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Conventional highly-nonlinear fiber (HNLF) designs are optimized for high field-confinement but are also inherently susceptible to dispersion fluctuations. The design compromise prevents fiber-optical parametric mixers from possessing high power efficiency and extended operating bandwidth simultaneously. Using a new fiber waveguide design, we have fabricated and tested a new class of HNLF that possesses a significantly lower level of dispersion fluctuations while maintaining a high level of field-confinement comparable to that in conventional HNLFs. The fiber was used to demonstrate an all-fiber parametric oscillator operating in short-wavelength infrared (SWIR) band with a watt-level pump, for the first time.
©2012 Optical Society of America
1. Introduction
Recent advances in communications, signal processing and sensing [1–4] have relied on parametric devices to generate and manipulate coherent optical fields in spectral bands extending beyond the conventional telecom windows. With octave-spanning bandwidth and power efficiency driven by effective interaction length longer than any other known waveguide platform, fiber-optical parametric mixers were used to set recent records in terabit channel transport [5], transmission impairment reversal [6,7], phase-sensitive amplification [1,8], and wideband parametric generation [9]. Highly nonlinear fibers (HNLF) possessing an elevated nonlinear coefficient will further reinforce the advantage of fiber parametric devices in terms of power efficiency over competing mixer alternatives [10].
Unfortunately, higher field confinement has necessarily meant higher sensitivity to radial geometry fluctuations in waveguides [11]. The latter is directly mapped to dispersive fluctuations along the mixer length [12]. In practice, dispersion fluctuations along the fiber length considerably reduce the efficiency of the mixing process [13,14] and sets a fundamental limit on the device performance. Strong parametric interaction relies on proper phase matching between participating waves, with global mixer efficiency depending on local dispersion characteristics of the nonlinear medium [15]. Even though contemporary fiber fabrication techniques has allowed for precise control of global dispersion parameters, the miniscule variation of the core radius along the fiber perturbs the local characteristics, thus derailing the parametric photon exchange process from the ideal (maximal-gain) trajectory. Indeed, rather than achieving a deterministic phase-matching, the response of a practical mixer device is convolved by a stochastic evolution of the phase mismatch vector [12]. Strong field confinement in a HNLF amplifies the stochastic component of the phase matching by enhancing the dispersion sensitivity to core geometry fluctuations [11]. The relevance of dispersion fluctuations in wide-band parametric mixer construction is highlighted by the extreme fabrication tolerance it implies: with a typical HNLF design, the core diameter needs to be maintained within molecular-scale margins in order to derive appreciable efficiency [12], thus presenting an unphysical demand on fiber fabrication control.
Motivated by the disparity between fiber geometry control limit and dispersion stability requirement for practical parametric devices, we devised a new dispersion control mechanism for high-confinement fiber waveguides [16]. The new approach provides intrinsic dispersion resilience to waveguide geometric fluctuations, while simultaneously maintaining field confinement capability and manufacturability.
This paper reports the design, fabrication and characterization of the new HNLF type, with emphasis on the performance advantage in wide-band parametric mixer construction. The report first introduces the new dispersion-stabilized HNLF, and subsequently reports the first demonstration of HNLF-based fiber-optical parametric oscillator operating in the short-wavelength infrared (SWIR) band. Its performance is compared against a conventional FOPO construction using a standard dispersion-shifted fiber (DSF).
2. Dispersion-stabilized HNLF
Nonlinear fiber designs utilize high-contrast, small core radius, and a variety of claddings to achieve enhanced mode confinement [17]. In addition to the tight confinement, strong guiding effect in the HNLF-type waveguides provides a simple means to attain the desired dispersion characteristics, which are vastly different from the material dispersion [17]. Although it is theoretically straightforward, using conventional approaches, to achieve the waveguide dispersion needed for high-performance parametric mixers [18], the dependence of dispersion on the waveguide geometry tends to make these fibers intrinsically sensitive to perturbations. As a result, dispersion stability control needed for wide-band mixer construction is extremely challenging, as exemplified by the single-atomic margins revealed in [16].
