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Abstract
Optical fibers with a logarithmic index profile can provide invariant mode field diameters along a tapered fiber, which enables adiabatic mode transitions for higher-order mode (HOM) microfibers. A microfiber with a waist diameter of ∼2 µm is fabricated with an insertion loss lower than 0.03 dB for the LP01 and 0.11 dB for the LP11 mode. The concept of the low loss HOM microfibers can be further extended to include more than one fiber and a 2×2 few mode microfiber coupler is fabricated/characterized in our experiments. These single or multiple spatial channel HOM microfibers are beneficial for various applications, including in particle propulsion, atom trapping, optical sensing and space division multiplexed data transmission systems.
Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
1. Introduction
Optical microfibers or nanofibers (having outer diameters ranging from ∼100 nm to a few µm) [1–4] have attracted considerable attention in the fields of optical communications, optical sensors, nonlinear optics and quantum/atom optics due to their strong evanescent light field, wavelength-scale mode profiles and large waveguide dispersion. The majority of previous studies have been conducted with single mode microfibers supporting only the fundamental mode but few-mode microfibers having higher-order modes (HOMs) have recently gained increasing interest for use in particle propulsion [5], atom trapping [6], micro-resonators [7], optical sensors [8,9] and space division multiplexed (SDM) data transmission systems [10,11]. For example, HOMs in microfibers can provide greater evanescent field extension around the taper waist compared to the fundamental mode and faster particle propulsion speeds (roughly 5-8 times) have been observed [5]. In general, however, meeting the adiabatic taper criterion for HOMs in common optical fibers (e.g. step-index or graded-index fibers) is more challenging than for the fundamental mode because the mode field diameter (MFD) changes rapidly when the mode is cutoff from the core. Consequently, it is hard to achieve low loss HOM microfibers. Reduced cladding fibers (e.g. 80 µm cladding fibers) and/or high numerical aperture fibers have been proposed to ease the adiabatic criterion for HOMs but this still dictates the need for small (∼ few milliradian) and well controlled taper angles to realize low-loss HOM microfibers [12].
Very recently, the new concept of an optical fiber having a logarithmic (LOG) refractive index profile [13–16] has been proposed as a means to provide an endlessly adiabatic taper transition due to the invariant mode field diameter (MFD) on tapering. A short low-loss taper transition (∼2 mm) for the fundamental mode has been experimentally demonstrated validating the approach [13,14]. Importantly, these LOG fibers can support several spatial modes and all the guided modes are expected to have constant MFDs that are independent of the scale of the fiber, just as for the fundamental mode. In practice, however, the mode size increases rapidly with mode order and the higher-order modes become much more susceptible to bend loss, as briefly discussed in Ref. [13].
In this paper, we focus our attention on HOM microfibers and investigate the advantages provided by LOG fibers for low-loss HOM microfiber fabrication. Firstly, we analyze the adiabatic criterion of LOG fibers compared to conventional step-index few-mode fibers and illustrate the unique advantage of LOG fibers in supporting a constant MFD along the taper. Based on the theoretical design, HOM microfibers were experimentally fabricated and their optical performance was measured/compared with that of conventional step-index fibers for the same tapering condition. Low loss HOM microfiber (0.11 dB for the LP11 mode) was readily achieved from a LOG fiber and it was compactly packaged using standard commercially available fused fiber coupler packaging components. Furthermore, we have extended the approach to multiport HOM microfiber devices and a 2×2 few-mode microfiber coupler was successfully fabricated with a low excess loss (<0.2 dB) for both spatial modes.
2. Modal characterization of a LOG fiber
Figure 1(a) shows an optical microscope image of the cross section of the LOG fiber whose refractive index varies gradually as a logarithmic function of the radial distance from the fiber center. There is no core/cladding boundary in this fiber but light guidance along the central axis is clearly visible when fiber end is illuminated with a halogen lamp. The fiber was fabricated using a conventional plasma chemical vapor deposition (PCVD) process and the measured refractive index profile of the LOG fiber (red line in Fig. 1(b)) is reasonably well matched to the fiber design (gray line), which is defined by n2(r) = n02 − NA2 ln(r/ρ) [13] where NA is the numerical aperture and ρ is the cladding radius of the fiber. Note that this is the same fiber used in our recent publication [13] and more details on the fiber design and related theory can be found therein. From numerical simulation of the guided mode properties, the current LOG fiber can be used for effective two mode operation supporting LP01 and LP11 modes at 1550 nm.
Fig. 1. (a) The fiber cross-section and (b) measured fiber refractive index profile (FRIP) (red line) and idealized refractive index profile (grey line) of our logarithmic (LOG) fiber.
