van_der_linden_2025#
R. van der Linden, N. Kuzkova and P. M. Kraus, “Nonlinear refractive index measurements of solids and the impact of B-integral on the phase of generated high-order harmonics”, Opt. Express 33, 53268 (2025)
Source record · Catalogue · Review register
DOI: 10.1364/oe.579736
Source kind: measurement
Recorded technique: Birefringent common-path interferometry (TWINS: two pairs of alpha-BBO wedges) with a Ti:sapphire amplifier (Coherent Astrella) centred at 804 nm, 1 kHz; the pulse duration before focus measured by SHG FROG as a Gaussian FWHM of 47 +- 1 fs (p. 53271). Two phase-locked, spatially separated (247 um) pulse copies of adjustable intensity ratio are focused (f = 50 cm spherical mirror, 1/e^2 areas 6.45e3 and 6.73e3 um^2) into 5-mm-thick uncoated Thorlabs windows at the focus; the relative phase of the central interference fringe against the normalized intensity difference Delta I/I0 gives n2 from its slope a, n2 = a lambda / (2 pi L) (Eq. 3, p. 53272). Six peak intensities, 24 to 55 GW/cm^2, per sample; a sample-free background phase is subtracted at each intensity (p. 53272).
Materials in structured entries: BK7, CaF2, KBr, N-BK7, SiO2
Dataset quantities: nonlinear_index
Contents: 8 datasets; 0 formulas.
Curation notes#
Journal pages 53268-53278 = PDF pages 1-11. Identity checked against the first page.
DEFINING RELATION (p. 53269): P(3) = 3 eps0 sum chi(3)_ijkl(omega; omega, omega, -omega) E_j E_k E_l*, n~(r, t) = n0 + n2 I(r, t) (Eq. 1) with n2 = 3 chi(3) / (4 n0^2 eps0 c) for isotropic media and parallel linear polarizations; B = (2 pi / lambda) int n2 I(z) dz (Eq. 2). SI units; the tabulated n2 is in 10^-16 cm^2/W (Table 1 header, checked on the image). Each pulse copy acquires its own B-integral in the sample (the two foci are 247 um apart), so n2 is the self coefficient. Both copies are s-polarized (linear) after the polarizer that makes them interfere (p. 53270).
CORRECTIONS APPLIED BY THE AUTHORS (p. 53273): Fourier-optics simulations showed that the phase measured at the camera is systematically lower than that applied in focus, n2_in/n2_out = 1.9, and that the camera’s time averaging over the Gaussian pulse lowers it further, n2_out,FT/n2_out,G = 1.4; ‘Both factors are taken into account for the final n2, as presented in Fig. 4 and outlined in Table 1.’ The tabulated values are averages over the six intensities, from the central fringe only (p. 53272). No trend with intensity (no self-focusing), and constant transmission (no nonlinear absorption).
WAVELENGTH. The laser is centred at 804 nm (p. 53270, abstract); Table 1 prints 800 nm for this work, recorded as printed (0.5 % from 804 nm).
PART. 47 fs pulses; the paper does not discuss the Raman (nuclear) response: part = ‘unknown’.
UNCERTAINTY. ‘Uncertainties of the reported values from this work are defined as +-2 sigma. As for the references, no explicit definition was given’ (Table 1 note). From error propagation of every measured parameter, the intensity calibration dominating; ‘no correlation between uncertainty in I1 and I2 was assumed, which ... makes the given uncertainty an upper bound’ (p. 53273).
LITERATURE (Table 1). Z-scan values of Ref. [27] (Ensley & Bambha 2019, ensley_2019) for CaF2, SiO2 and NBK-7 at 800 nm, and of Ref. [41] (DeSalvo et al. 1996, desalvo_1996) for KBr at 1064 nm. Ensley’s own table (ensley_2019) prints these 800 nm values without an uncertainty; the +-15 % here (1.8 +- 0.27, 2.7 +- 0.41, 3.3 +- 0.50) is van der Linden’s reading. DeSalvo prints KBr at 1064 nm as (29 +- 6) x 10^-14 esu with n0 = 1.53 (its Tables I-II); 7.87 +- 1.62 x 10^-16 cm^2/W is van der Linden’s conversion (40 pi n2(esu) / (c n0) gives 7.95 +- 1.64 with n0 = 1.53; computed here 2026-09-26; the paper does not state the n0 it used, 7.87 corresponds to n0 about 1.545).
SAMPLES (p. 53271): 5-mm-thick uncoated Thorlabs ‘isotropic windows’; grades and glass maker not stated. ‘NBK-7’ is recorded as N-BK7 (the lead- and arsenic-free BK7).
refractiveindex.info (VanderLinden n2 pages, checked 2026-09-26): BK7 (from NBK-7) 3.33e-20, CaF2 1.47e-20 and SiO2 2.54e-20 m^2/W at 0.804 um, 47 fs: the same values; the page uses the 804 nm laser wavelength where the table prints 800 nm, files N-BK7 under BK7, and has no page for KBr (8.98e-20).
