## Abstract

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

## 1. Introduction

All-optical wavelength conversion will be necessary in high-speed optical networks to provide all-optical routing [1], prevent blocking [2] and provide fast recovery from fiber cable damage [3]. 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 [4]. PWCs with large conversion bandwidths have been demonstrated [5]. PWCs can potentially be polarisation independent [6] and have low noise-figures [7].

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 *λ*_{s} and to a new converted wave at
*λ*_{c} =1/(2/*λ*_{p} -1/*λ*_{s} ). 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*. [8]. 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 [10]. 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 [10] are consistent with those for high bandwidth in fixed-pump OPAs [11]. 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 [10] 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 *λ*_{s} to a single converted wavelength
*λ*_{c} is represented by a point on a plot of *λ*_{c} vs
*λ*_{s} . 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 *λ*_{c} vs *λ*_{s} 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.

## 2. Methods

Our experimental setup (Fig. 1) is similar to that of [5], 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
LiNbO_{3} 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) [12]. 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 *µ*W) 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^{-1}km^{-1}, *β*
_{3}=0.12 ps^{3}km^{-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 *λ*_{c} as:
*η*_{c} =${P}_{c}^{\text{pump}\phantom{\rule{.3em}{0ex}}\text{on}}$/${P}_{s}^{\text{pump}\phantom{\rule{.3em}{0ex}}\text{off}}$, where ${P}_{c}^{\text{pump}\phantom{\rule{.3em}{0ex}}\text{on}}$ is the power in *λ*_{c} , 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 *λ*_{c} .
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 ${P}_{s}^{\text{pump}\phantom{\rule{.3em}{0ex}}\text{off}}$. This was repeated for each signal wavelength. A similar procedure was used
to determine ${P}_{c}^{\text{pump}\phantom{\rule{.3em}{0ex}}\text{on}}$ for the converted wavelengths *λ*_{c}
, but with the pump turned on and the Gaussian centered at the appropriate wavelength.

## 3. Results

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
*λ*_{c} .

Each frame in Fig. 2(a) shows an OSA spectrum for different signal wavelengths but with a fixed *λ*_{p} 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 *λ*_{c} , The generation and growth of the cascaded signal *λ*_{cts}
=1/(2/*λ*_{s} -1/*λ*_{p} ) and cascaded idler *λ*_{cti}
=1/(2/*λ*_{c} -1/*λ*_{p} ) are not discussed here.

Figure 2(b) shows conversion efficiency *η*_{c} (black circles) as a function of signal wavelength
*λ*_{s} , 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 [13]. The theoretical maximum conversion efficiency in Fig. 2(b) of
${\eta}_{c}^{\text{max}}$
=sinh^{2}( _{γ}*P*_{p}*L*) occurs at

where *K*=1, *P*_{p} 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 *λ*_{p} , and that these gain peaks only exist in the anomalous dispersion regime, *i.e*. where
*β*
_{3}(*ω*
_{0}-*ω*_{p} ) >0.

Previously [10] we argued that the wavelength range of operation of a PWC excludes the set of wavelength pairs
*λ*_{s,c} for which *η*_{c} <${\eta}_{c}^{\text{min}}$
=( _{γ}*P*_{p}*L*)^{2}. We return to the choice of this level below. The boundary of this region was
shown in [10] to be given by Eq. (1), with *K*=4. The theoretical curve (solid black
lines) in Fig. 3(a) is for *P*_{p} =760 mW, and corresponds well to the experimental result (blue line) for
this power. Eq. (1) predicts a ${P}_{p}^{1/2}$
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 *λ*_{p} >*λ*
_{0}, that is, the anomalous dispersion regime for the fiber, which has a positive *β*
_{3}. This is consistent with Eq. (1).

Each *η*_{c} =${\eta}_{c}^{\text{min}}$
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 *λ*_{s} within a range, to a *λ*_{c} within this range, is the side
length of the largest square that can fit inside this *η*_{c} =${\eta}_{c}^{\text{min}}$
contour [10]. The side length of this square was shown to be

We observed conversion bandwidths varying from 8.2 nm to 12.3 nm for *P*_{p} =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*=${\eta}_{c}^{\text{max}}$
/${\eta}_{c}^{\text{min}}$
. An ideal wavelength converter has an *R*=1. Recall now our choice of ${\eta}_{c}^{\text{min}}$
=( _{γ}*P*_{p}*L*)^{2}, which occurs at *λ*_{s}
=*λ*_{p} on the conversion spectrum shown in Fig. 2(b). Had we chosen an ${\eta}_{c}^{\text{min}}$
> ( _{γ}*P*_{p}*L*)^{2} the conversion square would not be continuous about the line
*λ*_{c} =*λ*_{s} , which at least halves the available conversion bandwidth. Figure 2(b) also shows that the conversion bandwidth increases only slowly for ${\eta}_{c}^{\text{min}}$
< ( _{γ}*P*_{p}*L*)^{2}, while the increase in *R* is still proportional to the
decrease in ${\eta}_{c}^{\text{min}}$
. Hence we choose ${\eta}_{c}^{\text{min}}$
=( _{γ}*P*_{p}*L*)^{2} and find the ripple to be [10]

