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We demonstrate a single taper-based all-solid photonic bandgap (AS-PBG) fiber modal interferometer that consists of a central tapered fiber region connected to the untapered via two abrupt transitions. Modal interference is given by superimposing the bandgap-guided fundamental core mode with a lower effective index and a specific index-guided cladding supermode with a higher effective index. A series of interferometers with taper diameter of 50μm ~60μm and device length of ~3mm are fabricated and studied in contrast to the conventional counterparts. The temperature coefficient of the interferometer is closely determined by the fraction of the cladding supermode energy localized within the index-raised regions of the fiber. The refractive index (RI) responsivities associated to fiber taper sizes are investigated. The measured maximal RI sensitivity is ~3512.36nm/RIU at the taper diameter of 50μm around RI = 1.423. This research gives a deep understanding to the modal-interferometric AS-PBG structure, which we believe to be valuable for the future application of the related device.
© 2016 Optical Society of America
1. Introduction
Photonic bandgap (PBG) fibers, which confine light in the core by the PBG effect originated from the 2D photonic crystal cladding, have been of great interest due to their unique guidance properties and many potential applications in nonlinear optics, high power transmission, optical sensing, and etc [1–3 ]. An all-solid PBG (AS-PBG) fiber is such a kind of bandgap fiber which commonly comprises of a low-index solid core surrounded by isolated high-index rods embedded in the low-index background [3–6 ]. Different from those hollow-core bandgap fibers [2,3 ], an all-solid PBG fiber can be easily integrated with functional materials and fusion spliced to the conventional single-mode fibers without the arc-induced air-hole collapse [7]. More interestingly, the arrangement of the rods can provide great flexibility to control or shape light beam propagating along the fiber, which has special applications in the waveguide-array or discrete-optics fields [8,9 ].
On the other side, optical fiber modal interferometers, which utilize different modes with dissimilar effective indices in a single fiber device to produce interference fringes, have been intensively researched for both the optical communication and sensing applications. Various approaches have been proposed to excite differential modes by the use of long-period gratings [10], tilted fiber Bragg gratings [11], one or two abrupt fiber tapers [12–17 ], or splicing of the fibers with different mode field profiles [18]. Among them, a single taper-based fiber modal interferometer is much appealing mostly due to its simplification, compactness, high integration, easy fabrication, and broadband of operation in comparison with those grating-assisted devices [10,11 ], exhibiting great potential in realization of optical devices and sensors for measurement of external refractive index (RI), strain, bending, and etc.
However, most of the previous studies are concentrated on the utilization of index-guiding fiber configurations, such as single-mode fibers or photonic crystal fibers [15–17 ]. In this paper, we demonstrate with single taper-based AS-PBG fiber modal interferometers, which superimpose the bandgap-guided fundamental core mode having a lower effective index and a specific index-guided cladding supermode having a higher effective index to produce interference fringes, the unique characteristics in contrast to the conventional versions. Both the temperature and external RI responses associated to structure sizes are investigated and discussed.
2. Configuration and principle
Figure 1 shows the schematic of the single taper-based AS-PBG fiber modal interferometer, which is composed of a central tapered fiber connected by two transition regions. Insets are the micrographs of the cross sections for both untapered and tapered AS-PBG fibers. As shown in the insets, the original AS-PBG fiber (manufactured by Yangtze company, China) consists of a pure silica core and a cladding with the triangular arrangement of germanosilicate rods of five layers in the silica background. The cladding diameter is 125μm, the distance between two adjacent rods of is ~3.2μm, and the rod diameter is ~2.8 μm, respectively. According to the antiresonant reflection waveguide model [19], photonic bandgaps originated from antiresonance of each individual high-index rods can prohibit light within them from penetrating into the cladding so that it is trapped in the core. This AS-PBG fiber can be directly spliced to standard single-mode fibers with a common fusion splicer without interference fringes. Then the modal interferometer is fabricated by locally heating the AS-PBG fiber via arc discharge and tapering it with the assist of a commercial, computer-controlled fiber processing machine (Fujikura, FSM100P + ). With precise control of the pulling and feeding speeds of the two motors in combination of arc strength, the desired geometry is formed [20]. The relative errors in taper diameter are below 6% over the uniform region and below 3% over the transition regions, showing a good reproducibility in geometry. As seen in the insets of Fig. 1, the geometric fiber cross section is well preserved during the tapering process. A series of samples, with L 1 = 0.4~0.7mm, L 0 = 1.0~5.0mm, and d = 50~60μm, respectively, are fabricated, which exhibit relatively thick or robust diameters and compact device lengths in comparison with the conventional counterparts [15–17 ].
