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The first successful translation of a phase modulated optical signal over 80 THz, from the near infrared to the short-wave infrared (SWIR) band is demonstrated. A signal, phase-modulated at 10 Gbps, was received in an error-free manner in the SWIR(1.7–2.2 μm) band. A new class of highly nonlinear fiber with reduced dispersion fluctuation was utilized as the platform for this phase-preserving distant parametric conversion.
©2013 Optical Society of America
1. Introduction
Distant-band translation has allowed porting the mature transmission, modulation, and detection technologies pertinent to the telecommunication band, to an arbitrary spectral location spanning from the visible to infrared wavelength ranges in the electromagnetic spectrum [1,2]. These non-conventional bands are of interest for a wide range of applications such as free-space communications, biological and chemical sensing and spectroscopy. The sensitivity and efficiency of these applications would greatly benefit from the capability of encoding both amplitude and phase on an optical carrier [3,4]. For such conversions, an optimal translator possessing a net-positive optical gain, fast response, spectrally invariant nature, as well as capable of preserving optical phase, amplitude, and/or quantum state can, in principle, be realized as a parametric mixer [5,6]. Among the materials that have been investigated as platforms for parametric conversion to distant bands [7–9], silica highly nonlinear fiber (HNLF) has been both proposed and demonstrated [10,11] as one of the most important platforms that rigorously satisfies the conversion requirements by its inherent capability of mapping the entire signal state to a distant spectral range.
Recent developments in silica-based HNLF fabrication process offer precise dispersion engineering and phase matching control of the fiber as well as a remarkably low loss [12,13], which, despite the lower nonlinear Kerr index of silica, provide highly-efficient nonlinear interaction compared to other competing platforms. Translators constructed with HNLF exhibit desirable performance such as wide conversion bandwidth and high modal confinement due to the small core size and high index contrast between the core and cladding [13]. Such wide-band parametric HNLF mixers phase-matched by positive-β4 have enabled distant translation of continuous-wave [10] and/or amplitude modulated signals [11] from the near-infrared (NIR) to the short-wave infrared (SWIR) regions. However, for phase information translation into the SWIR frequency band, the wide-band parametric translator designed using conventional HNLF platform imposes considerable limitations due to a broad out-of-(pump)-band amplified quantum (AQN) noise generation. Indeed, the AQN depletes the pump and contributes to the signal and idler phase noise [14]. As a matter of fact, the latter limitation can be overcome by taking advantage of a narrow-band parametric mixer relying on negative fourth-order dispersion which eliminates the generation of a wide-band AQN.
An additional important impediment that needs to be taken into account in wide-band parametric convertors is that of the dispersion fluctuations of the mixing medium. In practice, the phase-matching in a conventional HNLFs is extremely sensitive to dispersive fluctuations caused by transversal geometry fluctuations resulting in the fiber drawing process [15,16]. Recently, a new class of highly nonlinear fibers possessing dispersive characteristics invariant to these transverse geometry fluctuations has been introduced [17,18]. The new fiber design is based on an index profile that reduces dispersion shifts as the transverse geometry of the fiber is varied, allowing for a precise and maintained control over the phase matching condition along the entire length of the waveguide. In particular, the fiber is specifically tailored for parametric generation phase-matched by negative fourth-order dispersion (β4). More importantly for practical considerations, the new waveguide design fully maintains the dispersive properties even under longitudinal strain, thus allowing for stimulated Brillouin scattering suppression [19] (by fiber straining) without affecting the phase-matching properties, making the novel fiber design a perfect phase-matching retaining translator with an increased Brillouin threshold [18].
In this paper, we first discuss the benefits and challenges of operating in a narrow-band phase-matched region for phase-preserving wavelength conversion. The first part describes the advantage of operation in a narrow-band phase matched regime over wide-band schemes. The second part investigates the effect of random dispersion fluctuations on conversion efficiency of the mixer as well as the tolerance to dispersion fluctuations within a narrow bandwidth. Finally, we demonstrate that the combination of characteristics of the new dispersion fiber enables a pristine conversion of phase-coded optical signal to a spectrally distant (SWIR) band, with an error-free performance, for the very first time, by employing an optical parametric translator operating in the pulsed regime.
