We propose and demonstrate an inline fiber optic power sensor (IFPS) resorting to an embedded waveguide tap, which is formed to traverse across the cladding and core of a standard single-mode fiber. The tap was produced via a single-step inscription based on the femtosecond laser direct-writing method. A tightly focused pulsed laser beam has been particularly exploited to suppress the elongation along the laser propagation direction, thereby improving the cross-sectional symmetry of the created tap waveguide. The fabricated fiber optic tap has been stably combined with a photodiode via a compact package. The achieved tap ratio could be tuned from 1.0% to 5.9% at the wavelength of 1550 nm by adjusting the applied laser power, while the induced excess loss was kept below 0.6 dB. The proposed IFPS will be highly suitable for real-time power monitoring in a variety of applications, including optical communication networks and systems.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Fiber core and cladding photonics, which is perceived as a vital part of integrated photonics to extend the functionality of optical fiber, has received growing attention from a broad range of fields including optical communications [1–5], microfluidics [6–9], compact sensing [10–13], and lab-in-fiber applications [14,15]. In order to optically access the fiber core and cladding, the direct-writing technology assisted by a femtosecond laser (fs-laser) has accomplished significant advances in the flexible integration of three-dimensional photonic components and precise focal confinement of laser interaction volume with high resolution [15–18]. Unlike the fs-laser based inscription in diverse vitreous bulk substrates, fiber optic lightwave circuits induced by a fs-laser are principally based on smooth type I modification, which leads to a localized increase of material refractive index relative to the unirradiated region. Positive index modification is fundamentally driven by an energy transfer process from the ultrashort optical pulses to the dielectric material lattice, which incorporates a series of nonlinear absorption through photo-ionization, such as multiphoton, tunneling, and avalanche ionization, depending on the materials of inscription and exposure conditions [18–21]. Besides the heat accumulation, the local melting, thermal diffusion, and rapid resolidification of the material are deemed to subsequently take place for the tight-focusing and high-pulse-rate laser writing [18,21–23].
Recently, optical communication networks and systems based on a single-mode fiber (SMF) have been extensively deployed for providing broadband services over a long distance in various applications, including schools, enterprises, intranets, data centers, governments, and communities [24–26]. Rapid increase in the data traffic and density of fiber optic networks has created a demand for a device which plays the role of checking on the optical power flowing through an optical fiber, providing a reliable network monitoring and maintenance [27–29]. For the conventional fiber optic power monitoring systems, fused couplers or splitters are mainly utilized to split a fixed amount of light into another fiber, which collects the optical power into a power meter. This method is cumbersome and commonly comprised of several discrete components. In contrast, an inline fiber optic power sensor (IFPS), which takes advantage of architectures such as microbends  and offset fusion-splicing [28,29], is deemed to tap a fraction of optical power out of a fiber without interrupting the main transmission path. Hence, the IFPS can be directly incorporated into the pre-existing optical networks so as to fulfill real-time, continuous power measurement and feedback, offering salient features in terms of compactness and cost. Meanwhile, a built-in power sensor which is embedded in the fiber is capable of adaptively tapping a specific amount of light from the fiber core to the cladding, causing no significant loss. Hence, fiber cladding photonic circuits including a guided-wave coupler were reported to allow for a flexible coupling of light travelling in the core with the help of a spur-waveguide [16,30] or a total-internal-reflection (TIR) mirror that is embedded in the fiber cladding . However, the coupled light was only detected at the polished facets of the bare fiber or redirected by the TIR mirror, thus rendering direct power probing practically complicated. Alternatively, a side tapping was reported by incorporating an elongated ellipsoidal waveguide, which is written by a loose focusing optics that features a numerical aperture (NA) of 0.1 . However, loose focusing is possibly subject to poor positional alignment because the depth-of-focus is relatively long compared to the size of optical fiber.
