poulvellarie_2018

N. Poulvellarie, C. Ciret, B. Kuyken, F. Leo and S.-P. Gorza, “Highly nondegenerate two-photon absorption in silicon wire waveguides”, Phys. Rev. Appl. 10, 024033 (2018)

Source record · Catalogue · Review register

DOI: 10.1103/PhysRevApplied.10.024033

Source kind: measurement

Recorded technique: Pump-signal transmission of a silicon-on-insulator wire waveguide (2 cm long, 220 nm high, 780 nm wide; the Fig. 1 caption says 220 x 789 nm2), quasi-TE mode, dispersion-engineered so that ~1850 nm and ~1300 nm are group-velocity matched. An optical parametric oscillator synchronously pumped by a mode-locked Ti:sapphire laser (82 MHz) gives the pump at 1848 nm (chirped Gaussian, 200 fs FWHM unchirped, quadratic spectral phase b = 4.3e-27 s2) and the signal at 1322 nm (GVM) or 1298 nm (chirped sech, 152 fs unchirped, b = 2.3e-27 s2), combined on a dichroic mirror with a variable delay; output by lensed fibre into an optical spectrum analyser. Signal spectra and signal energy against delay are compared with coupled generalized nonlinear Schroedinger equations (pp. 024033-2 to -4).

Materials in structured entries: None recorded.

Dataset quantities: None recorded.

Contents: 0 datasets; 1 formula.

Curation notes

Article pages 024033-1 to -9 = PDF pages 1-9. Identity checked against the first page. No tables. The Supplemental Material (the relation between the coupled equations and the single GNLSE, Ref. [35]) is not in the library.

NOTHING IS EXTRACTED AS DATA: the paper measures a waveguide, not bulk silicon, and gives no material coefficient of its own. Its nonlinear coefficients are computed from Bristow et al.’s degenerate data (bristow_2007, ‘on the basis of the data from Ref. [13]’, p. 024033-4) under the approximation it tests, and the experiment is reproduced by simulation with ‘the input pump power as the only free parameter (all the other parameters are either computed or precisely measured)’ (p. 024033-5). The waveguide values, as printed (p. 024033-4): effective areas A_pp = 0.241, A_ss = 0.147, A_ps = 0.176 um2; gamma_pp = (164 + 14i), gamma_ss = (154 + 59i), gamma_ps = (97 + 31i), gamma_sp = (138 + 45i) W^-1 m^-1 (p pump 1848 nm, s signal 1322 nm); linear loss alpha_p = alpha_s = 2 dB/cm (measured); carrier lifetime tau_c and free-carrier sigma, k_c not given. Fig. 5 and 6: the dispersion of gamma and the GNLSE shock times s_R, s_I (first order 1.5 and 9 fs; ‘s_R = 0 fs and s_I = 7.5 fs’; ‘approx-cross’ s_R = -0.39 fs and s_I = 5.15 fs).

THE FINDING THAT BEARS ON A MODEL (p. 024033-6 and conclusion): ‘the excellent agreement between theory and experiment confirms that the simplification of reducing the nondegenerate nonlinear coefficients n2(omega_p, omega_s) and beta_TPA(omega_p, omega_s) to their value at the average frequency omega-bar is valid for indirect-band-gap semiconductors, at least for photon energy in the range from 0.6 E_g to 0.85 E_g’ (the pump at 1848 nm is 0.60 E_g and the signal at 1322 nm 0.84 E_g for E_g = 1.12 eV); ‘in silicon nanophotonic waveguides, the dispersion of the nonlinear absorption is much larger than the dispersion of the Kerr effect’ (abstract); the self-TPA coefficient ‘varies by more than a factor of 4’ between pump and signal, ‘and the signal cross-TPA coefficient is three times larger than the self-TPA coefficient at the pump wavelength’ (p. 024033-5). The Raman effect is neglected (‘negligible when one is dealing with short pulses in silicon [5,23]’, p. 024033-3). A 10-dB attenuation of the signal with a 1.2-pJ (6-W peak) pump; free-carrier absorption ‘responsible for only 2% of the signal attenuation’ (p. 024033-6). This contrasts with direct-gap semiconductors, where extreme nondegenerate 2PA is enhanced up to 1000 times (Refs. [18], [19], p. 024033-1).

CONSISTENCY WITH bristow_2007 (computed here, 2026-09-27, assuming the self-overlap factors eta_pp = eta_ss = 1, which the paper does not print): Im gamma = beta / (2 A) gives beta = 0.67 cm/GW at 1848 nm and 1.73 cm/GW at 1322 nm; Bristow’s fitted form (bristow_2007/beta_indirect_gk) gives 0.60 and 1.73. Re gamma = 2 pi n2 / (lambda A) gives n2 = 1.16e-13 cm2/W at 1848 nm and 4.8e-14 cm2/W at 1322 nm, against Bristow’s peak 1.2e-13 at 1800 nm and 4.7e-14 at 1220 nm. So the gammas are Bristow’s degenerate values at the mean frequency, as stated: no independent material datum.

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

Datasets

No datasets are recorded.

Formulas

poulvellarie_2018/gamma_mean_frequency

{
  "id": "gamma_mean_frequency",
  "equation": "Eq. (5), p. 024033-4",
  "printed": "gamma_mu_nu = omega_mu eta_mu_nu nbar^2 n2(omegabar) / (c sqrt(A_mu_mu A_nu_nu) n_mu n_nu) + i omega_mu eta_mu_nu nbar^2 beta_TPA(omegabar) / (2 omegabar sqrt(A_mu_mu A_nu_nu) n_mu n_nu)",
  "variable": "omegabar = (omega_mu + omega_nu) / 2; n_nu the mode index at omega_nu, nbar at omegabar; A the effective areas; eta_mu_nu the mode-overlap factors of Lin et al. (lin_2007, Ref. [20]); n2 and beta_TPA the degenerate Kerr and 2PA coefficients of the material",
  "coefficients": {
    "A_pp_um2": "0.241",
    "A_ss_um2": "0.147",
    "A_ps_um2": "0.176"
  },
  "check": "Not reproducible from the paper alone (the mode indices and eta are not printed). The self terms, with eta = 1, give back Bristow's degenerate beta and n2 (see notes): consistent with the stated use of bristow_2007."
}

The nondegenerate (cross) coefficients taken as the degenerate ones at the mean frequency; the paper’s experiment supports this for silicon for photon energies 0.6-0.85 E_g (p. 024033-6). Coupled equations (1)-(2) and the carrier rate equation (4) as printed on p. 024033-3.

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.