2. Narrow-band parametric translators
The parametric interaction inside a fiber between an optical pump, centered at ωP, and a spectrally distinct signal wave, with frequency ωS, leads to the amplification of the signal and the creation of a new idler wave at a frequency ωI equal to 2ωP – ωS. If the total power acquired by the signal and idler constitutes an insignificant fraction of the pump, then the signal gain, GS, and the idler generation efficiency, GI, can be represented by the following expressions [20]:
The length of fiber, L, the nonlinear parameter, γ, the incident pump power, Pp and a frequency-dependent factor ∆k, denoted as total phase mismatch, affect the efficiency of the nonlinear interaction. The spectral response of the parametric amplification (conversion) is determined by the total phase mismatch factor ∆k:
For silica fiber, the phase mismatch for pump at ωp and signal at ωs can be described accurately by taking into account only the second, β2, and fourth-order, β4, dispersion coefficients and neglecting higher order dispersion terms:
The recently developed capability to accurately tailor the dispersion of silica-based HNLF allows for precise control of the dispersion coefficients [12,13]. In the most commonly used parametric translators, for which a broadband gain is sought, the optimal phase matching is achieved by choosing the fiber with a positive β4 and situating the pump frequency at the anomalous dispersion region resulting operation in negative β2 dispersion regime. The simultaneous occurrence of positive β4 and negative β2 provides spectrally flat, vanishingly small phase mismatch over a wide spectral band as shown in the theoretical conversion efficiency spectra demonstrated in Fig. 1(a). The HNLF used for this simulation was characterized by a low positive β4 = 4.2∙10−7 ps4/km. In this wide-band phase matching mode, a broad out-of-(pump)-band AQN is generated which is present at the detector and significantly deteriorates the performance of the translator [2].
Fig. 1 Theoretical conversion efficiency (CE) spectra for (a) wide band, and (b) narrow-band parametric converter (λp = 1556.5nm and Δλp is the shift from this wavelength).
An alternative approach is to adopt a negative β4 fiber and a pump frequency at the normal dispersion region (resulting in positive β2) which leads to a pair of narrow spectral bands formed at spectrally distant frequencies. Figure 1(b) shows an example of the theoretical conversion efficiency spectra obtained for a fiber designed for operation in the negative β4 phase matching mode. The fiber used for this simulation is a recently designed highly nonlinear fiber [18] which was employed later in this work for distant-band phase-preserving translation. The fiber (at 1550 nm) was characterized by a nonlinear coefficient of 5.2 W−1km−1, a propagation loss of 0.4 dB/km, a zero-dispersion wavelength of 1593 nm, and a dispersion slope of 0.067 ps/nm2/km [21].
Figure 1 clearly shows a potentially wide tuning and far reaching range of the process: The result in Fig. 1 implies that tuning the pump wavelength by 60nm results in phase-matched doublets at 1200 and 2100 nm. It is important to emphasize that this operational mode for a fiber-optical parametric converter allows access to distant bands devoid of generating excessive AQN, inherent to wide-band parametric wavelength translators [2]. Moreover, in the case of a wide-band translation (i.e. wide-band phase matching), the AQN depletes the pump, thus imposing a higher pump power requirement for an equally efficient conversion. In practice, the latter condition, unfortunately, limits the generated idler power since the pump power must be kept well below the Brillouin threshold, lest significant degradations of the translated signal integrity materialize. Additionally, in the case of phase modulated signals, the AQN noise contributes to the phase noise transferred to the signal and idler waves during the distributed interaction in a HNLF [14], and should, thus, be kept at a minimum level.
In spite of the above mentioned translator performance improvement by operating in the negative-β4 phase matched regime, a typical HNLF which is designed based on the conventional single-core design strategy, is highly sensitive to dispersion fluctuations due to the transversal geometry fluctuations along the fiber [15,16]. In the analysis which follows, we investigate the translator performance degradation due to dispersion fluctuations along the fiber and we demonstrate that by employing the recently designed multi-layered waveguide design [17], which allows for high dispersion stability, specific mixer performance limitations can be significantly suppressed.