In this work, we present an IFPS which takes advantage of a built-in tap across the cladding and core of a standard SMF. A fs-laser direct-writing scheme capitalizing on a strongly focused optics was employed to manufacture the in-fiber tap. For the proposed method resorting to the tightly focused femtosecond laser inscription, elongation along the laser propagation direction has been substantially suppressed to improve the cross-sectional symmetry, as compared with the case of loose focusing optics. Thus, the tap structure becomes more compact and better suited for enabling high-density integration, which is especially noteworthy in the case of space-division multiplexing systems based on multi-core fibers [32,33]. The tapping efficiency was efficiently tuned by adjusting the irradiation power of fs-laser pulses. The fiber optic tap was integrated with a photodiode (PD) via a compact housing. Factors determining the tapping efficiency were particularly explored theoretically and experimentally. The propagation characteristics of fiber mode were calculated using RSoft BeamPROP (Synopsys), a commercially available modeling tool based on an implicit finite-difference scheme.
2. Proposed IFPS capitalizing on a laser-written waveguide tap
The proposed IFPS draws upon an embedded waveguide tap in combination with a PD. Figure 1 shows that the fiber optic tap is formed to traverse across the cladding and core of a standard SMF, playing the role of routing a fraction of power delivered in the core, as indicated by the red arrow. In order to traverse across the core, the tap created in the laser-writing plane is located 62.5 μm below the top surface of the cladding. The tap exhibits a cylindrical configuration with a quasi-circular cross-section and higher refractive index compared to that of the surrounding medium (ns). For the tap, the index modifications as a result of the different photo-sensitivities are ntap-in-cladding and ntap-in-core in the regions of fiber cladding and core respectively. The tap is designed to be slightly slanted with respect to the direction of the core at a crossing angle of θ, while the critical angle pertaining to the boundary between the tap and air is around 43°. Considering that the TIR at the boundary might prohibit light from escaping out of the tap created in the cladding region, an index-matching epoxy is introduced to fill the gap between the cladding and PD, thereby mitigating the constraint imposed by the TIR and alleviating the Fresnel reflection. In this respect, the tap directly couples light propagated in the core to the PD, and a real-time monitoring of the light signal carried over the fiber can be fulfilled.
Coupling between the intersecting waveguides corresponding to the fiber core and the proposed tap is primarily related to interactions of the modes of the compound structure, according to the supermode approach . The coupling efficiency is determined by the accumulated phase difference between the first two supermodes. The normalized output powers for the through- and tap-port are given by and , respectively. The total accumulated phase difference between the first two supermodes is . The analytical approximation neglects the radiation-mode coupling, and it is valid for values of H in the range of . Here, β1(x) and β2(x) represent the propagation constants of the first and second supermode along the x-axis, respectively. is the relative index difference, is the normalized frequency with the tap width of Wtap and free-space wavelength of λ, and is the normalized profile height. c0, c1, c2, and c3 are the numerical coefficients. From the perspective of enhanced power tapping, the index profile and the width of the fiber optic tap has been controlled, when the crossing angle is fixed at .
As depicted in Fig. 1, the proposed inline tap is constructed by moving the fiber with respect to the focused laser beam as indicated by the pink arrow, in an attempt to invoke permanent refractive index modifications in accordance with the transverse writing. The produced waveguide thus is not limited in length, contingent upon the working distance of the focusing objective lens. When it comes to the transverse writing scheme, the created waveguide might provide an asymmetric cross-section, which is disadvantageous in terms of optical coupling [19–21,35]. This issue can be significantly mitigated by resorting to a tightly focused lens with a high NA over 1.0 so as to minimize the confocal parameter [5,18,23]. Or an astigmatic beam shaping may be exploited in front of the focusing objective to revise the spatial beam profile [36–38], which requires a rigorous orientation depending on the laser scanning direction and potentially degrades the laser power . To the contrary, focusing optics featuring a low NA is prone to suffering from nonlinear effects which compete with the energy deposition, such as self-focusing, white-light generation, and laser beam filamentation [18,19]. Therefore, a strongly focusing scheme relying on an oil-immersion objective lens is desired for the laser-writing system.
