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This paper reports the demonstration of a widely-translatable fiber-optic mirror based on the motion of liquid metal through the hollow core of a photonic bandgap fiber. By moving a liquid metal mirror within the hollow core of an optical fiber, large, continuous changes in optical path length are achieved in a comparatively small package. A fiber-optic device is demonstrated which provided a continuously-variable optical path length of over 3.6 meters, without the use of free-space optics or resonant optical techniques (i.e. slow light). This change in path length corresponds to a continuously-variable true-time delay of over 12 ns, or 120 periods at a modulation frequency of 10 GHz. Wavelength dependence was shown to be negligible across the C and L bands.
©2013 Optical Society of America
1. Introduction
Optical-domain, radio-frequency (RF) true-time-delay (TTD) lines with programmable time delays, wide bandwidth and low optical loss are key components of microwave photonic signal processing systems [1–4] and future optical communications networks [5]. Their unique advantages, including low loss (independent of RF frequency), large instantaneousbandwidth, immunity to electromagnetic interference, and parallel signal processing capability, have led to the realization of high-performance, tunable microwave filters, phased array beamformers, fast analog-to-digital converters, arbitrary waveform generators, signalcorrelators, and frequency converters and mixers [1–4]. For such applications, it is critical that the delay lines exhibit low loss, wide RF bandwidth, minimal frequency-dependent loss and dispersion. Furthermore, continuous TTD tuning over many RF periods is of interest for enabling high-resolution, reconfigurable optical-domain signal processing and beam-forming systems.
This paper reports the demonstration of a continuously and widely-tunable optical-domain TTD developed to address such needs. It is shown schematically in Fig. 1(a) , and is based on the translation of a liquid metal mirror along the hollow core of a photonic bandgap fiber. A fiber-optic device is demonstrated that provides a continuously-variable optical path length of over 3.6 meters, without the use of free-space optics or optical-resonance techniques (i.e. “slow light”). This change in path length corresponds to a continuously-variable true-time delay of over 12 ns, which at a 10 GHz modulation frequency amounts to 120 periods of tunable delay.
Fig. 1 Schematic diagram of the liquid metal fiber mirror. The hollow core of a HCPBG fiber, shown with expanded cross-section, is partially-filled by a droplet of liquid metal. Light propagating in the core of the HCPBG fiber (red) reflects from the surface of the liquid metal (gray) and back along the fiber core. The liquid metal can be moved along the fiber to reposition the mirror surface, such as by gas pressure. Motion of the liquid metal alters the round-trip optical path length, or equivalently, the round-trip phase and group delay.
2. Liquid metal fiber mirror
A schematic diagram of the liquid metal fiber mirror (LMFM) is shown in Fig. 1(a). It is based on a hollow-core, photonic bandgap (HCPBG) fiber [6], a specialty, single-mode optical fiber that guides light along its central hollow core. By inserting a droplet of liquid metal into this hollow core, a mirror surface is produced which reflects the light propagating along the fiber core back towards its source. More importantly, since the mirror is comprised of liquid metal, the mirror can be actively or passively repositioned within the HCPBG fiber. This results in a widely-translatable, fiber-optic mirror. Any translation of this mirror will alter the round-trip optical path length, or equivalently the round-trip phase and group delay of the HCPBG fiber. Figure 2(a) illustrates the use of such a mirror to produce a continuously-variable, fiber-optic true-time-delay.
Fig. 2 (a) LMFM connected to a fiber-optic circulator to produce a fiber-optic continuously-variable true-time delay. (b) Analogous device based on free-space optics (lens and translatable mirror). Unlike the LMFM, the free-space device is fundamentally limited by misalignment, size constraints, and diffractive loss.
A key advantage of the liquid metal fiber mirror is that it allows the mirror’s position to be varied over a wide range without the use of free-space optics. Whereas fiber-coupled, free-space optical systems such as that shown in Fig. 2(b) are sensitive to both misalignment and diffractive losses, especially for mirror translation over large distances, the liquid metalfiber mirror remains self-aligned to the fiber core, and benefits from diffraction-free wave-guiding. Thus, in principle the liquid metal mirror can be translated over the entire length of a HCPBG fiber, without limitations imposed by diffraction or misalignment. Furthermore the HCPBG fiber can be coiled on a spool, so that long-distance mirror translation, over the range of meters and beyond, can be achieved in a relatively compact fiber package.
Droplet translation along the fiber can be controlled by gas pressure, as illustrated in Fig. 1. Pressure actuation was utilized in this paper to demonstrate the LMFM concept. However, alternative tuning methods may also be envisioned, including the use of electromagnetic forces or thermo-capillary action to translate the droplet along the fiber.
