Interplay of four-wave mixing processeswith a mixed coherent-incoherent pump
Jochen Schroder,1,3,∗ Anne Boucon,2,4 Stephane Coen,1
and Thibaut Sylvestre2
1 Physics Department, The University of Auckland, Private Bag 92019, Auckland,New Zealand
2 Departement d’Optique P. M. Duffieux, Institut FEMTO-ST, Universite de Franche-Comte,CNRS UMR 6174, F-25030 Besancon, France
3 Now with IPOS, School of Physics, University of Sydney, Sydney, NSW 2006, Australia4 Now with the ICB, Universite de Bourgogne, 21 078 Dijon Cedex - France
Abstract: We experimentally demonstrate the existence of multiple,simultaneous, independent four-wave mixing processes in optical fibers. Inparticular we observe competition between phase-matched and non-phase-matched processes involving the same mixed coherent-incoherent pump.Further investigation reveals that narrow-band degenerate four-wave mixingwith an incoherent pump can lead to efficient wavelength conversion.
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1. Introduction
The nonlinear phenomena of four-wave mixing (FWM) and parametric interactions in opticalfibers have attracted considerable research interest for several decades. Investigations started asearly as 1974 when Stolen et al first observed FWM in a glass fiber [1], initially referring to itas three-wave mixing. The efficiency of FWM in generating waves at new optical frequencieshas then led to an enormous amount of research [2–9]. Today, FWM is the underlying processof a large number of applications ranging from parametric amplification [9, 10] to wavelengthconversion [11, 12] or high repetition rate pulsed light sources [13–15].
Here we focus on two lesser known aspects of FWM, namely the interplay of multiple FWMprocesses and FWM based on an incoherent pump. Early theoretical and experimental studiesconsidered only one FWM process at a time [5,8,16]. In 1991, however, Thompson et al demon-strated FWM with two pump waves, which leads to a cascaded generation of sidebands [17],and theoretically described the interplay between the multiple FWM processes involved [18].Since then, several authors have expanded these results, predicting instabilities such as side-band oscillations along the fiber propagation [3, 19] as well as a self-stabilization effect [20].The concept of two pump FWM was also recently expanded to very broadband cascaded FWMproducts [2, 21]. In contrast to the cascaded generation of FWM sidebands, we demonstrate
#135435 - $15.00 USD Received 20 Sep 2010; revised 10 Nov 2010; accepted 16 Nov 2010; published 24 Nov 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25834
the simultaneous occurrence of largely independent FWM processes. Two processes stand outin particular: a non-phase-matched interaction between three wavelengths and the wavelengthconversion of a signal with a broadband incoherent pump beam comprised of an amplifiedspontaneous emission (ASE) source.
As a matter of fact, little attention has been paid to non-phase-matched FWM pro-cesses [7,22,23] and it is only recently that FWM with an incoherent pump beam has attractedsome interest [24–29]. Moreover most of those previous investigations have been conducted forweakly incoherent waves, i.e. waves with a spectral width of a few hundred GHz or less, andnever considered FWM in the presence of other processes. In contrast, in our experiment, weobserve both non-phase-matched FWM and FWM with a broadband incoherent pump simulta-neously. Parametric processes with large phase-mismatches are generally ignored due to theirsignificantly lower efficiency [22]. They can however be strongly enhanced in the presence ofadditional gain mechanisms such as stimulated Raman scattering (SRS) [7,23]. Nevertheless, inour experiment this effect is pronounced enough to observe competition between a non-phase-matched product and a incoherently-pumped phase-matched one.
2. Experiment
The experimental setup is depicted in Fig. 1. It is based on a continuous-wave (cw) Raman fiberlaser (RFL) with a fixed wavelength of 1455 nm and a cw Erbium-doped fiber laser (EDFL),wavelength tunable between 1535 and 1565 nm. The EDFL is followed by an Erbium-dopedfiber amplifier (EDFA) generating up to 33 dBm of output power, including some amplifiedspontaneous emission (ASE) noise. The ASE noise appears around 1550 nm with a spec-tral width of approximately 50 nm (at −10 dB level). The two light sources are combinedinto 3.1 km of dispersion-shifted fiber (DSF) by a wavelength division multiplexer (WDM).The fiber has a nonlinear parameter γ = 2 W−1 km−1, a zero-dispersion wavelength (ZDW)of 1550 nm (right within the tuning range of the EDFL and the bandwidth of the ASE), anddispersion coefficients β2 =−0.473 ps2/km, β3 = 0.119 ps3/km, β4 =−5.66×10−4 ps4/km(at 1555 nm). The output spectrum is recorded using an optical spectrum analyzer (OSA).