A standard step-index SMF has been adopted for the embodiment of the IFPS, for which the core and cladding are 8.2 μm and 125 μm in diameter, respectively, and the corresponding refractive indices are 1.449 and 1.444 at the wavelength of 1550 nm. For the theoretical analysis, the laser-written tap is simply assumed to provide a circular cross-section, in which the refractive index modification is uniform and isotropic both in the core and cladding. Figure 2(a) plots the index profile of the fiber optic tap, indicating a uniform width of Wtap = 4 µm and distinct index modifications of Δntap-in-cladding = 0.004 and Δntap-in-core = 0.007 in the cladding and core. Considering the crossing angle between the tap and the core, the tap is designed to be approximately 2.4 mm long. As shown in Fig. 2(b), a fundamental mode at λ = 1550 nm is incident upon the core along the x-axis. The coupling is observed at different sites marked “A”, “B”, and “C” corresponding to the pathways of the core, the forward (Fwd.) tap, and the backward (Bwd.) tap, respectively. The tapping efficiency is particularly equivalent to the coupling efficiency for the forward tap. About 88.3% of the launched light is transported in the core, while the forward tap accounts for a portion of 3.8% to incur an excess loss of 0.5 dB. There is no noticeable power delivery via the backward tap. It is thus concluded that the fiber optic tap is directional in nature with respect to the propagation direction associated with the incident light. As anticipated, the tapped light seems to preferentially travel along the direction of the incident light.
Under the given cladding index modification of Δntap-in-cladding = 0.004, the tapping efficiency could be readily tuned in the range from 0.1% to 59.4% when Δntap-in-core is increased from 0.006 to 0.015 in the cases of tap widths of Wtap = 3 µm, 4 µm, and 5 µm, as described in Fig. 3(a). The tapping does not necessarily increase in a consistent manner with the core index modification, instead it diminishes for excessive modifications. To the contrary, the coupling efficiency for the core declines from 96.3% to 4.9%, while the excess loss caused by the tap deteriorates from 0.2 dB to 13.1 dB. The guiding properties of the original fiber might be adversely affected under the strong modification. Therefore, the configuration of the tap should be meticulously devised in consideration of the tap ratio in conjunction with the excess loss. As plotted in Fig. 3(b), for the taps with Δntap-in-core = 0.009 and Wtap = 3 µm, 4 µm, and 5 µm, the calculated tapping efficiencies are presented when tap deviations away from the center of the core, ranging from −3 µm to 3 µm, are deliberately introduced along the vertical z-direction. The vertical positioning offset is thought to result in roughly symmetric degradations in the tapping capability. The tapping efficiencies are altered from 1.2%, 10.2%, and 29.3% to 0.8%, 8.0%, and 25.8% for Wtap = 3 µm, 4 µm, and 5 µm, respectively, for the offsets of z = ± 3 μm. It is implied from these calculation results that the proposed fiberoptic tap is expected to feature a substantially high structural tolerance.
3. Fabrication of the proposed IFPS and its optical characteristics
The proposed fiber optic tap was created in an SMF by performing a single step of inscription assisted by a fs-laser beam, which is tightly focused via an oil-immersion objective lens. As shown in Figs. 4(a) and 4(b), with its coating and jacket stripped off in the region of laser-writing window, the fiber was first placed in the slot of a customized fiber holder, which will be mounted on the motorized stage during the laser scanning. The fiber was kept under tight tension to prohibit its displacement during the laser writing process. The fiber cladding was efficiently and reliably aligned in relation to the focused laser beam with an accuracy of ~1 μm, with the help of a visual pen marking instead of a mechanical marking. Under this condition, the fs-laser beam was precisely focused on the fiber center, which is 62.5 μm below the top surface of the cladding. Hence the laser scanning was carried out to traverse across the core of SMF in a reliable manner.
