santran_2004#
S. Santran, L. Canioni, L. Sarger, T. Cardinal and E. Fargin, “Precise and absolute measurements of the complex third-order optical susceptibility”, J. Opt. Soc. Am. B 21, 2180-2190 (2004)
Source record · Catalogue · Review register
Source kind: measurement
Recorded technique: Collinear pump-probe (transient absorption) experiment (pp. 2180-2185): a mode-locked Ti:sapphire oscillator (800 nm; frequency doubled for 400 nm) or an optical parametric oscillator (1500 nm), pulses of about 100 fs; the beam is split into a p-polarized pump and an s-polarized probe (perpendicular linear polarizations), made exactly collinear and focused into the sample (about 1 mm thick); the probe intensity is recorded against the pump-probe delay, and the amplitude of the nonlinear fringes (at twice the optical frequency) and the dc level give the real and imaginary parts of chi(3), by Fourier filtering (Eq. 13). Average power and pulse width are monitored with Si and GaAsP (two-photon) photodiodes calibrated against a power meter and an autocorrelation. Absolute: all laser parameters measured.
Materials in structured entries: SiO2
Dataset quantities: nonlinear_index
Contents: 11 datasets; 2 formulas.
Curation notes#
Journal pages 2180-2190 = pdf pages 1-11 (p. 2185 = pdf page 6). Identity checked against the first page.
DEFINITIONS (p. 2185). The measured quantity is chi(3)_1212 (pump and probe perpendicular; Eq. 3), with chi(3)_1111 = 3 chi(3)_1212 for an isotropic medium (p. 2182). ‘For comparison purposes, we deduce the usual nonlinear index ... (in SI)’: n2 (m^2/W) = 3 chi(3)_1111 (m^2/V^2) / (2 c eps0 n0^2) (Eq. 14), the self coefficient of n = n0 + n2 I; and n2 (m^2/W) = (80 pi/(n0 c)) n2 (esu) (Eq. 15). Eq. (15)’s factor is twice the 40 pi of DeSalvo et al. (desalvo_1996) and White et al. (white_1984), whose esu n2 is defined by n = n0 + n2 <E^2>; this paper does not define its esu n2 and tabulates none. Polarization: linear (pump p, probe s).
PART (pp. 2186-2189). In silica and oxide glasses ‘the amplitude of the nuclear phenomena is too weak to be evaluated in this experimental setup. So, electronic and nuclear phenomena are measured as a whole and are collected in one single parameter’ (p. 2186). From the Raman spectra of Suprasil (Fig. 8) and Stolen and Tomlinson’s approach, the Raman contribution ‘begins to be significant for pulses longer than 100 fs and reaches the maximum for a pulse width of 10 ps’; ‘the nuclear contribution to the signal cannot be more than 5%. As Hellwarth et al. has found that approximately 18% of the nonlinear index of refraction in fused silica is attributed to the Raman effect, we can conclude that a maximum Raman contribution is approximately 1% in our signal’ (pp. 2187-2188); Fig. 11 puts it at 1.5 %; ‘we can conclude that pure electronic nonlinear susceptibility measurements are possible in fused silica’ (p. 2188). Recorded as part ‘electronic’ on the paper’s argument (the values include at most ~1-1.5 % of Raman response).
UNCERTAINTY. Table 1 (p. 2185), ‘Synthesis of Error Studies’: full accuracy, relative 2-16 % (800 and 1500 nm) and 3-17 % (400 nm); absolute 10-28 % (800 and 1500 nm) and 12-34 % (400 nm); ‘the relative and absolute accuracy ranges ... strongly depend on the sample optical quality and on the laser wavelength’. ‘Table 1 presents our efforts to reach a (record) value of 10%. Nevertheless, the relative error bars ... is routinely well below 2% even for weakly nonlinear samples’ (p. 2185). Table 2 footnote: ‘Relative accuracy between the different samples is inferior to 1%.’ No uncertainty is given per value, so none is recorded; the level is not stated. Components (Table 1, absolute): average power 5-7 %, beam waist 2-3 % (3-4 % at 400 nm), temporal width 3-5 % (4-10 % at 400 nm), nonlinear fringe amplitude 0.1-10 %, sample thickness 0.1-1 %, linear index 0.1-2 %.
