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Abstract
All-optical wavelength conversion technology based on four-wave mixing (FWM) effect is a promising development need of the modern high-speed optical signal processing system. In this work, we report on the polarization insensitive four-wave mixing based on graphene for all optical wavelength conversion. To overcome the polarization sensitivity of FWM, a dual-pump configuration was proposed based on the combination of graphene and the optical fibers. Our experimental results illustrate that by using the dual pump configuration, the FWM-based wavelength conversion efficiency, can be enhanced by graphene with about 8 dB when the state of polarization of the two pumps are parallel. This proposed all-optical wavelength converter based on graphene may provide a new approach for the next generation optical communications and signal processing.
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1. Introduction
Wavelength division multiplexing system has evolved to an all-optical network, which is effective for increasing the capacity of network communication systems. All-optical wavelength conversion is a critical and promising technology in all-optical wavelength division multiplexing communication networks [1]. Wavelength conversion technology has become a hot spot in the basic research of optical communications, and has been adopted in some all-optical test networks. The ideal all-optical wavelength conversion requires strict transparency to optical signals, low polarization sensitivity, wide wavelength conversion range, low or zero deterioration of optical signal-to-noise ratio and extinction ratio [2]. Wavelength converters had received extensive and in-depth research, particularly based on semiconductor optical amplifier has made major breakthroughs and obtained many amazing achievements. All-optical wavelength conversion technology mostly uses the nonlinear effects of light, including: cross-gain modulation (XGM) [3], four-wave mixing (FWM) [4,5], and cross-phase modulation (XPM) effects [6]. The all-optical wavelength conversion technology based on SOA-XGM has the advantages of high conversion efficiency and independence of polarization. However, there are also disadvantages such as serious deterioration of signal extinction ratio and low signal-to-noise ratio. Based on XPM effect, a higher output extinction ratio and transmission signal-to-noise ratio can be obtained, and it is able to convert signals in phase or reverse phase. This method has stricter requirements on the incident signal light and has a small adjustable range. The nonlinear optical loop mirror (NOLM)-XPM [7] method which based on the Sagnac interference-effect of the fiber and the nonlinear phase shift implemented by XPM in the fiber to achieve wavelength conversion. As a passive medium, NOLM-based all optical wavelength conversion is not only with low conversion efficiency but also difficult to integrate. Four-wave mixing wavelength conversion based on nonlinear media is completely transparent to the modulation format and the signal bit rate, which is considered as an attractive method.
Over the last decades, researchers have been exploring the use of two-dimensional materials as a nonlinear media to achieve higher conversion efficiency. Since 2004, for the first time, researcher has discovered that graphene [8,9] with only one carbon atom thickness, which opened the exploration and application investigation of graphene. In the field of nonlinear optics, graphene is with great potential in the optical signal processing system as its many excellent linear and nonlinear optical properties, such as saturated absorption, tunable light absorption, small scattering loss, etc. It is well known that graphene is an excellent nonlinear optical material, which is suitable for the excitation and device research of nonlinear optical signal processing, such as optical switching, optical wavelength conversion, optical signal regeneration, and so on. In addition, as a kind of ultra-thin flexible material, graphene is very easy to be employed in silicon-based wave-guides [10] and optical fibers, which greatly extends the potential applications of graphene, and makes it possible to invent graphene–based hybrid wave-guide devices.
