stolen_1973#
R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides”, Appl. Phys. Lett. 22, 276-278 (1973)
Source record · Catalogue · Review register
DOI: 10.1063/1.1654637
Source kind: measurement
Recorded technique: Two independent determinations of the small-signal Raman gain of fused quartz. (1) Direct: a single-mode clad glass fibre (core 3.8 um, ‘fused quartz which was the primary constituent of the fiber core’, length 590 cm, effective length 308 cm by Eq. (2) from the measured loss) pumped by the 526.0-nm line of a pulsed Xe laser (bandwidth 1.5 GHz; the line isolated by a narrow-band filter that also passed ~1 % of the 535.3-nm line as the signal, a shift of 330 cm^-1). The output signal-to-pump ratio was measured with a neutral density of one in front of the fibre (low gain) and at its output (high gain), the input pump changing from about 2 to 24 W: amplification factor 2.2. The gain follows from Eq. (1), P_s/P_s0 = exp(g I_p0 L), with the effective intensity of Eq. (3) (Boyd and Kleinman) from the computed mode profile. (2) From the spontaneous cross section: the polarized spontaneous Raman scattering of fused quartz measured relative to the 992-cm^-1 line of benzene with a cw argon laser at 514.5 nm (double spectrometer, 100-um slits, triangular response; spectrometer response calibrated with an NBS standard lamp; the refractive-index dependence of the solid angle and the omega^4 factor corrected), converted to gain by Eq. (4). Room temperature (not stated).
Materials in structured entries: SiO2
Dataset quantities: raman_gain
Contents: 4 datasets; 0 formulas.
Curation notes#
Journal pages 276-278 = pdf pages 2-4 (journal page = 274 + pdf page); pdf page 1 is the publisher’s cover sheet. Identity checked against the first page (title, authors, Appl. Phys. Lett. Vol. 22, No. 6, 15 March 1973; received 20 November 1972). All numbers below were read on the page images (pdftoppm, 150-400 dpi), not only on the text rendering.
THE DEFINITIONS (p. 276). Eq. (1): P_s/P_s0 = exp(g I_p0 L), P_s and P_s0 the output and input signal powers, I_p0 ‘the effective input pump intensity’, L ‘the effective gain length’. Eq. (2): L = [1 - exp(-alpha l)]/alpha, l the actual length; ‘The effective length calculated from Eq. (2) was 308 cm.’ Eq. (3): I_p0 = P_p0 int 2 pi f(r)^2 r dr / [int 2 pi f(r) r dr]^2, f(r) the mode intensity normalised to 1 at r = 0 (a Gaussian gives I_p0 = P_p0/2 pi r^2, r the 1/e intensity radius). The mode profile was computed for a 3.8-um core and the known index difference, and its far field compared with the measured one: ‘Best agreement was obtained when the value of the core diameter was increased by 6%. This result led to the definition of intensity I_p0 = P_p0/(1.34 x 10^-7 cm2). With these numbers the gain coefficient becomes g = 1.5 x 10^-11 cm/W’ (p. 277). CHECK (computed 2026-09-28): ln(2.2) x 1.34e-7 cm2/(22 W x 308 cm) = 1.56e-11 cm/W, taking the amplification 2.2 over the pump change ‘from about 2 to 24 W’; the printed 1.5 is reproduced. 1.34e-7 cm2 is a Gaussian of 1/e intensity radius 1.46 um.