TABLE 2 (p. 2186): ‘Absolute Measurements of the Nonlinear Index of Refraction of Several Samples of Fused Silica’ at 800 and 400 nm, one dataset per sample (the grade as printed; ‘F851053’ is printed without a maker). The unit cells print 10^-16 cm^2/W (image; extracted as ‘10216’): a structural fix in the script. ‘Synthetic samples present a smaller value than natural ones but a difference larger than 30% is clearly demonstrated, although the linear index will be affected only by less than 1%’ (p. 2186); which samples are natural is not said. Fig. 6 plots the samples’ density against n2 (not digitised; densities not tabulated).
DISPERSION (p. 2186): ‘the nonlinear index of one standard fused-silica sample - Suprasil - at three wavelengths: ... 3.4 x 10^-20 m^2/W at 400 nm, 3.2 x 10^-20 m^2/W at 800 nm, and 2.5 x 10^-20 m^2/W at 1500 nm’. The 400- and 800-nm values are Table 2’s Suprasil row (the same measurement); only the 1500-nm value is entered, inline. Fig. 7 (p. 2187) plots these with the published values of Milam 1998 (Ref. 18, milam_1998; figure only, not digitised) and PERT and Kramers-Kronig fits (parameters not given).
FORMULAS. The two-band Kramers-Kronig scaling (Eq. 19, Sheik-Bahae et al., Ref. 17) and the PERT equation (Eq. 20, Adair, Chase and Payne 1992, Ref. 13) are printed (p. 2187) and recorded as formulas; the paper gives no fitted parameters for Fig. 7, so neither can be checked against its numbers.
OXIDE GLASSES (pp. 2188-2189). Niobium-containing sodium and calcium borophosphate glasses: Fig. 12 plots the real part of chi(3) at 800 nm against the niobium concentration (figure only, no table, no named compositions); ‘The nonlinearity of a calcium borophosphate glass with the largest concentration of niobium can reach values around 25 times the fused-silica response’ (p. 2189); the Raman contribution in these glasses can be four times that of silica, so at most 4 % of the signal (pp. 2188-2189). The tellurium glasses of the abstract are not tabulated either. No values are recordable (no composition is given with a number), so no material is registered. The silicon wafer of Figs. 4-5 is an example signal (no value). CS2 (Figs. 2-3, a simulation from Canioni’s thesis values: electronic 19 %, fast nuclear 64 % with 170 fs, orientational 17 % with 880 fs) is a liquid: skipped.
REFRACTIVEINDEX.INFO has no n2 page for this source.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
santran_2004/heraeus_s300#
{
"id": "heraeus_s300",
"material": "SiO2",
"file": "SiO2/santran_2004__heraeus_s300.csv",
"table": "tbl_ece90cb0d86a",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"part": "electronic",
"coefficient": "self",
"technique": "collinear pump-probe (transient absorption, nonlinear fringes)",
"pulse_fs": 100,
"polarization": "linear; pump and probe perpendicular",
"grade": "Heraeus S300",
"form": "bulk"
}
}
Table 2 (p. 2186), sample ‘Heraeus S300’: n2 at 800 and 400 nm. Relative accuracy between samples < 1 %; absolute accuracy 10-28 % (800 nm) and 12-34 % (400 nm), per sample quality (source notes).
santran_2004/herasil#
{
"id": "herasil",
"material": "SiO2",
"file": "SiO2/santran_2004__herasil.csv",
"table": "tbl_ece90cb0d86a",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"part": "electronic",
"coefficient": "self",
"technique": "collinear pump-probe (transient absorption, nonlinear fringes)",
"pulse_fs": 100,
"polarization": "linear; pump and probe perpendicular",
"grade": "Herasil",
"form": "bulk"
}
}
Table 2 (p. 2186), sample ‘Herasil’: n2 at 800 and 400 nm. Relative accuracy between samples < 1 %; absolute accuracy 10-28 % (800 nm) and 12-34 % (400 nm), per sample quality (source notes).
santran_2004/suprasil#
{
"id": "suprasil",
"material": "SiO2",
"file": "SiO2/santran_2004__suprasil.csv",
"table": "tbl_ece90cb0d86a",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"part": "electronic",
"coefficient": "self",
"technique": "collinear pump-probe (transient absorption, nonlinear fringes)",
"pulse_fs": 100,
"polarization": "linear; pump and probe perpendicular",
"grade": "Suprasil",
"form": "bulk"
}
}
Table 2 (p. 2186), sample ‘Suprasil’: n2 at 800 and 400 nm. Relative accuracy between samples < 1 %; absolute accuracy 10-28 % (800 nm) and 12-34 % (400 nm), per sample quality (source notes).