Wavelength conversion based on the FWM effect in graphene can not only reach complete transparency of the modulation format and the bit rate, but also the converted light retains the phase and amplitude information of the original signal [5]. There have several works reported on FWM wavelength conversion based no nonlinear optical materials [11–16]. However, the FWM effect based on a single-pump of graphene has obvious shortcomings: firstly, the conversion efficiency is negatively correlated with the wavelength difference between the pump light and the signal light; secondly, the conversion efficiency is also easily affected by the polarization state of incident pump light and signal light. Later, the four-wave mixing effect has been studied by researcher more extensively and deeply, and proposed a dual-pump experimental scheme. Studies have shown that both orthogonal-dual-pump [17] (the polarization directions of the two pumps are orthogonal) and parallel-dual-pumps [18] (the polarization directions of the two pumps are parallel) cases are insensitive to polarization. Meanwhile, it is also demonstrated that the two co-polarized pumps scheme shows smallest polarization sensitivity. Besides, it is noted that FWM efficiency also depends on the wavelength spacing between the pump and signal (for the case of only one pump). In dual-pump schemes, the conversion efficiency also depends on the frequency spacing between the two pumps (for parallel pumps) or between the signal light and pump light (for orthogonal pumps).
In this work, we propose the employment of graphene as a nonlinear optical material for polarization insensitive wavelength conversion. The wavelength conversion is based on FWM in a dual-pump configuration which is polarization independent and conversion efficiency can be significantly enhanced by graphene deposited on the optical fiber. This is the first report on the graphene applied in dual-pump FWM for wavelength conversion, to the best of our knowledge. The experimental results showed that the graphene can be applied as nonlinear materials for the enhancement of wavelength conversion efficiency.
2. Theory of FWM for all-optical wavelength conversion
Four-wave mixing is a third-order nonlinear effect arising from Kerr effect [12]. When light-waves of multiple frequencies are injected into a nonlinear optical medium, due to the interaction of multiple lights in the medium, under certain phase and wavelength conditions, these input light waves will generate beats, and each beat can generate multiple converted lights by modulating input light. Their frequency and phase are linear combinations of the corresponding quantities of incoming light waves. Therefore, this kind of wavelength conversion can retain the information about amplitude and phase of the original signal, which is a strictly transparent wavelength transform. According to the number of input light waves, the FWM can be realized with one pump light and one signal light, or realized by two pump lights and one signal light. For the all-optical wavelength conversion, the conversion efficiency is defined as the ratio of the output light power to the input signal power at the end of a fiber of length L. The conversion efficiency ηc depends on the various parameters, such as input pump power, optical fiber length L, optical fiber dispersion, wavelength difference between pump light and signal light, etc. In our experiment, Conversion efficiency is defined as the ratio of the intensity of converted light to the input signal light, which can be estimated from optical spectra measured by optical spectrum analyzer.
In the single-pump configuration, there are two beams of light with frequencies ωs and ωp which are injected into nonlinear optical fiber, the new converted light ω1 = 2ωp-ωs will be generated when phase-matching condition is satisfied. The disadvantage of a single pump is that polarization sensitivity and conversion efficiency to signal-to-noise ratio decrease with the increase of the wavelength conversion amount, and it is difficult to maintain the flatness of the conversion efficiency in a larger range. Therefore, researchers proposed a double pumping method, which can solve these problems effectively. In these relevant works, two schemes for pumping have been theoretically analyzed and experimentally demonstrated, including parallel-dual-pump and orthogonal-dual-pump based on the FWM effect. In a previous study [19], the author found that using double pump in an SOA-fiber ring laser can improve the conversion efficiency, and analyzed theoretically noise figure of wavelength converters based on FWM. In 2006, Jianxin Ma investigated experimentally and theoretically that the polarization sensitivity of the wavelength converter based on dual-pump figuration in high-nonlinear dispersion shifted fiber. The expression tables of frequency and amplitude of the converted light based on the all-optical wavelength conversion in the highly nonlinear fiber are derived in this contribution [20]. At present, people have attached more importance to the dual-wave pumping technology to further optimize the all-optical wavelength converter. Figure 1 shows the schematic diagram based on dual-pump structure. More details on the theoretical study of FWM conversion have been concluded in previous works [21].
Fig. 1. Schematic diagram of all-optical wavelength conversion based on FWM effect (a) when the polarization states of the two pumps are parallel (b) and orthogonal.
