1. Introduction

Raman fiber amplifiers (RFAs) are widely studied and applied in optical communications in order to increase the bandwidth and span lengths of long haul WDM transmission systems [1]. The decreasing cost of high-power semiconductor lasers and increasing need in larger gain bandwidth of optical fiber transmission, lower gain-ripple, and lower noise figure make RFAs a more attractive technology than the traditional erbium-doped fiber amplifier (EDFA). At the same time, Raman fiber lasers (RFLs) are treated as advanced sources for RFA pumping due to high power capabilities and possibility to generate several wavelengths simultaneously [2].

For WDM transmissions systems it is important to know an amplifier spectrum, i.e. dependence of the gain coefficient on signal frequency, g_s (Δω), where Δω=ω_p -ω_s is a frequency shift between pump and signal frequencies. The gain spectrum depends on fiber type and may be saturated at high pump and signal powers. The nature of the gain saturation is one of the key questions for telecommunication system development. It is well known that the inhomogeneous gain saturation in EDFA changes essentially the gain contour: spectral hole burning (SHB) may induce local distortions in the amplifier gain spectrum around different channels, see, for example, [3, 4]. This phenomenon can cause crucial limitations for the accuracy of spectral gain control of the fiber amplifier, particularly in the case of ultra long haul WDM transmission systems with high signal powers.

Small-signal Raman gain coefficient for conventional germanosilicate fibers has broad complicated structure with the main maximum at Δω ~ 440 cm^-1: it may be approximated by multiple (~ 13) vibrational modes [5]. The spectral shape of the modes is adopted by the authors of paper [5] as gaussian, that corresponds to purely inhomogeneous broadening. Recently, this model has been extended to intermediate broadening [6], but the fitting of the experimental data is better when inhomogeneous contribution is ~ 3 times larger than homogeneous one. This fact makes principally possible some manifestations of spectral hole burning (SHB) effects in Raman gain spectrum [6]. A possibility of SHB effects are also discussed for Brillouin gain profile, having pure homogeneous broadening. It is shown theoretically [7] that in a long fiber a spectral hole may be burnt in the Brillouin gain profile due to modulation instability, analogous effects are possible in Raman gain profile too.

Though the question of the Raman gain saturation is of great importance for RFAs and RFLs development, no accurate experimental test of its nature and mechanisms have been made to present time. It is supposed, that the Raman gain is saturated homogeneously at low signal power [8]. On the other hand, the experimental results concerning a RFL output spectra formation and broadening at high intra-cavity Stokes wave power allow to suggest that different longitudinal modes generate independently, which may be treated as some indication of SHB effect [9].

It is well known, that one of the main gain saturation mechanisms is pump depletion, [8]. One could write the Stokes signal gain in the following form:

where $\overline{P_p}$ is the average pump power, g_R is the Raman gain coefficient normalized by effective cross-section, L is the fiber length. The main question is: does the spectral profile g_R (Δω) change its shape with increasing input pump power P ₀ and Stokes wave power P_s , i.e. does SHB occur or not? Another question is: does the amplitude of the gain coefficient at maximum $g_R^{\mathit{\text{max}}}$ change with increasing power, i.e. is the Raman gain coefficient saturated? In the present paper, we have studied for the first time the Raman gain saturation at high pump and signal powers.

2. Experimental technique

We have measured the Raman gain in a phosphosilicate fiber having single amplification peak at Δω ~ 1300 cm^-1. Saturation of small-signal Raman gain with increasing pump power in P₂O₅-doped fiber was first studied experimentally in [10]. To study spectral features of the saturation at high Stokes wave power we need an additional low-power probe field tunable laser either around the signal (Stokes) frequency or around anti-Stokes frequency, see Fig. 1. The last technique is known as coherent anti-Stokes Raman scattering (CARS) spectroscopy. It is usually used in gaseous media and may be applied to fibers too, see e.g. [11]. Around the anti-Stokes frequency the Raman spectrum has opposite sign that means pump-induced absorption. Its shape copies the gain spectrum around Stokes frequency with an account of difference in overlap factor depending on wavelength.

 

Fig. 1. CARS scheme: ω_p , ω_s and ω_as are pump, Stokes and anti-Stokes frequencies.

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Fig. 2. Experimental setup.

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The experimental setup is shown in Fig. 2. We have used a LD-pumped double clad Ytterbium-doped fiber laser (YDFL) generating at wavelength λ_p = 1060 nm as a pump source. High power Stokes wave at λ_s = 1234 nm is generated inside the Raman fiber laser (RFL) cavity [12] formed by two highly reflective (HR) fiber Bragg gratings (FBGs) and the fiber with 13mol% of P₂O₅ in the core and MFD of 6.3 μm at 1060 nm. A probe-field source is tunable Ti:Sa laser (TechnoScan Co.) pumped by argon ion laser (Inversion Co.). The Ti:Sa laser radiation with power of ~ 10 mW tests pump-induced absorption coefficient g_as around anti-Stokes wavelength λ_as ≃ 930 nm, see Fig. 1. At this power level the probe field does not saturate the two-photon transition at difference frequency Δω that has been tested experimentally.

We have measured the Raman gain spectral profiles Ag_s (ω_p - ω_s ) = -g_as (ω_as - ω_p ) scanning probe field frequency ω_as , here A is overlap factor. The profiles obtained at different pump and Stokes wave powers and normalized to unity at its maximum are shown in Fig. 3. Resonant CARS frequency ${\omega }_{\mathit{\text{as}}}^{\mathit{\text{res}}}$ = 2ω_p - ω_s corresponds to wavelength ${\lambda }_{\mathit{\text{as}}}^{\mathit{\text{res}}}$ ≃ 929 nm. Inhomogeneous saturation should induce spectral hole burning (SHB) at this wavelength. It is clearly seen in Fig. 3, that within the experimental accuracy no SHB effect has been observed, i.e. the Raman gain profile does not change its shape with increasing power. At the same time, amplitude of the gain profile $g_s^{\mathit{\text{max}}}$ changes with power, but not linear. Therefore, the gain profile is saturated homogeneously.

