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A novel fiber structure, coreless side-polished fiber (CSPF), is proposed and investigated to implement multimode interference (MMI) and high sensitive refractive index (RI) sensors. For such CSPF, the part of the cladding and the core of a single-mode fiber are side-polished off so as to make the remained cladding a D-shaped multimode waveguide. The excitation and evolution of MMI in the CSPF are simulated numerically. The simulation results show that the high-order modes excited within the D-shaped multimode waveguide are mainly TE0,1 (TM0,1)~TE0,6 (TM0,6) modes. Moreover, the RI sensing characteristics and the influences of residual thickness and dip wavelength on the sensitivity are investigated both numerically and experimentally. The experimental results show that the CSPF with a residual thickness of 43.1 μm can reach an ultra-high sensitivity of 28000 nm/RIU in the RI range of 1.442~1.444. It is also found that the sensitivity can be further increased by reducing the residual thickness and choosing the dip at a longer wavelength. Thanks to the ultra-high RI sensitivity and the ease of fabrication, the CSPF could provide a cost-effective platform to build high-performance fiber devices of various functions.
© 2017 Optical Society of America
1. Introduction
Multimode interference (MMI) is an important mechanism for various applications ranging from optical filters [1, 2], beam splitter [3], photonic switcher [4] to sensors [5–13]. Oftentimes single-mode-multi-mode-single-mode fiber (SMSF) is employed to implement MMI-based optical fiber devices, such as wavelength filters [1, 2], vibration sensor [5], micro-bent sensor [6], micro-displacement sensor [7], strain and temperature sensor [8], humidity sensor [9], liquid concentration sensor [10] and refractive index sensors [11–13].
Refractive index (RI) fiber sensor of high sensitivity is very desirable thanks to the advantages of compact size, immunity to electromagnetic field, and chemical inertness. It has many potential applications such as detecting chemical molecule and bio-molecule, monitoring environmental poison and food safety. For MMI-based RI fiber sensors, the efficient excitation of high-order modes and strong evanescent field in the multimode waveguide section is more desirable since it can help to enhance the sensitivity. Therefore, many methods have been reported to enhance the efficiency of exciting high-order modes and the strength of evanescent field, such as misalignment [14], tapering the splicing points [15], chemical etching [12], tapering the multimode fiber (MMF) [16], side-polishing the MMF [17] and coating a thin film of high RI onto the MMF [18]. On the other hand, some special fibers such as coreless MMF [12], small core fiber (SCSMF) [19], photonic crystal fiber (PCF) [15] and thin core fiber [20] are also employed to enhance the sensitivity. However, these methods oftentimes require two types of optical fibers spliced together to obtain MMI phenomenon. Therefore, it needs fabrication techniques such as splicing, precise alignment and other additional processes, which leads to high fabrication complexity and cost.
Here, we report a novel and simple fiber structure, referred to as coreless side-polished fiber (CSPF), to implement MMI in only a single mode fiber (SMF). It allows us to achieve an extremely high sensitivity of 28000nm/RIU in surrounding RI (SRI) range of 1.442~1.444. To the best of our knowledge, the highest reported sensitivity in MMI-based RI fiber sensors is 19212.5nm/RIU [19], while the higher RI sensitivity can be achieved by the CSPF. In addition, the CSPF structure, compared to other conventional structures, greatly lowers the fabrication complexity and cost because wheel-based side polishing on a single section of SMF is only required and it does not need any precise alignment, splicing and other additional processes. Moreover, the polishing technique can flexibly tailor the polished length and depth [17], which offers more freedom for the fiber sensor design. Thanks to the D-shaped structure, the CSPF provides a versatile platform on which other materials, such as two-dimensional material [21], photosensitive material [22] and particular biomaterial [23], can be integrated to implement various high-performance optical fiber devices of different functionalities.
In this paper, the excitation of the high-order modes and evolution of MMI along the CSPF are investigated both theoretically and numerically. In addition, three CSPF with different residual thickness are fabricated using the wheel-based side-polishing technique, and the RI sensing characteristics of the three CSPFs are also investigated both numerically and experimentally. It is found that reducing the residual thickness and choosing the dip at a longer wavelength will further enhance the sensitivity of the CSPF.