A fs-laser system was used to provide a linearly polarized collimated beam centered at a wavelength of 1035 nm, exhibiting a mean M2 value of 1.16. For the generated laser pulses, the repetition rate and the pulse duration were 510 kHz and 260 fs, respectively. The pulsed laser beam was delivered through a chain of turning mirrors, then tightly focused on an SMF (Corning SMF-28e) via an oil-immersion lens, which possesses a magnification of 100X with NA = 1.25, a working distance of 0.36 mm, and a focal length of 1.996 mm. An immersion oil (MOIL-30, Olympus), with a refractive index of 1.518 (@ λ = 546 nm) was used to fill the gap between the front surface of the objective lens and the SMF. In an effort to realize an effective fiber optic tap without adversely affecting its functionality, the laser power was appropriately tailored to assume 115 mW, 105 mW, and 95 mW. The overall focusing elements exhibited 50% loss and the corresponding pulse energies that are available on the target were observed to be 112 nJ, 103 nJ, and 93 nJ. Following the alignment, the laser beam was lowered by 62.5 μm from the top surface of the cladding to be focused on the center of the fiber core. The SMF, mounted on a motorized translation stage (XYCV630-C-N, Misumi), was horizontally rotated to make a crossing angle of 3° and subsequently scanned under the incident laser beam along the x-direction at a speed of 100 μm/s. In order to improve the production efficiency for the current tap and make even longer taps, we have attempted to alter the laser scanning speed from 100 μm/s to 300 μm/s in steps of 50 μm/s, taking into account the viscosity and binding strength of the index-matching oil. The optimal scanning speed was found to be 200 μm/s in terms of the polarization sensitivity of the inscribed tap.
When a visible light with a wavelength of 650 nm was shone on the SMF as indicated by the red arrow, a fraction of the light was evidently observed to be routed through the laser-formed tap. Light was also scattered due to the non-uniform and rough tap structure associated with the induced index perturbations [15,19,22]. The pattern of the fs-laser-written fiber optic tap was then inspected under a microscope. As revealed in the right hand side of Fig. 4(c), for the sample processed with a fs-laser power of 115 mW, an inscribed tap conduit with an approximately 4-μm width can be vividly witnessed displaying a slant angle of 3° with respect to the direction of the core. Figure 4(c) shows the cross-sectional facet of the fiber, where the laser-writing plane as indicated by the pink dotted line is 62.5 μm below the top surface of the cladding and the tap is written by traversing across the center of the fiber. The core is clearly observed in conjunction with the created tap of a quasi-circular shape, while the elongation along the laser propagation axis is monitored to be substantially suppressed. As shown in Fig. 5 of the x-z plane microscope image, the laser-written tap and fiber core are observed to overlap each other, confirming that the tap exactly is made to traverse across the core of SMF.
A PD was tethered to the prepared fiber optic tap via a UV curable epoxy (NOA68; Norland Products Inc.) within a compact package, as displayed in Fig. 6(a). A 1550-nm light from a laser diode (3CN00410DY, Alcatel Optronics) was coupled to the laser-processed SMF. The incident light power was varied from −20.0 dBm to 6.6 dBm. As plotted in Fig. 6(b), for the three taps that were treated with different fs-laser powers, the optical power was recorded at the output ports of the core and the inscribed tap as a function of the input light power. The tap ratio, which is defined as the ratio of the forward tap power to the input power, was measured to 5.9%, 2.6%, and 1.0% for the cases of fs-laser powers of 115 mW, 105 mW, and 95 mW, respectively. It was observed that the excess losses incurred by the fiber optic tap were accordingly 0.6 dB, 0.2 dB, and 0.2 dB. The output of the forward tap might have dwindled due to its own propagation loss on top of the Fresnel reflection pertaining to the imperfect interfaces between the cladding and the PD. The backward tap power was checked by coupling light to the SMF in the reverse direction, which was discovered to be negligible for the input light power weaker than −4.5 dBm and linearly increased with the stronger input power, which is attributed to the return loss and the propagation of cladding modes. Considering the asymmetry of the inscribed fiber as well as the non-uniform tap structure induced by the laser-writing, the forward and backward outputs of the tap exhibited a polarization sensitivity, as indicated by the error bars. When a polarization controller (FiberPro, PC1000) was used to adjust the state of the input light polarization, the measured polarization sensitivities for the forward and backward tap outputs were nearly the same at 1.6 dB for the three cases, while the polarization dependency for the core output was negligibly small as expected. In an effort to reduce the polarization sensitivity of the proposed tap, the scanning speed was optimized so that we could achieve a sensitivity of as small as 0.8 dB at the speed of 200 μm/s. The sensitivity might be further improved by exploiting a fs-laser with a shorter pulse duration (< 200 fs), which generates a smoother refractive index profile [40,41]. The directivity, defined as the contrast between the forward and backward tap powers, was measured to be 18.8 dB, 9.2 dB, and 6.0 dB for the taps corresponding to fs-laser powers of 115 mW, 105 mW, and 95 mW, respectively. Taking into account the results given in Fig. 6(b), the proposed IFPS could realize a highly linear relationship between the powers delivered through the core and the tap when the input power was ranging from −20.0 dBm to 6.6 dBm, as intended.
