A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> Micro Fiber Coupler (MFC) Structure <s> The polarisation properties of both strongly fused and weakly fused single-mode tapered fibre couplers have been analysed. A comparison with experimental results shows excellent agreement with our analysis. <s> BIB001 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> Micro Fiber Coupler (MFC) Structure <s> We present simple and accurate relations for the study of parallel and curved tunable single-mode fiber directional couplers employing step-index or graded-index fibers. Analytical results for the various coupler parameters such as coupling coefficient, effective interaction length, tunability, and channel wavelength separation in directional coupler wavelength filters are presented. These results must prove very useful for an easy, quick, and accurate prediction or design of tunable single-mode fiber directional couplers. <s> BIB002 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> Micro Fiber Coupler (MFC) Structure <s> The optical microfiber coil resonator with self-coupling turns is suggested and investigated theoretically. This type of a microresonator has a three-dimensional geometry and complements the well-known Fabry-Perot (one-dimensional geometry, standing wave) and ring (two-dimensional geometry, traveling wave) types of microresonators. The coupled wave equations for the light propagation along the adiabatically bent coiled microfiber are derived. The particular cases of a microcoil having two and three turns are considered. The effect of microfiber radius variation on the value of Q-factor of resonances is studied. <s> BIB003 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> Micro Fiber Coupler (MFC) Structure <s> Optical fiber tapers with a waist size larger than 1microm are commonplace in telecommunications and sensor applications. However the fabrication of low-loss optical fiber tapers with subwavelength diameters was previously thought to be impractical due to difficulties associated with control of the surface roughness and diameter uniformity. In this paper we show that very-long ultra-low-loss tapers can in fact be produced using a conventional fiber taper rig incorporating a simple burner configuration. For single-mode operation, the optical losses we achieve at 1.55microm are one order of magnitude lower than losses previously reported in the literature for tapers of a similar size. SEM images confirm excellent taper uniformity. We believe that these low-loss structures should pave the way to a whole range of fiber nanodevices. <s> BIB004 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> Micro Fiber Coupler (MFC) Structure <s> Various methods to overcome the difficulties in the fabrication of high-quality (Q) optical nanofiber microcoil resonators are investigated. Modifications of the resonator geometry by wrapping the nanofiber over nonuniform rods and/or by varying the pitch alter the resonator Q-factor significantly. These effects are quantified, and geometries, which allow for enhanced tolerance to fabrication uncertainties, are identified. These simulations apply equally to the fabrication of high-Q microcoil resonators with nanofibers suspended in air or embedded in low-refractive-index materials. <s> BIB005 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> Micro Fiber Coupler (MFC) Structure <s> We present a broadband single-mode bi-conical microfiber coupler (MFC) with a specifically designed transition region that effectively suppresses any higher-order modes present at the input fiber and provides efficient power splitting into the fundamental mode at the two output ports. As a practical example, single-mode 3-dB splitting operation over a broad spectral window (400 approximately 1700 nm) was demonstrated for a very thin taper waist approximately 1.5 microm) MFC made from conventional telecom optical fibers. <s> BIB006 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> Micro Fiber Coupler (MFC) Structure <s> A compact thermometer based on a broadband microfiber coupler tip is demonstrated. This sensor can measure a broad temperature interval ranging from room temperature to 1283 °C with sub-200 µm spatial resolution. An average sensitivity of 11.96 pm/°C was achieved for a coupler tip with ~2.5 µm diameter. This is the highest temperature measured with a silica optical fiber device. <s> BIB007 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> Micro Fiber Coupler (MFC) Structure <s> A compact temperature sensor based on a broadband microfiber coupler tip is demonstrated. The thermometer dynamic range spans from room temperature to 1511 with a response time of tens of milliseconds. This is the highest temperature measured with a silica optical fiber device. A resolution of 0.66 was achieved for a coupler tip diameter of . Better resolution can be achieved with smaller sized microfiber coupler tips. <s> BIB008 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> Micro Fiber Coupler (MFC) Structure <s> A compact and low