lin_2006 ======== Q\. Lin and G\. P\. Agrawal, "Raman response function for silica fibers", Opt\. Lett\. 31, 3086 \(2006\) `Source record `__ · :doc:`Catalogue ` · :doc:`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 ~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 :doc:`review register ` for the checks and decisions.