We present an experimental study of a systematic design procedure for achieving high bandwidth wavelength conversion with low ripple in a fiber parametric device with a single tunable pump. We find good agreement with established theory. Fourth order dispersion and fluctuations in the zero-dispersion wavelength have little effect on final conversion bandwidth. Strategies for ripple reduction and pump filtering in a practical device are proposed.
© 2004 Optical Society of America
All-optical wavelength conversion will be necessary in high-speed optical networks to provide all-optical routing , prevent blocking  and provide fast recovery from fiber cable damage . Fiber optic parametric wavelength converters (PWCs) are based on the ultrafast electronic χ (3) nonlinearity in glass, with a response time much less than 100 fs.
A major advantage of PWCs over other all-optical, fiber-based technologies is that both amplitude and phase information can in principle be preserved, making PWCs useful for all-optical label swapping . PWCs with large conversion bandwidths have been demonstrated . PWCs can potentially be polarisation independent  and have low noise-figures .
In a one pump parametric wavelength converter, a strong pump and a weaker signal are launched into a fiber. Power is transferred from the pump wavelength λ p to the signal wavelength λs and to a new converted wave at λc =1/(2/λp -1/λs ). Therefore a one-pump PWC able to convert a fixed signal wavelength to an arbitrary converted wavelengths requires a tunable pump wavelength. We stress that the requirement of a tunable pump is different from parametric amplifiers used solely for amplification, which can be optimized for gain bandwidth and flatness at a particular λ p, e.g. . Previous investigations into parametric wavelength conversion with a tunable pump and a tunable signal [5, 9] have presented experimental demonstrations without discussing the design of these devices for high-bandwidth, low ripple operation.
The aim of this paper is to verify the systematic design procedure for achieving high bandwidth wavelength conversion with low ripple in a fiber parametric device with a single tunable pump, that was introduced earlier in . We experimentally verify many of the theoretical arguments, including the expression for device bandwidth and ripple. We show experimentally that the design requirements of high fiber nonlinearity, high pump power and low dispersion slope to achieve high bandwidth, tunable-pump PWCs proposed in  are consistent with those for high bandwidth in fixed-pump OPAs . Furthermore, it is shown that the additional requirement for PWCs to have low ripple imposes a restriction on fiber length. We do not seek to demonstrate state-of-the-art parametric wavelength conversion.
In our earlier work  we proposed a systematic procedure for achieving a high bandwidth tunable PWC with low ripple. We established that any wavelength converter that converts from a single signal wavelength λs to a single converted wavelength λc is represented by a point on a plot of λc vs λs . From this we concluded that a wavelength converter that converts from any wavelength within a range to any other wavelength within that same range is defined by a solid square on a plot of λc vs λs and that the bandwidth of such a converter is the side length of this square. We derived an expression for the theoretical bandwidth of a wavelength converter and suggested ways to maximise it, while maintaining low conversion efficiency ripple.
Our experimental setup (Fig. 1) is similar to that of , having both a tunable signal and a tunable pump. The pump was a tunable external cavity laser (ECL1). A pulse generator allowed quasi-CW operation by modulating the laser drive current with rectangular pulses with a width of 460 ns and a period of 4.6 µs. Quasi-CW operation (10%duty cycle)was used for high pump powers because the filters used have a low damage threshold. The pulse generator was not used for pump powers of 650 mW and 760 mW, thus the pump was truly CW for these powers. We found no difference between the CW and quasi-CW results. CW output from ECL1 was coupled into a LiNbO3 phase modulator (PM), which was driven by sinusoidal signals at 70, 245, 860 and 2700 MHz to suppress stimulated Brillouin scattering (SBS) from the dispersion shifted fiber (DSF) . Tunable optical bandpass filters (TOBF 1 and 2), with bandwidths of 1 nm and 3 nm respectively, were used to remove amplified spontaneous emission from each EDFA stage.