which increases superlinearly with _{γ}*P*_{p}*L*. We cannot directly measure ${\eta}_{c}^{\text{min}}$
because of the strong pump at *λ*_{s} =*λ*_{p} . Instead, we infer ${\eta}_{c}^{\text{min}}$
from measuring the pump power and using ${\eta}_{c}^{\text{min}}$
=( _{γ}*P*_{p}*L*)^{2}. This estimate is valid for experiments described here. For example in Fig. 2(b), the theoretical ${\eta}_{c}^{\text{min}}$
=14.0 dB agrees well with the experimental *η*_{c} of about 15 dB at *λ*_{s} 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 ${\eta}_{c}^{\mathit{\text{max}}}$ 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
${\eta}_{c}^{\mathit{\text{max}}}$ =sinh^{2}(
_{γ}*P*_{p}*L*) for maximum conversion efficiency and *R*=${\eta}_{c}^{\text{max}}$
/${\eta}_{c}^{\text{min}}$
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 [10], 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 *λ*_{p} =*λ*_{c}
=*λ*_{s} 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 *λ*_{s} =*λ*_{c} , the channel for which no conversion is required.

In conclusion, we have verified the systematic design procedure proposed in [10] 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.

## References and links

**1. **T. Yamamoto, T. Imai, Y. Miyajima, and M. Nakazawa, “High speed optical path routing by using four-wave mixing and a wavelength
router with fiber gratings and optical circulators,” Opt. Commun , **120**, 245–248
(1995). [CrossRef]

**2. **N. Antoniades, S. J. B. Yoo, K. Bala, G. Ellinas, and T.
E. Stern, “An architecture for a wavelength-interchanging cross-connect utilizing parametric wavelength converters,”
J. Lightwave Technol. **17**, 1113–1125 (1999). [CrossRef]

**3. **G. Conte, M. Listanti, M. Settembre, and R. Sabella, “Strategy for protection and restoration of optical paths in WDM
backbone networks for next generation Internet infrastructures,” J. Lightwave Technol. **20**, 1264–1276 (2002). [CrossRef]

**4. **N. Chi, L. Xu, L. Christiansen, K. Yvind, J. Zhang, P. Holm-Nielsen, C. Peucheret, C. Zhang, and P. Jeppesen, “Optical label swapping and packet transmission based on ASK/DPSK orthogonal
modulation format in IP-over-WDM networks,” in *Proceedings of the Optical Fiber Communications Conference*, vol. Vol. 86 of OSA Proceedings Series, pp. 792–794 (Optical Society of America, Washington
D.C., 2003).

**5. **M. Westlund, J. Hansryd, P. A. Andrekson, and S. N. Knudsen, “Transparent wavelength conversion in fibre with 24nm pump
tuning range,” Electron. Lett. **38**, 85–86 (2002). [CrossRef]

**6. **K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization-independent one-pump fiber-optical parametric
amplifier,” IEEE Photon. Technol. Lett. **14**, 1506–1508 (2002). [CrossRef]

**7. **J. L. Blows and S. E. French, “Low-noise-figure optical parametric amplifier with a continuous-wave frequency
modulated pump,” Opt. Lett. **27**, 491–493 (2002). [CrossRef]

**8. **L. Provino, A. Mussot, E. Lantz, T. Sylvestre, and H. Maillotte,
“Broadband and flat parametric amplifiers with a multisection dispersion-tailored nonlinear fiber arrangement,” J. Opt. Soc. Am. B **20**, 1532–1537 (2003). [CrossRef]

**9. **E. A. Swanson and J. D. Moores, “A fiber frequency shifter with broadband, high conversion efficiency, pump and
pump ASE cancellation and rapid tunability for WDM optical networks,” IEEE Photon. Technol. Lett. **6**, 1341–1343 (1994). [CrossRef]

**10. **R. W. McKerracher, J. L. Blows, and C. M. de Sterke,
“Wavelength conversion bandwidth in fiber based optical parametric amplifiers,” Opt. Express **11**, 1002–1007 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-9-1002. [CrossRef] [PubMed]

**11. **M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric
amplifiers,” Opt. Lett. **21**, 573–575 (1996). [CrossRef] [PubMed]

**12. **S. K. Korotky, P. B. Hansen, L. Eskildsen, and J. J. Veselka, “Efficient phase modulation scheme for supression of
stimulated Brillouin scattering,” IOOC 1995 **WD2-1**, 109–111 (1995).

**13. **G. P. Agrawal, *Nonlinear Fiber
Optics*, 2nd ed. (Academic Press, 1995).

**14. **R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical
fibers,” IEEE J. Quantum Electron. **QE-18**, 1062–1072 (1982). [CrossRef]