Better fiber design resolves the entanglement between dispersion synthesis and stability control by introducing a double-layered core structure, as shown in Fig. 1 [16,19]. The new core structure and the cladding layers provide two distinct guiding regimes for low- and high-frequency fields, each of which conveys a dispersion shift in an opposite direction when the entire waveguide geometry is scaled radially. Thus, although perturbation sensitivity tends to arise from standard HNLF designs, it is not unavoidable, and can be engineered as part of the fiber design. Proper selection of the transition frequency and coupling strength between these two guiding regimes through layer indices and radii tuning can result in cancellation of the dispersion shift in the entire waveguide operating window, and consequently, provides substantial improvement in dispersion stability solely through waveguide design.
Fig. 1 Schematic index profile for the dispersion-stabilized HNLF, showing the outer core that provides dispersion control.
In order to verify the benefits of the new HNLF design, several fibers with index profiles conforming to the new design were fabricated using modified chemical vapor deposition. The fibers had identical index profiles besides differences in radial scaling, which allowed direct measurements of the dispersion sensitivity to waveguide geometrical variation. The measured properties of the fabricated fibers are summarized in Table 1 .
Table 1. Typical measured properties of the fabricated fibers at 1500 nm
Figure 2(a) shows the dispersion profiles at three different scaling factors with 1% difference in core radius, interpolated from the measurements of several radially-scaled fibers. Across the samples, the dispersion shifted by less than 0.13 ps/nm/km in response to a 1% stretch of transversal geometry. This value corresponded to an 86% reduction in dispersion shift when compared to a conventional HNLF [12]. The global dispersion stability was also reflected in the localized dispersion characteristics. The distribution of the zero-dispersion wavelength (ZDW) along a 100-m fiber section was characterized using the pump-wavelength scan method [19, 20], in which the extent of ZDW fluctuations was depicted by the width of the otherwise delta-like phase-matched conversion spectrum. In this characterization experiment, the fiber was pumped by a tunable source in the vicinity of 1537 nm and seeded by a fixed-wavelength probe at 1358 nm. The resulting idler was centered at 1770.6 nm. The conversion efficiency plot in Fig. 2(b) estimated the zero-dispersion wavelength variation to be 0.2 nm, thus inferring the dispersion varied only by 0.014 ps/nm/km. We note that the dispersion fluctuations represent a considerable reduction in comparison to conventional HNLFs and are comparable to the previously observed variations in standard DSFs [21].
Fig. 2 (a) Dispersion profiles of fiber samples with various core size deviation from the nominal value (∆r = 0%). dD/dr denotes the dispersion shift at 1543 nm in response to radial scaling. (b) Plot of conversion efficiency versus pump wavelength. The ordinates were normalized to the peak value corresponding to pump wavelength of 1537.1 nm .
The importance of the new HNLF design lays as well in the new means for Brillouin suppression. Efficient parametric mixing typically requires pump power exceeding the stimulated Brillouin scattering (SBS) threshold of the untreated fiber medium. Brillouin scattering in a HNLF can be suppressed by applying a varying tensile stress along the fiber span due to the stress-induced Brillouin frequency shift [22–24]. Unfortunately, in case of a conventional HNLF, the varying tensile stress also leads to unwanted changes in the local dispersion. Typical conventional HNLFs have shown a stress-induced SBS shift of 290 MHz/% and a corresponding change in dispersion by −0.65 ps/(nm∙km)/% [24]. While the new HNLF exhibited similar SBS-frequency-shift sensitivity to stress as the conventional HNLFs, amounted to 280 MHz/%, the change in dispersion due to straining in the new fiber is merely −0.05 ps/(nm∙km)/%, inferring more than ten-fold improvement over conventional HNLFs.
The effectiveness of the tensioning approach with the new HNLF is assessed in measurements shown in Fig. 3 , where the transmission and backscattered power levels were plotted against input power to depict the SBS threshold. The experiment compared two 100-m fiber sections, with one having tensile stress applied in an alternating staircase pattern, with maximum tension set at 18 N. With the tension applied, the SBS threshold was visibly higher than that of the untreated fiber – the measured Brillion threshold was increased by 7 dB.
Fig. 3 Transmitted and reflected power of 100-m stretched (filled markers) and untreated (empty markers) fiber. Blue diamond and red squares denotes the transmitted and reflected power respectively.