2. Principle
2.1 The structure of CSPF
Figure 1(a) shows schematically the three-dimensional structure of CSPF where the fiber core is shown in yellow. The structure can be easily fabricated by wheel-based side polishing a single SMF. Unlike the typical side-polished fiber (TSPF) with an intact fiber core [22], the CSPF has no fiber core. The part of the cladding and the core in the CSPF are polished off to make the remained cladding a D-shaped multimode waveguide. The residual thickness of CSPF (inset in Fig. 1(a)) is referred hereinafter as RT, which can be decreased by prolonging the duration of polishing process. Figure 1(b) is the vertical section (yz-plane) of the CSPF, from which we can see that the CSPF structure consists of five sections: lead-in SMF, transitional section I, coreless flat section, transitional section II and lead-out SMF. As shown in the below simulations, the coreless flat section works as a D-shaped multimode waveguide. The curve polished surface of the transitional section I provides an efficient way to excite the high-order modes and strong evanescent field of the D-shaped multimode waveguide, which gives rise to the high RI sensitivity. The fiber core in the transitional section II will recollect the light from the D-shaped flat section for output measurements.
Fig. 1 Schematic diagrams of coreless side-polished fiber (CSPF): (a) three-dimensional view and (b) vertical section.
2.2 Simulations
Beam propagation method (commercial BPM module from Rsoft Inc) is employed to simulate the transmission spectra and field evolution of the CSPF. In the simulation, the geometrical parameters of the CSPF are: length of the flat section Lf = 8 mm, lengths of the two transitional sections Lt1 and Lt2 = 4 mm; the core RI = 1.4681, the cladding RI = 1.4628 [24], the core diameter is 8.2 μm and the cladding diameter is 125 μm. Here, the RTs in the simulations are respectively set to be 43.1 μm, 50.1 μm and 53.3 μm to analyze the three CSPFs fabricated in the experiments (presented later in section 3.1). The curved polished surfaces of the transitional section I and II are modeled by a surface of an elliptic cylinder with a major axis of Lt1 and a minor axis of (125 - RT) μm. The material under sense is set to be of SRI and surround the CSPF in our simulation model.
Figure 2 shows the simulated results of the CSPF with a RT of 53.3 μm. The transmission spectra in Fig. 2(a) shows that a dip with an extinction ratio of about 15 dB redshifts from 1292 nm to 1322 nm when the SRI increases from 1.454 to 1.456. Here, transmission T is negative value as shown in Fig. 2(a) because transmission definition of T = 10⋅log(Pout/Pin) is used in the simulations, where Pin and Pout are respectively input and output power of the CSPF. Figures 2(b) and 2(c) show the field evolutions in vertical sections (yz-plane) along the CSPF respectively for the dip wavelength of 1292 nm and the peak wavelength of 1322 nm. The corresponding evolutions of field in the cross section (xy-plane) are respectively shown in Visualization 1 (for the dip wavelength) and Visualization 2 (for the peak wavelength) in supplementary materials. The incident light propagates in the fundamental mode along the lead-in SMF, and then be totally reflected by the polished surface. Consequently, the reflected light will be efficiently coupled into the coreless flat section, and thus the high-order modes are excited. These high-order modes interfere with each other when propagating along the flat section. Finally the multimode interference (MMI) results in a destructive interference at the core of the lead-out SMF (see Fig. 2(b)) at the dip wavelength, and a constructive interference (see Fig. 2(c)) at the peak wavelength. Besides, Fig. 2 (a) shows that a relative low insertion loss of ~7.5 dB for the CSPF structure can be achieved, which is in good agreement with the experimental results as shown later in section. 4.
Fig. 2 Simulated results of the CSPF with a residual thickness (RT) of 53.3 μm. (a) Transmission spectra with SRI = 1.454 and SRI = 1.456; (b) field evolutions along the CSPF at dip wavelength of 1292nm (see Visualization 1) and (c) peak wavelength of 1322nm (see Visualization 2), respectively.