3. Effect of dispersion fluctuations on phase-preserving narrow band translators
The high modal confinement of a conventional HNLF induces a high sensitivity of its dispersive properties to the ever present microscopic random fluctuations of the core geometry created in the drawing process. These intrinsic core fluctuations cause considerable dispersion variation [13]. Ultimately, these dispersion fluctuations not only affect the conversion efficiency of the translator, but also lead to undesirable high dispersion accumulation within the narrow band phase-matched window. The following two sections discuss these important system degradations.
3.1. Impact of random dispersion fluctuations on conversion efficiency
The longitudinal dispersion fluctuations of the HNLF are a result of small fluctuations in the fiber’s core diameter. To incorporate the random dispersion variations into the evolution of the interacting waves along the fiber, a random perturbation to the mean second-order dispersion is introduced as follows [22]:
In Eq. (4) Lc corresponds to the correlation length of the random fluctuation, whereas the perturbation is represented by p; a random process with ensemble-wise Gaussian statistics of N(0,σb), i.e. zero-mean Gaussian random variable with standard deviation of σb, and an auto-correlation σb2exp(-Δz/Lc). When Eq. (4) is incorporated into the well-known coupled-mode equations for degenerated (single-pump) parametric interaction, the resulting stochastic model describes the effect of dispersion fluctuations on conversion efficiency. Figure 2 shows simulation results of the impact of random dispersion fluctuation on the conversion efficiency of a narrow-band fiber converter. In particular, the result in Fig. 2 shows an ensemble average of the CE of one hundred realizations in a waveguide whose dispersion was a Gaussian random variable, with a correlation length set to 1m, and a pump peak power of 4W.Fig. 2 Theoretically calculated average conversion efficiencies as a function of random dispersion fluctuations. Red dotted line denotes the conversion efficiency for an ideal fiber in the absence of dispersion fluctuations.
Figure 2 clearly shows a significant effect of dispersion perturbation on the attainable CE in non-ideal fibers. While the conversion window is confined to a single peak in ideal case, the presence of substantial dispersion fluctuations splits the conversion window into fine structures, as shown in the inset of Fig. 2. The spread of conversion window in the dispersion-fluctuations-impaired mixer results in efficiency reduction. The observed trend in Fig. 2 clearly emphasizes the benefit of the newly designed fiber exhibiting more than one order of magnitude lower dispersion fluctuations along its length compared to conventional HNLFs. Moreover, the result illustrated in Fig. 2 can be used to demonstrate the advantage of the new fiber when tension-based Brillouin suppression technique [19] is employed in a parametric mixer; while both conventional HNLFs and new fiber [17] can be stretched to suppress stimulated Brillouin scattering (SBS), large dispersion variation in conventional HNLFs due to the applied stress will indeed prohibit parametric mixing across the spectral span demonstrated in this work. To illustrate the challenge in synthesizing Brillouin-suppressed parametric mixer with conventional HNLF, it should be noted that the dispersion of a conventional HNLF will vary by at least 0.1 ps/nm/km if the same stress profile used in this work is applied [23]. Using the analysis presented in Fig. 2, the introduced dispersion variation will imply 20-dB penalty from the ideal conversion efficiency, even before the intrinsic dispersion fluctuations are taken into account. In sharp contrast, the exceptional resistance to dispersion change demonstrated by the new HNLF avoids the efficiency penalty associated with stretching for suppressing SBS [18], thereby allowing phase-preserving conversion in this demonstration by alleviating the needs for pump phase dithering.
In addition to the effect on the conversion efficiency degradation, dispersion fluctuations lead to another impairment in the case of a phase preserving translator which arises from dispersion accumulation along the fiber. In the following section we investigate this important system degradation which has never previously been addressed in the literature.