The output from a second tunable external cavity laser, ECL2, was used as the signal. (400 µW) was launched into the dispersion-shifted fiber. Adjustment of the polarisation controller in the signal arm ensured the pump and signal wave were co-polarised when launched. The circulator (Circ.) and power meter OPM 1 were used to monitor SBS. The fiber was 1.5 km of Corning DSF with nonlinearity γ=2.2 W-1km-1, β 3=0.12 ps3km-1 and a zero dispersion wavelength λ 0=1549.25 nm. The output of the DSF was attenuated by 28 dB before being coupled into an optical spectrum analyser (OSA).
The phase modulator was not required for quasi-CW operation because the pulse generator produced a current-induced frequency chirp of approximately 800 MHz on the pump laser linewidth. This raised the SBS threshold above the peak powers required for this experiment. The phase modulator was still used for the truly CW pump.
We define the experimental conversion efficiency from a λ s to the converted wavelength λc as: ηc =/, where is the power in λc , recorded at point B in Fig. 1, with the pump turned on.
Implementation of this device as a wavelength converter in a WDM network would have a band-pass filter placed after the fiber to pass only λc . To approximate this, the spectrum at B (Fig. 1) was multiplied by a Gaussian, centered at the nominal signal wavelength, and having a full-width half-maximum of 0.5 nm. The result was integrated to give . This was repeated for each signal wavelength. A similar procedure was used to determine for the converted wavelengths λc , but with the pump turned on and the Gaussian centered at the appropriate wavelength.
An OSA was used to record spectra at B in Fig. 1 for a range of signal wavelengths between 1525 nm and 1575 nm. This procedure was repeated for pump wavelengths between 1548 nm and 1565 nm, all with constant pump power, to cover many combinations of λ s and λc .
Each frame in Fig. 2(a) shows an OSA spectrum for different signal wavelengths but with a fixed λp of 1551 nm. 28 dB has been added to the OSA powers recorded at B to compensate for the attenuation between the dispersion shifted fiber and the OSA. Black plus (+) symbols trace the power at each λc , The generation and growth of the cascaded signal λcts =1/(2/λs -1/λp ) and cascaded idler λcti =1/(2/λc -1/λp ) are not discussed here.
Figure 2(b) shows conversion efficiency ηc (black circles) as a function of signal wavelength λs , for one pump wavelength (1551 nm). The pink cross on Fig. 2(b) indicates the data point that corresponds to the current frame in Fig. 2(a).
In Fig. 2(a), the power in the converted signal wave varies with the input signal wavelength, consistent with the theoretical description of parametric wavelength conversion in . The theoretical maximum conversion efficiency in Fig. 2(b) of =sinh2( γPpL) occurs at
where K=1, Pp is the pump power, γ is the fiber nonlinearity, β 3 is the third-order dispersion parameter of the fiber, at the zero dispersion frequency ω 0 and can be positive or negative. We have assumed that the fourth order dispersion β 4 is negligible. Eq. (1) shows that the peak separation, and therefore the width of the region where conversion occurs, increases with increasing pump power, for all λp , and that these gain peaks only exist in the anomalous dispersion regime, i.e. where β 3(ω 0-ωp ) >0.
Previously  we argued that the wavelength range of operation of a PWC excludes the set of wavelength pairs λs,c for which ηc < =( γPpL)2. We return to the choice of this level below. The boundary of this region was shown in  to be given by Eq. (1), with K=4. The theoretical curve (solid black lines) in Fig. 3(a) is for Pp =760 mW, and corresponds well to the experimental result (blue line) for this power. Eq. (1) predicts a scaling of these curves. The remaining experimental curves have been scaled according to this, such that they should overlap. Indeed they coincide well with each other, and with the theoretical result.
The origin (0,0) of Fig. 3(a) corresponds to the zero-dispersion wavelength λ 0 of the fiber. The dashed line in Fig 3(a) is where signal, converted and pump wavelengths coincide. In Fig. 3(a) the anomalous dispersion region lies above-right of the line that runs from the top left to the bottom right corner of the figure. The region of acceptable gain is located entirely where λp >λ 0, that is, the anomalous dispersion regime for the fiber, which has a positive β 3. This is consistent with Eq. (1).