noise dual-wavelength fiber laser is demonstrated using a 70-cm-long Erbium-doped fiber loop attached to a microfiber coupler. The coupler functions to inject a 980-nm pump light as well as to tap out the output. At the maximum pump power of 8.4 mW, dual-wavelength laser is obtained at 1537.7 and 1551.4 nm with peak powers of 20.5 and 20.9 dBm, respectively. Both laser outputs are stable with a signal to noise ratio of more than 35 dB at room temperature. Both 1537.7 and 1551.4 nm lasers start to lase at threshold pump power as small as 2.5 mW with efficiencies of 0.14% and 0.10%, respectively. <s> BIB009 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> Micro Fiber Coupler (MFC) Structure <s> We experimentally demonstrate 2 × 2 and 3 × 3 fused fiber couplers made from dual mode fiber. A unique mode dependent power transfer characteristics as a function of pulling length is obtained that support various optical functionalities. Exploiting this we demonstrate several devices of interest for mode division multiplexed data transmission including LP11 mode filter, LP11 mode tap coupler, and 50:50 power splitter for both LP01 and LP11 modes. <s> BIB010 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> Micro Fiber Coupler (MFC) Structure <s> An optical microfiber coupler-based refractive index sensor is proposed and experimentally demonstrated in this letter. A microfiber coupler with a minimum diameter of 2.5 μm and a uniform waist with a length of 2 mm is fabricated and used for sensing surrounding refractive index. Both theoretical and experimental results have shown that the spectral response of the proposed microfiber coupler is highly sensitive to the surrounding refractive index over the range from 1.3340 to 1.3800. An average sensitivity of 2723 nm/RIU over this entire refractive index range has been achieved experimentally. Furthermore, for the refractive index range from 1.3340 to 1.3515, this sensor has demonstrated high sensitivity of 4155 nm/RIU. <s> BIB011 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> Micro Fiber Coupler (MFC) Structure <s> A compact micro-ball lens structure is fabricated at the cleaved tip of microfiber coupler (MFC) waist for displacement sensor application. The MFC is made by fusing and tapering two optical fibers using a flame brushing technique. It is then cleaved at the center of the minimum waist region. Then a micro-ball lens is formed at the tip of the microfiber by an arcing technique using a fusion splicing machine. The proposed displacement sensor uses the micro-ball lens as a probe and a reflector as a target. As the target is moved from the micro-ball lens, an interference fringe is obtained due to the interference between two reflected beams from the micro-ball lens and the reflector. At the smallest displacement of 0.6 mm, the output spectrum shows the interference fringes with highest extinction ratio and largest free spectral range (FSR). Both extinction ratio and FSR reduces following the power trend line with correlation coefficient of 0.99 as the displacement increases. The Q resonant factor of the comb spectrum increases from 1628 to 38,286 as the displacement increases from 0.6 to 3.6 mm. <s> BIB012 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> Micro Fiber Coupler (MFC) Structure <s> A compact highly sensitive microfiber coupler based reflective micro-force sensor is presented. The device is fabricated by fusing two twisted optical fibers and then connecting two of the pigtails to form a Sagnac loop. The sensor has a high force sensitivity of ~3754 nm/N which is three orders of magnitude larger than traditional optical fiber force sensors, and a low detection limit of ~1.6 µN. The good repeatability is also shown in this paper. <s> BIB013 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> Micro Fiber Coupler (MFC) Structure <s> A non-adiabatic microfiber coupler is fabricated by flame brushing technique and then theoretically and experimentally analyzed. The effective length of the microfiber coupler is determined by simulation, and a low-noise laser is demonstrated using various lengths of erbium-doped fiber (EDF) when incorporated in a laser setup. At 18.6-mW input pump power, the maximum output power of 20 \mu W and the lowest lasing threshold of 3.8 mW are obtained with a 90-cm-long EDF. <s> BIB014 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> Micro Fiber Coupler (MFC) Structure <s> A compact singlemode - photonic crystal fiber - singlemode fiber tip (SPST) refractive index sensor is demonstrated in this paper. A CO2 laser cleaving technique is utilised to provide a clean-cut fiber tip which is then coated by a layer of gold to increase reflection. An average sensitivity of 39.1 nm/RIU and a resolvable index change of 2.56 x 10-4 are obtained experimentally with a ~3.2 µm diameter SPST. The temperature dependence of this fiber optic sensor probe is presented. The proposed SPST refractometer is also significantly less sensitive to temperature and an experimental demonstration of this