AbstractâPump-to-Stokes and Stokes-to-Stokes relative inten- sity noise (RIN) transfer is discovered now for cascaded Raman fiber lasers (RFLs) with ...
IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 17, NO. 12, DECEMBER 2005
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Relative Intensity Noise in Cascaded Raman Fiber Lasers S. A. Babin, Member, IEEE, D. V. Churkin, A. A. Fotiadi, Member, IEEE, S. I. Kablukov, O. I. Medvedkov, and E. V. Podivilov
Abstract—Pump-to-Stokes and Stokes-to-Stokes relative intensity noise (RIN) transfer is discovered now for cascaded Raman fiber lasers (RFLs) with multimode laser pumping. We report on the first experimental study of this effect observed with two-stage phosphosilicate RFL and also propose its analytical explanation. It is shown that the peaks of radio-frequency (RF) spectrum associated with longitudinal mode beating in the pump laser cavity almost uniformly transfer to the first and second Stokes RF-spectra, thus increasing RIN of the RFL in megahertz-frequency domain.
Fig. 1. Experimental setup.
Index Terms—Raman fiber laser (RFL), relative intensity noise (RIN).
R
AMAN 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. A high-power pump for the RFA is now available from laser diode (LD) or Raman fiber laser (RFL). RFLs have higher power capabilities and possibility to generate several wavelengths simultaneously, but at the same time they have higher relative intensity noise (RIN) than LDs, which limits the bit-error rate of transmission systems due to the pump to signal RIN transfer effect in the RFA [1]. Recently, it has been demonstrated that enhanced RIN of the RFL observed at kHz- [2] and MHz-frequencies [3], [4] can be associated with a noise of the pump laser source. Therefore, the origin of the pump RIN significantly determinates the noise proprieties of the RFL. In this letter, we present a study of noise characteristics of the RFL as dependent of the noise features of multimode Yb-doped fiber pump laser (YDFL). We have found, for the first time to our knowledge, that RIN associated with longitudinal mode beating in YDFL cavity almost uniformly transfers from the YDFL to the first and second Stokes waves of the RFL leading to enhanced RIN peaks observed in MHz-frequency domain. We propose an adequate analytical explanation of this effect and discuss possible ways to reduce RIN level in the RFL. Manuscript received July 26, 2005; revised September 13, 2005. This work was supported by the Siberian Branch of Russian Academy of Sciences, Governmental Program of Support of Leading Scientific Schools in Russia. The work of A. A. Fotiadi was supported by Interuniversity Attraction Pole Program (IAP V 18) of the Belgian Science Policy. S. A. Babin, D. V. Churkin, S. I. Kablukov, and E. V. Podivilov are with the Institute of Automation and Electrometry, Russian Academy of Sciences, Novosibirsk 630090, Russia. A. A. Fotiadi is with the Service d’Electromagnétisme et de Télécommunications, Faculté Polytechnique de Mons, B-7000 Mons, Belgium, and also with Ioffe Physico-Technical Institute, Russian Academy of Sciences, Saint-Petersburg 194021, Russia. O. I. Medvedkov is with the Fiber Optics Research Center, General Physics Institute, Russian Academy of Sciences, Moscow 119991, Russia. Digital Object Identifier 10.1109/LPT.2005.859547
Fig. 2. RF beat spectrum for (a) the residual pump, (b) the first, and (c) the second Stokes wave intensity (linear scale) at input pump power 2.7 W.
