A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> A Singlemode-Multimode-Singlemode (SMS) Structure <s> We report the observation of whispering-gallery-mode lasers based on Er(3+) -doped ZBLAN microspheres coupled with half-tapered and tapered optical fibers. A multimode lasing effect is observed at 1.56mu when the taper diameters are properly adjusted so that their fundamental propagation constants match those of the resonant modes of interest. Overlap between the pump and the laser geometrical modes is optimized by pumping at 1.48mu . <s> BIB001 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> A Singlemode-Multimode-Singlemode (SMS) Structure <s> We describe the fundamentals of two new types of fiber, photonic crystal fiber (PCF) and photonic bandgap fiber (PBF). PCF is fabricated by forming small air holes in the cladding of the fiber rather than doping the fiber core with high-index materials. This fiber has very interesting new features including endlessly single-mode operation, zero GVD in the visible region, and an easily controllable spot-size due to the strongly guiding characteristics that result from the very high relative refractive index between the core and air-holed cladding. By contrast, PBF has air holes not only in its cladding but also in its core, and this enables us to confine an optical beam by using the principle of two-dimensional Bragg diffraction. The air core structure greatly reduces fiber nonlinearity and suggests the feasibility of high power transmission. <s> BIB002 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> A Singlemode-Multimode-Singlemode (SMS) Structure <s> Silica waveguides with diameters larger than the wavelength of transmitted light are widely used in optical communications, sensors and other applications. Minimizing the width of the waveguides is desirable for photonic device applications, but the fabrication of low-loss optical waveguides with subwavelength diameters remains challenging because of strict requirements on surface roughness and diameter uniformity. Here we report the fabrication of subwavelength-diameter silica 'wires' for use as low-loss optical waveguides within the visible to near-infrared spectral range. We use a two-step drawing process to fabricate long free-standing silica wires with diameters down to 50 nm that show surface smoothness at the atomic level together with uniformity of diameter. Light can be launched into these wires by optical evanescent coupling. The wires allow single-mode operation, and have an optical loss of less than 0.1 dB mm(-1). We believe that these wires provide promising building blocks for future microphotonic devices with subwavelength-width structures. <s> BIB003 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> A Singlemode-Multimode-Singlemode (SMS) Structure <s> A tunable photonic crystal fiber (PCF) coupler, which couples part of the optical power in one PCF with that in another PCF, has been made by side polishing. We fabricated the PCF coupler by mating two side-polished PCFs. We achieved evanescent field coupling between the core modes of the two PCFs by using side polishing to bring the cores close to each other. By adjusting the mating angle between the two side-polished PCFs we obtained as much as 90% tunability in the coupling ratio. The spectrum of the coupling ratio was almost flat, with small ripples, over a 400-nm wavelength range. <s> BIB004 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> A Singlemode-Multimode-Singlemode (SMS) Structure <s> We report on research towards application of birefringent photonic crystal fibers as active and passive elements of fiber optic sensors for measurements of different physical parameters. Using experimental and theoretical methods, the sensing characteristics of different photonic structures are studied, including spectral behavior of phase and group modal birefringence, polarization dependent losses, sensitivity to temperature and hydrostatic pressure. <s> BIB005 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> A Singlemode-Multimode-Singlemode (SMS) Structure <s> This paper presents an investigation on a single-mode-multimode-single-mode fiber structure. A one-way guided-mode propagation analysis for the circular symmetry waveguide is employed to model the light propagation and the approximated formulations are derived and evaluated concerning the accuracy. Phase conjunction of the multimode interference within the fiber structure is revealed. A simple way to predict and analyze the spectral response of the structure is presented through the space to wavelength mapping with the derived approximated formulations. The prediction of spectral response is verified numerically and experimentally. <s> BIB006 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> A Singlemode-Multimode-Singlemode (SMS) Structure <s> Here we demonstrate a supercontiuum spectrum generated in a tapered fiber pumped by a Ti sapphire laser with 130fs pulse width at 800nm