With the intention of gaining further insight into the index modification induced by the tightly focused fs-laser illumination, three optical waveguide patterns were similarly written along the core at depths of 30.0 µm, 62.5 µm, and 70.0 µm below the top surface of the cladding, as indicated by the pink circles of (I), (II), and (III) in Fig. 7. The laser writing condition is the same as that of the fiber optic tap fabrication. The refractive index profile of the laser-processed SMF was scrutinized in a non-destructive manner by means of a fiber index analyzer (IFA-100, Interfiber Analysis). As shown in Fig. 7(a), for the case of 95-mW fs-laser power, three distinct inscribed patterns are seen from the cross-sectional microscope image. The measured refractive index morphologies are accordingly served as well. The corresponding results are shown in Fig. 7(b) for the case of 115-mW fs-laser power. As compared with a virgin fiber, it appears that the tightly focused laser writing is supposed to produce a non-uniform index perturbation, entailing both positive and negative modifications. Such negative index alteration is particularly reported to be stem from thermally regenerated photosensitivity . Along the laser beam direction, as marked by the pink arrow, the created structures (I-III) are varying in their shapes and dimensions depending on the depth, which is attributed to the spherical aberration. This may be caused by the mismatch in the refractive indices of the oil and fiber [23,35]. For the patterns which are written 70.0 µm below the cladding with laser powers of 95 mW and 115 mW, the estimated dimensions are 3.9 × 4.1 μm2 and 4.1 × 6.3 μm2, respectively, which are slightly extended on the laser propagation direction. In general, for the patterns (I & III) formed in the cladding with the laser powers of 95 mW and 115 mW, analogous index changes were obtained, where positive and negative index variations range from 0.003 to 0.004 and from −0.002 to −0.005, respectively. However, the pattern (II) written in the core with the laser power 115 mW exhibited a dramatically amplified magnitude of index modification both in the positive and negative regimes. It is remarked that the pattern located at the core plays a chief role in tapping the light since the fiber tap is formed across the core. In the core region, the maximum positive index modification was enhanced from 0.009 to 0.015 when the laser power was raised from 95 mW to 115 mW. We could conclude that a highly increased index perturbation in the core and a slightly increased width of the laser-written waveguide led to the enhanced tap ratio ranging from 1.0% to 5.9%.
An IFPS, integrated with a PD within a compact package, was embodied by introducing a fiber optic tap traversing across the cladding and core of the SMF. The inline tap was fabricated through a fs-laser direct-writing scheme without fatally interrupting the fiber transmission. The strong focusing of an oil-immersion lens enables the creation of smaller and symmetric waveguide, which is highly suitable for high density integration. A reliable and straightforward method was developed to align the focal point and keep the fiber in place during the scanning process, rendering an accurate and repeatable fabrication. As intended, variable tap ratios of 5.9%, 2.6%, and 1.0% were practically achieved by altering the exposed fs-laser power. The proposed IFPS could possibly offer a perfect linearity between the powers delivered through the core and the tap, without incurring unbearable excess loss. The proposed device should pave the way of enabling real-time monitoring the optical fiber power conditions in cost effective manner.
Cooperative R & D between Industry, Academy, and Research Institute by Korea Small and Medium Business Administration in 2016 (No. S2385119); Kwangwoon University research grant in 2018.
The authors are grateful to Mr. Seung-Chan Lim for his helpful discussions.
