Miniature highly-birefringent microfiber loop with extremely-high refractive index sensitivity

doi:10.1364/OE.20.010180

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Miniature highly-birefringent microfiber loop with extremely-high refractive index sensitivity

Lipeng Sun, Jie Li, Yanzhen Tan, Xiang Shen, Xiaodong Xie, Shuai Gao, and Bai-Ou Guan »View Author Affiliations

Optics Express, Vol. 20, Issue 9, pp. 10180-10185 (2012)
http://dx.doi.org/10.1364/OE.20.010180

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▸ Article Outline
– Abstract
1. Introduction
2. Fabrication
3. Principle
4. Response to refractive index and temperature
5. Conclusion
– References and links

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Abstract

A miniature polarimetric interferometer with the twist of a highly-birefringent microfiber is demonstrated. Good transmission spectral characteristics, which are co-governed by the birefringence and the twist degree of the microfiber, are investigated. The structure exhibits extremely-high sensitivity of around 24,373 nm per refractive-index unit and excellent temperature stability of better than 0.005nm/°C. Featured with compactness, reconfigurability, stability, robustness, and compatibility with other fiberized components, our device has potential in tunable filtering, sensing, multi-wavelength lasing, and etc.

1. Introduction

Polarimetric interferometer that employs separation and interference of orthogonally polarized states of light has great application potential in tunable comb filtering, sensing, multi-wavelength lasing, nonlinear resonating, and etc. Nowadays microfibers on the subwavelength scale are attracting much research attention due to their compactness and very large evanescent field effect [1

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003). [CrossRef] [PubMed]

]. Various compact microfiber devices in the form of loops/knots [2

Y. Wu, X. Zeng, C. L. Hou, J. Bai, and G. G. Yang, “A tunable all-fiber filter based on microfiber loop resonator,” Appl. Phys. Lett. 86, 191112 (2008).

X. S. Jiang, L. M. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang, and D. R. Yang, “Demonstration of optical microfiber knot resonators,” Appl. Phys. Lett. 88(22), 223501 (2006). [CrossRef]

], coils [4

F. Xu, P. Horak, and G. Brambilla, “Optical microfiber coil resonator refractometric sensor,” Opt. Express 15(12), 7888–7893 (2007). [CrossRef] [PubMed]

M. Sumetsky, “Uniform coil optical resonator and waveguide: transmission spectrum, eigenmodes, and dispersion relation,” Opt. Express 13(11), 4331–4340 (2005). [CrossRef] [PubMed]

], or reflectors [6

S. S. Wang, Z. F. Hu, Y. H. Li, and L. M. Tong, “All-fiber Fabry-Perot resonators based on microfiber Sagnac loop mirrors,” Opt. Lett. 34(3), 253–255 (2009). [CrossRef] [PubMed]

–8

S. D. Lim, K. J. Park, B. Y. Kim, K. Lee, and S. B. Lee, “An optical microfiber Sagnac interferometer with adjustable transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JWA7.

] have been implemented. However, all those previous configurations basically rely on the resonance or reflection of optical cavity without consideration of polarization properties, which yields refractive index (RI) sensitivity of up to 10³ nm/RI-unit [4

F. Xu, P. Horak, and G. Brambilla, “Optical microfiber coil resonator refractometric sensor,” Opt. Express 15(12), 7888–7893 (2007). [CrossRef] [PubMed]

]. Differently, this letter demonstrates a miniature polarimetric interferometer using the twisted highly-birefringent microfiber (HBMF). Experiment displays extremely-high sensitivity of ~24,373nm/RI-unit and excellent temperature stability of <0.005nm/°C, enabling the potential application in wide wavelength tuning or (bio) chemical sensing. Besides, the designed structure is featured with reconfigurability, stability, robustness, and compatibility with other fiberized components.

2. Fabrication

Figure 1 depicts the schematic of our interferometer, which consists of the loop and the twist sections of microfiber. For the purpose of polarization interference, the birefringence of the microfiber should be high sufficiently, which can be realized by using a noncircular microfiber [9

A. M. Zheltikov, “Birefringence of guided modes in photonic wires: Gaussian-mode analysis,” Opt. Comrnun. 252(1–3), 78–83 (2005). [CrossRef]

]. In our experiment, the high-birefringent microfiber is obtained by tapering a rectangular preform, having a circular Ge-doped core with diameter of 6.0μm and a rectangular silica cladding with widths of a = 113μm and b = 70μm, into the micron size utilizing the flame-brushing technique [10

J. Li, L. P. Sun, S. Gao, Z. Quan, Y. L. Chang, Y. Ran, L. Jin, and B. O. Guan, “Ultrasensitive refractive-index sensors based on rectangular silica microfibers,” Opt. Lett. 36(18), 3593–3595 (2011). [CrossRef] [PubMed]

]. The rectangular profile can be well preserved by optimizing the heating temperature and the fiber-tapering speed, as shown in Fig. 1. Thanks to the noncircular symmetry and the large refractive index contrast between the fiber and the surrounding environment, the microfiber generates very high birefringence (~10⁻³) as the fiber size is reduced sufficiently. Similar to the well-established bi-conical taper model [2

Y. Wu, X. Zeng, C. L. Hou, J. Bai, and G. G. Yang, “A tunable all-fiber filter based on microfiber loop resonator,” Appl. Phys. Lett. 86, 191112 (2008).