At the same time, the applied longitudinal stress is transformed into a lateral stress when the fiber is wound on a spool, and induces a stress-induced birefringence which manifests as a measurable increase in the polarization mode dispersion (PMD). The differential group delay (DGD) plot shown in Fig. 4 depicts an increase in the DGD magnitude, which is accompanied with a spread of DGD across the measured wavelength as contributed by a second-order PMD. Similar behavior is observed when straining conventional HNLFs [24]. The PMD degradation due to straining can be diminished by using spools with larger core radius.
Fig. 4 Differential group delay (DGD) of stretched and untreated fibers, showing the effect of applied longitudinal stress on fiber PMD.
The measured PMD degradation also had a measurable impact on parametric mixing efficiency, particularly in wide-band setting. Indeed, while the wavelength conversion efficiency was largely maintained within the 30-nm bandwidth for untreated fiber (Fig. 5(a) ), the conversion peak phase-matched by the fourth-order dispersion vanished when the fiber was stretched (Fig. 5(b)). Nevertheless, the SBS threshold increase should outweigh the PMD impairment in most of mixing applications that do not involve distant-band photon exchange. For instance, phase-sensitive amplification [1,8] and wavelength-conversion devices for coherent channel transport in the conventional telecom-bands are not trivially compatible with conventional pump-dithering techniques [25], and therefore are the applications most likely to immediately benefit from the new HNLF type.
Fig. 5 Conversion spectra of mixers pumped at (a) 1548.1 nm and (b) 1542.9 nm. Diamond and circles denotes untreated and stretched fibers.
3. Application: distant-band parametric light generation
Broadband light sources covering unconventional spectral bands have fuelled multiple advances in areas including sensing, spectroscopy, bio-photonics, and among others. Possessing octave-wide tunable bandwidth and generation efficiencies unparalleled by crystal-based counterparts, fiber optical parametric oscillators (FOPOs) represent a promising solution for these emerging applications.
FOPOs are constructed of microstructure fibers [26,27] or solid structure fibers as the parametric gain media [9,28]. Applications demanding ultra-fast pulses as well as visible-band generations are typically supported by microstructure fibers – their high nonlinearity and atypical dispersion characteristics allow for ultra-short pulses generation in a short-fiber device, as well as generation in unconventional bands [29,30]. However, the loss elevation in the long-wavelength bands (λ > 1700 nm) renders microstructure fibers suboptimal for operation in these bands [31,32]. While solid-structure fibers exhibit substantially lower attenuation in the long-wavelength bands, maintaining an unperturbed dispersion along an extended distance for high-efficiency parametric generation remains challenging for the conventional fiber types.
The development of the new HNLF type was motivated, in part, by the fundamental limit set by conventional HNLF fibers on NIR-driven FOPO devices [9,28]. Indeed, wide-band fiber-optical parametric oscillators tuned by higher-order dispersion present one of the most demanding requirements in terms of local dispersion invariance [16]. These widely-tunable light sources rely on precise balancing of the positive second-order dispersion and the negative fourth-order dispersion to produce a pair of GHz-wide gain windows separated by 40 THz or more. This regime of parametric amplification is very sensitive to the local dispersion characteristics, thus mandating dispersion stability better than any existing HNLF types by approximately an order of magnitude [16]. Indeed, this is the sole reason for the absence of HNLF-based FOPO operating with negative fourth-order dispersion: all reports to date have used large-core mixer waveguides such as DSFs [9,28].
The dispersion-stabilized HNLF described here opens a new path towards power-efficient FOPO construction. In order to quantify the benefit in this regard, a NIR-pumped mixer operating in the SWIR band was constructed. The mixer was used to compare the generation efficiency of a FOPO based on the new HNLF against a standard construction using telecom DSF. The FOPO test-bench is shown in Fig. 6 .
Fig. 6 FOPO setup. ECL: External cavity laser; MZM: Mach-Zehnder modulator; EDFA: Erbium-doped fiber amplifier; TBPF: Tunable band-pass filter; WDM: Wavelength-division multiplexing band filter; FUT: Fiber-under-test; ODL: Optical delay line; PC: Polarization controller; VOA: Variable optical attenuator.
