Co- and cross-polarized Raman spectra have been obtained previously in bulk glass [1] and in polarization-maintaining fiber [2]. However, no polarization resolving measurements have been reported either at the zero-dispersion wavelength of fibers or for non-polarization maintaining fibers. Such measurements are of increased interest because recent research in producing entangled-photon pairs in standard optical fiber [3, 4, 5, 6, 7, 8, 9, 10] has highlighted the need to precisely measure co- and cross-polarized Raman scattering (RS) in such fiber at small detunings. The experiment reported in Ref. [5] clearly indicates that Raman scattering sets a limit on the purity of entanglement generated in the fiber. Therefore, a detailed investigation of the small-detuning co- and cross-polarized Raman-gain spectra in dispersion-shifted fiber (DSF) will help improve the quality of the generated entanglement of the photon pairs. These measurements are also necessary for characterizing the limits on the noise figure of fiber-optical parametric amplifiers [11, 12].

Recently, measurements of the polarization-averaged spectra of Raman scattering on both the Stokes and anti-Stokes sides have been made and compared to the Raman gain spectra with excellent agreement [13]. However, this work was unable to resolve the co- and cross-polarized components, owing to polarization-mode dispersion (PMD) in the long fiber lengths that were used. Here we report precise measurements of the co- and cross-polarized Raman-gain spectra on both the Stokes and anti-Stokes sides at the zero-dispersion wavelength of standard dispersion-shifted fiber by use of a photon-counting technique. Our use of a pulsed pump eliminates Brillouin scattering and forming a Sagnac loop with the fiber suppresses self-phase-modulation (SPM) induced spectral broadening from contaminating the measurements, thus enabling precise measurement of the Raman gain down to a detuning of 0.17 THz (5.7cm^-1). Moreover, in our recent research in the context of noise-figure limit of fiber-optical parametric amplifiers [12], the measurement of parametric fluorescence, which was produced by 4.4-km-long DSF having similar parameters as the DSF we used here, clearly showed that the PMD was negligible when the detuning was less than 1.3 THz (see Fig. 1 in Ref. [12]). Judging from that measurement and the fact that PMD scales proportionally to the square-root of fiber length, we believe that for the measurements reported in this paper with use of a Sagnac loop made of 300-m-long DSF, the co- and cross-polarized Raman-gain spectra have been resolved without contamination from the PMD effect since the reported detunings are less than the PMD-free detuning of 4.9 THz.

A simplified diagram of our setup is shown in Fig. 1. Stokes and anti-Stokes photons at frequencies ω _s and ω _a , respectively, are produced in a nonlinear-fiber Sagnac interferometer (NFSI) through the χ ⁽³⁾ (Kerr) nonlinearity. The NFSI, as described in detail in Ref. [14], consists of a fused-silica 50/50 fiber coupler spliced to 300m of DSF having a zero-dispersion wavelength at λ₀=1535±2nm. A fiber polarization controller (FPC1) placed within the Sagnac loop provides a phase bias between the counter-propagating waves, allowing the device to be operated as a total reflector [15]. Because of the non-zero response time of the χ ⁽³⁾ nonlinearity, when a pulsed pump is injected into the NFSI, two nonlinear processes take place. One is RS: the imaginary part of χ ⁽³⁾ couples the pump through thermally-populated optical-phonon modes to Raman-scattering modes on both the Stokes and anti-Stokes sides.

The other is four-photon scattering (FPS): two pump photons at frequency ω_p scatter through the real part of χ ⁽³⁾ to create a simultaneous pair of Stokes and anti-Stokes photons, where ω_a -ω_p =ω_p -ω_s ≡Ω. The process of FPS is enhanced when the central wavelength of the pump is close to the zero-dispersion wavelength of DSF, where phase-matching can be satisfied. We have previously used this effect to generate quantum-correlated twin beams [14], correlated photon-pairs [3, 5], and polarization entanglement [9].

 

Fig. 1. Experimental setup; scattered Stokes and anti-Stokes photons emerging from the port labelled “Out” are detected. FPC, fiber polarization controller; FPBS, fiber polarization beam splitter; F, filter.