3.2 Impact of random dispersion fluctuations on phase preserving translation
The constricted bandwidth provided by narrow-band phase-matched translators leads to rapid phase variations over the conversion spectral window, as a consequence of causality conservation described by Kramers-Kronig relations [24]. In fact, the narrow-band nature of the conversion process may leads to highly dispersive characteristics, particularly in the presence of dispersion fluctuations where the conversion windows split into fine structures. To understand the severity of dispersion accumulation in the conversion process, the additional dispersion within the translation bandwidth was studied using the stochastic model introduced in Section 3.1. The dispersion introduced by the conversion process D is determined from the following relationship by considering the phase rotation β of the optical field relative to the phase at the conversion peak with wavelength λ:
Figure 3 shows the effect of dispersion fluctuations on the accumulated dispersion, obtained by the described approach. The result in Fig. 3 was obtained as an average of 100 realizations of a Gaussian-perturbed stochastic parametric converter. The result shown in Fig. 3 clearly demonstrates the manner in which dispersion fluctuations can significantly increase the amount of accumulated dispersion of a narrow-band parametric convertor within the phase-matched window. The trend can be attributed to rapid phase rotation within the converted signal bandwidth in the presence of dispersion fluctuations, thereby adding significant dispersion. In consequence, this result implies that the fluctuation-resilient characteristics of the newly developed HNLF, with more than an order of magnitude lower dispersion fluctuation compared to conventional HNLF, also lead to a low chromatic dispersion accumulation along the translator, thus identified the novel fiber design as a highly suitable platform for a phase-preserving conversion.
Fig. 3 Accumulated dispersion within the narrow phase-matching window in the presence of fiber dispersion fluctuation, calculated for a fiber length of 45m and a fluctuation correlation length of 1m.
4. Realization of a phase-preserving distant parametric wavelength convertor
The excellent dispersion stability in the stretched new HNLF was employed to construct a differential phase-shift keying (DPSK) short-wave infrared (SWIR) parametric frequency converter. Figure 4 shows a demonstration experiment of the DPSK SWIR translator constructed with a 45-m section of the new fiber. A varying tension profile [23] was applied to the fiber to increase the Brillouin scattering threshold. Although the applied stress raised the SBS threshold of the new fiber by a considerable margin (7 dB demonstrated in Ref [18].), the resultant conversion efficiency remained inadequate to overcome the excessive loss in the telecom-band passive devices along the mixer output path (1.5 dB) as well as the loss in the DPSK demodulator (6 dB). Consequently, this demonstration was performed with pulsed pump to further enhance the conversion efficiency.
Fig. 4 Experimental setup schematic of the parametric SWIR converter. Acronyms: MZM: mach–zehnder modulator; SOA— semiconductor optical amplifier; EDFA—erbium-doped fiber amplifier; PC—polarization controller; WDM—wavelength multiplexer; DPSK—differential phase-shift keying; HNLH—highly nonlinear fiber; LPF—long pass filter; C—collimator; M1,M2—mirrors; PD—photo detector; BER—bit-error rate; OSA—optical spectrum analyzer; PRBS – pseudo-random bit sequence.
The pump source was a fixed distributed feedback (DFB) laser, which was amplitude modulated for Brillouin suppression, resulting in quasi-continuous-wave (CW) 102.4-ns long pulses with a 1/16 duty cycle that was subsequently amplified to 4W. An external-cavity laser (ECL), tunable from 1260 to 1360 nm, was chosen as the signal source. A MZM driven at twice its Vπ characteristic was employed to imprint a differentially-encoded phase-shift-keyed (DPSK) 10 Gb/s pseudo-random bit sequence (PRBS) onto the signal carrier. The signal seed was subsequently amplified to 50mW using an O-band semiconductor optical amplifier (SOA). The amplified 1550 nm pump pulse was coupled with the 10 Gb/s DPSK signal into a 45 m-long segment of longitudinally tensioned HNLF with a nonlinear coefficient of 5.2 W−1km−1, characterized by a zero dispersion wavelength (ZDW) at 1593 nm, a slope of 0.067 ps/nm2-km, and a negative fourth-order dispersion coefficient measured at −5 × 10−4 ps4/km. After filtering out the seed and the pump using a long-pass filter (LPF) at 1640 nm, a 99/1 tap was used, which enabled an unimpeded monitoring of the SWIR idler (2.002 µm) on an optical spectrum analyzer (OSA). The idler was then directed to a free-space (one-bit) delay Michelson interferometer (shown in Fig. 4) that was used to decode and successfully receive the differentially encoded phase modulated information stream. The mirror M1 was placed on a controlled motorized stage to enable flexible adjustment of the optical path mismatch between the two arms of the interferometer. The decoded (and phase to intensity converted by the interferometer) wave was received by a single 10 GHz InGaAs PIN-detector (PD) and sampled using a digital oscilloscope and/or received by the analyzer section of the bit-error-ratio tester (BERT) to rigorously evaluate the transmitter performance. The O-band receiver simply circumvented the parametric stage.