3. Fiber mirror implementation
In order to implement the liquid metal fiber mirror, a hollow-core HCPBG fiber with 10 µm core diameter, 9 µm mode field diameter (MFD), and 1.49-1.68 µm wavelength transmission range (NKT Photonics HC-1550-02) was cleaved at both ends to a length of approximately 2.0 m. One end of the HCPBG fiber was then placed against the cleaved end of a 15 µm inner diameter fused silica capillary tube which had been filled with a 25 µm-long droplet of electronics grade mercury (Alfa Aesar, 99.999995% purity). The mercury droplet was then transferred into the core of the HCPBG fiber using a combination of air pressure applied to the capillary and suction applied to the HCPBG fiber. In this step, the tendency for mercury not to wet a fused silica surface was utilized (a property analogous to hydrophobicity [7]). This provided reverse capillary pressure that inhibited mercury from filling the smaller tubes of the HCPBG fiber cladding. The resulting capillary pressure (which scales inversely with tube diameter [7]) was significantly larger for the 3.8 µm holes of the cladding as compared to the 10 µm fiber core, thus allowing the fiber core to be preferentially filled. This step was also assisted by the high surface tension of the droplet. A microscope image of the HCPBG fiber cross-section, cleaved (using a larger droplet after testing) at a point where mercury filled the fiber core, is shown in Fig. 3(a) . This indicates that the mercury was placed within the HCPBG fiber core using this procedure, but not within the surrounding air-filled cladding.
Fig. 3 (a) Microscope image of the HCPBG fiber cross section, cleaved where mercury filled the fiber core. (b) Surface profile of the mercury-air meniscus within the cleaved, mercury-filled HCPBG fiber, measured using a scanning confocal microscope. The dotted lines indicate the limits of the 9 µm mode field diameter (1/e2 intensity) of the HCPBG fiber, over which the meniscus varied by approximately 1.0 µm.
The shape of the mercury-air interface (meniscus) within the HCPBG fiber was optically-profiled using a scanning confocal microscope, and the resulting surface profile is shown in Fig. 3(b). This surface profile demonstrates that the mercury-air interface was flat to within 1.0 µm over the 9 µm mode field diameter of the fiber (the extents of which are indicated by the vertical dashed lines). The presence of any meniscus was not ideal, however, as the mirror surface should be flat to maximize reflection into the guided mode of the HCPBG fiber. Thus, some optical loss at the air-mercury interface was to be expected due to inter-modal coupling.
The optical reflectivity of the LMFM was measured by butt-coupling the HCPBG fiber to a flat cleaved SMF28 fiber, and measuring the reflectivity at 1.55 µm. A fiber-coupled, multi-mode laser with 0.8 mm coherence length was used for this measurement, which eliminated cavity interference between the reflections from the SMF28 end face and the liquid metal surface. This allowed the device reflectivity to be measured, as defined by the expression
where Pin is the power launched into the SMF28 fiber, Pf the returned power from the fiber-fiber interface, Pm the returned power from the air-mercury interface, and Pt = Pf + Pm. Using this method the device reflectivity was measured to be −10.9 dB when the mercury droplet was located 12 cm from the fiber-fiber interface. After accounting for 1.5 dB of fiber-to-fiber coupling loss per pass (estimated from transmission measurements of an empty HCPBG fiber), the reflectivity of the liquid metal mirror into the guided mode of the HCPBG fiber was estimated to be −7.9 dB. Given that the reflectivity of mercury is 80% at 1.55 µm [10], it follows that the majority of the optical loss at the mirror, 6.9 dB, was attributable to the curvature of the meniscus.That loss was dominated by the meniscus is significant, because various methods exist to control the shape of a meniscus, including temperature [11], surface treatments [12], surfactants [13], and electromagnetic fields [14]. Although meniscus control (particularly in the context of hollow core fiber) was beyond the scope of this paper, the experimental results indicate its potential for improving device reflectivity.
4. Demonstration of widely-tunable true-time-delay
Translation of the liquid metal droplet along the HCPBG fiber was monitored using the setup shown in Fig. 4 . The input end of the fiber mirror was butt-coupled to a SMF28 fiber, which was in turn connected to an optical frequency-domain reflectometer (OFDR). The flat-cleaved ends of the HCPBG and SMF28 fibers were then manually aligned to maximize the reflection from the liquid metal droplet, discernible at the end of the HCPBG fiber using the OFDR. The droplet was then pushed along the HCPBG fiber via air pressure, and after coming to a stop its position was monitored using the OFDR. Measurements were performed over the wavelength range 1.525 to 1.613 µm, which covered the C-band and most of the L-band. The 2.0 m HCPBG fiber was coiled on a 1.0 inch diameter spool during measurements, with a total volume of less than 1 cubic inch.
