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We experimentally study four-wave mixing in highly nonlinear fibers using two independent and partially coherent laser pumps and a third coherent signal. We focus our attention on the Bragg-scattering frequency conversion. The two pumps were obtained by amplifying two Intracavity frequency-shifted feedback lasers working in a continuous wave regime.

Over the last decades, the nonlinear phenomena of parametric four-wave mixing (FWM) have been intensively studied in view of their great potential to provide a large variety of all-optical functionalities for ultrafast signal processing [

The adoption of incoherent pumps may represent a cost-effective solution to study FWM in different scenarios and may open a novel kind of applications, even if this may take place at the expense of low conversion efficiency and spectral broadening of the converted signal. The interplay between four-wave mixing processes with mixed coherent-incoherent pumps may also open entirely new features as reported very recently in [

In this paper, we study the case of BS-FWM with partially coherent pumps in HNLF. For this purpose we used two broadband intra-cavity frequency-shifted feedback lasers (IFSFLs) that operated in the continuous wave (CW) regime. Although these pumps are independent and exhibit low coherence time, we experimentally observed a clear signature of frequency conversion. In addition, we discuss the competition between BS-FWM and other types of FWM simultaneously occurring in HNLFs. In particular, we experimentally demonstrate the competition with degenerate (i.e., single pump) FWM.

In the case of a parametric frequency conversion, the coherence time of the pump

To study the case of BS-FWM frequency conversion in such a different regime we propose the experimental setup presented in Figure

Experimental setup; IFSFL: intra-cavity frequency-shifted feedback laser, BPF: bandpass filter, EDFA: erbium-doped fiber amplifier, ISO: isolator, ECL: extended cavity tunable laser, HNLF: highly non-linear fiber, OSA: optical spectrum analyzer, and OSC: oscilloscope.

The coherence properties of IFSFLs have been widely investigated and exploited in metrology and in astronomical imaging [

The spectrum at the output end of the fiber was analyzed by an optical spectrum analyzer (OSA) and by a 1 GHz photodiode connected either to an oscilloscope (OSC) or to a radio frequency (RF) analyzer. In what follows we will refer to a set of measurements in which the average powers of pump 1, 2, and signal at the input end of HNLF were 43 mW, 62 mW, and 0.12 mW, respectively.

The two central elements of our experimental setup are the fiber IFSFLs. We present their synoptic scheme in Figure

Setup of each IFSFL; MUX: multiplexer, PM: polarization maintaining, and AOFS: acousto-optic frequency shifter.

The free-space optics section reported in Figure

(a) Experimental RF spectrum for IFSFL 1 with a preamplified RF analyzer: the frequency comb free spectral range is of 3.6 MHz; (b) numerical simulation of RF photodiode current (spectrum of equation (3) of [

We observe the presence of a comb of frequencies regularly spaced by 3.6 MHz, which compares well with the reciprocal of the round trip time of the fiber cavity. We compare these results with the direct numerical calculation coming from a model described in [

The dynamical evolution of the IFSFLs is also a key point for applications in nonlinear optics. Indeed we observed as many other authors that our IFSFLs may operate in a CW or in a pulsed regime (see, e.g., [

Four-wave mixing is usually characterized as 3 distinct processes depending on the relative positions of the pumps, signal, and idler frequencies (see Figure

(a) Four-wave mixing processes, from [

For BS-FWM energy and momentum conservation give for angular frequencies

The dependence of wave vectors on angular frequency leads to the determination of the best conditions for frequency conversion. In close proximity to the ZDW, the dispersion coefficient of an HNLF is generally approximated by a linear function of wavelength. Under this approximation, if one fixes for instance the wavelength of the pump 1, one can build a chart of optimization for the remaining wavelengths combining (^{2}). The horizontal axis represents a common reference wavelength: its corresponding angular frequency is the mean value between the frequency of the idler and that of pump 2. One can start to choose a value for the wavelength for pump 2 by covering the corresponding thick dashed curve: the wavelength for pump 2 will be the vertical coordinate of the selected point. Then from the chart one can automatically predict the best signal wavelength and hence the position of the corresponding idler. One should draw first a vertical line that matches the selected choice of pump 2. The wavelengths for signal and idler will be read at the intersection points with the other curves. More specifically the signal will be read at the intersection with the thin solid line while the idler will come from the intersection with the thin dashed curve. In practice, it is likely that the ZDW may fluctuate by about 1 nm along the fiber length, according to the analysis presented in [

Let us first focus on the spectral region between 1520 nm and 1535 nm, where the BS-FWM appears whenever the signal is varied between 1547.3 nm and 1554.3 nm. The collection of these experimental results is shown in Figure

(a) Collection of experimental spectra upon different input signal wavelengths; (b) BS-FWM idler wavelength upon signal wavelength; dots: experimental results; solid line: equation (

Therefore if we keep fixed the spectral position of pumps and we gradually reduce the angular frequency

As we show in Figure

(a) experimental output spectrum obtained for the signal wavelength at 1550.3 nm: maximal conversion of BS-FWM; phase-matching conditions for BS-FWM. (b) experimental output with two pumps only.

Note that in our experiment we can shift the signal within the relatively wide spectral range and still obtain efficient BS-idler generation (see Figure

Let us now report on the case of the two external sidebands (see

Experimental output spectrum obtained for signal wavelength at 1547.3 nm (a) and 1556.3 nm (b); existence of multiple simultaneous FWM processes.

In this paper, we studied BS-FWM in HNLF with a novel cost-effective and partially coherent pumping scheme. We experimentally demonstrated efficient and tunable BS-FWM despite the large bandwidth of the pumps and their complete statistical independence. The spectral peak of the converted BS-FWM is 20 dB below that of the original signal and 16 dB above the background noise level. We noted coexistence of multiple independent FWM processes. In particular, we observed a relevant competition BS-FWM and MI-FWM. Our measurements agree well with a theoretical analysis based on the phase-matching diagram for the case of monochromatic waves. In conclusion, nonlinear fiber optics frequency converters based on broadband pumps appear to be promising for their implementation in all-optical signal processing devices.

The authors acknowledge the financial support from the Region Limousin and from the French National Research Agency under Grant ANR-08-JCJC-0122 PARADHOQS. They thank Alain Dexet for his assistance in manufacturing some of the mechanical parts used in the experiment.

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