lin_2006#
Q. Lin and G. P. Agrawal, “Raman response function for silica fibers”, Opt. Lett. 31, 3086 (2006)
Source record · Catalogue · Review register
DOI: 10.1364/ol.31.003086
Source kind: fit
Recorded technique: A model of the Raman response of silica fibre with an isotropic part (Blow and Wood’s damped oscillator) and an anisotropic part (a Boson-peak term plus a share of the oscillator), fitted to Stolen’s measured copolarized and orthogonal Raman gain spectra (ref. 6: R. H. Stolen, in Raman Amplifiers for Telecommunications 1, M. N. Islam, ed. (Springer, 2003); spectra provided by Stolen) over 0-15 THz.
Materials in structured entries: SiO2
Dataset quantities: nonlinear_index, raman_fraction, raman_response_time
Contents: 5 datasets; 1 formula.
Curation notes#
Journal pages 3086-3088 = PDF pages 1-3. Identity checked against the first page. f_b = 0.21 is garbled in the extracted text (‘0.\bar{2}1’) and was read from the PDF text layer (pdftotext, p. 3087).
THE RESPONSE (verbatim, with the page). Eq. (1), p. 3086: R_ijkl(tau) = [(1 - f_R)/3] delta(tau)(delta_ij delta_kl + delta_ik delta_jl + delta_il delta_jk) + f_R R_a(tau) delta_ij delta_kl + (f_R/2) R_b(tau)(delta_ik delta_jl + delta_il delta_jk), i, j, k, l = x or y; R_a the isotropic and R_b the anisotropic Raman response. The scalar form: R_xxxx(tau) = (1 - f_R) delta(tau) + f_R [R_a(tau) + R_b(tau)]. Gains: g_a(Omega) = 2 gamma f_R Im[R_a~(Omega)], g_b(Omega) = 2 gamma f_R Im[R_b~(Omega)], gamma = n2 omega_0/c, R~(Omega) = int R(tau) exp(i Omega tau) dtau; g_par = g_a + g_b, g_perp = g_b/2. Eq. (2), p. 3087: h_a(tau) = tau_1 (tau_1^-2 + tau_2^-2) exp(-tau/tau_2) sin(tau/tau_1) (Blow and Wood, ref. 10), R_a = f_a h_a. Eq. (3): h_b(tau) = [(2 tau_b - tau)/tau_b^2] exp(-tau/tau_b). R_b(tau) = f_b h_b(tau) + f_c h_a(tau). Eq. (4): R_xxxx(tau) = (1 - f_R) delta(tau) + f_R [(f_a + f_c) h_a(tau) + f_b h_b(tau)], with f_a + f_c + f_b = 1. h_a and h_b each integrate to 1 over tau > 0 (h_b’s integral is 2 - 1 = 1).
VALUES (p. 3087). tau_1 = 12.2 fs and tau_2 = 32 fs (Blow and Wood, reproduced); f_a = 0.75 (fits g_a below 14 THz); tau_b = 96 fs, f_b = 0.21, f_c = 0.04 (fit g_par and g_perp over 0-15 THz). ‘If we use n2 = 2.6 x 10^-20 m2/W for silica fibers [ref. 1, Agrawal’s book], the choice f_R = 0.245 in our model yields a peak Raman gain equal to the experimental value of g_R = 1.2 x 10^-11 cm/W at 795.5 nm [ref. 4: Dougherty et al., Opt. Lett. 20, 31 (1995)], corresponding to g_R = 1.81 x 10^-11 cm/W at 526 nm [ref. 6].’ ‘Our value of f_R is slightly higher than the experimental value of about 0.2 (Refs. 9 and 10), because our model overestimates the Raman gain in the spectral region beyond 15 THz. This causes an underestimation of the electronic contribution to nonlinear refractive index by 5% or so’ (p. 3087). The model is expected to hold ‘for pulses as short as 30 fs’ (p. 3088).
NOT EXTRACTED. The fractions f_a, f_b, f_c have no quantity (they partition the Raman response, not the total): they are the coefficients of the formula below. The peak Raman gain coefficients g_R (1.2e-11 cm/W at 795.5 nm, 1.81e-11 cm/W at 526 nm, both reproduced) have no quantity in the vocabulary (TC-384). The gain spectra, the nonlinear index against shift (Fig. 3) and the RIFS rates (Fig. 4; the single-Lorentzian model underestimates RIFS by ~40 % for 100-500 fs solitons, and by ~20 % in the 300-fs, 1200-nm simulation, whose soliton shifts 175 nm) are figures only.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
lin_2006/f_R#
{
"id": "f_R",
"material": "SiO2",
"table": "text",
"quantity": "raman_fraction",
"abscissa": "label",
"use": "primary",
"parameters": {
"definition": "R(tau) = (1 - f_R) delta(tau) + f_R h_R(tau) (p. 3086), the copolarized scalar response R_xxxx of Eq. (4); f_R set by the peak Raman gain with n2 = 2.6e-20 m2/W",
"form": "fibre"
}
}
1 inline points in the source record.