We experimentally investigated the effect of polarization on conversion efficiency when a wavelength converter based on the FWM with only two pump lights configuration is employed. The related experimental result detected by the optical spectrum analyzer is shown in Fig. 2. By slowly adjusting the angle between the polarization directions of the two pumps (pump1 at 1550.89 nm, pump2 at 1551.32nm), when the polarizations of two input lights are parallel, the converted signal power gets the maximum value. When the polarizations of two input lights are orthogonal, the output power is minimum, indicating that FWM effect can be neglected. This result coincides with the prediction that FWM between two beams are polarization sensitive.
Fig. 2. Optical spectra of Four wave mixing effects when the polarizations of the two input lights are a) parallel and b) orthogonal.
The expression of the two pump lights and signal light are given by
where ${k_i}$, ${A_i}$ ${\omega _i}$, ${\varphi _i}$ are the wave vector along the fiber, amplitude of the light, the angular frequencies of the two pumps, and phase respectively. i =1, 2, 3 which respectively represents pump1, pump2 and signal. As described in the literature, after FWM effect in nonlinear medium, new converted lights are obtained by modulating the pump light and the signal light respectively with three beat waves. The frequencies of the three beats are ω1-ω2, ω1-ω3, ω2-ω3 separately. The FWM schematic diagram based on parallel-dual-pump structure is shown in the Fig. 1(a). Among these input beams, frequencies of pump1 and pump2 are fixed, and the polarization states of the two pumps keep parallel. The wavelength spacing between the signal light and pump2 is tunable. According to the theory of the FWM effect, this case can get nine spectral components. What we are interested in are the optical frequencies ω3±(ω1-ω2) as they remain independent of polarization. The optical frequency ω3+ω1-ω2 is generated by the beat |ω1-ω2| modulating ω3 and beat |ω3-ω2| modulating ω1. And the power of the frequency is given asWe can see that if the polarization directions of the two pumps are parallel, the output power obtains maximum, and these two new optical powers is independent θ. That is to say, the all-optical wavelength conversion system based on parallel dual-pump can achieve polarization insensitivity of the system.
The case of orthogonal-pump, as shown in Fig. 1(b), three light waves with the frequencies of ω1, ω2, and ω3 will generated three beats |${\mathrm{\omega }_1} - {\mathrm{\omega }_2}$|,|${\mathrm{\omega }_1} - {\mathrm{\omega }_3}$|and |${\mathrm{\omega }_2} - {\mathrm{\omega }_3}$|. Each beat can modulate each input light to produce sidebands. In our work, we focus on the frequency(ω1+ω2-ω3), which is contributed by the beating grating |${\mathrm{\omega }_1} - {\mathrm{\omega }_3}$| modulating input signal ${\mathrm{\omega }_3}$ and the beating grating |${\mathrm{\omega }_2} - {\mathrm{\omega }_3}$| modulating pump1 ω1. It can be written that the output power of the optical frequency is:
If |${\mathrm{\omega }_1} - {\mathrm{\omega }_3}$|≈|${\mathrm{\omega }_2} - {\mathrm{\omega }_3}$|, then r(ω1-ω3) ≈ r(ω2-ω3). Therefore, Eq. (4) can be reduced to
It is illustrated that output signal optical power is polarization insensitive. From Eqs. (3) and (5), we can predict that the all-optical wavelength conversion system of FWM based on parallel pump and orthogonal-pump structures both can be polarization insensitive.