santran_2004/heraeus_homosil#
{
"id": "heraeus_homosil",
"material": "SiO2",
"file": "SiO2/santran_2004__heraeus_homosil.csv",
"table": "tbl_ece90cb0d86a",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"part": "electronic",
"coefficient": "self",
"technique": "collinear pump-probe (transient absorption, nonlinear fringes)",
"pulse_fs": 100,
"polarization": "linear; pump and probe perpendicular",
"grade": "Heraeus Homosil",
"form": "bulk"
}
}
Table 2 (p. 2186), sample ‘Heraeus Homosil’: n2 at 800 and 400 nm. Relative accuracy between samples < 1 %; absolute accuracy 10-28 % (800 nm) and 12-34 % (400 nm), per sample quality (source notes).
santran_2004/heraeus_s1#
{
"id": "heraeus_s1",
"material": "SiO2",
"file": "SiO2/santran_2004__heraeus_s1.csv",
"table": "tbl_ece90cb0d86a",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"part": "electronic",
"coefficient": "self",
"technique": "collinear pump-probe (transient absorption, nonlinear fringes)",
"pulse_fs": 100,
"polarization": "linear; pump and probe perpendicular",
"grade": "Heraeus S1",
"form": "bulk"
}
}
Table 2 (p. 2186), sample ‘Heraeus S1’: n2 at 800 and 400 nm. Relative accuracy between samples < 1 %; absolute accuracy 10-28 % (800 nm) and 12-34 % (400 nm), per sample quality (source notes).
santran_2004/herasil_s1v#
{
"id": "herasil_s1v",
"material": "SiO2",
"file": "SiO2/santran_2004__herasil_s1v.csv",
"table": "tbl_ece90cb0d86a",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"part": "electronic",
"coefficient": "self",
"technique": "collinear pump-probe (transient absorption, nonlinear fringes)",
"pulse_fs": 100,
"polarization": "linear; pump and probe perpendicular",
"grade": "Herasil S1V",
"form": "bulk"
}
}
Table 2 (p. 2186), sample ‘Herasil S1V’: n2 at 800 and 400 nm. Relative accuracy between samples < 1 %; absolute accuracy 10-28 % (800 nm) and 12-34 % (400 nm), per sample quality (source notes).
santran_2004/suprasil_en1027a#
{
"id": "suprasil_en1027a",
"material": "SiO2",
"file": "SiO2/santran_2004__suprasil_en1027a.csv",
"table": "tbl_ece90cb0d86a",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"part": "electronic",
"coefficient": "self",
"technique": "collinear pump-probe (transient absorption, nonlinear fringes)",
"pulse_fs": 100,
"polarization": "linear; pump and probe perpendicular",
"grade": "Suprasil EN1027A",
"form": "bulk"
}
}
Table 2 (p. 2186), sample ‘Suprasil EN1027A’: n2 at 800 and 400 nm. Relative accuracy between samples < 1 %; absolute accuracy 10-28 % (800 nm) and 12-34 % (400 nm), per sample quality (source notes).
santran_2004/f851053#
{
"id": "f851053",
"material": "SiO2",
"file": "SiO2/santran_2004__f851053.csv",
"table": "tbl_ece90cb0d86a",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"part": "electronic",
"coefficient": "self",
"technique": "collinear pump-probe (transient absorption, nonlinear fringes)",
"pulse_fs": 100,
"polarization": "linear; pump and probe perpendicular",
"grade": "F851053",
"form": "bulk"
}
}
Table 2 (p. 2186), sample ‘F851053’: n2 at 800 and 400 nm. Relative accuracy between samples < 1 %; absolute accuracy 10-28 % (800 nm) and 12-34 % (400 nm), per sample quality (source notes).