 

Fig. 3. Raman gain spectral profile (attributed to P ₂0₅ peak) tested by CARS technique at different pump power P ₀ and intra-cavity Stokes wave power P_s .

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3. Theoretical analysis

The next question is: what is the reason of this saturation — saturation of Raman gain coefficient g_R (P ₀,P_s ) with increasing signal power P_s or just pump power depletion $\overline{P_p}(P_0,P_s)$? Let us perform a theoretical treatment. The following set of equations describes the pump wave and probe wave power variation, [13].

where $P_p^{\pm }$, $P_s^{\pm }$ represent power of the pump and the first Stokes wave in RFL cavity, correspondingly, ± denote forward and backward propagation relatively to the z-axis direction along the fiber, P_p is the total pump power (P_p = $P_p^{+}$+$P_p^{-}$), P_s is the total intracavity power at Stokes frequency (P_s = $P_s^{+}$ + $P_s^{-}$), P_as is a probe wave power, α_p and α_as are the absorption coefficients for the pump wave and probe anti-Stokes wave, A is the constant which accounts for the difference between overlap integrals for pump/Stokes and anti-Stokes/pump, that is roughly proportional to λ_s /λ_as . In Eqs. (2) we do not take into account the reverse influence of probe wave on pump wave because of P_as /P_s ≪1.

Due to the output HR FBG reflecting at wavelength around 1060 nm, there are two counter-propagating pump waves, $P_p^{+}$ and $P_p^{-}$, which obey Eq. (2):

 

Fig. 4. Intracavity Stokes wave power P_s versus input pump power P ₀.

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Taking into account the boundary conditions $P_p^{+}$(0) = P ₀, $P_p^{-}$(L) = $P_p^{+}$(L), one can derive the following expression for the pump wave power averaged over the fiber length

Note, that this expression is valid within the limits of assumption P_s = $P_s^{+}$+$P_s^{-}$ = const, which is well-justified in our case of a highly-reflective cavity for Stokes wave [9].

Equation (5) describes average pump power depletion with increasing Stokes wave power P_s . We have directly measured intracavity RFL power P_s via 99:1 coupler and obtained the dependence P_s (P ₀), see Fig. 4. Using this data we can plot theoretical prediction for the integral Raman gain $g_{s}L=g_R\overline{P_p}L$ at different power levels in the assumption of the constant value of g_R . The theoretical curve, calculated using Eq. (5) with experimental values α_p = 1.8 dB/km, g_R = 1.29 (kmW)^-1, L = 0.37 km and the measured dependence P_s (P ₀) without fitting parameters is shown at Fig. 5 by solid line.

We can compare the prediction with direct experimental measurement of the Raman gain. One can derive from Eq. (3) the power of the probe wave at the exit:

Using this expression, the Raman gain coefficient can be easily obtained, $g_s\equiv g_R\overline{P_p}=\frac{\left(\delta -{\alpha }_{\mathit{as}}\right)}{A}=-\frac{g_{\mathit{as}}}{A}$ using measured values of g_as . The results are shown in Fig. 5 (boxes). Comparison of the theoretical prediction and the experimental data shows very good agreement with constant A = 1.35 which is quite close to the relation Stokes and anti-Stokes wavelengths, λ_s /λ_as = 1.328.

Without Stokes wave, the integral Raman gain $g_{s}L=g_R\overline{P_p}L=g_R{P}_0\frac{1-\exp \left(-{\alpha }_{p}2L\right)}{{\alpha }_p}$ grows linearly versus pump power (dashed line). Corresponding experimental data (stars) agree with the theory with the same constant A being used. At these measurements HR FBGs for Stokes wave ω_s have been removed from the experimental setup, see Fig. 2.

 

Fig. 5. Integral Raman gain g_sL measured at the presence (boxes) and at the absence (stars) of the Stokes wave, solid and dashed lines are the results of calculation from Eq. (4).

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4. Conclusion

Thus, we have observed that the Raman gain $g_s=g_R\overline{P_p}$ for the Stokes wave in the phosphosilicate fiber depends on the power via average pump power $\overline{P_p}(P_0,P_S)$ only. The spectral shape of the gain coefficient g_R (Δω, P ₀, P_s )=$g_R^0$ (Δω) is not changed even at high pump and Stokes wave powers P ₀ ~ P_s ~ 3 W, here $g_R^0$(Δω) is the small signal Raman gain coefficient. Therefore, the Raman gain profile is saturated homogeneously. Taking this into account, possible reasons for the inhomogeneous-like RFL output spectra formation should be further clarified. The obtained experimental results have clearly demonstrated that the main gain saturation mechanism is the pump power depletion. Let us mention that the RFL scheme applied for the experimental test of saturation mechanisms have advantages over a simple amplifier scheme in high pump/signal power domain. The signal power P_s is nearly constant along the fiber in HR cavity and may exceed pump power P ₀, so there appears a possibility of analytical description and direct comparison with experiment. At the same time, the CARS technique applied is very sensitive tool that may reveal even very small spectral holes which are not resolvable in normal Stokes wave spectrum. Though the spectrum is measured at anti-Stokes wavelength (~ 0.93 μm), it characterizes the gain at Stokes wavelength being close to 1.3 μm transmission window. The obtained results and developed technique are generally applicable to other types of fibers and wavelength domains, specifically to 1.5 μm telecom window. But exact level of pump and Stokes power at which the gain saturation remains homogeneous should be measured in each concrete case.