stolen_1989#

R. H. Stolen, J. P. Gordon, W. J. Tomlinson and H. A. Haus, “Raman response function of silica-core fibers”, J. Opt. Soc. Am. B 6, 1159 (1989)

Source record · Catalogue · Review register

DOI: 10.1364/josab.6.001159

Source kind: measurement

Recorded technique: The Raman response function of silica-core fibre computed by the sine transform, Eq. (9), of the imaginary third-order susceptibility taken from room-temperature spontaneous Raman-scattering spectra of silica-core fibres (ref. 15: Stolen, Lee and Jain, J. Opt. Soc. Am. B 1, 652 (1984); Stolen and Bosch, Phys. Rev. Lett. 48, 805 (1982)), converted to gain by dividing by 1 + n(Omega, T), n the thermal phonon population factor (p. 1161). The Raman fraction is estimated from Raman cross-section and gain measurements (refs. 6, 16). The response is then used in nonlinear-Schroedinger simulations (pp. 1162-1164).

Materials in structured entries: SiO2

Dataset quantities: nonlinear_index, raman_fraction, raman_response_time

Contents: 5 datasets; 1 formula.

Curation notes#

Journal pages 1159-1166 = PDF pages 1-8. Identity checked against the first page. The material is ‘pure silica-core fibers’: ‘Some of the details of the gain spectrum will vary from fiber to fiber depending on dopants in the core as well as drawing temperature, but these data are a fairly representative curve’ (p. 1161).

DEFINITIONS (all waves linearly polarized, parallel polarizations; p. 1161). Expression (6), p. 1160: N2 |u(t)|^2 -> N_2inf |u(t)|^2 + N_2R int_{-inf}^{t} dt’ |u(t’)|^2 f(t - t’), ‘where the response function f(t - t’) is real and is normalized such that its integral is unity’. N_2inf is the (nearly instantaneous) electronic part, N_2R the delayed part. Eq. (7): N2(Omega) = N_2R int_0^inf f(s) exp(i Omega s) ds, Omega = omega_p - omega_s. Eq. (5): the Raman power gain g = (2 omega_p/c) N2’’(Omega). Eq. (9), p. 1161: N_2R f(s) = (2/pi) int_0^inf dOmega N2’(Omega) cos(Omega s) = (2/pi) int_0^inf dOmega N2’’(Omega) sin(Omega s). ‘In the opposite limit of long pulses all the nonlinearity is essentially instantaneous, with a strength N2(0) = N_20 = N_2inf + N_2R. It is N_20 that is usually measured in self-focusing or self-phase modulation experiments ... N_2inf = N_20(1 - alpha) and N_2R = alpha N_20’ (p. 1161). The relation to Hellwarth’s response: ‘the present N_2R f(t - t’) is equal to the expression a(t - s) + b(t - s) of Refs. 5 and 6 times a factor 2 pi/n’ (p. 1165).

THE RESPONSE FUNCTION ITSELF is given only as Fig. 2 (and Fig. 3 for spectral features removed); not digitised. The gain spectrum (Fig. 1(a), normalised to unity at its peak at 440 cm^-1) and its Kramers-Kronig real part (Fig. 1(b)) are figures only. Fig. 3: (a) full gain and response, (b) sharp features removed, (c) the 604 cm^-1 line, (d) bands beyond 750 cm^-1, (e) a Lorentzian through the half-gain points. The text calls the line both 604 (caption) and 603 cm^-1 (p. 1162).

EXPONENTIAL MODELS. Eq. (2) with Eq. (4), p. 1160: N2’(Omega) = N_2inf + N_2R/(1 + Omega^2 tau^2), N2’’(Omega) = N_2R Omega tau/(1 + Omega^2 tau^2); tau = 76 fs matches the peak of the silica gain curve (Fig. 1, dashed). In the pulse-compression simulation (p. 1162) an artificial tau = 391 fs with 40 % of the nonlinearity was used because the 122-fs grid could not resolve the real response (‘This produces a peak Raman gain close to that of fused silica’). Both are recorded as check values, the second as assumed.

NONLINEAR INDEX. ‘For silica the nonlinear index N2 is 3.2 x 10^-16 cm2/W. [Note that in electrostatic units the nonlinear index is 1.1 x 10^-13 esu and is related to N2 by the factor (4 pi/nc) x 10^7.]’ (pp. 1159-1160), and n2 = 1.1e-13 esu ‘for silica’ in Eq. (13) (p. 1162). No reference, wavelength or measurement is given: a model input. Check: 1.1e-13 x 4 pi/(1.45 x 2.998e10) x 1e7 = 3.18e-16 cm2/W with n = 1.45 (n is not stated). Which part it is (N_20 or N_2inf) is not said.

SOLITON SELF-FREQUENCY SHIFT (p. 1164, a check of the normalisation): 9.2 MHz/m at z/z0 = 4.0 for a 40-fs sech pulse at 1.5 um with 15 ps/(nm km); Gordon’s formula gives 8.5 MHz/m for a 45-fs pulse. Not a material property; not extracted.

Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.