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We report a chalcogenide suspended-core fiber with ultra-high nonlinearity and low attenuation loss. The glass composition is As38Se62.With a core diameter as small as 1.13 µm, a record Kerr nonlinearity of 46 000 W–1km–1 is demonstrated with attenuation loss of 0.9 dB/m. Four-wave mixing is experimented by using a 1m-long chalcogenide fiber for 10 GHz and 42.7 GHz signals. Four-wave mixing efficiencies of –5.6 dB at 10 GHz and –17.5 dB at 42.7 GHz are obtained. We also observed higher orders of four-wave mixing for both repetition rates.
©2011 Optical Society of America
1. Introduction
Chalcogenide fibers with nonlinear refractive index up to 1000 times greater than fused silica, and fast response time [1,2], have attracted much interest to exacerbate high Kerr nonlinearity. Chalcogenide glasses, possessing optical bandgaps in the range of twice the energy of the communication photon energies [3], are ideally suited for high-bit-rate nonlinear optics (>20 Gbit/s) near the telecommunications wavelengths (between 1.3 µm and 1.6 µm). The nonlinear response time of chalcogenide glasses is very fast, in the femtosecond range. It is much faster than semiconductor optical amplifiers (SOA) or saturable absorber (SA) and leads much more interests in high-bit-rate telecommunications applications.
Chalcogenide fibers, tapers as well as waveguides have been fabricated with the aim to be applied in all-optical signal processing. Self-phase-modulation-based 2R-regeneration has been implemented by M. R. E. Lamont et al. in a chalcogenide As2Se3 fiber [4]. Supercontinuum generation has been demonstrated in chalcogenide tapers [5,6]. Four-wave-mixing-based wavelength conversion and optical sampling have been experimented in chalcogenide waveguides and tapers [7–10]. With a 7-cm chalcogenide As2S3 rib planar waveguide, T. D. Vo et al. have successfully demultiplexed 10-Gbit/s from 1.28 Tbit/s signal in 2011 [11]. By using chalcogenide glasses with high nonlinearity and small core diameter, the Kerr nonlinearity of chalcogenide fibers can be increased to 31 000 W–1km–1 [12]. It makes a bright way ahead to use chalcogenide fibers and waveguides in telecommunications systems.
The first chalcogenide fiber was reported in 1960s by J.A. Savage and S. Nielsen [13]. Then, with the purpose of improving the ability of propagating, attenuation loss of chalcogenide fibers was investigated [14,15]. With the trend of microstructured fibers, the first chalcogenide microstructured fiber was demonstrated in 2000 by T. M. Monro [16]. Then, many microstructured chalcogenide fibers were fabricated in the tendency of boost-up nonlinearity [17]. In 2010, by improving the fabrication process [18], an AsSe suspended-core microstructured fiber, composed of a solid core surrounded of three holes, was presented [12]. A large nonlinear coefficient of 31 300 W–1km–1 due to an effective area as small as 1.7 µm2 was reported. However, the attenuation loss of 4.6 dB/m and the coupling loss of 10 dB restricted applications for telecommunications.
With the purpose of exploiting the high-nonlinearity of chalcogenide fibers, tapers or waveguides for all-optical signal processing in telecommunications, optical functions such as amplification, 2R-regeneration, time-domain demultiplexing and wavelength conversion have been implemented [2–11]. Among those, all-optical wavelength conversion plays a useful role in the future optical network with requirement of wavelength flexibility. Moreover, a key to transparency to both data rate and modulation format can be achieved by optically mixing the signal with a continuous-wave (CW) pump beam in a nonlinear fiber. However, in previously reported microstructured AsSe fibers, the quantity of Kerr nonlinearity does not compensate enough the attenuation loss and coupling loss thus restricts the feasibility for telecommunications.
The aim of our work is to boost up Kerr nonlinear coefficient together with the decrease of attenuation loss of the fiber. In this paper, we present a 1m-long chalcogenide suspended-core fiber with a core diameter as small as 1.13 µm leading to a Kerr nonlinearity of 46 000 W–1km–1. To reduce the coupling loss, the fiber is expanded at its two ends by mode-adaptation parts. Thanks to this tapering process, the core diameter of the fiber at the adaptation-mode parts is enlarged up to 5 µm. Then, microlensed fibers [19] with mode diameter around 5 µm are used to couple with the AsSe fiber.
In this paper, section 2 is dedicated to introduce the wavelength conversion based on four-wave-mixing (FWM). The fabrication process and the characterization of the fiber are presented in section 3. In section 4, the high performance of this fiber in terms of Kerr nonlinearity is demonstrated. We present four-wave mixing experiments for 10 GHz and 42.7 GHz clock signals. The FWM-based conversion gain is much improved compared to previously reported results.