Fig. 1 Schematic of the single taper-based AS-PBG fiber modal interferometer. Insets are the electron micrographs of the cross sections for both untapered and tapered AS-PBG fibers, respectively.
To understand the guidance properties of the interferometer, Fig. 2(a) plots the modal dispersion diagrams for both the untapered AS-PBG fiber with diameter of 125μm and the tapered fiber with diameter of 60μm, respectively, by use of a full-vector finite-element method [21]. The material dispersion for the silica fiber is taken into account. The arrangement of dielectric rods in the transverse direction is kept invariable with the scale-down of fiber diameter. The 90 index-raised rods in the silica background determine 90 index-guiding eigen modes, known as cladding supermodes, in each individual photonic band. For example, in the 1st photonic band, there are 90 LP01 supermodes of different orders. The couplings between the neighboring rods establish the specific mode profiles over the whole microstructure. With reduction of fiber size, the indices of the supermodes shift down as a whole and the photonic band is broadened. And more cladding supermode energies extend into the low-index silica regions. Figure 2(b) gives field distributions for some typical supermodes and the fundamental mode of the AS-PBG fiber corresponding to points A~H, respectively, shown in Fig. 2(a). Only the fundamental core mode is present within the first bandgap. As the fiber cladding size decreases, the confinement of the fundamental mode becomes weak gradually, until the mode dispersion curve vanishes as the fiber size is small sufficiently. When the fiber diameter changes dramatically in the transition of the taper to break the adiabaticity [15,16 ], modal coupling could occur between the core mode and a specific cladding supermode which has the similar azimuthal symmetry [16]. The modal coupling coefficient κ can be expressed as
where Δε is the change of dielectric constant, E(x,y) is the field profile of the modes involved in the modal coupling process, and the subscripts f and s denotes the fundamental mode and the supermode, respectively. As shown in Fig. 1(a), the light power is partially split into the core mode and the cladding supermode at the incident transition and then experiences different effective indices in the tapered fiber region. The interference is given by recombining the modes at the other transition region of the taper. The phase difference between the core mode and the cladding supermode is given bywhere Δn is the index difference between the interference modes, L is the interaction length of modes, and λ is the wavelength, respectively. The transmittance is I = I 1 + I 2 + 2(I 1⋅I 2)1/2cos(Φ), where I 1 and I 2 are the intensities for the core mode and the cladding supermode, respectively. The transmission maxima occur when Φ equals an even number of π and the minima occur when Φ equals an odd number of π.Fig. 2 (a) Modal dispersion diagrams for the AS-PBG fiber with diameters of 125μm and 60μm, respectively. (b) Electric field distributions for some typical supermodes and the fundamental mode of the AS-PBG fiber with relation to the diagrams of (a).
The introduction of the taper may induce excitation of different periodical arrays of the high-index cladding rod modes, leading to groups of resonance dips in the transmission spectrum in practice. In our experiment, the spectral characteristics can be controlled by optimizing the fiber processing procedure and monitored by use of a broadband light source in junction to an optical spectrum analyzer. Figure 3(a) plots two transmission spectra for the single taper-based AS-PBG fiber modal interferometers with L 1 = 0.628mm, L 2 = 0.61mm, L 0 = 1.85mm, d = 60μm and L 1 = L 2 = 0.50mm, L 0 = 2.0mm, d = 50μm, respectively. Distinct interference fringes are observed. As shown in the figure, the measured transmission loss is ~10dB and the extinction ratio is over 10dB. The measured wavelength spacing between two adjacent peaks are ~105nm and ~78nm for the thicker and thinner tapers, respectively. From Eq. (2), the positions of transmission dips are co-determined by the diameter and the length of the taper. Considering the mode dispersion property, the wavelength spacing Δλ between the neighboring transmission maxima can be expressed as Δλ = λ 2/(Δn g⋅L), with Δn g the group index difference [16]. From Fig. 3(a), we can estimate the group index differences of around 0.0116 and 0.0144 for the thicker and thinner tapers, respectively.