The spectral dips could be explained by the MMI in the CSPF. Thus, the input optical field of the coreless flat section of the CSPF can be written as
where Ѱm,n(r,θ) is the guided mode of TEm,n (predominately in x polarization) or TMm,n (predominantly in y polarization) supported by the coreless flat section of the CSPF, since the flat section is considered as a D-shaped multimode waveguide; The subscripts m and n are the node numbers of a specific guided mode, where the mode field distribution respectively varied with the azimuthal angle and along the radial direction. The exciting coefficient bm,n for the Ѱm,n(r,θ) mode is expressed as:Considering the symmetry properties of the input field Ein(r,θ) excited by the fundamental mode of the lead-in SMF, TE0,n or TM0,n modes are mainly excited in the CSPF (see details in Visualization 1 and Visualization 2 in supplementary materials). As shown by simulation in Fig. 3, distribution of TE0,n mode field is same as that of TM0,n mode. Therefore, we can neglect the vector properties and denote the TE0,n and TM0,n mode field by a scalar function Ѱ0,n(r,θ). The evolution of optical field along the flat section of CSPF is determined by the interference between the excited high-order modes:
where β 0,n is the propagation constant of TE0,n and TM0,n modes in the flat section.Fig. 3 (a) One-dimensional field intensity distributions extracted along the symmetrical axis of mode fields; (b) TE and TM propagation mode fields in the coreless flat sections of the CSPF; Here, RT = 53.3 μm for the CSPF.
To present deep insight into the multimode interference in the flat section of the CSPF, we investigate the field evolution along the flat section of CSPF by using Fourier transformation, since the different TE0,n (TM0,n) modes correspond to different spatial frequencies as shown in Fig. 3 and Fig. 4. Firstly, we use finite element method (Comsol Multiphysics) to calculate the TE0,n (TM0,n) modes (n = 0~8) of the flat section for the CSPF with a RT of 53.3 μm when SRI = 1.454, as shown in Fig. 3(b). The one-dimensional field intensity of TE0,n (TM0,n) modes, which are extracted along the symmetrical axis (y-axis), are shown in red dash line (black line) in Fig. 3(a). The black dashed line in the Fig. 3(a) indicates the position of the polished surface. Note that the evanescent field of the TE0,6 (TM0,6)~TE0,8 (TM0,8) modes can penetrate into the outside of the CSPF by at least 4μm, leading to a strong interaction between the mode field and surrounding material, and thus a high sensitivity for the CSPF. It is seen again that the field distributions of TE0,n and TM0,n are same. Therefore, for the sake of simplicity, we only analyzes the TE0,n mode instead of the TM0,n mode without considering polarization effect. Using Fourier transformation of the field intensity of the TE0,n modes, as shown in Fig. 4, we can obtain the spatial spectra of TE0,n modes. For the TE0,n modes of n = 1~8, the predominant spatial frequencies are respectively 0.0293 μm−1, 0.04883 μm−1, 0.06836 μm−1, 0.08789 μm−1,0.10742 μm−1, 0.12695 μm−1,0.13672 μm−1 and 0.15625 μm−1. The higher order mode has a higher spatial frequency along the y-axis. As a result, we can distinguish the modes by the predominant spatial frequencies.
Figure 5(a) shows the field evolution along the CSPF with a RT of 53.3 μm at the dip wavelength of 1292 nm. The field distributions at several cross sections of different propagation lengths are shown in the insets of Fig. 5(a). It can be seen that, as mentioned previously, the dominant high-order modes are the TE0,n and TM0,n modes, whose nodes is in radial direction instead of azimuthal direction. To give deep insight into the evolution of modes along the flat section of the CSPF, the evolution of spatial spectrum, as shown in Fig. 5(b), is obtained by Fourier transformation of one-dimensional field distribution. The predominant spatial frequencies for the mode fields of TE0,1~TE0,8 are indicated by white dashed lines in Fig. 5(b). Figure 5(b) shows clearly that when the incident field enters into the flat section, the spatial frequencies of TE0,1~TE0,8 modes are mainly excited. When propagating from z = 4100 μm to 6100 μm, light carried by the higher-order modes of TE0,7 and TE0,8 will be coupled to the lower-order modes of TE0,3,TE0,4,TE0,5 and TE0,6. With propagating across z = 7100 μm, the higher-order modes of TE0,7 and TE0,8 will decay, and most of light energy will be stably carried by TE0,1~TE0,6 modes. It shows that the highest order mode efficiently excited in the flat section is TE0,6 (TM0,6) mode, which has a strong evanescent field and thus gives rise to the high sensitivity。
Fig. 5 (a) Field evolution along the CSPF with a RT of 53.3 μm at the dip wavelength of 1292 nm; (b) Corresponding mode evolution along the CSPF, which is analyzed by spatial spectra of the TE0,n (TM0,n) modes.
