We have developed a depolarization technique to achieve polarization-insensitive wavelength conversion using four-wave mixing in an optical fiber. A maximum conversion efficiency of -11.79 dB was achieved over a 3 dB bandwidth of 26 nm in a 100-m-long dispersion-flattened photonic crystal fiber. The polarization-dependent conversion efficiency was less than 0.38 dB and the measured power penalty for a 10 Gbit/s NRZ signal was 1.9 dB. The relation between the conversion efficiency and the degree of polarization of the pump was also formulated.
©2005 Optical Society of America
Wavelength conversion plays an important role in all-optical wavelength-division-multiplexed (WDM) networks. Among the different conversion approaches, four wave mixing (FWM) is attractive for being transparent to bit rate and modulation format. Two common device media for FWM are the semiconductor optical amplifier (SOA) and the optical fiber. The latter is attractive for its low noise performance that leads to a smaller power penalty.
Photonic crystal fiber (PCF) technology has advanced significantly in recent years and the production of high quality PCF with low loss and high nonlinearity has become available. J. H. Lee et al. demonstrated wavelength conversion in a 15-m-long polarization maintaining PCF and obtained a maximum conversion efficiency of -16 dB over a 3 dB bandwidth of ~10 nm . With a special design, a very small dispersion slope of 1×10-3 ps/(km.nm2) has recently been realized in a PCF . The PCF also has a small dispersion coefficient and a large nonlinear coefficient. The combined features of small dispersion, low dispersion slope, and large nonlinearity are favorable for wide band and highly efficient wavelength conversion using four-wave mixing . However, the large fiber nonlinearity is achieved at the expense of a small mode field diameter. The pump power density will be very high, resulting in significant stimulated Brillouin scattering (SBS), which thus drain most of the pump power to the backward-propagating Stokes light.
In this work, we demonstrated wide-band polarization-insensitive wavelength conversion using a highly nonlinear dispersion-flattened PCF. Two phase modulators were adopted to increase the spectral width of the pump, hence increasing the threshold of the SBS process by about 10 dB. A depolarization technique was also applied to eliminate the polarization sensitivity using an optical delay line and a polarization beam combiner. A 100-m-long dispersion-flattened PCF was used in the experiment for wavelength conversion of 10 Gbit/s pseudorandom non-return-to-zero (NRZ) data. A maximum conversion efficiency of -11.79 dB has been achieved with a 3 dB bandwidth over 26 nm. The polarization-dependent conversion efficiency was 0.38 dB.
2. Principle and theory
The efficiency of FWM is intrinsically dependent on the polarization states of the input fields , . To eliminate the polarization sensitivity, polarization diversity technique can be adopted in the process . However, since the optical components that are used to realize polarization diversity will inevitably introduce insertion loss to the pump, the input signal, and the converted output, the conversion efficiency will decrease accordingly. Also, the settings of the three polarization controllers in the setup are inter-related and it is difficult to adjust all of them to the optimized settings simultaneously. An alternative approach is to simplify the adjustment using a birefringence fiber as the nonlinear medium for FWM.
Instead of using polarization diversity, we present an alternative scheme to achieve polarization insensitivity by the use of depolarization technique. As shown in Fig. 1, the pump beam was divided into two branches by a 3 dB optical coupler. An optical delay line (ODL) with a length larger than the coherence length of the pump was inserted into one of the arms between the coupler and the polarization controller (PC). A single mode fiber was used here to serve as the ODL. After the two PCs, the two optical branches were combined together again by a polarization beam combiner (PBC).
By adjusting the two PCs, the amplitudes of the two orthogonally linear-polarized p- and s-waves can be set nearly the same. If the length of the ODL also satisfies the condition that it is much larger than the coherence length of the pump, depolarization can be effectively achieved . The corresponding reference length in fiber is given by
where Lcoh, λ, Δλ, and n are the coherence length, the wavelength, the pump linewidth, and the fiber refractive index, respectively. In our experiment, the frequency linewidth was about 10 MHz and the ODL was 100 meter. Hence, the ODL was an order of magnitude longer than L in Eq. (1). The lowest degree of polarization (DOP) obtained in our experiment was 2.3%.