The wavelength conversion characteristics of the system were captured after the HNLF (before filtering the pump and seed), which is illustrated in Fig. 5. All spectra were measured using an OSA operating in a continuous 1.2-2.4 µm range. Figure 5 clearly demonstrates the benefit of adopting the negative-β4 phase-matching scheme due to the absence of parametric fluorescence noise.
Fig. 5 Spectra measured at the output of the HNLF reflecting the response of 20dB attenuator compared with spectrum after the LPF with pump and seed filtered out. The extent of the measurement is limited by the OSA operation range.
A 1550-nm band 99/1 coupler was used to capture the spectrum at high power. The coupler induced a uniform 20 dB attenuation from 1400 nm to 1700 nm, but, as strictly determined in a separate characterization, departed from a uniform attenuation characteristic outside of its specified operation band. Hence, the diminished power reading around the seed wavelength in Fig. 5. In addition, the idler after the telecom-band long pass filter experienced an additional 1.5 dB loss at 2002 nm. The best conversion efficiency was obtained by positioning the pump at 1556.5 nm and the signal at 1273 nm. The attained conversion efficiency of −15 dB, taking into account the excess loss of the coupler, was almost in accordance with the theoretical projection (13-dB below the ideal CE at 0.6 dB) in Fig. 2, when the intrinsic dispersion fluctuations (0.016 ps/nm/km) were taken into account.
The performance of the DPSK translation was measured for a 10 Gbps signal beam phase modulated with a 214 long NRZ PRBS (the order of which was dictated by the quasi-CW pump condition). The DPSK data cast on the signal wave were translated to the SWIR idler and the performance of the DPSK translation was then strictly quantified. Note that the single-port-based DPSK receiver introduced an excess 3 dB power loss, clearly implying a higher achievable sensitivity by a balanced detector. Consequently, the total forward loss in the system was characterized at 6 dB. A performance contour plot stringently characterizing the performance margin of the system is shown in Fig. 6.
Figures 7(a) and 7(b) shows the typical eye diagram in the O- and SWIR bands. The slow rise and fall times are typical for the 10 GHz band-limited detector. To quantify the sensitivity and demonstrate the robustness of the transmitter, a bit-error rate (BER) measurement was performed on the received signal. Due to the 100ns duration of the pulsed envelope of the idler data sequence, the first and the last two bits within the pump-defined envelope were ignored, in order to allow for proper synchronization of the BERT. The idler power incident onto the receiver was varied by tuning the signal power. Figure 7 (c) shows the plots of BER as a function of the received signal power for both O- and SWIR-bands.
Fig. 7 Data stream waveform and eye diagrams of the 10Gbps DPSK signal (a) signal in the O-band and (b) idler in SWIR region., c) BER plots of the 10Gb/s O-band signal (red circles) and SWIR idler (blue squares).
As demonstrated by the measurement, the BER curves exhibit an error-free performance at 2002 nm. The observed negative penalty (for the converted SWIR signal) is due to a lower detector responsively at 1273 nm, as compared to that at 2002 nm. The total SWIR power penalty compared to signal at 1273 nm, taking into account the detector sensitivity, amounts to 1.8 dB.
5. Conclusion
We have for the first time, to the best of our knowledge, demonstrated an error-free translation of the 10 Gb/s phase-modulated information from the O- to SWIR (2μm)-band. The critical element in the experiment was the newly developed dispersion fluctuation resilient HNLF with a negative β4, that served as a vehicle for a narrow-band distant parametric conversion. The impact of dispersion fluctuations on narrow band phase preserving parametric translators based on four-wave mixing was also investigated. The results further reinforce the benefit of adopting a newly designed highly nonlinear fiber with low dispersion fluctuations, observed in the experiments.
Acknowledgments
Authors gratefully acknowledge Sumitomo Electric Industries for supplying the HNLF used in this study.
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