centre wavelength. The tapered fiber with the diameter of 1.25µm and the length of 16cm was made by using a tapered machine. The supercontiuum range is from 500nm to 900nm. We simulated the supercontinuum with the nonlinear Schrodinger Equation and discussed the affecting factors. In some conditions, the experimental results are agreed very well with the theoretical analyses. <s> BIB007 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> A Singlemode-Multimode-Singlemode (SMS) Structure <s> An optical fiber sensor based on the change of optical confinement in a subwavelength tip is presented. The optical spot is substantially increased when the environmental refractive index (RI) increases from 1.3 to 1.4. By measuring the intensity of low angular spectral components, an intensity sensitivity up to 8000% per RI unit is achieved. The fiber tip sensors take advantage of the small detection volume and real-time responses. We demonstrate the application of the nanofiber sensors for measuring concentrations of acids and evaporation rates of aqueous mixtures. <s> BIB008 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> A Singlemode-Multimode-Singlemode (SMS) Structure <s> We have investigated the influence of multimode fiber core (MMFC) diameters and lengths on the sensitivity of an SMS fiber based refractometer. We show that the MMFC diameter has significant influence on the refractive index (RI) sensitivity but the length does not. A refractometer with a lower MMFC diameter has a higher sensitivity. Experimental investigations achieved a maximum sensitivity of 1815 nm/ RIU (refractive index unit) for a refractive index range from 1.342 to 1.437 for a refractometer with a core diameter of 80 μm. The experimental results fit well with the numerical simulation results. <s> BIB009 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> A Singlemode-Multimode-Singlemode (SMS) Structure <s> We have proposed the use of a single bent singlemode -multimode-singlemode (SMS) fiber structure to measure both displacement and temperature simultaneously and independently. Our experimental results show that this sensor has a sensitivity of 5.89 pm/μm for displacement and 11.6 pm/°C for temperature. <s> BIB010 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> A Singlemode-Multimode-Singlemode (SMS) Structure <s> Abstract The development of highly-sensitive miniaturized sensors that allow real-time quantification of analytes is highly desirable in medical diagnostics, veterinary testing, food safety, and environmental monitoring. Photonic Crystal Fiber Surface Plasmon Resonance (PCF SPR) has emerged as a highly-sensitive portable sensing technology for testing chemical and biological analytes. PCF SPR sensing combines the advantages of PCF technology and plasmonics to accurately control the evanescent field and light propagation properties in single or multimode configurations. This review discusses fundamentals and fabrication of fiber optic technologies incorporating plasmonic coatings to rationally design, optimize and construct PCF SPR sensors as compared to conventional SPR sensing. PCF SPR sensors with selective metal coatings of fibers, silver nanowires, slotted patterns, and D-shaped structures for internal and external microfluidic flows are reviewed. This review also includes potential applications of PCF SPR sensors, identifies perceived limitations, challenges to scaling up, and provides future directions for their commercial realization. <s> BIB011
Untapered SMS fiber structures have been intensively investigated and developed into a range of optical fiber devices, such as filters, splitters, combiners, actuators and sensors BIB006 BIB009 BIB010 , due to their many merits of easy fabrication, low-cost and stable configuration. As depicted in Figure 1 , an SMS fiber structure comprises a multimode fiber (MMF) sandwiched between two singlemode fibers (SMFs). Sensors 2018, 18, x FOR PEER REVIEW 2 of 28 such as lasers, couplers, and sensors BIB002 BIB005 BIB004 BIB011 . However, given its high-cost and poor compatibility to existing fiber types, PCF does present challenges for sensing applications. Compared with the conventional fiber structures above, tapered optical fibers (TOF) can provide a number of useful features including a large evanescent field, strong mode confinement capability and small-scale diameter. Thus, TOF exhibits great potential for applications in communication systems and optical sensing, since it was reported for first time in 2003 BIB003 . Over the past few decades, TOFs have been investigated and widely used in many fields ranging from telecommunications to sensing. For instance, supercontinuum (SC) generation in TOFs was reported in BIB007 ; whispering gallery mode (WGM) lasers based on Er 3+ doped ZBLAN microspheres coupled with half-TOFs and TOFs were observed in BIB001 and a sensitive liquid refractive index sensor using TOF tips was demonstrated in BIB008 . These TOF based devices have exhibited