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The NFSI is a bi-directional amplifier, in the sense that a signal injected from either port can be amplified. This means that half of the spontaneously scattered Stokes and anti-Stokes photons, created either one at a time via RS or pair-wise via FPS, are directed towards the pump source, and the other half towards the detection setup. It is worth stressing that due to the process of quantum interference both photons of a pair scattered via FPS are directed in the same direction.

To measure the scattered Stokes (anti-Stokes) photons, one must effectively prevent the pump photons from reaching the detector. Since only about 0.1 photon on average is scattered by a typical 5-ps-duration pump pulse that contains approximately 10⁸ photons, a pump-Stokes (anti-Stokes) photon rejection ratio in excess of 100 dB is required. We achieve this by first exploiting the mirror-like property of the NFSI, which provides a pump rejection greater than 30 dB [15]. In this case, there are three kinds of photons that emerge from the port labelled “out: (i) Stokes and anti-Stokes photon-pairs produced by the FPS process; (ii) Stokes and anti-Stokes photons produced by the RS process, which in the low-pump region are half of the total RS photons produced by the incident pump power; and (iii) leaked pump photons that are 30 dB less than the incident pump. All these photons are sent through a specially made filter (F₂), which provides a pump-rejection ratio greater than 75 dB. F₂ is realized by one of two configurations: either by a free-space double-grating spectral filter (DGSF) [3, 5], wherein the passband of the filter is determined by the numerical aperture of the fiber along with the geometrical settings of the optical elements composing the filter; or alternatively by a cascaded array-waveguide-grating spectral filter (CAWGSF), which is made by cascading two 40-channel array-waveguide gratings (AWG) (Wavesplitter, WAM-10-40-G) with a C-band filter (JDSU, FWS-D20020000) in between.

The pump is a mode-locked pulse train at 75.3MHz rate, which is obtained by spatially dispersing the output of an optical-parametric oscillator (OPO) (Coherent Inc., model Mira-OPO) with a diffraction grating, whose central wavelength can be tuned from 1536 to 1545 nm. To achieve the required power, the pump pulses are amplified by an erbium-doped-fiber amplifier (EDFA). Photons at the Stokes and anti-Stokes wavelengths from the OPO that leak through the spectral-dispersion optics and from the amplified spontaneous emission (ASE) produced by the EDFA are eliminated by passing the pump through a filter (F₁).

A photon counter consisting of an InGaAs/InP avalanche photodiode (APD, Epitaxx, model EPM 239BA) operated in a gated-Geiger mode is used to detect the Stokes (anti-Stokes) photons [3]. The 1-ns-wide gate pulses arrive at a rate of 588 kHz, which is 1/128 of the repetition rate of the pump pulses. The quantum efficiency of the detector is 20%. The total detection efficiency for the Stokes (anti-Stokes) photons is about 7% (2% with CAWGSF), when the efficiencies of the NFSI (82%), 90/10 coupler, DGSF (⋍57%) [CAWGSF (⋍25%)], and the fiber polarization beam splitter (FPBS) (about 90% and 60% in front of DGSF and CAWGSF, respectively) are taken into account.

 

Fig. 2. Fitting parameters s ₁ and s ₂ versus the detuning, Ω. Solid (hollow) squares-blue and solid (hollow) circles-pink are the fitting parameters s ₁ and s ₂, respectively, for co- (cross)-polarized photons relative to the pump polarization.

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Fig. 3. (a) Transmission spectrum of one channel in the CAWGSF. (b) Spectra of the leaked pump at the port labelled “Out” at pump levels of 0.22×10⁸ photons/pulse (dark gray), 0.6×10⁸ photons/pulse (gray), and 1.0×10⁸ photons/pulse (black).

