We report polarization independent wavelength conversion based on one-pump fiber optical parametric amplifiers. A spectrum-sliced amplified spontaneous emission (ASE) light source is used to provide a non-polarized pump. The signal is coherent lights coming from a tunable laser. When adjusting the polarization of the signal using a polarization controller, the variation of wavelength conversion efficiency is less than 0.2 dB. We use the vector theory of four-wave mixing to analyze the polarization independent nature of wavelength conversion by using randomly polarized pumps.
© 2008 Optical Society of America
Wavelength conversion plays an important role in wavelength division multiplexed (WDM) optical networks. In recent years, all-optical wavelength converters have attracted a great deal of interest for their potential extensive applications in the next generation of all-optical networks. There are many methods to achieve all-optical wavelength conversion, such as cross-gain modulation , cross-phase modulation  and four-wave mixing . Plenty of media can be used, for example, fibers, semiconductor optical amplifiers , and waveguides . Fiber optical parametric amplifier (FOPA), based on highly efficient four-wave mixing (FWM) in fibers, is one of the promising technologies to achieve wavelength conversion. It offers many advantages, for instance, nearly instantaneous response, transparently connecting with the optical transmission system, bit rate and modulation format transparency, low noise and so on. .
Unfortunately, the wavelength conversion efficiency is related to the state of polarization (SOP) of the input signal. In conventional FOPAs, coherent and linear-polarized laser sources are used as pumps. Conversion efficiency reaches the maximum when the SOP of the signal is the same linear polarization as that of the pump (for two-pump FOPA, the SOPs of the three waves should be the same linear polarization), while decreases more or less in other situations. This polarization-dependent feature limits the application of this technique. To solve the problem, Wong and co-workers used a polarization-diversity technique for one-pump FOPA  and orthogonal liner polarization configuration for two-pump FOPA . Lin and colleagues found that any pairs of orthogonal polarized pumps can provide polarization independent conversion in the absence of self- and cross-phase modulations . But there are also some drawbacks in the above schemes. For one thing, the conversion efficiency is less than the maximum value that the conventional co-linear polarized FWM can reach under the same pump power. For another, the SOPs of pumps should be adjusted carefully and maintain stable before injecting the nonlinear fibers, which is not easy. Thirdly, the polarization-independent feature is realized on the assumption that the SOPs of pump lights keep unchanged along the fibers, which may be not true when the fibers are disturbed by temperature and stress, or have random birefringence.
In this paper, we report polarization independent wavelength conversion based on one-pump fiber optical parametric amplifiers. A spectrum-sliced amplified spontaneous emission (ASE) light source is used as the pump. In our former experiment, the ASE light was used as the signal . Here the signal is coherent lights coming from a tunable laser. When adjusting the signal polarization randomly using a polarization controller, the variation of wavelength conversion efficiency is less than 0.2 dB. Furthermore, the conversion efficiency is almost the same as that using a coherent laser pump under the same power.
The experiment setup is shown in Fig. 1. A broadband ASE light source (Opticwave BLS-C ASE Light Source, 3-dB spectrum width is about 40 nm, C-band) was firstly amplified by EDFA1, and then spectrum-spliced by an array wave grating (AWG). The Channel 20 of AWG was picked up as the pump. Its wavelength was 1545.04 nm with 3 dB-bandwidth 0.8 nm. After being amplified by EDFA2, the pump was multiplexed using a 90:10 coupler, and launched into a 1-km-long highly nonlinear fiber (HNLF) with zero-dispersion wavelength around 1543 nm, nonlinear coefficient 10 W-1km-1. The signal was provided by a continuous wave tunable laser. Its SOP can be adjusted by a polarization controller (PC). The wavelength conversion efficiency was measured by an optical spectrum analyzer (OSA).
We fixed the pump power before entering the HNLF at 6.8 dBm and tuned the wavelength of signal. For each signal wavelength, the PC was rolled optionally for a while to change the SOP of signal randomly. The SOP of pump lights was not controlled at all. The powers of the pump, signal, and idler were measured with an optical spectrum analyzer (OSA). The maximal and minimal wavelength conversion efficiency, defined as the idler power divided by the input signal power in logarithmic scale, was measured. The results are shown in Fig. 2. Though the SOP of the signal was adjusted randomly, the ripple of the conversion efficiency was less than 0.2 dB. The present wavelength converter was thus polarization independent.
Then we fixed the signal wavelength at 1553 nm and tuned the pump power. The conversion efficiency was nearly linear relationship with pump power in logarithmic scale, as is shown in Fig. 3.
