV) and 1.4-2.5 (A. J. Glass, unpublished memorandum, Ref. 15).
DUPLICATE COPY. The library holds a second pdf, original/source_02 (ol-9-1-10.pdf, rewritten by Aspose.PDF for Java 24.9), beside the main source_01 (OL.9.000010.pdf, 2002). Their text layers (pdftotext) are identical and their pages render identically at 100 dpi (compared 2026-09-26): the same scan, no difference in content.
REPRODUCTIONS. milam_1998 Table 1 (ref. 13) reproduces the silica value as ‘2.5 +- 1.2 at 351 nm’ (the wavelength is Milam’s slip). refractiveindex.info’s SiO2 ‘White’ n2 page gives 2.5e-20 m^2/W at 0.355 um, time-resolved interferometry, no pulse duration: consistent with Table 1 (the pulse, 0.15-0.20 ns, is stated here).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
white_1984/this_work_355_SiO2#
{
"id": "this_work_355_SiO2",
"material": "SiO2",
"file": "SiO2/white_1984__this_work_355_SiO2.csv",
"table": "tbl_985eae28abf9",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"part": "total",
"coefficient": "self",
"technique": "two-beam time-resolved interferometry",
"grade": "Suprasil II, Dynasil 4000",
"form": "bulk"
}
}
Table 1, ‘gamma (355 nm) (This Work)’ (p. 11): time-resolved interferometry on Suprasil II (31.0 cm) and on Dynasil 4000 with Suprasil II end to end (25.4 cm). Uncertainty +-45 %, a root-sum-square estimate (source notes). Pulses 0.15-0.20 ns FWHM.
white_1984/this_work_355_BK-10#
{
"id": "this_work_355_BK-10",
"material": "BK-10",
"file": "BK-10/white_1984__this_work_355_BK-10.csv",
"table": "tbl_985eae28abf9",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"part": "total",
"coefficient": "self",
"technique": "two-beam time-resolved interferometry",
"form": "bulk"
}
}
Table 1, ‘gamma (355 nm) (This Work)’ (p. 11): two 10.0-cm pieces of BK-10 end to end. BK-10 absorbs at 355 nm (alpha = 0.0107 cm^-1, beta = 0.0055 cm/GW), which the reduction includes through Eq. (3). Uncertainty +-45 % (source notes). Pulses 0.15-0.20 ns FWHM.
white_1984/time_integrated_355_SiO2#
{
"id": "time_integrated_355_SiO2",
"material": "SiO2",
"table": "text",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "check",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"part": "total",
"coefficient": "self",
"technique": "time-integrated interferometry",
"grade": "Suprasil II",
"form": "bulk"
}
}
1 inline points in the source record.
‘To check our results ... we remeasured gamma (355 nm) in Suprasil II using time-integrated interferometry ... We obtained gamma = (2.7 +- 0.8) x 10^-16 cm^2/W’ (p. 11). The authors’ check of Table 1; rms scatter of the time-integrated data +-30 %.
white_1984/previous_1064_SiO2#
{
"id": "previous_1064_SiO2",
"material": "SiO2",
"file": "SiO2/white_1984__previous_1064_SiO2.csv",
"table": "tbl_985eae28abf9",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"weber_1978",
"milam_1976"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"part": "unknown",
"coefficient": "self"
}
}
Table 1, ‘gamma (1064 nm) (Previous Work)’, footnote b: Ref. 2 (p. 11), weber_1978, whose Table 1 reprints milam_1976’s fused-silica value 2.73 +- 0.27 x 10^-20 m^2/W (Dynasil 4000, 125 ps, linear polarization). DISAGREEMENT: printed here as 2.7 +- 0.5, the value rounded and the uncertainty larger than the original’s +-0.27 (not explained).
white_1984/previous_1064_BK-10#
{
"id": "previous_1064_BK-10",
"material": "BK-10",
"file": "BK-10/white_1984__previous_1064_BK-10.csv",
"table": "tbl_985eae28abf9",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "check",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"part": "unknown",
"coefficient": "self"
}
}
Table 1, ‘gamma (1064 nm) (Previous Work)’: not a measurement but a prediction, ‘predicted from Eq. (38) of Ref. 10 and is believed to be accurate to about 20%’ (p. 11; Ref. 10 = Boling, Glass and Owyoung 1978, boling_1978); the table’s footnote c names Ref. 11 (C. C. Wang, Phys. Rev. B 2, 2045 (1970)) instead (source notes). The +-0.6 is the stated ~20 %.
white_1984/absorption_355_BK-10#
{
"id": "absorption_355_BK-10",
"material": "BK-10",
"table": "text",
"quantity": "absorption_coefficient",
"unit": "cm-1",
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"base": "e",
"form": "bulk"
}
}
1 inline points in the source record.
‘Separate absorption measurements at 355 nm yielded alpha << 0.001 cm^-1 in fused silica and alpha = 0.0107 cm^-1 in BK-10’ (p. 11). Base e: the reduction (Eq. 3) uses exp(-alpha L). No uncertainty stated.
white_1984/two_photon_355_BK-10#
{
"id": "two_photon_355_BK-10",
"material": "BK-10",
"table": "text",
"quantity": "two_photon_absorption_coefficient",
"unit": "cm/GW",
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"W. L. Smith, \"Absolute two-photon absorption coefficient at 355 nm in UV glasses,\" in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1981), Postdeadline paper ThB21"
]
}
1 inline points in the source record.
‘We obtained the two-photon absorption coefficients from published values, using ... for BK-10 beta = 0.0055 cm/GW’ (p. 11, Ref. 9), used in the reduction (Eq. 3).
Formulas#
No formulas are recorded.
Corrections#
No dataset errata are recorded in this source record.
Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.