THE CALCULATED GAIN (p. 277). Ratio of peak cross sections sigma(fused quartz)/ sigma(benzene) = 0.0031; with the benzene 992-cm^-1 value sigma_p = 7.14 x 10^-8 /cm sr cm^-1 at 488 nm (Refs. 5, 8, which ‘agree within 7%’) and the omega^4 correction, ‘a peak cross section for the polarized scattering in fused quartz at 535.3 nm’ of 1.86 x 10^-10 /cm sr cm^-1 (a scattering coefficient per unit length, solid angle and wavenumber; no quantity in the vocabulary: notes only). Benzene linewidth taken as 2.15 cm^-1 FWHM (Ref. 7). Cross-checks via crystal quartz: sigma(crystal quartz)/ sigma(benzene) = 0.084 at 488 nm reported (Ref. 8), 0.087 measured for sigma_zz, and sigma(fused quartz)/sigma_zz(crystal quartz) = 0.036 (0.087 x 0.036 = 0.0031, computed); the 467-cm^-1 crystal line width 6.7 cm^-1 (Ref. 9); area conservation (Ref. 10) gives 0.03-0.05. Eq. (4): g(cm/W) = sigma lambda_s^3/c^2 h epsilon (n + 1), lambda_s the Stokes wavelength, epsilon the dielectric constant at the Stokes wavelength, n the Bose-Einstein factor. ‘For a pump at 526.0 nm and a signal at 535.3 nm the frequency shift is 330 cm^-1. This is not quite the peak of the gain curve and sigma = 0.80 sigma_p. The calculated gain at 535.5 for a pump at 526.0 nm is g = 1.49 x 10^-11 cm/W. This compares to the amplifier measurement of 1.5 x 10^-11 cm/W.’ The ‘535.5’ is printed so on the page image (p. 277, no unit), where every other statement says 535.3 nm (p. 276 twice, p. 277 twice); 526.0 -> 535.3 nm is a shift of 330.3 cm^-1, 526.0 -> 535.5 nm of 337.3 cm^-1: taken as a slip for 535.3 (not a value; no erratum). CHECK (computed 2026-09-28): Eq. (4) with sigma = 0.80 x 1.86e-10, lambda_s = 535.3 nm, epsilon = n^2 = 1.4607^2 and T = 295 K (n_BE = 0.250) gives 1.44e-11 cm/W, 3.5 % below the printed 1.49; the index and temperature used are not stated. The PEAK gain implied, 1.49/0.80 = 1.86e-11 cm/W, is not printed (computed, notes only); Fig. 2’s curve peaks at about 1.87e-11 cm/W near 400 cm^-1 (read by eye, not digitised).
UNCERTAINTY (pp. 277-278). Amplifier: ‘The uncertainties in measurement of the gain from the amplifier are of the order of 10%.’ Two effects could only lower it (strain birefringence, ‘The gain is almost zero for the case of 90 degree relative polarizations’; a higher-order mode at 526.0 nm): ‘the gain should not be reduced by more than 5%’. Stimulated Brillouin depletion negligible. Calculated: benzene cross section ~7 %, benzene linewidth ~7 % (3 % in the peak cross section), others < 3 %. ‘The two values of gain are in better agreement than would be expected from the estimated uncertainties.’ Fig. 2’s error bar (‘a combination of the uncertainties both in the measurement of the gain and the spontaneous cross section’) spans about 1.31 to 1.71 (read by eye).
FIGURES (not digitised). Fig. 1: the apparatus and the Xe laser lines (495.4, 500.8, 515.9, 526.0, 535.3, 539.4 nm; ‘The output at 526 nm is typically 100 W’). Fig. 2: the gain of fused quartz against shift 0-900 cm^-1 for a 526-nm pump, with the amplifier point at 330 cm^-1; ‘this gain curve does not appear to depend on the type of fused quartz used’ (p. 277). Fig. 3: oscilloscope traces.