Figure 2 depicts the spectra at the output of the DSF when scanning the EDFL wavelengthfrom 1536 to 1554 nm, both as (a) a line and (b) a color plot. Here the power of the RFL wasset to 1.3 W and the EDFA was adjusted to yield approximately 500 mW of output power. Thespectra reveal a number of new frequency components created by independent FWM processes.The individual processes are easily distinguishable and this is to the best of our knowledge thefirst observation of such a large number of independent, simultaneous FWM processes. In thefollowing we will discuss each of these in more details.
For long EDFL wavelengths, the most obvious feature in the spectra are the two sidebandscreated by the spontaneous scalar modulation instability (MI) of the EDFL. These sidebandsare symmetrically located around the EDFL frequency. The lower and upper limits delineating
#135435 - $15.00 USD Received 20 Sep 2010; revised 10 Nov 2010; accepted 16 Nov 2010; published 24 Nov 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25835
Spectralpower[dB]
(a)
1400 1500 1600 1700
1554.5
1548.8
1546.4
1536.0
(b)
Fig. 2. Output spectra for EDFL wavelengths 1536 to 1554 nm: (a) line plot, (b) color plot.
the frequency region of positive MI gain are given by the two inequalities [30]:
β2 +β4Ω2/12 < 0 (1)∣∣β2 +β4Ω2/12
∣∣Ω2 < 4γP (2)
where Ω is the angular frequency detuning of the sidebands from the pump wave (here theEDFL). The frequency region defined by these inequalities is very narrow for large normaldispersion while it gets significantly wider around the ZDW [30]. This is well reproduced inour experiment, as highlighted by Fig. 3 that shows an enlargement of the relevant part of thespectra of Fig. 2, again both as (a) a line and (b) a color plot. In the color plot of Fig. 3(b)[which is plotted versus the detuning Ω rather than the wavelength], the dashed and solid linescorrespond to the boundaries of the theoretical MI gain region defined by the two inequalities,Eqs. (1) and (2), respectively. We can see that theoretical and experimental results agree well,and that the generated sidebands lie within the expected bandwidth. We would like to point outthe structure of the MI gain bands. When the pump is well within the anomalous dispersionregime (λEDFL > 1550 nm) we observe a single wide gain region extending on both sides ofthe pump. However, when the EDFL experiences normal dispersion, the gain structure changessignificantly into two sidebands that are detached from the pump. This behavior results from thecontribution of fourth-order dispersion [31] and it is essential that this contribution is includedin Eqs. (1) and (2).
We now examine the long wavelength side of the spectra shown in Fig. 2. Two Stokes peaksare observed above 1600 nm: one (S1) remains stationary at 1651.5 nm upon tuning of theEDFL, while the wavelength of the other (S2) varies. Figures 4(a) and 4(b) show details of the
Spectralpower[dB]
(a)
1548
1550
1552
(b)
Fig. 3. (a), (b) Enlargement of Figs. 2(a) and (b) around the MI region respectively. In (b),the solid and dashed lines correspond to the boundaries of the MI gain band, i.e. solutionsof Eqs. (1) and (2) respectively. The dotted vertical and horizontal lines indicate the ZDW.
#135435 - $15.00 USD Received 20 Sep 2010; revised 10 Nov 2010; accepted 16 Nov 2010; published 24 Nov 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25836
Spectralpower[dB]
(a)
1620 1650 16801536.0
1546.4
1548.8
1554.5
(b)
Fig. 4. Enlargement of Fig. 2 around the two Stokes waves, S1 (fixed) and S2 (variable).(a) Line plot, (b) color plot. In (b), the theoretical wavelength of S2 calculated from energyconservation considerations (2ωEDFL = ωRFL +ωS2 ) is superimposed as a black line.
relevant part of the spectra both as line and color plots. In Fig. 4(b), we have also superim-posed as a black line the idler wavelength calculated from the energy conservation condition ofa degenerate FWM process involving the EDFL and the RFL respectively acting as pump andsignal, ωS2 = 2ωEDFL −ωRFL. As it perfectly overlaps with the observed peak S2 for all EDFLwavelengths, we can safely assume that this is the likely origin of S2. It must be clear howeverthat this process cannot be phase-matched for all EDFL wavelengths (it is only phase-matchedwhen S2 matches S1). In the general case, we therefore interpret it as resulting from a com-bination of non-phase-matched parametric FWM and SRS, i.e., Raman-assisted FWM [23].The SRS gain from the EDFL pump overcomes the strict limitations imposed by the phase-matching condition and we observe the generated Stokes wave even with a relatively largephase-mismatch.