Since we consider the case that the change in the polarization state is independent of the wavelength, the relationship of the polarization states between the pump and the signal is maintained along the fiber. The FWM interaction can then be described by 
Here, ÊP, ÊS and ÊFWM are vectors representing the fields of the pump, the signal, and the FWM output, respectively; κ is a proportional constant related to the FWM efficiency, and [·] denotes the inner product of two vectors. The pump is now composed of two components that are orthogonal and non-coherent with each other, and can be expressed by
Here, E P1 and E P2 are complex amplitudes; ê1 and ê2 are unit vectors representing the polarization states of the two orthogonal pump components, respectively. Vectors ê1 and ê2 satisfy the following relations:
The signal field can be expressed as
E S1 and E S2 are the complex amplitudes of the signal along the ê1 and ê2 axes respectively. Their relative magnitudes determine the polarization state of the signal. Substituting (4) and (6) into (3) and use (5a) and (5b), we obtain the converted signal field as:
The symbol 〈 〉 represents an average over the time period T of the light fields. P P1, P P2, P S1, and P S2 are the pump and signal powers along the ê1 and ê2 axes, respectively; PS is the total signal power; θ is a phase angle relating the values of P S1 and P S2 to PS. The power of the converted signal can then be obtained as:
Here ϕ denotes the phase angle of E P1 E P2*E S1*E S2. Owing to the incoherence between E P1 and E P2, ϕ is a random value and hence 〈cos(ϕ)〉=0. Thus,
For the pump light, assuming P P1≥P P2, the degree of polarization can be expressed as:
After substituting (11) into (10), we obtain
where PP=P P1+P P2 is the total pump power. By considering the maximum and the minimum values of PFWM, we obtain the following relation between the polarization-dependent conversion efficiency and the DOP:
Since the depolarizer is placed in front of a saturated EDFA, the loss that is introduced in the setup can be compensated by the amplifier gain. In comparison, in the polarization diversity technique, the associated optical components have to be placed after the EDFA, hence resulting in additional loss and lower conversion efficiency. Furthermore, with the depolarization technique, a double-pass configuration can be used to increase the conversion efficiency of FWM by means of an optical circulator and a fiber reflector.
The schematic of our experimental setup is shown in Fig. 2. The pump and the signal were each obtained from a tunable cw external cavity laser operating within the range of 1510 to 1605 nm. The pump was modulated by 2 cascaded LiNbO3 phase modulators driven respectively at 0.7 and 2.3 GHz. The increased linewidth enhances the SBS threshold by around 10 dB . After passing through the depolarizer, the pump was amplified by a tunable Er–Yb doped fiber amplifier (EDFA1). The maximum saturated power of the amplifier is 2W. The signal was modulated with a 231-1 pseudo-random bit sequence (PRBS) at a data rate of 10 Gbit/s using a Mach-Zehnder interferometer (MZI) modulator. It was then boosted to 23 dBm using another fiber amplifier (EDFA2).
Two optical tunable band pass filters (TBF1 and TBF2) with a 3 dB bandwidth of 1 nm were used to remove the amplified spontaneous emission noise from the fiber amplifiers. A 90/10 optical coupler is then used to combine 90% of the pump and 10% of the signal into the 100-m-long PCF. The converted signal was extracted using a tunable filter (TBF3) that blocks the residue pump and signal from the output.
The PCF has a small dispersion coefficient of -1.3 ps/(km nm) at 1550 nm and a very small dispersion slope of 1×10-3 ps/(km nm2) within the operating wavelength range from 1500 to 1600nm. Its nonlinear coefficient is about 11 (W km) -1 and the attenuation is less than 10 dB/km over the C-band.
As the PCF has a very small mode field diameter of about 2.5 um, SBS is ready to occur. Fig. 3 plots the reflected pump power versus the launched pump power into the PCF before and after the introduction of linewidth enhancement using phase modulators. The SBS threshold was increased from around 20.0 to over 29.6 dBm, indicating that SBS has been effectively suppressed.