In order to compare the conversion efficiency with that using coherent pump, a tunable laser pump was utilized instead of ASE light source in Fig. 1. The pump wavelength and power were tuned to the same value as the incoherent pump used above. When the PC was rolled, the idler power fluctuated quickly. The ripple of wavelength conversion efficiency was more than 8dB, which is apparently polarization dependent. The maximal conversion efficiency was recorded in Fig. 4. For comparison, the average conversion efficiency in the case of ASE pump was also presented, which shows nearly the same as the one with a laser pump. The inset of Fig. 4 shows two typical conversion spectrums, in which the pumps and signals have the same wavelength and power respectively. It can be seen from the inset that the spectrum of ASE pump is a little wider than the laser pump. Therefore, the spectrum of the corresponding converted idler is also wider.
3. Theoretical analysis
In our polarization independent scheme, the signal is polarized lights. The pump coming from the ASE light source is incoherent and non-polarized lights. Generally, the pump wavelength can be considered as the central wavelength in conventional treatment of FWM process. Thus for simplicity, we regard the pump as a single frequency pump with random polarization. The FWM process can be described as follows, which is derived from the vector theory of FWM in Ref. , Eqs. (7) and (8)
Where(Apx,Apy)T, (Asx,Asy)T and (Apx,Apy)T are the Jones vectors for the pump, signal and idler respectively. Here we have made an assumption that the pump power is much higher than the signal and not depleted, also the fibers have no birefringence and loss. For a given signal with fixed SOP, we change the SOP of the pump randomly, covering the whole Poincaré sphere while keeping the pump power constant. The wavelength conversion efficiency is calculated with the average idler power. In our simulations, all the parameters are the same as that in our experiment and the signal wavelength is chosen to be 1550 nm. The conversion efficiencies are calculated for 50 different signal SOPs (randomly selected), as is shown in Fig. 5 (a). The SOPs of the signal are plotted in Fig. 5 (b). For each point in the figure, 2000 different pump SOPs (also randomly selected) are considered. We found the conversion efficiencies fluctuation is within 0.3 dB.
If we put the simulation results both for laser pump and ASE pump together with the corresponding experiment results in Fig. 6, we found the experimental results for the case of ASE pump are 3.5~6 dB higher than those from our simulations. This may attribute to the simplification of the ASE pump as single frequency in the simulations. In Ref. , it has been shown that the FWM efficiency for incoherent co-linear polarized ASE pump is 5~6 dB higher that in the case of co-linear polarized laser pump. For the same reason, the actual experiment results will be a little higher than that in our simplified pump model.
The similar conversion efficiency with a coherent laser pump and an incoherent ASE pump can be understood by the following intuitive picture. FWM efficiency is maximized when the signal is co-polarized with the pump, but becomes negligible when their SOPs become orthogonal to each other. As a result, in a statistically average sense, only half of the non-polarized incoherent pump contributes to the FWM process for a given signal SOP. On the other hand, the FWM process introduced by an incoherent co-polarized pump is dominated by the non-degenerate FWM process (as shown in Ref. ), which has double efficiency compared with the degenerate FWM introduced by a coherent pump.
Though the pump we used is an incoherent light, FWM is a coherent process which occurs nearly instantaneously. As a result, all the temporal fluctuations on the pump wave (amplitude, phase, SOP) would be directly transferred to the idler during FWM process, as partially indicated by its broad spectrum shown in Fig. 4. In this sense, the polarization independent performance observed is only in the statistically average sense. However, for each frequency branch of the ASE pump at every moment, there exist tremendous photons with randomly distributed SOPs. Therefore, in the present scheme the “statistically average” time can be so short that any real detector can distinguish.
A polarization independent wavelength converter based on one-incoherent pump fiber optical parametric amplifier was reported both experimentally and theoretically. We used a spectrum-sliced ASE light source as the pump and a laser light as the signal. When tuning the SOP of the signal but without any control of pump polarization, nearly constant conversion efficiency was observed. The ripple was less than 0.2 dB. For comparison, in a separate experiment, another laser pump was used instead of ASE light with the same wavelength and power. The conversion efficiencies in the two cases are nearly the same. The polarization independent nature of wavelength conversion with randomly polarized pumps was discussed in the vector theory of four-wave mixing.
The work is supported in part by the National Natural Science Foundation of China (NNSCF 60478003) and the “Specialized Research Fund for the Doctoral Program of Higher Education” (SRFDP 20040003064).
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