We have studied the effect in the two-stage RFL (Fig. 1) based on an 370-m-long phosphosilicate fiber pumped by LD-pumped YDFL [5]. The first and second Stokes generation thresholds are 1 and 2.1 W of the YDFL power at m. The cascaded cavities of RFL are formed by pairs of the fiber Bragg gratings (FBGs) with reflectivity 99%, except the output FBG with reflectivity 42% at m (second Stokes wavelength). The output radiation of the RFL is separated into components with different wavelengths by a prism. The noise spectrum is monitored by means of avalanche photodiode with 50-ps response and electric radio-frequency (RF) spectrum analyzer (ESA). In our RFL, the noise amplitude does not exceed 1%–2% of the steady-state value for all three waves, in contrast to the experiments [6], where unstable behavior of the Stokes wave with large low-frequency fluctuations has been studied. For the pump YDFL (see Fig. 2), we observe high-frequency longitudinal mode beating with resonances separated by MHz ( is refractive index), which correspond to the round-trip along the YDFL cavity of the length m. This structure is observable up to frequencies of 1 GHz that is
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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 17, NO. 12, DECEMBER 2005
the upper limit of our ESA. We did not find a noticeable difference between the RF spectrum of the residual pump and of the incident pump. For the first Stokes component, we observe the RFL cavity resonances with period MHz m), and what is more important, (RFL cavity length the structure with period MHz, i.e., the same as in pump wave, is observed also. These “resonant” peaks are observable in the first Stokes output up to 1 GHz, too. At the same time, dynamic behavior analyzed by oscilloscope clearly indicates 6-MHz oscillations modulated by 0.3-MHz signal. For the second Stokes wave the picture is similar: The beat spectrum of the second Stokes wave reflects also the pump mode beating. Thus, the intensity fluctuations in the pump wave induced by mode beating transfer into intensity fluctuations of the first Stokes wave and then to the second Stokes wave. Direct comparison of the RF-spectra has allowed us to conclude that the transfer is almost uniform, i.e., the transfer coefficients are frequency independent in the scale of the pump mode structure. To explain the observed effect, we have developed an analytical model that describes interaction between the pump and Stokes intensity fluctuations inside the RFL cavity. Our approach is based on the set of Raman propagation equations [7] that are linearized around steady-state RFL solutions [8]. Similar method has already proved to be efficient at describing Brillouin noise spectra [9], [10]. For simplicity, we limit our consideration by the pump and first Stokes component. In the RFL cavity, there are two running Stokes waves: one coand counterpropagating interacting with the running pump wave , their mutual dynamics is described by the equations [7]
then the Raman cavity, so the terms responsible for interaction between counterpropagating waves could be omitted. Indeed, a temporal scale of the pump fluctuations associated with longitudinal mode beating is determined by round-trip in the . It means that the fluctuations are always cavity, much shorter than the integration time in the mentioned terms that is associated with the long Raman cavity. Applying the second average theorem, we could conclude that . It is clear that the these terms are averaged out as accuracy of our approach is determined by ratio of the Stokes round-trip frequency and the RF under study. For the first pump resonance at MHz, this relation is , so the accuracy in this case reduced to cavity length ratio is % and even smaller for higher frequencies. In this way, we obtain the expression for counterpropagating Stokes fluctuations and the set of equations describing a coupling between the pump and copropagating Stokes fluctuations
(2)
(3) where
, , and .
In the case of low velocity dispersion , the space and running time variables can be separated. Then the solutions are simple linear combinations of the boundary fluctuations (4) (5) (1)
Assuming that all intensities are independent on time (a stationary approach [8]), we can find the solution that essentially determine the time-averaged intensity distributions along the cavity. In order to describe the fluctuations , (1) should be linearized around the steady-state distributions so that , where . We should take into account, and it is the key point of our approach, that the pump cavity is much shorter
are functions determined by the stationary distribuwhere tions . So (4) and (5) directly yield the linear relation between the pump and Stokes RF-spectra in RFL and completely explains uniform pump-to-Stokes RIN transfer observed in the experiment. To be more concrete, let us consider the simplest situation when the reflection coefficients of the FBGs in RFL are high enough , so that the variation of the total Stokes wave intensity along the fiber is rather weak. Taking into account that , we can obtain from (3) the total income of the Stokes fluctuation for one round-trip inside the cavity (6) (7)
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(1 )
Fig. 3. (a) Relative amplitude I =I and (b) width of the envelope of RF MHz for the pump laser (dashed line) and peak with maximum at the first Stokes output wave (solid line) as dependent of the pump laser power. n A MHz and (c) ratio of amplitudes of “resonant” peaks at m n A “nonresonant” fluctuations at k MHz versus pump power.