3. Graphene-enhanced all-optical wavelength conversion
Figure 3 shows the experimental setup for graphene-enhanced all-optical wavelength conversion in view of FWM effect. Two light waves operating at 1550.89 nm and 1551.32 nm generated from two distributed feedback laser diodes (DFB-LD), namely DFB-LD1 and DFB-LD2 are served as pumps. The wavelength spacing of the two pumps is fixed to be 0.43 nm. They were combined by a 50/50 optical coupler, followed by their corresponding polarization controllers (PCs) that are employed to control the polarization state to meet different experimental conditions. The signal light is obtained by a tunable laser (TL) following by the polarization controllers. The optical signal and the high-power pump lights are combined by a 3-dB optical coupler (OC) before an erbium-doped fiber amplifier (EDFA). The EDFA is providing gain amplification of the lights, and the final all-optical wavelength conversion happens in the graphene. Graphene is synthesized by using the chemical vapor deposition method. The graphene sheets have several layers and are carefully deposited on the end facet of an optical fiber patch cord, which is inserted in a fiber connector. As a nonlinear optical material, insertion of graphene into the optical path can increase third-order nonlinearity of the optical system which can enhance the efficiency of four wave mixing. Polarization degree between pumps on the optical conversion efficiency of signal can be studied by adjusting polarization controllers. The optical power of two pump lights and signal light injected into the graphene are 12.2 dBm,13 dBm and 11 dBm, respectively.
Fig. 3. Experimental setup for an all-optical wavelength conversion based on FWM. TL: Tunable laser; DFB-LD: Distributed feedback laser diode; PC: Polarization controller; OC: Optical coupler; EDFA: Erbium doped fiber amplifier; OSA; Optical spectrum analyzer.
In this work, optical spectra of the lights are measured by using an optical-spectrum analyzer (OSA) with a resolution of 0.02 nm. The experimental optical spectra with dual-pump configuration are shown in Fig. 4. As shown in Fig. 4(a), there are nine newly generated light when the two pumps are co-polarized. Particularly, we focus on the two symmetric sides of the original signal include the upper and lower sidebands at the wavelength 1554.16 nm and 1553.30 nm (marked as λ4 and λ5 in Fig. 4(a)). According to the above theoretical analysis, the power of the two converted signal lights should be independent of the polarization direction of the pump light and signal light. In addition, the wavelength shift of the converted signal which is just equal to the wavelength spacing of the two pumps. By adjusting the PCs to ensure the polarization direction of pump1 and pump2 holding orthogonal. As presented in Fig. 4(b), it is clearly to see that the conversion efficiency of signal light is obviously reduced under the orthogonal pumps configuration, and the number of newly generated wavelengths also decreases. The experimental results are consistent with the previous studies, there are seven new wavelengths will be generated. According to theoretical and experimental analysis, the converted light of frequency (ω1+ω2-ω3) can be used (marked as λ4 in Fig. 4(b)), to realize the polarization insensitivity of the wavelength conversion, in the all-optical wavelength conversion system based on the vertical dual-pump FWM.
Fig. 4. Experimental optical spectra of FWM based wavelength conversion (a) co-polarized-pump configuration. (b) orthogonal-pump configuration.
Polarization sensitivity of wavelength conversion for the cases was measured, as shown in Fig. 5. The two pumps can be co-polarized or cross-polarized. To test the polarization sensitively of wavelength conversion, for each case the polarization states of the two pumps are fixed and the polarization state of the signal is tunable. When the two pumps are parallel, the FWM effect between the two pumps are maximum, as shown in Fig. 5(a). After the signal lights are injected, the two converted wavelengths λ4 and λ5 can be found. As the polarization of the signals changed by rotating the PCs, it can be found that the intensity of λ4 and λ5 are kept while other wavelengths in the spectra has significant intensity change. When the two pumps are orthogonal, the FWM effect between the two pumps are minimum, as shown in Fig. 5(e). The spectra change as the polarization of signal light change is shown in Fig. 5(f)-(h). It is easy to see that intensity of target wavelength λ4 can be kept as the polarization of signal light changes. It is verified that the wavelength conversion of the dual pump configuration for the two cases can be polarization independent.
Fig. 5. Experimental optical spectra of polarization sensitivity of wavelength conversion when the polarization states of the two pumps are (a)-(d) parallel. The polarizations of the signals light changed (e)-(h) when the polarization states of two pumps are orthogonal.