2. Four-wave mixing based wavelength conversion
Nonlinear effects rely on the response of bound electrons to an intense electromagnetic field. Depending on the response of the second-order susceptibility χ(2) or the third-order susceptibility χ(3), they can be classified into second-order or third-order processes. Because the second-order susceptibility χ(2) is eliminated in optical fibers or appears with relatively low efficiency, it hence can be ignored. The third-order process includes nonlinear interaction among four optical waves. It consists of phenomena such as four-wave mixing (FWM) and third-harmonic generation. In general, we can consider that a wave at frequency ω4 is generated by the interaction of three waves at frequencies ω1, ω2, and ω3. The total energy of the new wave at frequency ω4 can be written as [20,21]:
where ε0 is the vacuum permittivity, Ej (j = 1 to 4) is the electric field of the frequency ωj, and θ+ and θ– are defined as: where kj = njωj/c, with nj being the refractive index at the frequency ωj.The energy of new wave ω4 depends on all the third-order nonlinear processes. In the Eq. (1), the terms containing E4 are responsible for the self-phase modulation and cross-phase modulation effects. The remaining terms result from the frequency combinations of all the four waves. The efficiency of the FWM process depends on the phase-matching conditions expressed by Eqs. (2) and (3).
Typically, from Eq. (1), two types of FWM terms can be classified. The term containing θ+ corresponds to the case in which three photons (at frequencies ω1, ω2, and ω3) transfer their energy to a new single photon at frequency ω4 = ω1 + ω2 + ω3. This term corresponds to two cases of nonlinear phenomena. The first one is third-harmonic generation when the three photons are at the same frequency (ω1 = ω2 = ω3). The second one occurs when ω1 = ω2 ≠ ω3. A frequency conversion is implemented to a new wave at frequency 2ω1 + ω3. However, the condition of phase-matching for these cases is not easy to be fulfilled. The difficulty to have high efficiency restricts the use in practise. The term containing θ– in Eq. (1) describes the interaction between two photons (ω1 and ω2) yielding two new photons (ω3 and ω4). In this case, two new photons at frequencies ω3 and ω4 are created simultaneously:
The phase-matching requirement for this process is
OrBecause of the symmetric condition of the phase-matching requirement, it is relatively easy to satisfy. Based on this last type, FWM-based wavelength conversion is able to fulfill completely. Practically, in order to easily meet the phase-matching condition, one uses typically a combination of two pumps such as modulated pump (need to be wavelength-converted) and a continuous-wave (CW) pump as ω1 and ω2.
Figure 1a shows a schematic diagram of FWM in theory. The two waves ω1 and ω2, after propagating through a nonlinear medium, generate two new frequencies ω3 and ω4 (named as Stokes and anti-Stokes) as seen in Fig. 1b. In the simulation, the wavelength of the modulated pump is 1553 nm (ω1) and the wavelength of the CW pump is 1556 nm (ω2). The Stokes and anti-Stokes waves appear at 1559 nm (ω3) and 1550 nm (ω4), respectively. Simulated results in Fig. 1b show that at the output of nonlinear medium, Stokes and anti-Stokes frequencies appear as in symmetrical pairs (2ω1 = ω2 + ω4 and 2ω2 = ω1 + ω3). We can also observe higher-order FWM waves due to different combinations of ω1 and ω2 (3ω1 = 2ω2 + ω4, 3ω2 = 2ω1 + ω3 and so on). In practical, one can use an optical filter to extract out the converted signal at both band sides Stokes or anti-Stokes. The wavelength of converted signal can be controlled by detuning the wavelength of CW pump.
Fig. 1 (a) Theoretical schematic diagram for four-wave mixing generation; (b) Simulated spectra of four-wave mixing for modulated pump ω1 and CW pump ω2.
3. Suspended-core Chalcogenide fiber
Fiber fabrication method is based on a casting glass which is described in [18]. A preform of chalcogenide glass in a structure of suspended-core is prepared. The As68Se62 suspended core fiber is then obtained by applying a suitable pressure in the 3 holes of the preform during the drawing. With a suspended-core structure, the fiber contains 3 holes around a solid core as shown in Fig. 2 . The external diameter ϕF is 62 µm and the core diameter ϕC is around 1.13 µm. The fiber loss is found to be 0.9 dB/m which is a large improvement compared to that of the previous AsSe fiber (4.6 dB/m) [12]. The mode field diameter of the fiber, measured by a far field method, is 1.21 µm (Aeff = 1.15±0.1 µm2). This is one of the smallest values reported in a chalcogenide microstructured fiber.