many superior properties over conventional optical fiber structures and for this reason our group has investigated the TOF structure. In this paper, we systematically summarize the various TOF technologies that exploit multimodal interference and also the range of sensing applications for TOF technology. In Section 2 "TOF Structures and Their Fabrication" the fundamental principles of light propagation within TOF structures and associated fabrication techniques are introduced. Section 3 "Applications of TOFs as Optical Fiber Sensors" provides an overview of sensing applications for structures in sensing for measurands such as refractive index (RI), temperature, humidity and biochemical. Finally Section 4 provides a conclusion and some comments on the future directions of TOF technology. Untapered SMS fiber structures have been intensively investigated and developed into a range of optical fiber devices, such as filters, splitters, combiners, actuators and sensors BIB006 BIB009 BIB010 , due to their many merits of easy fabrication, low-cost and stable configuration. As depicted in Figure 1 , an SMS fiber structure comprises a multimode fiber (MMF) sandwiched between two singlemode fibers (SMFs). In a previous work BIB006 , a guided-mode propagation analysis (MPA) was adopted to comprehensively investigate an SMS fiber structure. Furthermore, a comparison of the calculated self-imaging positions of an SMS fiber structure employing MPA and beam propagation method (BPM) was presented  . In a previous work BIB006 , a guided-mode propagation analysis (MPA) was adopted to comprehensively investigate an SMS fiber structure. Furthermore, a comparison of the calculated self-imaging positions of an SMS fiber structure employing MPA and beam propagation method (BPM) was presented  . In BIB006 light transmission within an SMS fiber structure was firstly investigated theoretically, within which the SMF and MMF used are SMF28e (Corning) and ASF 105/125, respectively. Their parameters are follows: the SMF and MMF core/cladding diameters and RI values are 8.3/125 µm and 1.4504/1.4447, and 105/125 µm and 1.4446/1.4271, respectively. As the light propagates from the SMF to the MMF, the fundamental mode E(r, 0) is decomposed into M eigenmodes φ m (r), thus: where m and a m respectively denote the excited mode number and excitation coefficient. Both of the parameters can be calculated from: where V denotes the normalized frequency parameter, a is the MMF core radius, and n co and n cl are the RI values of the MMF core and cladding, respectively. The optical amplitude distribution of the transmitted light at a propagation distance z within the MMF section can be expressed as: where β m represents the propagation constant of m-th mode. Based on this equation, the optical amplitude distribution pattern at a propagation distance z within the SMS fiber structure can be simulated, and the simulated result is shown in Figure 2 .  where and respectively denote the excited mode number and excitation coefficient. Both of the parameters can be calculated from: where denotes the normalized frequency parameter, is the MMF core radius, and and are the RI values of the MMF core and cladding, respectively. The optical amplitude distribution of the transmitted light at a propagation distance within the MMF section can be expressed as: where represents the propagation constant of -th mode. Based on this equation, the optical amplitude distribution pattern at a propagation distance within the SMS fiber structure can be simulated, and the simulated result is shown in Figure 2 . When light is launched from the MMF section into the output SMF, the eigenmodes within the MMF are recoupled into the SMF fundamental mode and the relationship between the coupling loss and the MMF length can be calculated from: From the above equations, the relationship between the coupling loss and the MMF length can When light is launched from the MMF section into the output SMF, the eigenmodes within the MMF are recoupled into the SMF fundamental mode and the relationship between the coupling loss and the MMF length can be calculated from: From the above equations, the relationship between the coupling loss and the MMF length can be calculated and presented in Figure 3 . The self-imaging position is denoted as the propagation distance at which both a maximum coupling efficiency and a minimum coupling loss occur. Practically edge filters and bandpass filters based on an SMS fiber structure have been proposed utilizing the spectral characteristics over a wavelength range of the multimode interference pattern at some specific MMF lengths. Sensors 2018, 18, x FOR PEER REVIEW 4 of 28 distance at which both a maximum coupling efficiency and a minimum coupling loss occur. Practically edge filters and bandpass filters based on an SMS fiber structure have been proposed utilizing the spectral characteristics over a wavelength range of the multimode interference pattern at some specific MMF lengths. 