1 6
1 6= 1 (
1 = 1( )
)
where , and is the time averaged input pump power. The first term in the RHS of (6) describes the RFL intensity fluctuations induced by pump intensity fluctuations. The second term appears because of inverse process: increase in the first Stokes wave intensity leads to pump depletion and decrease of the Raman gain coefficient, as a result the fluctuations are damped . After Fourier transformation of (6), one can obtain the expression for the beat spectrum of the copropagating Stokes wave
(8) MHz, This is a function with period with period modulated by pump beatings MHz just like in the experiment (see Fig. 2). Squared amplitude in th maximum of the envelope at freis quency (9) The amplitude and width of the Stokes RF spectrum envelope follow the amplitude and width of the pump RF spectrum, that is also confirmed in the experiment [Fig. 3(a) and (b)]. On this plot, the measured peak amplitude is normalized by a value of CW power of corresponding beam. Near the RFL threshold, only one RFL-cavity peak exists inside the envelope, so we give the width of this peak, which is narrower than the envelope [see Fig. 3(b)]. If we divide the relative noise amplitude value by the peak width value, we can estimate the RIN value as 100 dB/Hz at 2-W pump power, which is completely determined by the pump noise. Note, that an analogous model may be developed for the RIN transfer from the first to the second Stokes wave, but it is more complicated. It is interesting to compare the noise induced by the pump mode beating and the own RFL mode beating noise. With increasing excess above the threshold the pump-induced noise de-
creases as respect to own RFL noise [see Fig. 3(c)]. The own Stokes noise makes a considerable contribution to the total noise level at high pump power, estimated as 30% of pump-induced noise at 4-W power. Ultimate RIN value is determined by Stokes noise, estimated as 120 dB/Hz at pump power 4 W. In the opposite case of low-frequency noise , one must take into account the counterpropagating wave too. In that case, in (8) term should be replaced by and . The low-frequency noise is important for RFA pumped in counterpropagating geometry while high-frequency noise that we have studied is more important for codirectional RFA pumping. Thus, we have shown experimentally and theoretically that the RIN of the cascaded RFL is mainly defined by the high-frequency RIN of the pump laser that is induced by its longitudinal mode beating. The longitudinal mode beating in the YDFL has been observed earlier in the YDFL [11], and it has been also mentioned that intermode beat resonances are observable in the one-stage RFL with its own round-trip frequency [2], [12], but the pump-to-Stokes mode beating transfer and its uniform characteristics have not been mentioned so far. It is important that the role of the pump noise may be reduced by increasing pump power. Well above the threshold, its own intermode beating at RFL round-trip frequency determine ultimate noise characteristics of the RFL. REFERENCES [1] C. R. S. Fludger, V. Handerek, and R. J. Mears, “Pump to signal RIN transfer in Raman fiber amplifiers,” J. Lightw. Technol., vol. 19, no. 8, pp. 1140–1148, Aug. 2001. [2] M. Krause, S. Cierullies, H. Renner, and E. Brinkmeyer, “Pump-toStokes transfer of relative intensity noise in Raman fiber lasers,” in Proc. Conf. Lasers and Electro-Optics, 2004, Paper CMD5. [3] S. A. Babin, D. V. Churkin, and S. I. Kablukov, “Longitudinal mode structure of the two-stage Raman fiber laser,” 13th Int. Laser Physics Workshop, p. 217, 2004. in: Book of abstracts. [4] S. A. Babin, D. V. Churkin, S. I. Kablukov, E. V. Podivilov, O. I. Medvedkov, and A. A. Fotiadi, “Pump-to-Stokes relative intensity noise (RIN) transfer in Raman fiber lasers: Observations and modeling,” Proc. Optical Fiber Communication Conf., 2005. [5] V. I. Karpov, E. M. Dianov, V. M. Paramonov, O. I. Medvedkov, M. M. Bubnov, S. L. Semyonov, S. A. Vasiliev, V. N. Protopopov, O. N. Egorova, V. F. Hopin, A. N. Guryanov, M. P. Bachynski, and W. R. L. Clements, “Laser-diode-pumped phosphosilicate-fiber Raman laser with an output power of 1 W at 1.48 m,” Opt. Lett., vol. 24, pp. 887–889, 1999. [6] A. Doutté, P. Suret, and S. Randoux, “Influence of light polarization on dynamics of continuous-wave-pumped Raman fiber lasers,” Opt. Lett., vol. 28, no. 24, pp. 2464–2466, 2003. [7] J. Auyeung and A. Yariv, “Theory of CW raman oscillation in optical fibers,” J. Opt. Soc. Amer., vol. 69, pp. 803–807, 1979. [8] S. A. Babin, D. V. Churkin, and E. V. Podivilov, “Intensity interactions in cascades of a two-stage Raman fiber laser,” Opt. Commun., vol. 226, pp. 329–335, 2003. [9] A. A. Fotiadi, E. A. Kuzin, M. P. Petrov, and A. A. Ganichev, “Amplitude-frequency characteristic of an optical-fiber stimulated-Brillouin amplifier with pronounced pump depletion,” Sov. Tech. Phys. Lett., vol. 15, pp. 434–436, 1989. [10] E. A. Kuzin, M. P. Petrov, and A. A. Fotiadi, “Phase conjugation by SMBS in optical fibers,” in Optical Phase Conjugation, M. Gower and D. Proch, Eds. New York: Springer-Verlag, 1994, pp. 74–96. in. [11] R. Selvas, J. K. Sahu, L. B. Fu, J. N. Jang, J. Nilsson, A. B. Grudinin, K. H. Ylä-Jarkko, S. A. Alam, P. W. Turner, and J. Moore, “High-power, low-noise, Yb-doped, cladding-pumped, three-level fiber sources at 980 nm,” Opt. Lett., vol. 28, no. 13, pp. 1093–1095, 2003. [12] S. V. Chernikov, N. S. Platonov, V. P. Gapontsev, D. I. Chang, M. J. Guy, and J. R. Taylor, “Raman fibre laser operating at 1.24 m,” Electron. Lett., vol. 34, no. 7, pp. 680–681, 1998.