Fig. 3 (a) Transmission spectra of the single taper-based AS-PBG fiber modal interferometers with L 1 = 0.628mm, L 2 = 0.61mm, L 0 = 1.85mm, d = 60μm and L 1 = L 2 = 0.5mm, L 0 = 2.0mm, d = 50μm, respectively. (b) Near-field images of transmitted power at wavelengths of 1534nm (point A) and 1544nm (point B), respectively.
To identify what kind of supermode is involved in the interference, we use a wavelength-swept laser to illuminate the interferometer via the lead-in single-mode fiber. Figure 3(b) gives the near-field images of the transmitted light power at points A (corresponding to the wavelength of 1534nm) and B (corresponding to the wavelength of 1544nm), respectively. Point A has a relatively larger fraction of mode power localized inside the index-raised rods due to the suppression of the core mode at the resonance dip as analyzed in Eq. (1). Comparatively, point B has a larger fraction of mode power in the core than the high-index rods approaching the transmission maxima. The modal interference occurs between the fundamental core mode and an LP01-order cladding supermode.
3. Temperature coefficient
The temperature coefficient is investigated by placing the structure into a resistance furnace in air, with the furnace temperature controlled by an electric circuit and recorded by a thermometer. Figure 4(a) shows the interferometric dip wavelength shift as a function of temperature for the taper diameters of d = 50μm and 60μm, respectively. The other parameters are L 1 = L 2 = 0.5mm and L 0 = 2.0mm, respectively. Figures 4(b) and 4(c) detail the transmission spectra with respect to different temperatures at d = 50μm and 60μm, respectively. With the increasing temperature from 25°C to 95°C, the dip wavelength redshifts for ~1.40nm (from 1506.60nm to 1508.0nm) at d = 50μm and ~1.56nm (from 1432.28nm to 1433.82nm) at d = 60μm, respectively. By linear fitting the experimental data, we obtain the temperature coefficients of ~20.5 pm/°C at d = 50μm and ~22.2 pm/°C at d = 60μm, respectively. These coefficients are analogous to that of Bragg gratings in the conventional single-mode fibers and are mainly originated from the dissimilar thermal expansion and thermo-optic factors between the silica core and the germanosilicate cladding rods. The difference of temperature coefficients between the two different tapers is ∼8.29%. The thicker fiber taper has a larger temperature coefficient since it has a larger fraction of the cladding supermode distributed in the high-index rods than the thinner one. For example, utilizing the parameters of Fig. 2, we can calculate the fraction of cladding supermode energy within the index-raised rods, with the results being 16.92% and 24.95% for the upper and lower edges, respectively, for the 1st mode band shown in Fig. 2(a), with d = 50μm and λ = 1500nm, and 21.36% and 31.76% at the upper and lower edges, respectively, for the 1st mode band with d = 60μm and λ = 1500nm, respectively. The latter has a larger fraction of energy than the former, consistent to the observation shown in Fig. 4(a). Simultaneously, the measured temperature coefficient is ~18.9pm/°C at wavelength of 1424.50nm for d = 50μm. Such a coefficient is slightly smaller than that at wavelength of 1506.60nm for the same taper structure. The temperature coefficient can be modified by changing the diameter of the taper.
Fig. 4 (a) Dip wavelength shifts as functions of temperature corresponding to d = 50μm and 60μm, respectively, with L 1 = L 2 = 0.5mm and L 0 = 2.0mm. (b) Transmission spectra with respect to different temperatures at d = 50μm. (c) Transmission spectra with respect to different temperatures at d = 60 μm.