–10

], the fabricated microfiber comprises two transition regions with length of ~60 mm and a central uniform waist region with length of ~35 mm, respectively. The inset of Fig. 1 gives an image of realistic HBMF interferometer. For the purpose of fabricating the HBMF interferometer, we firstly create a tens-of-millimeter-order self-touching microfiber loop in the minimum waist of the microfiber taper with micromanipulation. Secondly, we mount the loose ends of the microfiber into the two rotatable fiber holders that are placed in 45° angle, as illustrated in Fig. 2(a) . As the fiber holders are turned slightly along the same direction, the microfiber begins to twist itself via the strong Van der Waals and the electrostatic attraction and the torsion force. During turning, it is observed that the twist length increases continuously but the shape of microfiber loop keeps unchanged in the free space, finally yielding a stable and robust device.

Fig. 1 Schematic of the HBMF interferometer. The cross-sectional fiber view and the photograph of a fabricated structure are also provided as insets.

Fig. 2 (a) Fabrication setup of the HBMF interferometer. (b) Transmission spectra in respect of the turn angle. (c) Transmission spectra for the interferometers with d = 13mm, a = 3.0μm and d = 2.3mm, a = 2.7μm, respectively.

The spectral characteristics of the interferometer are monitored using a broad-band light source (BBS) and an optical spectrum analyzer (OSA), as shown in Fig. 1, where the untapered lead ends of microfiber are connected to the standard single-mode fibers with a connection loss smaller than 0.5dB at each splice point by carefully aligning the fiber cores. During the fiber holders’ rotating, as shown in Fig. 2(a), the transmission spectrum is generally unstable at the beginning due to the uncertainty of the microfiber contact, but after two or three rounds it tends to stable and varies with relation to the turn angle. As shown in Fig. 2(b), the extinction ratios of the spectrum increase continuously with the turn angle increasing from 820° to 870° and the value can be better than 20dB with optimization of the turn angle. But as the angle is further increased, the extinction ratios first decay and then increase alternately with a period of ~90°. In this process the wavelength points of resonance transmission dips keep unchanged. Experiment also shows that twisting the microfibers may modify the transmission values in Fig. 2(b). By tuning the twist degree, both the extinction ratio and the transmission can be optimized. Figure 2(c) provides two resultant transmission spectra of the fabricated interferometers corresponding to d = 13mm, a = 3.0μm, and d = 2.3mm, a = 2.7μm, respectively. Considering the material dispersion of the fused silica fiber [11

M. Bass, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009).

], by the use of a full-vector finite element method [12

M. Koshiba and Y. Tsuji, “Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol. 18(5), 737–743 (2000). [CrossRef]

], we calculate the free space ranges in transmission spectrum to be 7.3nm (experiment: 7.0 nm) and 34.7nm (experiment: 36 nm) for the interferometers with d = 13mm and d = 2.3mm, respectively. The calculation agrees with the experimental results. The discrepancy between the calculation and experimental results can be attributed mostly to the difference between the measured and the true sizes of microfiber loop. From Fig. 2(c), the larger microfiber loop can correspond to the more narrowed wavelength spacing of transmission dips.

3. Principle

To understand the spectral characteristics of the HBMF loop, the touching of microfibers can correspond to a strong light coupling due to the very large evanescent field effects [1

–10

]. As shown in Fig. 1, at the twist of microfiber, the input light is split into the two beams of clockwise and anticlockwise propagation. Each of the resultant beams is decomposed into two beams after traveling around the highly-birefringent loop [13

D. B. Mortimore, “Fiber loop reflectors,” J. Lightwave Technol. 6(7), 1217–1224 (1988). [CrossRef]

]. The interference is then given by recombination of the counter-propagating beams as similarity to the conventional fiber Sagnac loop. Regarding the fiber loop as an equivalent waveplate having phase retardation of ϕ and oriented at an angle of θ, we have

ϕ = (2 π / λ) B L

(1)

where λ is the wavelength, B = |n_a− n_b| is the modal birefringence with n_a and n_b representing the effective refractive indices at the slow and fast axes, respectively, and L (≈πd) is the effective length of the fiber loop. It has been known that the coupling of touched microfibers is much complicated [14