For the application of wavelength conversion, information loaded on the light is typically required. Experimental research about the wavelength conversion efficiency for the radio frequency signals is conducted. Figure 6 illustrates the related experimental results. Figure 6(a) shows the output spectra without loading with modulated signal, under the influence of co-polarized pump1 and pump2, the signal light can be expected to be converted to two adjacent wavelengths λ4 and λ5. When the input light was added 8 GHz signal, as shown in Fig. 6(b), wavelengths λ4 and λ5 are with modulations in the optical spectrum, indicating the information carried in signal is successfully converted to two wavelengths λ4 and λ5.
Fig. 6. Experimental optical spectra of FWM based wavelength conversion (a) without signals. (b) with 8 GHz signals.
4. Discussion
In this work, we employ an all-fiber structure that consists of a graphene film on the patch cord. Graphene based wavelength conversion indeed is not only attributed to the nonlinear optical property of graphene, optical fibers and amplifiers are also contributed to the FWM based wavelength conversion. Figure 7(a) and Fig. 7(b) shows that wavelength conversion efficiency can be significantly enhanced by the graphene-based device for the both two cases. The conversion efficiency under parallel dual-pump and orthogonal dual-pump is shown in Table 1. From Table 1 we can see that when the two pumps are co-polarized with graphene, wavelength conversion efficiency is maximum with -28.3 dB, which is enhanced by graphene around 7.7 dB. For the cross-polarized pumps, graphene-enhanced conversion efficiency is 1.4 dB.
Fig. 7. Output spectra of wavelength conversion signal of the graphene-enhanced four wave mixing. a) parallel-pumps; b) orthogonal-pumps.
Table 1. Conversion efficiency of dual-pump configuration with/without graphene
According to the above theoretical analysis, with the increase of the distance between the pump light and signal or the decrease of the incident power, the power of converted light will be reduced. Relation between wavelength conversion efficiency and the wavelength spacings between the signal and the pumps is investigated and shown in Fig. 8. Figure 8 shows the wavelength conversion of graphene at different wavelength spacings when the two pumps are co-polarized. The wavelengths of the two pumps are fixed at 1550.94 nm and 1551.34 nm, respectively. The wavelength of signal light is tuned from 1551.74 nm to 1554.16 nm. It illustrates that the wavelength conversion efficiency of graphene can be kept within 3 nm tuning range and the efficiency starts to decrease when the wavelength spacing is becoming larger.
Fig. 8. Graphene-enhanced four wave mixing based all-fiber wavelength conversion at different wavelength spacings.
In general, the conversion efficiency is influenced by pump power, wavelength spacing between signal and pump. The nonlinear optical property of graphene will also influence the conversion efficiency. Considering the conversion efficiency and wavelength tunability, a parallel pump structure is preferred for the graphene enhanced all optical wavelength conversion.
5. Conclusion
The use of dual pump waves can effectively solve the polarization sensitivity problem. By taking advantage of the strong optical nonlinearity of graphene and the polarization insensitivity of FWM with a dual-pump configuration, the few-layer graphene deposited on the fiber patch cord based on the FWM with a dual-pump configuration is employed. In dual-pump scheme (be co-polarized or cross-polarized), in which the polarization states of the two pumps are fixed and the polarization state of the signal is tunable, the target wavelength can be polarization independent. These experimental results agree with the theoretical analysis. Experimental results show that the co-polarized-pump scheme can obtain a larger conversion efficiency, and because of graphene, the wavelength converter with a conversion efficiency up to -28.3 dB. With the increase of the wavelength spacing between signal and pump, the conversion efficiency of the converted signal reduces. This work demonstrated that nonlinear optical materials like graphene are effective in optical signal processing and the co-polarized pump is an attractive scheme for the polarization insensitive wavelength conversion.
Funding
National Natural Science Foundation of China (62005178); Shenzhen Fundamental Research Program (JCYJ20190808143611709, JCYJ20200109105216803).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request
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