Section 3.2 (HHG in gas, the B-integral of the fundamental) holds no material values.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
van_der_linden_2025/twins_CaF2#
{
"id": "twins_CaF2",
"material": "CaF2",
"file": "CaF2/van_der_linden_2025__twins_CaF2.csv",
"table": "tbl_a71e46ef0edc",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "2 sigma"
},
"parameters": {
"part": "unknown",
"coefficient": "self",
"technique": "common-path (TWINS) interferometry",
"pulse_fs": 47,
"polarization": "linear",
"form": "bulk"
}
}
Table 1, this work (TWINS), average over 24-55 GW/cm^2; 5 mm Thorlabs window. Laser centred at 804 nm (printed 800).
van_der_linden_2025/twins_SiO2#
{
"id": "twins_SiO2",
"material": "SiO2",
"file": "SiO2/van_der_linden_2025__twins_SiO2.csv",
"table": "tbl_a71e46ef0edc",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "2 sigma"
},
"parameters": {
"part": "unknown",
"coefficient": "self",
"technique": "common-path (TWINS) interferometry",
"pulse_fs": 47,
"polarization": "linear",
"form": "bulk"
}
}
Table 1, this work (TWINS), average over 24-55 GW/cm^2; 5 mm Thorlabs window, grade not stated. Laser centred at 804 nm (printed 800).
van_der_linden_2025/twins_N-BK7#
{
"id": "twins_N-BK7",
"material": "N-BK7",
"file": "N-BK7/van_der_linden_2025__twins_N-BK7.csv",
"table": "tbl_a71e46ef0edc",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "2 sigma"
},
"parameters": {
"part": "unknown",
"coefficient": "self",
"technique": "common-path (TWINS) interferometry",
"pulse_fs": 47,
"polarization": "linear",
"form": "bulk"
}
}
Table 1, this work (TWINS), printed ‘NBK-7’; average over 24-55 GW/cm^2; 5 mm Thorlabs window. Laser centred at 804 nm (printed 800).
van_der_linden_2025/twins_KBr#
{
"id": "twins_KBr",
"material": "KBr",
"file": "KBr/van_der_linden_2025__twins_KBr.csv",
"table": "tbl_a71e46ef0edc",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"column": true,
"level": "2 sigma"
},
"parameters": {
"part": "unknown",
"coefficient": "self",
"technique": "common-path (TWINS) interferometry",
"pulse_fs": 47,
"polarization": "linear",
"form": "bulk"
}
}
Table 1, this work (TWINS), average over 24-55 GW/cm^2; 5 mm Thorlabs window. Laser centred at 804 nm (printed 800).
van_der_linden_2025/ensley_2019_CaF2#
{
"id": "ensley_2019_CaF2",
"material": "CaF2",
"file": "CaF2/van_der_linden_2025__ensley_2019_CaF2.csv",
"table": "tbl_a71e46ef0edc",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"ensley_2019"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"part": "unknown",
"coefficient": "self",
"technique": "z-scan"
}
}
Table 1, Z-scan value of Ref. [27] (Ensley & Bambha 2019) at 800 nm; the +- is van der Linden’s (Ensley prints none at 800 nm; source notes).
van_der_linden_2025/ensley_2019_SiO2#
{
"id": "ensley_2019_SiO2",
"material": "SiO2",
"file": "SiO2/van_der_linden_2025__ensley_2019_SiO2.csv",
"table": "tbl_a71e46ef0edc",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"ensley_2019"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"part": "unknown",
"coefficient": "self",
"technique": "z-scan"
}
}
Table 1, Z-scan value of Ref. [27] (Ensley & Bambha 2019) at 800 nm; the +- is van der Linden’s (source notes).
van_der_linden_2025/ensley_2019_BK7#
{
"id": "ensley_2019_BK7",
"material": "BK7",
"file": "BK7/van_der_linden_2025__ensley_2019_BK7.csv",
"table": "tbl_a71e46ef0edc",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"ensley_2019"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"part": "unknown",
"coefficient": "self",
"technique": "z-scan"
}
}
Table 1, Z-scan value of Ref. [27] (Ensley & Bambha 2019) at 800 nm, printed on the NBK-7 row; recorded under BK7, the material of the original (Ensley and Bambha print ‘BK7’, from Thorlabs, and do not say N-BK7; ensley_2019). The +- is van der Linden’s (source notes).
van_der_linden_2025/desalvo_1996_KBr#
{
"id": "desalvo_1996_KBr",
"material": "KBr",
"file": "KBr/van_der_linden_2025__desalvo_1996_KBr.csv",
"table": "tbl_a71e46ef0edc",
"quantity": "nonlinear_index",
"unit": "cm2/W",
"scale": 1e-16,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"desalvo_1996"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"part": "unknown",
"coefficient": "self",
"technique": "z-scan",
"pulse_fs": 30000
}
}
Table 1, Z-scan value of Ref. [41] (DeSalvo et al. 1996) at 1064 nm: van der Linden’s conversion of DeSalvo’s (29 +- 6) x 10^-14 esu (source notes). DeSalvo’s pulses: 30 ps at 1064 nm.
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.