Each ηc = contour in Fig. 3(a) was recorded across a range of pump wavelengths, at a given pump power. As discussed in Section 1, the conversion bandwidth of a PWC that converts from an arbitrary λs within a range, to a λc within this range, is the side length of the largest square that can fit inside this ηc = contour . The side length of this square was shown to be
We observed conversion bandwidths varying from 8.2 nm to 12.3 nm for Pp =0.52 W and 1.78 W respectively. Figure 3 (b) shows good agreement between theory (dot-dash line) and experiment (triangles) even though no fitting parameters were used.
Ripple is the maximum variation in conversion efficiency within the square and is given by R= / . An ideal wavelength converter has an R=1. Recall now our choice of =( γPpL)2, which occurs at λs =λp on the conversion spectrum shown in Fig. 2(b). Had we chosen an > ( γPpL)2 the conversion square would not be continuous about the line λc =λs , which at least halves the available conversion bandwidth. Figure 2(b) also shows that the conversion bandwidth increases only slowly for < ( γPpL)2, while the increase in R is still proportional to the decrease in . Hence we choose =( γPpL)2 and find the ripple to be 
which increases superlinearly with γPpL. We cannot directly measure because of the strong pump at λs =λp . Instead, we infer from measuring the pump power and using =( γPpL)2. This estimate is valid for experiments described here. For example in Fig. 2(b), the theoretical =14.0 dB agrees well with the experimental ηc of about 15 dB at λs adjacent to the pump wavelength.
Figure 3(b) shows good agreement between theoretical (solid and dashed lines) and experimental (crosses and circles) values for the maximum conversion efficiency and ripple respectively for five pump powers ranging from 520 mW to 1.78 W. No fitting parameters were used. The highest recorded was 33.2 dB, where the ripple was 20 dB, which is too high for a practical device. Below we discuss how to reduce this ripple. Ripples of <5 dB were recorded at maximum conversion efficiencies below 10 dB. The theoretical fits to these data are =sinh2( γPpL) for maximum conversion efficiency and R= / for ripple.
4. Discussion and conclusions
Wavelength converters need a large bandwidth and low ripple, but do not necessarily require large conversion efficiencies. Figure 3(b) shows that both bandwidth and ripple increase with increasing pump power and fiber nonlinearity, and that ripple increases faster than conversion bandwidth, as predicted by Eqs (2) and (3). This result is also consistent with fixed-pump parametric amplifiers [11, 14],
We now have an experimentally verified systematic design procedure for PWCs with a single tunable pump. Given a fiber with a known γ and β 3, we set the bandwidth of the PWC by selecting the pump power according to Eq. (2). The maximum ripple for the device can then be set by choosing the device length, according to Eq. (3). While reducing the fiber length to control ripple does decrease the overall conversion efficiency of our device, we note that high conversion efficiencies are not an essential requirement of broadband wavelength converters.
Because Eq. (2), used to generate the theory curve in Fig. 3(b), ignores β 4 and fluctuations in λ 0, the good agreement between the theoretical and experimental bandwidths in Fig. 3(b) suggests that the bandwidths of our one-pump parametric wavelength converters are unaffected by λ 0 fluctuations and β 4. However, consistent with , we expect β 4 will play a role for larger excursions of λ p away from λ 0 and for larger conversion bandwidths.
The unusable range within ±1.5 nm of the line λp =λc =λs in Fig. 3(b) corresponds to the 3 nm bandwidth of the tunable filter. This range could be reduced to less than a 100 GHz channel by replacing our filters with, e.g. 0.5 nm-wide compression-tuned gratings. The unusable range is then only a single channel surrounding λs =λc , the channel for which no conversion is required.
In conclusion, we have verified the systematic design procedure proposed in  for achieving high bandwidth wavelength conversion with low ripple in parametric wavelength converters. We also proposed strategies for managing ripple and for circumventing the “unusable” band generated by filtering the strong pump.
This work was produced with the assistance of the Australian Research Council (ARC) under the ARC Centres of Excellence program. CUDOS (the Centre for Ultrahigh-bandwidthDevices for Optical Systems) is an ARC Centre of Excellence.
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