In order to experimentally characterize the modal properties of the LOG fiber the multimode impulse response of the fiber was first measured by selective modal excitation at the input and subsequent time-of-flight measurement at the output. As shown in Fig. 2(a), two distinguishable temporal peaks, corresponding to the LP01 and LP11 modes, are clearly observed and the differential group delay (DGD) between the two spatial modes is about -6.7 ps/m. Note that this is quite a large negative value, which means that the LP11 mode travels much faster than the LP01 mode. This feature means that LOG fiber could be in principle used for DGD compensation in space division multiplexed data transmission links based on step-index few mode fibers (typically DGD∼ 2-3 ps/m). In this case, whilst the local DGD is relatively large (a few ps/m) the total accumulated DGD over the link can be engineered to be close to zero by cascading suitable lengths of step-index and LOG fibers with opposing signs of DGD [17]. DGD compensation using fibers with high local values of DGD not only minimizes the complexity of the MIMO processing, but also the impact of intermodal nonlinear effects such as cross-phase modulation as compared to DGD compensated links made from graded-index few mode fibers (which can exhibit much lower values of DGD). As shown in Fig. 2(a), (a) high modal purity of >20 dB is readily achieved in this fiber and the guided modal intensity profiles are confirmed by a CCD camera (under 1550nm CW laser excitation). As shown in the inset of Fig. 2(a), two clean spatial modes (LP01 and LP11) were observed in the far field. The DGD at different wavelengths was further measured in the time domain as plotted in Fig. 2(b). By taking the derivative of the measured DGD with respect to wavelength, the chromatic dispersion was determined to be ∼19.8 ps/km·nm for the LP01 and ∼14.9 ps/km·nm for the LP11 mode, respectively.
Fig. 2. (a) Time-of-flight measurement for pure LP01 and LP11 mode excitation, with output far-field patterns inset, and (b) wavelength dependency of the differential group delay (DGD) in the LOG fiber.
In order to analyze the adiabatic criterion [18,19] of the LOG fibers compared to commercial step-index few mode fibers used in our work (two-mode step-index fiber from OFS), the mode field diameters (MFDs) of the fibers were calculated as a function of the outer diameter of the fiber taper using the beam propagation method (Synopsys BeamPROP). The more the MFD of a mode changes with fiber diameter, the harder it is to achieve an adiabatic taper for that mode [13]. As shown in Fig. 3(a) going from right to left, i.e. down the taper transition, the MFDs of both spatial modes initially decrease slightly for the step-index FMFs but then increase as the light guidance of the core becomes weaker and is gradually taken over by guidance at the cladding/air boundary. For the fundamental (LP01) mode the variation in MFD is modest and gradual, so it is relatively straightforward to make low-loss tapers for that mode in step-index fiber. However, in contrast, the LP11 modes cease to be guided along the core while the outer diameter is relatively large around 80 µm (i.e. the higher-order modes experience a cutoff) and the MFD increases sharply. This sudden big change in the MFD of the HOMs is the primary reason that it is difficult to achieve an adiabatic taper transition from conventional step-index (or graded-index) FMFs. However, the MFD curve of the LOG fiber is nearly flat for both spatial modes until the fiber outer diameter becomes comparable to the MFD. This unique characteristic of constant MFDs along the taper makes LOG fiber a good candidate for the fabrication of HOM microfibers with negligible insertion loss. Figure 3(b) shows the calculated mode field evolution in a tapered LOG fiber. The beam sizes of both modes show only modest changes along the taper region even though only a very short taper transition (∼1 mm) is employed in this simulation.
Fig. 3. (a) Change in mode field diameters (MFDs) for step-index few mode fiber (FMF) and LOG fiber along the taper and (b) mode field evolution of two transverse modes in a LOG fiber (the physical profile of the taper is indicated by the gray shading).
3. Microfiber fabrication and its optical performance
By using the well-established flame brushing technique [3,20], both optical fibers were gradually tapered from 125 µm to 2 µm with an exponential taper profile (uniform waist length = 4 mm, transition length = 15 mm) and the transmitted optical power was monitored as a function of the pull length. In order to investigate the mode dependent characteristics of the microfibers, a 1550 nm distributed feedback (DFB) laser was used as a light source and a simple phase-plate based free-space setup [21] was employed in front of the input facet of the optical fiber to excite either the LP01 or LP11 modes with a modal purity of >20 dB. As shown in Fig. 4(a), the LP11 mode of the step-index FMF experiences oscillatory power fluctuations due to the non-adiabatic taper transition during the tapering process, which is a signature of energy transfer from the core mode to the unwanted higher-order cladding modes. As such it continuously loses optical power, resulting in a higher insertion loss (13.9 dB). However, as expected, the LP11 mode of the LOG fiber in Fig. 4(b) shows no signature of power oscillation (i.e. the transition is adiabatic) and the total insertion loss of the LP11 mode was less than 0.11 dB, comparable to that of the LP01 mode (0.03 dB) in this experiment.