4. Response to external RI
As demonstrated in Fig. 2, when the AS-PBG fiber diameter is decreased, both the interfering core mode and cladding supermode fields can extend into the external medium and have strong interaction with the surroundings, making our structure sensitive to external RI perturbations. For example, utilizing the parameters of Fig. 2, we can estimate the fractions of evanescent mode energies for the fiber taper placed in water and the results are given by 0.0315%, 5.78 × 10−6%, and 0.0326% for the core mode (point E), the supermode at the upper edge of the 1st band (point F), and the supermode at the lower edge of the 1st band (point G), respectively. The fraction of evanescent mode energy for the core mode can be higher or lower than that for the cladding supermode. As shown in Fig. 2, the supermode F corresponds to a much higher effective index and accordingly a stronger mode confinement with the index-guiding mechanism, which leads to a much smaller fraction of evanescent mode energy compared with the other two modes. The dissimilarity between the interfering core mode and the cladding supermode determines the shift of transmission spectrum with the change in external RI. In fact, the spectral shift is related to the excited cladding supermode propagating in the cladding rods [22]. In our experiment, we make an investigation of RI responsivities associated to the different fiber taper sizes. To do so, we immerse our fabricated interferometer into an aqueous solution of sucrose and modify the surrounding RI by changing the sucrose concentration at the room temperature (~26°C). Figure 5(a) plots the dip wavelength shifts as functions of external RI for the taper diameters of d = 50μm and 60μm, respectively. The other parameters are L 1 = L 2 = 0.5mm and L 0 = 2.0mm, respectively. Figures 5(b) and 5(c) show the transmission spectra at different RIs with d = 50μm and 60μm, respectively. The dip wavelengths redshift gradually with an increase of external RI in a nonlinear relationship. For the RI increasing from 1.333 to 1.423, the dip wavelength shifts for ~73.92nm (from 1516.47nm to 1590.39nm) at d = 50μm and ~23.04nm (from 1443.26nm to 1466.30 nm) at d = 60μm, respectively. The obtained sensitivities are ~146.87nm/RIU at d = 50μm and ~86.92nm/RIU at d = 60μm around RI = 1.333 and ~3512.36nm/RIU at d = 50μm and ~403.59 nm/RIU at d = 60μm around RI = 1.423, respectively. The RI sensitivity becomes large gradually with an increase of RI. The thinner fiber has a larger RI sensitivity due to its higher evanescent mode interaction with external RI compared to the thicker one. Simultaneously, the measured RI sensitivities are ~97.70nm/RIU around RI = 1.333 and ~483.84nm/RIU around RI = 1.423 at wavelength of 1310nm for d = 60μm. The sensitivity varies slightly with wavelength due to the changes of evanescent mode fractions as previously demonstrated. The RI sensitivity can be improved by modifying the diameter of the taper at a fixed wavelength.
Fig. 5 (a) Dip wavelength shift as a function of external RI for d = 50μm and 60μm, respectively, where L 1 = L 2 = 0.5mm and L 0 = 2.0mm. (b) Transmission spectra with respect to different RIs at d = 50μm. (c) Transmission spectra with respect to different RIs at d = 60μm.
5. Conclusion
In this paper, a single taper-based AS-PBG fiber modal interferometer which consists of a central tapered fiber region and two abrupt transitions is demonstrated. Both the lower-index core mode guided by the bandgap effect and the higher-index cladding supermode guided by the index-guiding mechanism are involved to produce interference fringes. A series of interferometers with taper diameter of 50μm~60μm and device length of ~3mm are fabricated and studied. The temperature coefficient originated from the different thermal expansion and thermo-optic factors between the silica core and the germanosilicate rods is closely related to the fraction of the supermode energy distributed within the index-raised cladding rods. The RI responsivities associated to fiber taper sizes are investigated as well. The measured maximal RI sensitivity is ~3512.36nm/RIU at the taper diameter of 50μm around RI = 1.423. This work provides a useful investigation to the modal-interferometric AS-PBG structure, which is valuable for the future application of the device.
Acknowledgments
This work is supported by the National Science Fund for Distinguished Young Scholars of China (61225023), the National Natural Science Foundation of China (NSFC) (61235005 and 61575083), and the Guangdong Natural Science Foundation (S2013030013302 and 2014A030313364).
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