reduced sensitivity is presented in the paper. Because of its compactness, ease of fabrication, linear response, low temperature dependency, easy connectivity to other fiberized optical components and low cost, this refractometer could find various applications in chemical and biological sensing. <s> BIB015 </s> A Review of Multimode Interference in Tapered Optical Fibers and Related Applications <s> Micro Fiber Coupler (MFC) Structure <s> A magnetic field and electric current meter is proposed based on a differential twin receiving microfiber coupler (MC) sensor. The sensor is fabricated by bonding a MC and an aluminium (Al) wire together. With the small diameter of several micrometers, the output power at each port of the coupler shows high sensitivity to the distortion of Al wire from the Lorentz force induced by the magnetic field or the thermal expansion caused by the electric current. The ratio of the difference to the sum of the output signals from the two output ports can be used to eliminate the variation in the sensitivity. Using our proposed sensor, we measured a magnetic field sensitivity of ~0.0496 mT(-1), current sensitivity of ~1.0899 A(-1) without any magnetic field, and good repeatability are also shown in this paper. <s> BIB016
Compared with the conventional optical fiber coupler structures, a MFC structure can effectively be used in a wider range of applications including telecommunications lasers, polarizers, and sensors BIB006 BIB009 BIB013 BIB016   BIB010 . For example: A dual mode fused optical fiber coupler has been fabricated for WDM transmission BIB010 ; a non-adiabatic MFC was also used in implementing a compact, simple and high performance laser BIB014 ; and an optical microfiber coupler based RI sensor was reported for the first time in our previously published work BIB011 . In this subsection structure the basic operating principles and fabrication methods for a bi-conical 2 × 2 MFC are described. Within an MFC structure, there is light interchange between the two adjacent fibers due to of the propagation constant difference between the even and odd Figure 16 presents the schematic of the SPST structure as reported in our previous work BIB015 , and it is composed of an input/output SMF and a PCF half-taper section coated with gold film. The gold film is employed to increase the reflectivity of the tip end. Here, the SPST structure was fabricated by CO 2 laser irradiation and is presented in Figure 7 . The prefabricated singlemode-photonic crystal fiber-singlemode fiber structure is vertically fixed on a support, and a 50 g weight is hung at the other end of this fiber structure to apply a constant predictable tension. The combined effect of heating by the CO 2 laser and the constant tension applied was to cause the glass to become molten and stretch to a point where breakage occurred, resulting in half-tapered PCF tip with a diameter of circa 3.2 µm. Furthermore, the half-tapered PCF tip was coated with a gold film of circa 40 nm thickness by utilizing a thermal evaporator to improve reflectivity. The gold film on the PCF and the conical transitional region was then partially removed using a gold-etching solvent. Finally, a thin gold film was left on the half-tapered PCF tip end. In the next stage, we expect to fabricate a SPS tip with an increased reflectivity by employing a FIB milling and gold coating process, therefore its sensing performance can be also enhanced. Compared with the conventional optical fiber coupler structures, a MFC structure can effectively be used in a wider range of applications including telecommunications lasers, polarizers, and sensors BIB006 BIB009 BIB013 BIB016   BIB010 . For example: A dual mode fused optical fiber coupler has been fabricated for WDM transmission BIB010 ; a non-adiabatic MFC was also used in implementing a compact, simple and high performance laser BIB014 ; and an optical microfiber coupler based RI sensor was reported for the first time in our previously published work BIB011 . In this subsection structure the basic operating principles and fabrication methods for a bi-conical 2 × 2 MFC are described. Within an MFC structure, there is light interchange between the two adjacent fibers due to of the propagation constant difference between the even and odd modes  or symmetric and anti-symmetric modes as presented in previous literatures BIB001 . It is noteworthy that as the diameter of the microfiber reduces is decreased to a specific value, the transmission spectrum of the MFC structure shows a semi-periodically resonant behavior for each of the output ports. In a departure from the coupled wave equations derived in BIB005 BIB003 , we adopted a simple analytical method and an initial approximate theoretical analysis. When the scale of the TOF is comparable with the light wavelength, it can be approximated as a several micrometers of waveguide surrounded with an air cladding. Thus, the coupling coefficient can be calculated by BIB002 : where λ is the light wavelength, n 1 and n 2 are the RI values of the silica