Q. Wu, Y. Ma, J. Yuan, Y. Semenova, P. Wang, C. Yu, and G. Farrell, “Evanescent field coupling between two parallel close contact SMS fiber structures,” Opt. Express 20(3), 3098–3109 (2012). [CrossRef] [PubMed]

]. Without loss of generality, we express the relation between the input and output field amplitudes across the twist as E₃_x,y = k₁_x,y E₁_x,y + k₂_x,yE₂_x,y and E₄_x,y = k₂_x,y E₁_x,y + k₁_x,yE₂_x,y, with k₁_x,y and k₂_x,y the coupling for the x and y polarizations of the coupler [13

D. B. Mortimore, “Fiber loop reflectors,” J. Lightwave Technol. 6(7), 1217–1224 (1988). [CrossRef]

]. Similar to Ref. 10

, the output power P₂_x,y at port 2 can be related to the input power P₁_x,y at port 1 by

P_{2 x, y} = {(k_{1 x, y}^{2} + k_{2 x, y}^{2})}^{2} P_{1 x, y} - \sin^{2} 2 θ \sin^{2} \frac{ϕ}{2} [{(k_{1 x, y}^{2} + k_{2 x, y}^{2})}^{2} P_{1 x, y} - {(k_{1 x} k_{1 y} - k_{2 x} k_{2 y})}^{2} P_{1 y, x}]

(2)

For the unpolarized input light, the powers P₁_x and P₁_y are equal to each other. The transmission, T = P₂_x,y/P₁_x,y, is thereby governed by the coupling parameters k₁_x,y and k_2x,y, the orientation angle θ, and the phase difference ϕ. The terms of k₁_x,y, k₂_x,y, and θ are relatively wavelength-insensitive. In the case of θ = mπ + π/2 (m = integer), the retardation ϕ has no effect on the performance of the interferometer; otherwise, the transmission varies rapidly against λ, as shown in Eq. (2). The change of the orientation angle θ can vary the extinction ratios or visibilities of the interferometric spectrum. In Fig. 2(a), twisting the microfibers can modify the value of θ but has no influence on the length of the microfiber loop at head, which can in quality demonstrate the phenomenon as observed in Fig. 2(b).

When the birefringence is negligible, e.g., for circular microfibers, we obtain ϕ≈0 and Eq. (2) reduces to P₂_x,y = (k₁_x,y² + k₂_x,y²)²P₁_x,y. The input light is just reflected via the coupling after transmitting a round trip in the loop without polarization interference and the transmission is governed by the coupling of microfibers. Owing to the fact that the coupling is relatively wavelength insensitive, the transmission spectrum has a quite broad-band wavelength dip, as has been observed in [8

]. Twisting the microfibers can shift the transmission spectrum almost as a whole, which restricts the structure to function as an attenuator or a linear edge filter [8

4. Response to refractive index and temperature

The dependency of wavelength on the external RI can be measured by immersing the HBMF interferometer into an ethyl alcohol liquid with purity of 99.8%, with the index value of alcohol modified through control of the applied temperature. In the experiment we adopt a water bath method to tune the temperature of alcohol. The interferometer is placed into the alcohol in a small glass vessel and the vessel is placed in a big glass cup filled with water. The mouth of the small vessel is sealed to avoid the direct exposure of alcohol to outside air. With heat exchange between the alcohol, the water, and the environment, the alcohol temperature cools down from high to low in a quite slow, steady, and natural way. We measure the spectral characteristics of the interferometer using BBS and OSA, the refractive index of alcohol using a refractometer (Reichert AR200), and the temperature using a thermometer. Figure 3(a) records several transmission spectra in respect of external RI, for the HBMF loop with d ≈4.3mm and a ≈3.65μm. Considering the material dispersion of both fused silica fiber [11

M. Bass, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009).

] and alcohol liquid [15

T. E. Smith and R. F. Bonner, “Refractive index temperature data for anhydrous ethyl alcohol,” Anal. Chem. 24(3), 517–518 (1952). [CrossRef]