References and links
1. J. Thomas, C. Voigtländer, R. G. Becker, D. Richter, A. Tünnermann, and S. Nolte, “Femtosecond pulse written fiber gratings: a new avenue to integrated fiber technology,” Laser Photonics Rev. 6(6), 709–723 (2012). [CrossRef]
2. J. He, Y. Wang, C. Liao, Q. Wang, K. Yang, B. Sun, G. Yin, S. Liu, J. Zhou, and J. Zhao, “Highly birefringent phase-shifted fiber Bragg gratings inscribed with femtosecond laser,” Opt. Lett. 40(9), 2008–2011 (2015). [CrossRef] [PubMed]
3. R. G. H. van Uden, R. A. Correa, E. A. Lopez, F. M. Huijskens, C. Xia, G. Li, A. Schülzgen, H. de Waardt, A. M. J. Koonen, and C. M. Okonkwo, “Ultra-high-density spatial division multiplexing with a few-mode multicore fibre,” Nat. Photonics 8(11), 865–870 (2014). [CrossRef]
4. T. A. Birks, I. Gris-Sánchez, S. Yerolatsitis, S. G. Leon-Saval, and R. R. Thomson, “The photonic lantern,” Adv. Opt. Photonics 7(2), 107–167 (2015). [CrossRef]
7. K. Zhou, Z. Yan, L. Zhang, and I. Bennion, “Refractometer based on fiber Bragg grating Fabry-Pérot cavity embedded with a narrow microchannel,” Opt. Express 19(12), 11769–11779 (2011). [CrossRef] [PubMed]
8. C. Liao, L. Xu, C. Wang, D. N. Wang, Y. Wang, Q. Wang, K. Yang, Z. Li, X. Zhong, J. Zhou, and Y. Liu, “Tunable phase-shifted fiber Bragg grating based on femtosecond laser fabricated in-grating bubble,” Opt. Lett. 38(21), 4473–4476 (2013). [CrossRef] [PubMed]
9. L. Yuan, J. Huang, X. Lan, H. Wang, L. Jiang, and H. Xiao, “All-in-fiber optofluidic sensor fabricated by femtosecond laser assisted chemical etching,” Opt. Lett. 39(8), 2358–2361 (2014). [CrossRef] [PubMed]
10. K. K. C. Lee, A. Mariampillai, M. Haque, B. A. Standish, V. X. D. Yang, and P. R. Herman, “Temperature-compensated fiber-optic 3D shape sensor based on femtosecond laser direct-written Bragg grating waveguides,” Opt. Express 21(20), 24076–24086 (2013). [CrossRef] [PubMed]
11. Y. Liu and S. Qu, “Optical fiber Fabry-Perot interferometer cavity fabricated by femtosecond laser-induced water breakdown for refractive index sensing,” Appl. Opt. 53(3), 469–474 (2014). [CrossRef] [PubMed]
12. C. Waltermann, A. Doering, M. Köhring, M. Angelmahr, and W. Schade, “Cladding waveguide gratings in standard single-mode fiber for 3D shape sensing,” Opt. Lett. 40(13), 3109–3112 (2015). [CrossRef] [PubMed]
14. K. Cao, Y. Liu, and S. Qu, “Quantitative microfluidic delivery based on an optical breakdown-driven micro-pump for the fabrication of fiber functional devices,” Opt. Express 25(20), 23690–23698 (2017). [CrossRef] [PubMed]
16. G. Marowsky, Planar waveguides and other confined geometries: Theory, technology, production, and novel applications (Springer, 2014), Chap. 4.