Fig. 4 Test setup for translating the LMFM and characterizing its motion. Gas pressure applied by a piston pushed/pulled a liquid metal droplet along the HCPBG fiber core. The location of the mirror reflection point (air-metal interface) was monitored using an optical frequency-domain reflectometer (OFDR).
Figure 5 plots the results of nine OFDR scans, each corresponding to different positions of the liquid metal droplet as it was it was pushed along the HCPBG fiber. Each scan plots the amplitude of the optical impulse response versus position along the fiber, with position derived from the measured group delay assuming an effective mode refractive index of 1.00 for the HCPBG fiber [15]. The reflection from the SMF28 to HCPBG fiber interface, located at the origin of the horizontal axis, serves as a reference. The second reflection peak from the left corresponds to the location of the air-liquid metal interface within the HCPBG fiber. As shown, this interface was translated a distance of 1.8 m along the fiber by applied air pressure. This distance provided a continuously-variable round-trip optical path length of 3.6 m, or equivalently, a continuously-variable round-trip true-time-delay of 12 ns. By applying reverse pressure the liquid metal droplet could also translated in the opposite direction. No significant hysteresis was observed in the optical response upon change of direction, other than a slight reduction in device reflectivity as described below.
Fig. 5 OFDR scans recorded at different times as the liquid metal droplet was translated along the HCPBG fiber. The reflection from the SMF28-to-HCPBG fiber interface, located at the horizontal axis origin, serves as a reference. The location of the air-liquid metal interface (i.e. mirror reflection point) is indicated by second reflection peak from the left. This interface was translated 1.8 m along the HCPBG fiber, producing a round-trip true time delay tuning range of 12 ns.
The impulse response measured by the OFDR, shown in Fig. 5, is related to the optical reflectivity via a Fourier transform relationship. Transforming the impulse response data in Fig. 5 (using data only in the vicinity of the air-liquid metal interface), produced the device reflectivity values plotted in Fig. 6 . As shown, the device reflectivity tended to decrease with distance from SMF28-HCPBG fiber interface, decreasing by approximately 0.9 dB until stabilizing at a distance of 1.2 m from the fiber-fiber interface. This variation with position was presumably due to the excitation of leaky modes in the HCPBG fiber, which attenuated over a distance of approximately 1 meter. Moving the droplet in the opposite direction produced very similar values for the device reflectivity to those in Fig. 4, other than a slight hysteresis characterized by a 0.25 dB reduction in mean reflectivity when the droplet moved away from (as opposed to towards) the OFDR.
Fig. 6 Device reflectivity versus position of the liquid metal mirror within the HCPBG fiber. Device reflectivity decreased with distance from the SMF28-HCPBG interface (the horizontal origin), presumably due to attenuation of leaky modes excited in the HCPBG fiber. Device reflectivity stabilized at a distance of approximately 1.2 m from the fiber-fiber interface.
Figure 7 plots the measured group delay and device reflectivity versus wavelength, when the liquid metal mirror was located 1.89 m from the fiber-fiber interface. As shown, the group delay was relatively wavelength independent, varying by only 0.24% over the entire 88 nm measurement range. The device reflectivity was also relatively wavelength independent, varying by approximately 0.3 dB over a 70 nm wavelength range. Note that the data in Fig. 7 have been smoothed using a 1.0 nm window to reduce noise.
Fig. 7 (a) Group delay and (b) device reflectivity vs. wavelength, when the liquid metal mirror was located 1.89 m from the SMF28-HCPBG fiber interface. Data has been smoothed using a 1.0 nm window to reduce noise.
5. Conclusion
The liquid metal fiber optic mirror presented in this paper offers a novel method for widely and continuously-tunable optical-domain TTD. A fiber-optic device was demonstrated providing a continuously-variable optical path length of over 3.6 meters, or equivalently a continuously-variable TTD of over 12 ns. This was achieved without the use of free-space optics or resonant optical techniques (i.e. slow light), in a robust and compact package, and with minimal wavelength dependence. The ability to continuously-tune a TTD over many RF periods (12 ns is equivalent to 120 periods at 10 GHz) offers considerable potential for high-resolution, reconfigurable optical-domain signal processing and beam-forming systems.
Acknowledgments
The authors would like to thank Geoffrey Cranch at the U.S. Naval Research Laboratory for assistance with the OFDR measurements.
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