p. 3087: chosen so that the model’s peak copolarized Raman gain, with n2 = 2.6e-20 m2/W, equals g_R = 1.2e-11 cm/W at 795.5 nm. Slightly above the ‘experimental value of about 0.2’, because the model overestimates the gain beyond 15 THz (the electronic part is underestimated by ~5 %).
lin_2006/f_R_literature#
{
"id": "f_R_literature",
"material": "SiO2",
"table": "text",
"quantity": "raman_fraction",
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"stolen_1989",
"blow_1989"
],
"parameters": {
"definition": "R(tau) = (1 - f_R) delta(tau) + f_R h_R(tau)",
"form": "fibre"
}
}
1 inline points in the source record.
p. 3087: ‘the experimental value of about 0.2 (Refs. 9 and 10)’. Printed as ‘about 0.2’, a rounded summary: stolen_1989 gives 0.18; blow_1989 prints alpha = 0.7 for the instantaneous weight, i.e. a Raman weight of 0.3 in its field-squared response (Eq. 5) and a delayed share of 0.22 in its envelope equation (Eq. 8, a factor 2/3), neither 0.2 exactly.
lin_2006/blow_wood_times#
{
"id": "blow_wood_times",
"material": "SiO2",
"table": "text",
"quantity": "raman_response_time",
"unit": "fs",
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"blow_1989"
],
"parameters": {
"constant": "tau1, tau2 (per row)",
"model": "h_a(tau) = tau_1 (tau_1^-2 + tau_2^-2) exp(-tau/tau_2) sin(tau/tau_1) (Eq. (2), Blow and Wood)",
"form": "fibre"
}
}
2 inline points in the source record.
p. 3087: ‘By using the values tau_1 = 12.2 fs and tau_2 = 32 fs (Ref. 10)’ in h_a, Eq. (2). blow_1989 (p. 2666): tau_1 = 0.0122 ps, tau_2 = 0.032 ps: agrees.
lin_2006/tau_b#
{
"id": "tau_b",
"material": "SiO2",
"table": "text",
"quantity": "raman_response_time",
"unit": "fs",
"abscissa": "label",
"use": "primary",
"parameters": {
"constant": "tau_b",
"model": "h_b(tau) = [(2 tau_b - tau)/tau_b^2] exp(-tau/tau_b) (Eq. (3)), the anisotropic Boson-peak response of lin_2006",
"form": "fibre"
}
}
1 inline points in the source record.
p. 3087: ‘By choosing tau_b = 96 fs to account for the spectral width of the Boson peak together with f_b = 0.21 and f_c = 0.04’.
lin_2006/n2#
{
"id": "n2",
"material": "SiO2",
"table": "text",
"quantity": "nonlinear_index",
"unit": "m2/W",
"scale": 1e-20,
"abscissa_unit": "nm",
"use": "check",
"reproduced_from": [
"G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001), Chap. 2"
],
"parameters": {
"part": "unknown",
"coefficient": "self",
"form": "fibre",
"assumed": true
}
}
1 inline points in the source record.
p. 3087: ‘If we use n2 = 2.6 x 10^-20 m2/W for silica fibers [ref. 1]’, the input that fixes f_R. Wavelength and part not stated.
Formulas#
lin_2006/response#
{
"id": "response",
"material": "SiO2",
"equation": "Eqs. (2)-(4), p. 3087",
"printed": "R^{(3)}_{xxxx}(\\tau) = (1 - f_R)\\delta(\\tau) + f_R[(f_a + f_c) h_a(\\tau) + f_b h_b(\\tau)], h_a(\\tau) = \\tau_1(\\tau_1^{-2} + \\tau_2^{-2})\\exp(-\\tau/\\tau_2)\\sin(\\tau/\\tau_1), h_b(\\tau) = [(2\\tau_b - \\tau)/\\tau_b^2]\\exp(-\\tau/\\tau_b)",
"variable": "tau: delay (fs); the copolarized scalar response of silica fibre",
"coefficients": {
"f_R": "0.245",
"f_a": "0.75",
"f_b": "0.21",
"f_c": "0.04",
"tau_1": "12.2 fs",
"tau_2": "32 fs",
"tau_b": "96 fs"
},
"check": "f_a + f_b + f_c = 0.75 + 0.21 + 0.04 = 1.00, as the paper requires; h_a and h_b each integrate to 1 over tau > 0 (analytically). No printed number to reproduce (the gain comparisons are figures)."
}
The tensor form, Eq. (1), gives the orthogonal gain g_perp = g_b/2 with R_b = f_b h_b + f_c h_a. tau_1 and tau_2 are Blow and Wood’s; f_R, f_a, f_b, f_c and tau_b are this paper’s. f_R assumes n2 = 2.6e-20 m2/W. Valid 0-15 THz; overestimates the gain beyond 15 THz.
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.