santran_2004/heraeus_h1#
{
"id": "heraeus_h1",
"material": "SiO2",
"file": "SiO2/santran_2004__heraeus_h1.csv",
"table": "tbl_ece90cb0d86a",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"part": "electronic",
"coefficient": "self",
"technique": "collinear pump-probe (transient absorption, nonlinear fringes)",
"pulse_fs": 100,
"polarization": "linear; pump and probe perpendicular",
"grade": "Heraeus H1",
"form": "bulk"
}
}
Table 2 (p. 2186), sample ‘Heraeus H1’: n2 at 800 and 400 nm. Relative accuracy between samples < 1 %; absolute accuracy 10-28 % (800 nm) and 12-34 % (400 nm), per sample quality (source notes).
santran_2004/schott_sq1#
{
"id": "schott_sq1",
"material": "SiO2",
"file": "SiO2/santran_2004__schott_sq1.csv",
"table": "tbl_ece90cb0d86a",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"part": "electronic",
"coefficient": "self",
"technique": "collinear pump-probe (transient absorption, nonlinear fringes)",
"pulse_fs": 100,
"polarization": "linear; pump and probe perpendicular",
"grade": "Schott SQ1",
"form": "bulk"
}
}
Table 2 (p. 2186), sample ‘Schott SQ1’: n2 at 800 and 400 nm. Relative accuracy between samples < 1 %; absolute accuracy 10-28 % (800 nm) and 12-34 % (400 nm), per sample quality (source notes).
santran_2004/suprasil_1500#
{
"id": "suprasil_1500",
"material": "SiO2",
"table": "text",
"quantity": "nonlinear_index",
"unit": "m2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"part": "electronic",
"coefficient": "self",
"technique": "collinear pump-probe (transient absorption, nonlinear fringes)",
"pulse_fs": 100,
"polarization": "linear; pump and probe perpendicular",
"grade": "Suprasil",
"form": "bulk"
}
}
1 inline points in the source record.
‘2.5 x 10^-20 m^2/W at 1500 nm’ for Suprasil (p. 2186), measured with an optical parametric oscillator; the same sample’s 400- and 800-nm values in the same sentence are Table 2’s Suprasil row. Absolute accuracy 10-28 % (Table 1, 800 and 1500 nm).
Formulas#
santran_2004/two_band_kramers_kronig#
{
"id": "two_band_kramers_kronig",
"material": "SiO2",
"equation": "Eq. (19), p. 2187",
"printed": "n2(esu) = K' sqrt(E_p) / (n0 E_g^4) G2(hbar omega / E_g), with G2(x) = (1/(2 x^6)) [ -(3/8) x^2 (1 - x)^(-1/2) + 3 x (1 - x)^(1/2) - 2 (1 - x)^(3/2) + 2 theta(1 - 2x) (1 - 2x)^(3/2) ]",
"variable": "x = hbar omega / E_g; E_p = 2 |p_vc|^2 / m0 (p_vc the interband momentum matrix element, m0 the free-electron mass); E_g the gap energy; theta the step function",
"coefficients": {
"K_prime": "a constant that takes different values according to the material"
},
"check": "Not checkable: no values of K', E_p or E_g are given for the Fig. 7 fit (checked 2026-09-26)."
}
The two-parabolic-band scaling of Sheik-Bahae et al. (Ref. 17), as printed here (the same G2 as DeSalvo et al.’s Eqs. 3-4 in closed form). n2 in esu, of an unstated definition (see the record’s notes on Eq. 15).
santran_2004/pert#
{
"id": "pert",
"material": "SiO2",
"equation": "Eq. (20), p. 2187",
"printed": "n2(x)/n2(0) = [n(0)/n(x)] [ (n(x)^2 + 2)/(n(0)^2 + 2) ]^4 [1/(1 - x^2)] [ (1 - x^2)/(1 - 4 x^2) + (1/(2K)) ( (1 - x^2)/(1 - 4 x^2) - (1 + x^2/3)/(1 - x^2) ) ]",
"variable": "x: printed 'x is in inverse centimeters' (presumably the photon wavenumber over the resonance's, a ratio; the paper does not define the resonance here); n(x) the linear index",
"coefficients": {
"K": "0.5"
},
"check": "Not checkable: the resonance and n2(0) of the Fig. 7 fit are not given (checked 2026-09-26)."
}
The PERT equation of Adair, Chase and Payne (Optical Materials 1, 185 (1992), Ref. 13), which Milam 1998 used (milam_1998). ‘K is the kurtosis electron distribution, which has a value close to 0.5 for widebandgap glasses’ (p. 2187): K = 0.5 is the paper’s typical value, not a fit.
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.