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In the low-pumping regime, where the χ ⁽³⁾ interaction is weak, the number of RS photons generated in the DSF is linearly dependent on the number of pump photons. In contrast, the number of photon-pairs produced via FPS in the DSF is quadratically dependent on the number of pump photons, and they are also predominately co-polarized with the pump. To investigate the dependence of the co- and cross-polarized RS efficiency upon the detuning Ω, a FPBS is placed in front of F₂. With proper settings of FPC2, which is placed in front of the FPBS, the Stokes (anti-Stokes) photons that are either co- or cross-polarized with the pump can be selected. The detuning can be changed by adjusting the passband frequency of F₂. At each detuning, we measure the number of scattered photons per pump pulse, co- and cross-polarized with the pump, respectively, that are detected in the Stokes (anti-Stokes) channel, N_{s (a)}, as a function of the number of pump photons per pulse, N_p . In both co- and cross-polarized cases, we fit the measured data with N_{s (a)}=s ₁ N_p +s ₂ $N_p^2$ , where s ₁ and s ₂ are the linear and quadratic scattering coefficients, which respectively determine the strengths of RS and FPS in the DSF [3, 5]. In Fig. 2 we plot s ₁ and s ₂ so obtained for both the co- and cross-polarized cases as a function of the detuning Ω. For these measurements, the NFSI is pumped by Gaussion-shaped 5-ps-duration pulses, whose central wavelength is 1536 nm and the full-width at half-maximum (FWHM) is 0.8 nm. F₁ is a 1nm-bandwidth tunable filter (Newport, model TBF-1550-1.0) and F₂ is the DGSF adjusted to obtain a 0.8 nm-wide (FWHM) passband.

 

Fig. 4. Detected photons at detunings of 0.28 THz (circles-black), 0.38 THz (triangles-green), 0.48 THz (squares-pink), and 0.68 THz (diamonds-blue), as a function of the injected pump photons for (a) scattered photons co-polarized with the pump and (b) scattered photons cross-polarized with the pump.

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Because it is difficult to achieve a rejection ratio in excess of 75 dB with the DGSF when the detuning is less than ⋍0.5 THz (⋍4 nm), we replace the DGSF with a CAWGSF, and make the same measurement. In Fig. 3(a) we show the transmission curve of one channel in the CAWGSF, whose FWHM is about 0.4 nm. One sees that a rejection in excess of 75 dB can be obtained for the photons that are 0.1 THz away from the central wavelength of the channel. Figures 4(a) and (b) give the measurement results. We find that when the detuning is less than 0.38 THz, in both co- and cross-polarized cases, single counts start to exponentially depend on pump power. This is caused by an increasing amount of pump leakage—note that the pump spectrum is broadened due to SPM in the DSF, as shown in Fig. 3(b)—through the CAWGSF passband for dutunings smaller than 0.38 THz that prevents us from achieving a pump-rejection ratio greater than 75 dB.

 

Fig. 5. (a) Total detected photons at detuning 0.17 THz (black) and 0.47 THz (gray), respectively, as a function of the injected pump photons. Second-order polynomials, N_a =s ₁ N_p +s ₂ $N_p^2$ , are shown to fit the experimental data (dot-dashed line). The contributions of linear scattering, s ₁ N_p , (solid line) and quadratic scattering, s ² $N_p^2$ , (dotted line) are plotted separately as well. (b) Detected photons cross-polarized with the pump at different detunings as a function of the injected pump photons. First-order polynomials, N_a =s ₁ N_p , are shown to fit the experimental data (solid line).

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To measure the RS for smaller detunings, not only we replace the DGSF with a CAWGSF, we also pump the NFSI with a narrower-bandwidth pulse train to curtail the spreading of the pump photons owing to SPM-induced spectral broadening. The pump’s central wavelength is set to 1544.5nm and a bandwidth of ⋍0.2 nm (between -1 dB transmission points) is obtained by using an F₁ that is composed of a cascade of two WDM filters (JDSU, DWS-1F3403P90). Figures 5(a) and (b), respectively, show the number of scattered photons measured in several

different channels of the CAWGSF with and without the FPBS in the experimental setup. Linear dependence of the cross-polarized scattered photons on N_p (proportional to the average pump power), even when the detuning is as small as 0.17 THz, shows that the SPM-broadened pump pulses are effectively reflected back by the NFSI. The fitting parameters s ₁ and s ₂ obtained without the FPBS in the setup are plotted as a function of Ω in Fig. 6(a). While comparing s ₂ here with that in Fig. 2, one should note that the efficiency and the bandwidth of FPS are reduced because the phase-matching condition is not satisfied owing to the central wavelength of pump being far from the zero-dispersion wavelength of the DSF. Figure 6(b) shows s ₁ versus Ω, co- and cross-polarized with the pump, where the co-polarized s ₁ at each Ω is obtained by subtracting the corresponding data point in Fig. 5(b) from that in Fig. 5(a) after carefully normalizing for the differences in the detection efficiencies in the two cases. Comparing Fig. 6(b) with Fig. 2, we see that there is an overlapping region of Ω in the two figures; the data points for the same Ω have a ratio of 7.8 between them, which is in agreement with the measured efficiency differences of the F₂ used in the two experiments (taking into account the differing bandwidths and the transmission losses). Using this 7.8 factor to correct the data in Fig. 6(b), we can normalize the fitting parameters s ₁ for detunings less than 0.5 THz to the data sets in Fig. 2.