For the wavelength conversion, the input signal power was 10 dBm and its wavelength was fixed at 1550 nm. The pump power was about 29.6 dBm. Fig. 4 (a) shows the conversion efficiency, defined as the ratio of the power at the converted wavelength to the input signal power, versus the converted wavelength. A maximum conversion efficiency of -11.79 dB was achieved over a 3 dB bandwidth of 26 nm. The conversion range is limited by the EDFA gain bandwidth. We observed two small peaks located at 1522 and 1578 nm, which are at +/- 28 nm away from the signal wavelength. A possible explanation of the peaks is the occurrence of dispersion ripples at the wavelengths but the phenomenon is still under investigation.
Another experiment was carried out in which the pump was fixed at 1550 nm while the signal wavelength was detuned over the C-band. The dependence of the conversion efficiency versus the converted wavelength is shown in Fig. 4(b). Again, small peaks are also observed on both sides of the spectrum. The two first order peaks are located at +/- 14 nm away from pump wavelength, i.e., +/-28 nm from the signal wavelength. These two peaks correspond to the peaks observed in Fig. 4(a). A second order peak also appears in Fig.5 at 1569.24 nm.
To investigate the dependence of the conversion efficiency on the polarization state of the input signal, we measured the efficiency as the input polarization was varied. An Agilent 11896A variable polarization controller was used in place of PC3 in the setup. Fig.5 plots the relative variation of the efficiency at different input polarization angles. The pump and the signal wavelengths were set at 1555.4 and 1549.92 nm, respectively. The converted signal was at 1560.96 nm. The maximum variation of the conversion efficiency was 0.38 dB when the polarization angle was rotated through 180°. The value is larger than the theoretical value of 0.20 dB that can be deduced from Eq. (13). The difference is partly attributed to the polarization-dependent gain (about 0.2 dB) of EDFA1 and the polarization-dependent loss (about 0.2 dB) of TBF1 and the 90:10 optical coupler.
To analyze the system performance of the PCF-based FWM wavelength converter, we have performed a bit-error-rate (BER) measurement. The signal wavelength was set at 1550 nm and the converted output was obtained at 1560.96 nm. Fig. 6 shows the measured BER versus the received optical power using 10 Gb/s NRZ data signal. A pin photo-receiver was used in the experiment. Error-free (BER<10-9) wavelength conversion was obtained with a power penalty of 1.9 dB. The eye diagrams of the input signal and the converted output were also shown in the inset. A small amount of timing jitter and intensity noise was observed and was associated with the power penalty. We believed that the noise originated from amplitude modulation of the phase modulators as well as from EDFA1. There should be no modulation-instability-induced intensity noise in our setup since the PCF has a normal dispersion.
A depolarization technique was successfully applied to realize polarization-insensitive wavelength conversion based on FWM effect. The relation between the DOP of the pump and the polarization-dependent conversion efficiency was derived. With the large nonlinearity, low dispersion, and ultra-small dispersion slope of the dispersion-flattened PCF, we demonstrated a short-length fiber wavelength converter with a maximum conversion efficiency of -11.79 dB and a 3 dB bandwidth of over 26 nm. Two cascaded phase modulators have been used to increase the SBS threshold from 20 to over 29.6 dBm. By use of the depolarization technique, we obtained a DOP as low as 2.3% for the pump and the corresponding polarization-dependent conversion efficiency is 0.38 dB. Error-free wavelength conversion of 10Gbit/s NRZ signal was achieved with a 1.9 dB power penalty.
The authors wish to thank Crystal Fiber A/S for providing the dispersion-flattened PCF. Thanks are also given to Dr. T. K. Liang for assistance with the experiment, W. W. Tang for fruitful discussion, and M. P. Fok for encouragement.
The work described in this paper is supported by a grant from the Research Grants Council of Hong Kong (CUHK 4196/03E).
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