To investigate the impact of RT on the self-imaging length, the five CSPFs of RT = 50μm, 51μm, 52μm, 53μm and 54μm are simulated by BPM. The field evolutions of MMI for these CSPFs are shown in Fig. 6. It can be seen clearly that the position of destructive interference will shift towards longer direction with increase in RT, as indicated by the yellow dash line in Fig. 6. From this phenomenon, it is concluded that the self-imaging length of the MMI in CSPF will increase with RT because the position of the destructive interference is proportional to the self-imaging length [25]. This phenomenon can be explained by the fact that the difference between propagation constant of guided modes of the CSPF will decrease when the RT becomes thicker and the destructive interference requires a longer position to achieve π phase difference between the guided modes.
Fig. 6 Field evolution of the MMI for the CSPFs with RT = 50μm (a), 51μm (b), 52μm (c), 53μm (d) and 54μm (e), respectively. In the simulation, the wavelength is fixed at 1292nm.
3. Fabrication and experimental setup
3.1 Samples and fabrications
In the fabrication of CSPF, our home-developed fiber-polishing system as shown schematically in Ref [17]. is used to polish a section of conventional SMF (Corning SMF-28e) with a core diameter of 8.2 μm and a cladding diameter of 125 μm. During the fabrication, the two ends of SMF are doubly clamped on a movable stage, and the movable stages are controlled by computer to hold the longitudinal tension of the SMF. In the polishing system, a polishing wheel, on which an abrasive paper with a particle size of 6 μm is stuck, is moved from bottom close to the midpoint of the double-clamped SMF until the SMF is bent and has a 2~3cm long section overlapped with the abrasive paper, and then is controlled by a computer to rotate clockwise and anticlockwise to polish the surface of the SMF. The rotation speed is kept at 94 RPM by computer with RPM feedback to lower the possibility of breaking the SMF. After the wheel rotation continues for ~10 minutes, both the cladding on one side and the fiber core are polished off by the abrasive paper. By extending and controlling the polishing duration, three CSPFs with RTs of 43.1 μm, 50.1 μm and 53.3 μm are fabricated, respectively. It should be noticed that the CSPF is easily broken under large transverse deformation. Consequently, the fabricated CSPF is fixed on the glass slide to enhance its robustness. Figure 7(a) shows the zoom-in microscopic image of vertical section of the coreless flat section, from which the RT of 50.1 μm is measured. The flat polished surface of CSPF is shown in Fig. 7(b). Here, a 4.85 cm diameter wheel is used to polish the SMF and form the curve polished surface of a small tilted angle θ with respect to the flat polished surface. From Fig. 7(c), the tilted angles θ are measured to be 1.11°, 0.76° and 0.70° for the CSPFs of RTs = 43.1 μm, 50.1 μm and 53.3 μm, respectively. These small tilted angles, which is much less than the maximum titled angle of 2.76° as estimated in the Appendix, ensures the total reflection at the curve surface and high efficient excitation of high-order modes even when the SRI is up to 1.456, which is confirmed in Figs. 2(b) and 2(c). As discussed in the Appendix section, the larger tilted angle will help to excite higher order mode and thus enhance the sensitivity. Using light ray method shown in the Appendix, the maximum titled angle is up to 2.76° and the corresponding slope is up to 0.048 when the SRI = 1.456. The variations of residual thickness along the CSPF, as shown in Fig. 7(c), are measured by the microscopy (Zeiss Axio Scope A1) for the three CSPFs. From Fig. 7(c), lengths of the transitional sections for the three CSPFs are all measured to be ~4 mm, lengths of the flat sections are all measured to be ~8 mm, and RTs are respectively measured to be 43.1 μm, 50.1 μm and 53.3 μm.