The pump was generated by a tunable external cavity laser (ECL) with 15 dBm output power. The pump ECL output was carved by a Mach-Zehnder modulator (MZM), driven by flat-top electrical pulses with 1.2-ns pulse width, 53.3 MHz repetition rate and 1/16 duty ratio. Subsequent amplification by two erbium-doped fiber amplifiers (EDFAs) in tandem provided the FOPO pump with a peak power up to 12 W (1.1 W average) at the input facet of the FOPO cavity. The cavity was assembled in a ring topology, where the pump was launched into the fiber-under-test (FUT) through a wave-band combiner (WDM), and the 1.3-μm-band component in the FUT output was extracted and fed back to WDM. The intra-cavity optical delay line (ODL) provided fine alignment of the cavity round-trip time to the repetition rate, whereas the polarization controller (PC) was set to align the states of polarization of the pump and lasing waves. Input pump power and optical spectrum at the output of the FUT were monitored through the 1% couplers at the cavity input and FUT output facet.
With the new HNLF serving as the parametric gain medium in the cavity, the FOPO created two distinct tones in the near-infrared (NIR) and SWIR bands, as shown in Fig. 7 . The farthest SWIR and NIR tones were generated at 1802.1 nm and 1336.8 nm by the pump at 1535 nm. Since the degradation in parametric amplification efficiency due to dispersion fluctuations intensifies as distant pump-signal frequencies detune, this wavelength configuration also represented the worst-case operating condition for this FOPO system. Remarkably, the fiber maintained its capability to provide narrow-band phase-matched gain, as exemplified by the 0.2-nm spectral width of the SWIR-band output.
Fig. 7 FOPO output generated by a pump at 1535 nm. The pump peak power was set at 4.3 W. Inset shows a zoom-in view of the SWIR-band component possessing a 3-dB spectral width of 0.2 nm.
The FOPO characteristics in terms of pump-lasing wave power transfer were subsequently examined at the above wavelength configurations, as depicted in Fig. 8 . To demonstrate the benefit of HNLF over conventional DSF, the characterization was repeated using a 100-m DSF with a nonlinear coefficient of 2.5 (W∙km)−1. The pump used in the DSF-based parametric oscillator was shifted to 1549.2 nm in order to enforce the same frequency detune (29 THz). The benefit of the new HNLF in parametric generation is prominent – the threshold pump power was reduced by a factor of 2.5, as well as an enhancement of power efficiency by the same factor.
Fig. 8 Power transfer characteristics of FOPO using new high-confinement fiber (blue diamonds) and DSF (red squares). Pth denotes the threshold pump power.
On the other hand, the measured threshold power was considerably higher than the theoretical projection at 1.4 W, calculated by taking into account of the cavity round-trip loss of 6.1 dB. The source of this discrepancy was accounted for by using a statistical model of the parametric gain in the presence of dispersion fluctuations [33]. Shown in Fig. 9 , the mean gain level at 6 dB corresponded to a dispersion fluctuation level of 0.013 ps/nm/km. We note that the level of dispersion fluctuations predicted in the numerical model was in remarkable agreement with the measured value, thus suggesting that dispersion fluctuations were indeed the limiting factor in parametric device performance. More importantly, while the fluctuations exhibited by the fabricated fiber sample did not allow the parametric generation efficiency approaching the theoretical bound, this gap is likely to be closed by the improvement in geometry control accuracy enabled by advanced fabrication techniques.
Fig. 9 Calculated mean gain level attainable by the parametric amplifier at the threshold pump power, under the influence of dispersion fluctuations in terms of standard deviation of dispersion at the pump wavelength.
4. Conclusion
We have demonstrated a high power efficiency SWIR-band fiber optical parametric oscillator using the newly designed highly-nonlinear fiber. The new fiber exhibited approximately an order-of-magnitude improvement (86% reduction) in dispersion stability over the conventional designs, when subjected to transversal geometry variation. Furthermore, the fiber showed very small sensitivity of dispersion to longitudinal strain. This makes the fiber very well suited for SBS suppression by spooling the fiber with varying strain. The exceptional dispersion stability, coupled with the high field-confinement characteristics of the new fiber, has enabled low-pump-power parametric oscillation in the SWIR band. Compared to the standard SWIR FOPO using conventional DSFs, the power efficiency of the parametric oscillator based on the new fiber was improved by 2.5 times. Further improvement in the generation efficiency is expected with further optimization in the fiber fabrication control.
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