Fig. 2 Suspended-core chalcogenide fiber with mode adaptation ends. Where LF, LA, LTF: length of fiber, length of adaptation mode parts and length of taper parts, respectively; ϕC, ϕA: core diameters of fiber and adaptation mode parts, respectively.
In order to limit the coupling loss due to the difficulty to inject optical waves in such a very small core, the fiber is enlarged by mode-adaptation parts at each end of the 1m-long fiber during the fabrication process as shown in Fig. 2. The length of mode-adaptation parts LA are 5 cm, the length of the taper parts LTF are around 10 cm, and the length of fiber LF is 1 m. For both mode-adapted facets of the fiber, the core diameter and the external diameter are 5 µm and 280 µm, respectively.
With the advantage of mode-adaptation tapers, the coupling loss at both ends is reduced to less than 2 dB. This value includes the loss due to Fresnel reflection. The Fresnel reflection is given by R = [(n1−n2)/(n1 + n2)]2 when a light passes from one medium with the refractive index n1 to another medium with the refractive index n2. In our case, the refractive index of air n1 is approximate 1, and the refractive index of our chalcogenide material n2 is 2.805. The loss of Fresnel reflection is calculated to be 1.1 dB.
Self-phase modulation (SPM) has been observed by using a mode-locked laser emitting Gaussian pulses of 8 ps at 1550 nm with a repetition rate of 20 MHz. A good agreement between simulated spectra and experimental SPM-broadened spectra has been obtained for a nonlinear coefficient of 46 000 W–1km–1 and a group-velocity dispersion D in the waist of the fiber around −300 ps/nm-km. To the best of our knowledge, this is the highest nonlinear coefficient reported for a 1m-long optical fiber. This tapered microstructured fiber does not lead to nonlinear coefficient as high as the ones of tapered nanowire fibers (γ > 90 000 W–1km–1) [5,6] but offer longer interaction length and more robust structure as suggested by Chandalia et al. [22]. Note also that reducing the core diameter of the fiber allows reducing the dispersion by adding anomalous dispersion to the strong normal dispersion of this glass (around − 550 ps/km/nm).
4. Four-wave mixing experiments
In this section, we present FWM-based wavelength conversion of high-repetition-rate signals at 10 GHz and 42.7 GHz. The experimental setup of FWM characterization is shown in Fig. 3c . The free-space coupling in the mode-adapted ends of the fiber is performed using Gradhyp microlensed fibers [19] with a mode diameter of 5.2 µm. The coupling loss is then much improved. Including Fresnel reflection of 1.1 dB (refractive index nAsSe = 2.805) at each end of the fiber, the total loss between the output of the Gradhyp fiber and output of the AsSe fiber is measured to be 4.2 dB. It points out the advantage in diminishing the insertion loss by tapering the mode-adaptation parts to the fiber.
Fig. 3 Block diagram of pulse stream generation (a) at 10 GHz and (b) at 42.7 GHz; and (c) setup of FWM measurement at 10 GHz and 42.7 GHz.
4.1 Four-wave mixing at 10 GHz
Figures 3a and 3b show the schematic block setups to generate the modulated pumps at 10 GHz as well as 42.7 GHz. We use these signals as pulse sources cooperating with a continuous wave for our wavelength conversion experiments.
A 10 GHz clock signal is generated from a mode-locked fiber laser emitting 1.5 ps pulses with a time-bandwidth product of 0.35 centered at a wavelength of 1552.7 nm. This pump source is then amplified by an erbium-doped-fiber amplifier (EDFA) and filtered by an optical band-pass filter (OBPF) of 1 nm (Fig. 3a) [23]. The second pump source is a CW tunable laser amplified with a second EDFA. After amplifiers, both pulsed and CW pumps pass through polarization controllers (PC) and are combined with a 50:50 coupler.
The coupled signals are then filtered by an OBPF of 5 nm to reject the amplified spontaneous emission ASE noise of EDFAs. After the OBPF, the pulse width of the 10 GHz pump source is 8.3 ps and the average power of the CW source is set to 16 mW. In the experiment, no FWM is found at the input of AsSe fiber. At the output of the AsSe fiber, FWM Stokes and anti-Stokes waves appear in symmetrical pairs. The new wavelengths λanti-stokes and λstokes depend on the wavelength detuning Δλ = λ1 - λ2 between the pulsed pump and the CW pump such that 1/λanti-stokes + 1/λstokes = 1/λ1 + 1/λ2 as shown in Fig. 4a .
Fig. 4 Optical spectra at 10 GHz at the output of AsSe fiber (a) with appearance of the third-order FWM, (b) with various wavelengths of the CW pump, and (c) efficiency of the first-order FWM related to the wavelength detuning Δλ.