Fig. 7 (a) Microscopic image of the flat section of the CSPF with a RT of 50.1 μm; (b) Microscopic image of polished surface of the CSPF; (c) Variations of residual thicknesses for the three fabricated CSPFs.
3.2 Experimental setup
Figure 8 schematically illustrates the experimental setup used to investigate the RI sensing characteristics of the three CSPFs. In the experiment, the CSPF is fixed on the glass substrate by ultra-violet glue (UV glue, Norland Optical Adhesive 65). Basin formed by glass strips and fixed by the UV glue is fabricated to make the CSPF completely immersed in certified RI liquid (CRIL). Here, CRILs with a RI range from 1.3 to 1.444 (Cargille Labs) are used to measure the sensing characteristics of the CSPFs. In the measurement, light from a broadband source (BBS, ANDO AQ4305) with a broad wavelength range of 1000~1700 nm is launched into the CSPF. The transmission spectra of the CSPF, corresponding to different SRIs, are measured by an optical spectrum analyzer (OSA, YOKOGAWA AQ6370D). Before injecting new CRIL for every measurement, the basin and the CSPF are cleaned with alcohol carefully and repeatedly until the transmission spectrum goes back to the initial one.
4. Results and discussions
The RI sensing characteristics of the three fabricated CSPFs with RTs of 43.1 μm, 50.1 μm and 53.3 μm are investigated both numerically and experimentally. The measured transmission spectra with the increase of SRI in the range of 1.434~1.444 are shown in Figs. 9(a), 9(c) and 9(e), while the simulated spectra with the SRI in the range of 1.430~1.456 are shown in Figs. 9(b), 9(d), and 9(f). Wherein, the circles indicate the dips that are traced to sense the SRI. Tracing the shift of the dip, we obtain the dependencies of the dip wavelength on the SRI experimentally in Fig. 9(g) and numerically in Fig. 9(h). Although the simulated spectra are different from experimental ones, as shown in Figs. 9(a)-9(f), the simulated and experimental results show the same dependence: the dip wavelength increases exponentially with the SRI. The slight difference in SRI range between experiments and simulations is because the RIs of the core and the cladding in experiments are different from that in simulations. Despite the spectral difference between experiment and simulation, the dependence of dip wavelength on SRI is same for the three CSPFs with different RTs. Here, we mainly consider the dependence of dip wavelength on SRI since it determines the sensing characteristics of the CSPF. Besides, both simulations and experiments show that the sensitivity of the CSPF increases with the SRI and approaches its maximum when the SRI is close to the RI of the flat section. This is because the proportion of the evanescent field outside the CSPF will increase with the SRI, which results in a stronger interaction with surrounding media.
Fig. 9 The measured transmission spectra of the CSPFs with RTs of (a) 43.1 μm, (c) 50.1 μm and (e) 53.3 μm. Simulated transmission spectra of the CSPFs with RTs of (b) 43.1 μm, (d) 50.1 μm and (f) 53.3 μm. Measured (g) and simulated (h) dependencies of dip wavelength on surrounding refractive index (SRI).