 

Fig. 6. (a) Fitting parameters of s ₁ (squares) and s ₂ (circles) versus detuning without the FPBS is the setup. (b) Fitting parameter s ₁ co- (solid squares) and cross-polarized (hollow squares) with the pump versus detuning.

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It is well known that in the low-gain region, the RS photons measured by the detector can be expressed as [16, 13]

where n_i (Ω) (i=s,a) is the number of detected RS photons per second in the Stokes or anti-Stokes channel times a factor of 2 (included to account for the fact that half of the RS photons that go back towards the pump source are not detected), η is the total detection efficiency, Δf is the bandwidth of the optical filter, P is the total incident pump power in Watts, and n _th=1/[exp(hΩ/kT)-1] is the Bose population factor. In Eq. (3), L _eff is the effective length of the DSF, where α(ω_j ) (j=p,s,a) is the fiber attenuation coefficient—a mild function of optical frequency—which is about 0.21 dB/km, and L (=300 m) is the length of the DSF. In Eqs. (1) and (2), R_g (ω_p ,Ω) is the standard Raman gain, which is positive on the Stokes side (Ω<0) and negative on the anti-Stokes side (Ω>0). Substituting the experimental parameters into Eqs. (1)–(3), assuming that R_g does not very much within the 3-dB bandwidth of the optical filter used, and comparing the results with the measured fitting parameters s ₁ in Fig. 2, we find that R_g (ω_p ,Ω)=35.8s ₁. In this way we obtain the co- and cross-polarized Raman-gain spectra on both the Stokes and anti-Stokes sides for detunings from 0.17 THz to 3.1 THz, as plotted in Fig. 7. When the detuning is less than 1 THz, in both co- and cross-polarized cases, we find that the measured R_g (ω_p ,Ω) fits very well with the following third-order polynomial: R_g (ω_p ,Ω)=aΩ+bΩ²+cΩ³ without the need for any additional adjustable parameter. Such fit is shown by the red (green) solid curve in the top right (bottom left) inset of Fig. 7 for the co- (cross-) polarized Raman gain. One clearly sees the existence of asymmetry around the pump frequency in both the co- and cross-polarized Raman-gain spectra, which points to the pump-wavelength dependence of the Raman gain [17, 18]. The plots in Fig. 7 also show that the co- and cross-polarized spectra gradually converge as the detuning decreases, and that the co-polarized Raman gain grows faster than the cross-polarized Raman gain as the detuning increases.

 

Fig. 7. Measured Raman-gain spectra, co- (solid squares) and cross-polarized (hollow squares) with the pump, versus detuning. Insets: Curves fitted to the measured Raman gain for detunings up to 1 THz, where third-order polynomials, R_g (ω_p ,Ω)=aΩ+bΩ²+cΩ³, are shown to fit the experimental data. Red (green) solid curve is the fit for co- (cross-) polarized Raman gain with a=0.019 (0.021), b=0.0043 (0.0020), and c=0.045 (0.029).

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In conclusion, by using an NFSI to curtail the leakage from SPM-induced spectral broadening of the pump, by employing picosecond pulses to pump the NFSI to suppress Brillouin scattering, and by using a photon-counting technique to separate the RS from FPS, we have measured the co- and cross-polarized Raman spectra of the standard DSF at the fiber’s zero-dispersion wavelength on both the Stokes and anti-Stokes sides for detunings from 0.17 THz (5.7cm^-1) to 3.1 THz (103cm^-1). Detailed knowledge of these spectra are useful for optimizing the performance of entangled-photon sources based on the fiber’s Kerr nonlinearity.