LATER USE. hellwarth_1975 (p. 965): ‘Our measurements of the polarized Raman cross sections of fused quartz yield Raman gains in (4) about 20% greater than those reported by Stolen and Ippen, but within their limits of error’ (citing this paper as Appl. Phys. Lett. 22, 275). stolen_1989 cites this paper (its Ref. 16) with hellwarth_1975 for its Raman fraction 0.18. lin_2006’s ‘1.81 x 10^-11 cm/W at 526 nm’ is from Stolen’s later spectrum (lin_2006 Ref. 6), not this paper.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
stolen_1973/gain_amplifier#
{
"id": "gain_amplifier",
"material": "SiO2",
"table": "text",
"quantity": "raman_gain",
"unit": "cm/W",
"scale": 1e-11,
"abscissa_unit": "nm",
"use": "primary",
"uncertainty": {
"relative": 0.1,
"level": "not stated"
},
"parameters": {
"transition": "Stokes shift 330 cm-1 (526.0 -> 535.3 nm), on the flank of the main band below its peak",
"pump_nm": 526.0,
"shift_cm1": 330,
"form": "fibre",
"polarization": "pump and signal linearly polarized, parallel (nominal)",
"technique": "small-signal amplification in a 590-cm single-mode fibre (Eqs. 1-3)"
}
}
1 inline points in the source record.
p. 277: ‘With these numbers the gain coefficient becomes g = 1.5 x 10^-11 cm/W’, the small-signal amplifier measurement at 330 cm^-1 (not the peak of the gain curve), with I_p0 = P_p0/(1.34 x 10^-7 cm2) and L = 308 cm (Eqs. 1-3). Uncertainty ‘of the order of 10%’ (level not stated); depolarisation and higher-order-mode effects could lower it by at most 5 %. The abscissa is the pump wavelength (medium not stated).
stolen_1973/gain_cross_section#
{
"id": "gain_cross_section",
"material": "SiO2",
"table": "text",
"quantity": "raman_gain",
"unit": "cm/W",
"scale": 1e-11,
"abscissa_unit": "nm",
"use": "check",
"parameters": {
"transition": "Stokes shift 330 cm-1 (526.0 -> 535.3 nm), sigma = 0.80 sigma_p",
"pump_nm": 526.0,
"shift_cm1": 330,
"polarization": "polarized (parallel) scattering",
"technique": "spontaneous Raman cross section relative to the 992 cm-1 line of benzene at 514.5 nm, Eq. (4)"
}
}
1 inline points in the source record.
p. 277: ‘The calculated gain at 535.5 for a pump at 526.0 nm is g = 1.49 x 10^-11 cm/W’ (‘535.5’ as printed, a slip for 535.3: source notes), from the polarized spontaneous cross section relative to benzene by Eq. (4), with sigma = 0.80 sigma_p at 330 cm^-1. The paper’s comparison value for the amplifier measurement; its uncertainty is given only by parts (benzene cross section ~7 %, benzene linewidth 3 %, others < 3 %; pp. 277-278). Eq. (4) with n = 1.4607 and 295 K gives 1.44 (source notes).
stolen_1973/gain_band_1060#
{
"id": "gain_band_1060",
"material": "SiO2",
"table": "text",
"quantity": "raman_gain",
"unit": "cm/W",
"scale": 1e-11,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"transition": "peak of the band at 1060 cm-1",
"pump_nm": 526.0,
"polarization": "polarized (parallel) scattering",
"technique": "spontaneous Raman cross section relative to benzene, Eq. (4)"
}
}
1 inline points in the source record.
p. 277: ‘Not shown in the figure are two bands at 1060 and 1190 cm^-1 for which the peak gains would be 0.10 x 10^-11 and 0.07 x 10^-11 cm/W’: from the spontaneous spectrum by Eq. (4), for the 526-nm pump of Fig. 2 (the pump is implied by the context, not restated). No uncertainty stated for the bands.
stolen_1973/gain_band_1190#
{
"id": "gain_band_1190",
"material": "SiO2",
"table": "text",
"quantity": "raman_gain",
"unit": "cm/W",
"scale": 1e-11,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"transition": "peak of the band at 1190 cm-1",
"pump_nm": 526.0,
"polarization": "polarized (parallel) scattering",
"technique": "spontaneous Raman cross section relative to benzene, Eq. (4)"
}
}
1 inline points in the source record.
p. 277: the peak gain of the band at 1190 cm^-1, ‘0.07 x 10^-11 cm/W’, from the spontaneous spectrum by Eq. (4), for the 526-nm pump of Fig. 2 (implied, not restated). No uncertainty stated.
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.