Due to the MMI in the flat section of the CSPF, several dips will appear in the transmission spectrum, which is confirmed by the simulated and measured spectra in Fig. 10(a) and 10(d). Here, RT = 43.1 μm is chosen for the measured transmission spectra in Fig. 10(a), while RT = 53.3 μm is for the simulated in Fig. 10(d). The dip wavelength at SRI = 1.3, which is subtracted from that at SRI > 1.3 to obtain the dip shift, is defined as “reference wavelength” (RW). To investigate the influence of the RW on RI sensitivity, the shift of the dip with SRI are respectively obtained by tracing the dips a~c in the experiment shown in Fig. 10(b), and by the dips 1~4 in the simulation shown in Fig. 10(e). Here, the RWs are chosen at 1174.4 nm, 1214.6 nm and 1401.2 nm respectively for the dips a~c, while at 1008.8 nm, 1074.8 nm, 1188 nm and 1226.8 nm for the dips 1~4. Since the wavelength shift increases exponentially with SRI, we divide the SRI into three ranges to analyze the sensitivity of the CSPF. The three SRI ranges are respectively 1.3~1.4, 1.4~1.438, 1.438~1.444 for the experiments, and 1.3~1.4, 1.4~1.45, 1.45~1.456 for the simulations. The influence of RW on sensitivity is analyzed experimentally in Fig. 10(c) and numerically in Fig. 10(f). In Fig. 10(c), the average sensitivities in SRI range of 1.438~1.444 are respectively measured to be 8133 nm/RIU, 9433 nm/RIU and 15667 nm/RIU for the dips a~c. In Fig. 10(f), the average sensitivities in SRI range of 1.45~1.456 is calculated numerically to be 5867 nm/RIU, 7333 nm/RIU, 8117 nm/RIU and 10500 nm/RIU for the dips 1~4. Both the simulations and the experiments show that the sensitivity of the CSPF increases with RW, and approach the maximum when the SRI is close to the RI of the fiber cladding. This is because the larger RW will lead to a stronger evanescent field outside the CSPF. Surprisingly, it is shown in Fig. 10(b) that an ultra-high sensitivity of 28000 nm/RIU can be achieved for the CSPF with a RT of 43.1 μm when the SRI changes from 1.442 to 1.444.
Fig. 10 Influence of the RW on the sensitivity of the CSPF. Experimental results for the CSPF with a RT of 43.1 μm: (a) the measured spectra, (b) shift of the dip with SRI at different RWs, and (c) the corresponding sensitivities in three RI ranges. Simulated results for the CSPF with a RT of 53.3 μm: (d) the simulated spectra, (e) shift of dip wavelength with SRI at different RWs, and (f) the corresponding sensitivities in the three RI ranges.
Furthermore, we also investigate the influence of the RT on the RI sensitivity. The RWs of the dips are chosen at almost same wavelengths for the three CSPFs to minimize the RW impact. For the CSPFs with RTs of 43.1 μm, 50.1 μm and 53.3 μm, the RWs of the dips are respectively of 1401.2 nm, 1295.6 nm and 1214.2 nm for experiments, and of 1222.4 nm, 1184.4 nm and 1188 nm for simulations. The RI sensitivities measured from the simulations are shown in Fig. 11(a), and the experimental ones are shown in Fig. 11(b). Both simulation and experiment show that the reduction in RT will enhance the RI sensitivity. It is because the reduction in RT will, for a specific mode field, increase the proportion of evanescent field outside the CSPF.
Fig. 11 Sensitivities in three SRI ranges for spectral dips of CSPFs with different RTs: (a) experimental results and (b) simulated results.
In Table 1, we compare the performance and fabrication of MMI-based fiber sensors in different structures. It can be seen that the average sensitivity of the present CSPF varied from 346nm/RIU to 15667 nm/RIU in RI range from 1.300 to 1.444. As shown in the table, the highest sensitivity among these MMI-based fiber sensors can be achieved up to 28000 nm/RIU using the CSPF in the RI range of 1.442~1444. Although the RI range is very narrow, such ultra-high sensitivity will promise many important applications in detecting the concentration of organic liquid of RI around 1.44, since organic liquid is usually toxic to human. For example, the RI of ethylene glycol, hexadecane, 1,2-dichloroethane and chloroform, are respectively 1.4318, 1.4345, 1.4448 and 1.4459 [28]. Moreover, the CSPF has a sensitivity of 346 nm/RIU in RI range of 1.3~1.4, which is higher than some other structures of the SMF-tapered PCF-SMF [19], the splicing points tapered SMF-PCF-SMF [15], the core-offset SMF [14], the SMS [12, 13] and the SMF-TCF-SMF [20]. This allows the CSPF to be a relative good platform for biochemical and biological sensors. Besides, it should be noticed that the CSPF has a relative low insertion loss of 5~10dB because the total reflection at the curve polished surface ensures a high efficiency of coupling input light to the high-order modes in the coreless flat section. Thanks to the high efficient excitation of the high order modes, a high extinction ratio of ~22 dB at the dip can be achieved for the CSPF as shown in Figs. 9(a), 9(c), 9(e) and Fig. 10(a). The fabrication method of different MMI-based fiber sensors are also shown in the Table 1. Note that the fabrication of the CSPF is simplest and easiest among these sensors since the wheel-based side polishing on a single SMF is only required, which does not need other types of fibers and other precise processing such as alignment, splicing and tapering. Furthermore, unlike other fiber sensors, the CSPF has a D-shaped cross-section, which provides a platform onto which novel materials [21–23] and micro/nano-structures [29,30] can be easily integrated.