To assess the FWM conversion gain, we define the FWM efficiency as the ratio between the collected peak power of the anti-Stokes wave at the output of the AsSe fiber and the CW power injected in the AsSe fiber [12]. Efficiency of the first-order FWM at 10 GHz is found to be –5.6 dB with a total average power at the input of AsSe fiber of 17 mW and a detuning of 1.9 nm. This efficiency is much improved compared to the value of –27 dB with 20 mW of total average input power obtained with the previous fiber [12]. An improvement of 21 dB of the FWM efficiency is then obtained with this new fiber even if the total input power is lower. Furthermore, second-order and third-order FWM waves are also measured with efficiencies of –21 dB and –37 dB, respectively.
Figure 4b plots the output spectra for the CW signal detuning from 1554.6 nm to 1555.5 nm, corresponding to idler generation in the range of 1549.9-1550.8 nm. As shown in Fig. 4c, a good agreement between simulated FWM efficiency and measured data is obtained for a nonlinear coefficient γ = 46 000 W−1km−1 and a dispersion D = –300 ps/km-nm as previously calculated by SPM experiments.
4.2 Four-wave mixing at 42.7 GHz
We use the same experimental setup (Fig. 3c) for a FWM-based wavelength conversion experiment at 42.7 GHz. Figure 3b depicts the procedure for generating the 42.7 GHz pulse stream. The laser is a quantum-dash mode-locked laser diode (QD-MLLD) seeded by an optical clock [24]. The 42.7 GHz optical clock signal is generated at 1535 nm with a LiNbO3 modulator and is injected into the QD-MLLD module through an optical circulator. The laser is then injected into an optical amplifier and passes through a tunable band-pass filter of 3 nm centered at 1550 nm. This 42.7 GHz signal is used for FWM experiment in the chalcogenide AsSe fiber. The pulse width of the 42.7 GHz signal at the input of the chalcogenide AsSe fiber is 5 ps.
The total average power at the output of the variable attenuator is 33.1 mW with a CW power of 13.7 mW. Similarly to the 10 GHz setup, the polarization state of both pulsed pump and CW pump are aligned using polarization controllers (PC). The total average power launched into the AsSe fiber is 17.2 mW. This value is compatible with usual power in telecommunications systems. Note also that with these relatively low values of optical powers, the two-photon absorption, that usually occurs in AsSe glasses, is not visible in our case.
Figure 5a plots the total spectrum just before the AsSe fiber. No FWM signal appears. After the AsSe fiber, the output spectrum exhibits strong FWM waves (Fig. 5b). The second-order FWM is obtained with an efficiency of –36 dB. Figure 5c depicts the measured FWM efficiency and its simulated curve. At the wavelength shift of Δλ = 6.1 nm, a FWM efficiency of –17.5 dB is achieved. When the detuning Δλ increases to 7.3 nm, we still have a high FWM efficiency of –18.5 dB.
Fig. 5 (a) Spectrum of combined CW signal and 42.7 GHz pump at the input of the AsSe fiber; (b) Spectrum at the output of the AsSe fiber with FWM signal up to second-order; and (c) efficiency of the first-order FWM with respect to the wavelength detuning Δλ.
With the new structure of suspended-core, the core diameter of the fiber is considerably reduced (1.13 µm). The nonlinear coefficient hence is boosted up to 46 000 W−1km−1. The ultra-high nonlinearity allows reducing the power launching into fiber. It makes a power-compatibility for telecommunications systems. However, the suspended-core structure exhibits a multimode behavior. This leads to eye-diagram degradation when working with data signals rather than with clock signals. Further work has now to be carried out to ensure single mode propagation. One possible issue is to use microstructured chalcogenide fibers with 3 or 4 rings of holes.
5. Conclusion
We have reported a new chalcogenide suspended-core fiber with a very small core diameter of 1.13 µm and low attenuation loss of 0.9 dB/m. The strongly nonlinear coefficient is measured to be 46 000 W–1km–1. The dispersion is evaluated to be –300 ps/km-nm. With this fiber, FWM at 10 GHz and 42.7 GHz has been experimented. An efficiency improvement of 21 dB compared to the previous AsSe fiber [12] has been obtained. For 42.7 GHz signal, the highest –17.5 dB FWM efficiency for the detuning wavelength of 6.1 nm is achieved. With attenuation loss of only 0.9 dB/m, interaction lengths higher than 1 m are possible and would lead to less power consumption. This high efficiency fiber offers a strong potential for performing all-optical signal processing at high-bit-rates in terms of required optical power.
Acknowledgments
This work was supported by the Conseil Régional de Bretagne and the Conseil Général des Côtes d’Armor.
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