As regards the fixed peak S1, as it does not vary with the EDFL wavelength, it is clear thatthe EDFL is not involved in its generation. Presuming a would-be degenerate FWM process in-volving S1 and the RFL laser yields a pump wavelength at ωp = (ωS1 +ωRFL)/2 = 1547.0 nm.This wavelength generally lies within the low spectral power ASE pedestal generated by theEDFA. A phase-matching analysis using the fiber parameters given above yields a phase-matched wavelength of 1651 nm very close to the experimentally observed position of S1 at1651.5 nm (the discrepancy is probably due to uncertainties in the dispersion values). S1 thusresults from phase-matched narrow-band degenerate FWM with an incoherent pump seededby the RFL laser, i.e., induced MI. Note we have also considered the possibility of a non-degenerate FWM process with the RFL and a ASE slice acting as pump waves coupled with alower order emission line of the RFL around 1.3 μm acting as a seed. However this process isassociated with a very large phase-mismatch and thus is highly unlikely. The simultaneous gen-eration of the two waves S1 and S2 is rather remarkable. It demonstrates the co-existence of aphase-matched and a non-phase-matched FWM process sharing the same RFL seed and mixedcoherent-incoherent pump. The two waves only merge when the EDFL wavelength matcheswith the 1547.0 nm ASE slice involved in the generation of S1, as seen in the center of Fig. 4.It should be noted that the phase-matched process generating wave S1 seems less effective thanthe process generating S2. This can be attributed to the relatively low spectral power of the ASEslice at 1547.0 nm [PEDFL −PASE(λ = 1547.0 nm) > 20 dB]. Furthermore the two gaps withno power in S1 seen in figure 4 are due to the spectral power of the ASE slice at 1547.0 nmdropping further when the EDFL wavlength is close [PEDFL −PASE(λ = 1547.0 nm)> 40 dB].In this case the spectral power in the ASE slice is not sufficient for significant conversion oflight to wave S1.
We have investigated further the mechanism leading to the generation of S1 by conducting an
#135435 - $15.00 USD Received 20 Sep 2010; revised 10 Nov 2010; accepted 16 Nov 2010; published 24 Nov 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25837
1400 1450 1500 1550 1600 1650 1700 [nm]
¡ 60
¡ 50
¡ 40
¡ 30
¡ 20
¡ 10
0
P [d
Bm
]
(b)
1400 1450 1500 1550 1600 1650 1700 [nm]
¡ 60
¡ 50
¡ 40
¡ 30
¡ 20
¡ 10
0
P [d
Bm
]
(a)
λ λ
Fig. 5. (a) Output spectra demonstrating FWM between the RFL and the ASE pump fora constant RFL power of 1 W and ASE powers of 28 dBm (solid) and 33 dBm (dotted).(b) Output spectra for constant ASE pump power of 30 dBm and RFL power of 100 mW(solid) and 900 mW (dotted).
additional experiment in which the EDFL was switched off. In this way, we studied the FWMinteractions between the RFL and the ASE noise of the EDFA without the influence of thecoherent EDFL signal. Figure 5(a) depicts output spectra for two different ASE power levels.Notice the efficiency with which the 1651.5 nm Stokes wave is generated. For the highest ASEpower we considered (33 dBm), the power of the generated Stokes is significantly higher thanthe residual power of the RFL, the latter one appearing severely depleted. The level of depletionof the RFL at the fiber end actually increases with increasing ASE input power. This behavior ispartly due to SRS which induces an asymmetry between the Stokes and anti-Stokes sides of theASE pump by causing a net-energy transfer from lower to higher wavelengths [23]. In termsof efficiency, we must stress that we have also performed an experiment with a constant ASEpower of 30 dBm while varying the power of the RFL. The Stokes wave was still generatedquite efficiently (−20 dB with respect to the RFL output) with only 50 mW from the RFL.
3. Conclusion
In conclusion we have demonstrated that multiple independent FWM processes can co-exist in-side optical fibers. In particular, we have revealed a competition between phase-matched FWMwith an incoherent pump and non-phase-matched FWM with a coherent pump. Additionally,we examined induced MI with an incoherent pump which surprisingly leads to a quite highconversion efficiency. Clearly, FWM with incoherent pumps leads to surprising new featuresand deserves more investigation.
Acknowledgments
Thibaut Sylvestre thanks the programme de cooperation territoriale europeen france-suisse IN-TERREG IV and the Conseil Regional de Franche-Comte for financial support. The work ofStephane Coen is supported by a New Economy Research Fund (NERF) grant from The Foun-dation for Research, Science and Technology of the New Zealand government.
#135435 - $15.00 USD Received 20 Sep 2010; revised 10 Nov 2010; accepted 16 Nov 2010; published 24 Nov 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25838