Table 1. Performances and fabrications of MMI-based fiber sensors.
5. Conclusions
In summary, a novel fiber structure of CSPF is proposed to implement MMI for the first time. Three CSPFs with different RTs are fabricated with the wheel-based side polishing technique. The MMI mechanism of the CSPF is theoretically and numerically investigated. Evolution of MMI and spatial spectrum along the CSPF shows that the TE0,n (TM0,n) modes (n = 1~6) are efficiently and dominantly excited within the flat section of the CSPF, which gives rise to the high RI sensitivity. The RI sensing characteristics are investigated numerically and experimentally. The influence of RT and RW on the sensitivity is also analyzed. It is found that the highest sensitivity of 28000 nm/RIU can be achieved for the CSPF with a RT of 43.1 μm in the SRI range of 1.442~1.444. The analysis shows that reducing the residual thickness and choosing the dip at a longer wavelength could further enhance the sensitivity of the CSPF. Besides, such CSPF structure has a relative low insertion loss (5~10 dB) and a relative high extinction ratio (~22 dB) when compared to other MMI fiber structures. Thanks to its advantages of low loss, D-shape and high RI sensitivity, the CSPF provides a versatile platform to build high performance optical devices with various functionalities.
Appendix
Slope of polished surface in CSPF transitional section
Since the size of flat section of CSPF (RT=~40μm) is much greater than the light wavelength of 1.2μm ~1.6μm, geometrical light ray method can be used to analyze the CSPF case. Using the light ray method, Fig. 12 schematically shows that the input light beam guided by fundamental mode in lead-in SMF is reflected by the polished surface into the flat section of CSPF. It can be seen from Fig. 12 that more modes of the CSPF will be excited with larger tilted angle θ or slop t=tanθ because according to Snell’s law, larger tilted angle θ results in smaller incident angle α as shown in Fig. 12, and thus excites higher order modes with smaller propagation constants. Here, the propagation constant of m order mode can be estimated approximately by βm=ncl⋅k0⋅sinαm, where smaller αm corresponds to higher order mode and smaller βm. As shown in Fig. 2, ncl, nS, k0 are refractive indexes of the cladding and surrounding material under detection, and wavenumber in vacuum of light, respectively.
Fig. 12 Schematic of estimating the tilted angle θ (slope t = tanθ) of polishing surface to excite the highest order mode in the cladding of CSPF using optical ray approximation
It is very interesting to investigate the maximum of the tilted angle or slope to excite the highest mode in the CSPF. As shown in Fig. 12, the incident angle α is geometrically related to the tilted angle θ by
To excite the highest order guided mode, the tilted angle θ will reach up to the maximum,when the incident angle α approaches to the critical angle for the total internal reflection. For the CSPF with ncl = 1.4628 and nS = 1.456 in our simulation as shown in Fig. 2(b), the maximum of the tilted angle for the polished surface is calculated to be 2.76°, and the corresponding maximum slope of the polished surface is 0.048.Funding
National Natural Science Foundation of China (Grant No. 61675092, 61405075, 61475066, 61401176, 61505069, 61575084); Natural Science Foundation of Guangdong Province (Grant No. 2016A030313079, 2015A030306046, 2014A030313377, 2014A030310205, 2015A030313320, 2016A030311019, 2016A030310098); Science and technology projects of Guangdong Province (Grant No. 2013B090600045, 2015A020213006, 2015B010125007, 2016B010111003, 2016A010101017).
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