fiber cladding and the surrounding environment respectively, a is the radius of microfiber, τ = d/a , the distance between the two fused microfibers is denoted as d, and the normalized frequency is calculated The output power of the coupled port of the MFC structure can be calculated by: where P 0 and P respectively denote the input power and the output power of the MFC structure, and L e f f denotes the effective coupling length of two microfibers. When the RI, radius and effective coupling length are determined, the calculated transmission spectra can be obtained based on the theoretical analysis above. From this, as the surrounding environment changes, a significant wavelength shift can be monitored. Traditionally, an MFC structure is fabricated by employing a microheater brushing technique to taper and fuse two SMFs BIB004 . Figure 17 presents the experimental fabrication process for the MFC structure, and it mainly consists of two linear motorized translation stages and a ceramic microheater (CMH-7019, NTT-AT, Osaka, Japan), the temperature of which is regulated by adjusting the current provided by a power supply. where λ is the light wavelength, and are the RI values of the silica fiber cladding and the surrounding environment respectively, is the radius of microfiber, = ∕ , the distance between the two fused microfibers is denoted as , and the normalized frequency is calculated by = The output power of the coupled port of the MFC structure can be calculated by: where and respectively denote the input power and the output power of the MFC structure, and denotes the effective coupling length of two microfibers. When the RI, radius and effective coupling length are determined, the calculated transmission spectra can be obtained based on the theoretical analysis above. From this, as the surrounding environment changes, a significant wavelength shift can be monitored. Traditionally, an MFC structure is fabricated by employing a microheater brushing technique to taper and fuse two SMFs BIB004 . Figure 17 presents the experimental fabrication process for the MFC structure, and it mainly consists of two linear motorized translation stages and a ceramic microheater (CMH-7019, NTT-AT, Osaka, Japan), the temperature of which is regulated by adjusting the current provided by a power supply. As an initial fabrication step, two SMFs are placed in proximity together and twisted slightly to ensure close contact. After that, the fibers are placed on two linear motorized translation stages, which can be accurately adjusted by a LABVIEW program. When the temperature of the ceramic microheater reaches about 1300 °C, the tapering and fusing begin with the silica fiber glass becoming soft. By presetting a number of control parameters, the taper diameter, length, and shape of the MFC structure can be determined. In our previous paper BIB011 , the MFC used had a 2-mm long uniform As an initial fabrication step, two SMFs are placed in proximity together and twisted slightly to ensure close contact. After that, the fibers are placed on two linear motorized translation stages, which can be accurately adjusted by a LABVIEW program. When the temperature of the ceramic microheater reaches about 1300 • C, the tapering and fusing begin with the silica fiber glass becoming soft. By presetting a number of control parameters, the taper diameter, length, and shape of the MFC structure can be determined. In our previous paper BIB011 , the MFC used had a 2-mm long uniform waist region, which is fabricated by weakly fusing two microfibers with a diameter of 2.5 µm. The length of the transition region between the uniform region and input/output ports was 27 mm. The fabricated tapers should be adiabatic to support the LP 01 mode and the profile of the transitional region fell within the adiabatic regime demonstrated in BIB006 . A microfiber coupler tip (MFCT) was also investigated to broaden applications of MFC based devices, in relation to a high spatial resolution BIB007 BIB008 BIB012 . Figure 18 shows both an MFC and an MFCT fabricated by using a ceramic cleaver to divide the complete MFC structure into two equal parts. The fabricated MFCT comprised a uniform waist region, a conical transitional region and two input/output ports (P 1 and P 2 ). When the light is launched from port P1 to MFCT structure, and the reflected light from port P2 can be received as a result of the existed flat end surface. Moreover, the end of the MFC tip could be coated with gold film to improve its reflectivity, and therefore its sensing performance. The fabricated MFCT comprised a uniform waist region, a conical transitional region and two input/output ports (P1 and P2). When the light is launched from port P1 to MFCT structure, and the reflected light from port P2 can be received as a result of the existed flat end surface. Moreover, the end of the MFC tip could be coated with gold film to improve its reflectivity, and therefore its sensing performance. (a) (b) Figure 18 . Schematic of (a) a MFC structure and (b) a MFCT structure.