Fig. 4. (a) Transmitted power evolution of both (a) step-index FMF and (b) our LOG fiber for pure LP01 and LP11 mode excitation as a function of pull length. (c) The microscope image of the fabricated microfiber (left) with an outer diameter of ∼2 µm and a picture of the fully packaged device (right).
The microscope image of the fabricated microfiber is shown in Fig. 4(c). The outer diameter of the taper waist was ∼2 µm and the fabricated microfiber was protected/packaged using commercially available fused fiber coupler packaging components (i.e. U-shaped glass substrate tube and outer stainless steel housing). The length of the fully packaged prototype device was ∼10 cm with a 3 mm diameter metal housing tube, but this could be further shortened by reducing the length of the stripped bare section of fiber and by optimizing the taper profile. Also, note that the device is based on an adiabatic mode transition (i.e. smooth taper transition without any mode coupling) and consequently the transmission is inherently broadband (> a few hundred nanometers). These low loss HOM microfibers are particularly beneficial for particle propulsion, atom trapping, optical sensing and space division multiplexed transmission systems due to their enhanced efficiency, high sensitivity and lower crosstalk. For example, ultra-high sensitivity detection can be achieved by HOM micro-resonators (e.g. few-mode microfiber loops or coils) and low crosstalk fan-in/fan-out (FIFO) devices for high spatial density multicore fiber interconnect (e.g. FIFO for few mode multicore fibers) [22] can be readily realized for space division multiplexed transmission. In addition, these LOG fibers can support several spatial modes whilst providing an invariant MFD along the fiber taper, and spatial multiplexing devices on optical microfibers could further accelerate the wider application of the technology.
In addition, the concept of the low loss HOM microfiber can be further extended to include more than one fiber, and a 2×2 microfiber coupler was fabricated and examined as part of our experiments. The tapering process is almost identical to that used in single fiber tapering except that two LOG fibers are taken and twisted around each other (∼1.5 turns for efficient physical contact) and then fused/stretched to form a biconical microfiber coupler. With selective modal excitation (either LP01 or LP11 mode), light from a 1550 nm DFB laser diode was launched into one input fiber, and the two output fibers were monitored to determine the amount of light coupling. As shown in Fig. 5, the LP11 mode starts to couple first at a pulling length of around 17 mm whereas power transfer for the LP01 mode happens only after a pulling length of 22 mm. This is because the evanescent tail of the LP11 mode extends further into the cladding and light begins to couple from one optical fiber to another at an earlier pulling stage. Note, however, that only a smooth periodic power oscillation (owing to the mode coupling between two fibers) was observed for both spatial modes and there was no signature of a non-adiabatic transition (i.e. nothing similar to the fast power oscillation in Fig. 4(a)) due to excitation of higher-order cladding modes. Therefore, each spatial mode experiences a different power transfer but the total excess loss (i.e. the ratio of the total input power to the total output power) remains very low (∼0.05 dB for the LP01 and ∼0.2 dB for the LP11 mode). In comparison, as presented in Ref. [11], the HOMs in conventional FMFs frequently experience a non-adiabatic transition, making it very difficult to fabricate low loss FMF fused fiber components. Using our proposed LOG fiber, however, the adiabatic taper criterion of HOMs can be significantly relaxed and various functional fused FMF components (e.g. 2×2 fiber coupler, power splitter, mode converter) [11] can accordingly be developed for space division multiplexed data transmission systems.
Fig. 5. Coupling ratio evolution of a 2×2 LOG microfiber coupler for pure LP01 and LP11 modes at 1550 nm as a function of the pulling length.
4. Conclusion
In conclusion, we have successfully fabricated low loss microfibers supporting higher order spatial modes using a logarithmic index fiber. This specialty optical fiber can provide an invariant mode field diameter along the fiber taper for all spatial modes and enables a very smooth mode transition from core modes to cladding modes (i.e. adiabatic taper transition). We have focused on the characterization of the two lowest order transverse modes (LP01 and LP11) of this fiber and the microfibers were readily fabricated with very low insertion loss (typically less than 0.2 dB for both spatial modes). We believe that low-loss HOM microfibers could prove a very useful tool for particle propulsion, atom trapping, micro-resonators, optical sensing and space division multiplexed transmission systems.
Funding
Engineering and Physical Sciences Research Council (EP/N00762X/1, EP/P030181/1); Science and Technology Facilities Council (ST/N000544/1); Horizon 2020 Framework Programme (730890).
Acknowledgments
Data published in this paper are available from the University of Southampton repository at http://doi.org/10.5258/SOTON/D1360.
Disclosures
The authors declare no conflicts of interest.
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