17. T. Meany, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Gross, M. J. Steel, M. J. Withford, and A. Szameit, “Laser written circuits for quantum photonics,” Laser Photonics Rev. 9(4), 363–384 (2015). [CrossRef]
18. R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008). [CrossRef]
19. A. Saliminia, N. T. Nguyen, M. C. Nadeau, S. Petit, S. L. Chin, and R. Vallee, “Writing optical waveguides in fused silica using 1 kHz femtosecond infrared pulses,” J. Appl. Phys. 93(7), 3724–3728 (2003). [CrossRef]
20. D. Choudhury, J. R. Macdonald, and A. K. Kar, “Ultrafast laser inscription: perspectives on future integrated applications,” Laser Photonics Rev. 8(6), 827–846 (2014). [CrossRef]
21. K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, “Ultrafast processes for bulk modification of transparent materials,” MRS Bull. 31(8), 620–625 (2006). [CrossRef]
22. C. B. Schaffer, J. F. Garcia, and E. Mazur, “Bulk heating of transparent materials using a high-repetition-rate femtosecond laser,” Appl. Phys., A Mater. Sci. Process. 76(3), 351–354 (2003). [CrossRef]
23. S. Gross and M. J. Withford, “Ultrafast-laser-inscribed 3D integrated photonics: challenges and emerging applications,” Nanophotonics 4(3), 332–352 (2015). [CrossRef]
24. R. Ramaswami, “Optical fiber communication: from transmission to networking,” IEEE Commun. Mag. 40(5), 138–147 (2002). [CrossRef]
25. K. Himeno, S. Matsuo, N. Guan, and A. Wada, “Low-bending-loss single-mode fibers for fiber-to-the-home,” J. Lightwave Technol. 23(11), 3494–3499 (2005). [CrossRef]
26. R. Essiambre and R. W. Tkach, “Capacity trends and limits of optical communication networks,” Proc. IEEE 100(5), 1035–1055 (2012). [CrossRef]
27. C. D. Poole, “Broadband fiber optic tap,” U.S. patent 7,116,870 B2 (2006).
28. M. Suzuki, M. Ao, and T. Fukuyama, “Optical power monitor,” U.S. patent 7,412,137 B2 (2008).
29. J. Zhao, “Fiber optics fiber inline tap monitoring,” U.S. patent 9,535,218 B1 (2017).
30. P. R. Herman, K. H. Y. Cheng, J. R. Grenier, M. Haque, and K. K. C. Lee, “Femtosecond laser structuring in optical fiber and transparent films,” in MATEC Web of Conferences (EDP Sciences, 2013), Vol. 8, p. 05010. [CrossRef]
31. L. A. Fernandes, O. Sezerman, G. Best, M. L. Ng, and S. Kane, “Direct writing of fiber optic components in photonic crystal fibers and other specialty fibers,” Proc. SPIE 9740, 97400N (2016). [CrossRef]
32. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013). [CrossRef]
33. K. Saitoh and S. Matsuo, “Multicore fiber technology,” J. Lightwave Technol. 34(1), 55–66 (2016). [CrossRef]
34. F. Durr and H. Renner, “Analytical design of X-couplers,” J. Lightwave Technol. 23(2), 876–885 (2005). [CrossRef]
35. M. Will, S. Nolte, B. N. Chichkov, and A. Tünnermann, “Optical properties of waveguides fabricated in fused silica by femtosecond laser pulses,” Appl. Opt. 41(21), 4360–4364 (2002). [CrossRef] [PubMed]
36. R. Osellame, S. Taccheo, M. Marangoni, R. Ramponi, P. Laporta, D. Polli, S. D. Silvestri, and G. Cerullo, “Femtosecond writing of active optical waveguides with astigmatically shaped beams,” J. Opt. Soc. Am. B 20(7), 1559–1567 (2003). [CrossRef]
37. M. Ams, G. Marshall, D. Spence, and M. Withford, “Slit beam shaping method for femtosecond laser direct-write fabrication of symmetric waveguides in bulk glasses,” Opt. Express 13(15), 5676–5681 (2005). [CrossRef] [PubMed]
39. F. He, H. Xu, Y. Cheng, J. Ni, H. Xiong, Z. Xu, K. Sugioka, and K. Midorikawa, “Fabrication of microfluidic channels with a circular cross section using spatiotemporally focused femtosecond laser pulses,” Opt. Lett. 35(7), 1106–1108 (2010). [CrossRef] [PubMed]
40. C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, “Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica,” Appl. Phys. Lett. 87(1), 014104 (2005). [CrossRef]
41. M. Ams, G. D. Marshall, and M. J. Withford, “Study of the influence of femtosecond laser polarisation on direct writing of waveguides,” Opt. Express 14(26), 13158–13163 (2006). [CrossRef] [PubMed]
42. J. He, Y. Wang, C. Liao, C. Wang, S. Liu, K. Yang, Y. Wang, X. Yuan, G. P. Wang, and W. Zhang, “Negative-index gratings formed by femtosecond laser overexposure and thermal regeneration,” Sci. Rep. 6, 23379 (2016). [CrossRef] [PubMed]