], by the use of a full-vector finite element method, the free space range is calculated to be 304nm around λ = 1300nm at RI = 1.3586, which is consistent to the observation shown in Fig. 3(a). The widening of dip-wavelength spacing for the structure in alcohol compared to that in air can be attributed to the decreasing of the fiber birefringence with an increase in ambient RI. Figure 3(b) shows the relationship between the dip wavelength, the alcohol RI, and the alcohol temperature. The dots indicate the measured temperature points (circles), the first-round measured wavelength points (triangles), and the second-round measured wavelength points (squares), respectively, the solid line indicates the linear fit results, and the dashed curve indicates the simulation results. It turns out each measurement round has a fairly good repeatability. With the increasing of alcohol RI, the wavelength dip redshifts rapidly. The scanning time of OSA is not more than one second over the whole wavelength range of interest. Hence the response time of the device to the external RI change should be smaller than one second. As shown in Fig. 3, in the RI range from 1.3550 to 1.3886, the measured average sensitivity is 24,373nm/RI-unit, which is the higher than other microfiber configurations as reported to date, to our knowledge. As shown by the dashed curve in Fig. 3(b), the calculated results show an excellent agreement to the experimental values. It is also shown that the alcohol RI increases almost linearly with the decreasing of temperature from 37° to 28° with a coefficient of −4.01 × 10⁻⁴ RI-unit/°C similar to [15

T. E. Smith and R. F. Bonner, “Refractive index temperature data for anhydrous ethyl alcohol,” Anal. Chem. 24(3), 517–518 (1952). [CrossRef]

]. Owing to the slow heat exchange between the alcohol and the surrounding environment, each measurement round in Fig. 3(b) lasts for more than 3 hours. The time interval between the two measurement rounds is about 1.5 hours. Experimental investigation shows that the interferometer is fairly long-term stable and repeatable due to the strong Van der Waals force and electrostatic attraction between microfibers as previously demonstrated. One may fix the relative position of the microfibers using the CO₂ laser as reported in [16

P. Wang, L. Zhang, Z. Y. Yang, F. X. Gu, S. S. Wang, Q. Yang, and L. M. Tong, “Fusion spliced microfiber closed-loop resonators,” IEEE Photon. Technol. Lett. 22(15), 1075–1077 (2010). [CrossRef]

]. The package method of the interferometer can be considered. When functioning as a tunable optical filter, the interferometer can be packaged with a temperature-sensitive material together. When functioning as a RI sensor, the interferometer may have the coupling section packaged but left the sensing microfiber loop exposed to environment.

Fig. 3 (a) Transmission spectra of the HBMF interferometer in alcohol with the external RI rising from 1.3550 to 1.3586. (b) Relationship between the dip wavelength, the external refractive index, and the temperature. The dots indicate the experimental temperature points (circles), the first-round measured wavelength points (triangles), and the second-round measured wavelength points (squares), respectively, the solid line indicates the linear fit results, and the dashed curve indicates the simulation results by the use of a full-vector finite element method.

To experimentally investigate the temperature influence on the spectral characteristics, we place the interferometer into a resistance furnace in air. Figure 4 records a series of transmission spectra for the temperature increasing from 25°C to 140°C. It is shown that the temperature variation can have a negligible effect on the wavelength characteristics, which can be attributed to the low thermal-expansion coefficient (0.55 × 10⁻⁶/°C) of silica fiber. The measured absolute sensitivity is smaller than 0.005nm/°C, implying significant suppression of temperature-cross sensitivity during the RI modification.

Fig. 4 Transmission spectra of the HBMF interferometer with the temperature range from 25°C to 140°C.

5. Conclusion

In conclusion, we demonstrate a miniature polarimetric interferometer with twist of a continuous highly-birefringent microfiber. Both the fabrication method and the interferometric principle are presented. The device performance is co-governed by the birefringence and the twist degree of microfiber. In particular, extremely-high RI sensitivity of around 24,373nm/RI-unit and suppressed temperature-cross sensitivity of better than 0.005nm/°C are achieved. Featured with reconfigurability, stability, robustness, and compatibility with other fiberized components, our structure can exhibit great application potential in tunable filtering, sensing, multi-wavelength lasing, and etc.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (60736039, 11004085), the Research Fund for the Doctoral Program of Higher Education of China (20114401110006), and the Fundamental Research Funds for the Central Universities of China (21609102).

References and links

1.	L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003). [CrossRef] [PubMed]
2.	Y. Wu, X. Zeng, C. L. Hou, J. Bai, and G. G. Yang, “A tunable all-fiber filter based on microfiber loop resonator,” Appl. Phys. Lett. 86, 191112 (2008).
3.	X. S. Jiang, L. M. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang, and D. R. Yang, “Demonstration of optical microfiber knot resonators,” Appl. Phys. Lett. 88(22), 223501 (2006). [CrossRef]
4.	F. Xu, P. Horak, and G. Brambilla, “Optical microfiber coil resonator refractometric sensor,” Opt. Express 15(12), 7888–7893 (2007). [CrossRef] [PubMed]
5.	M. Sumetsky, “Uniform coil optical resonator and waveguide: transmission spectrum, eigenmodes, and dispersion relation,” Opt. Express 13(11), 4331–4340 (2005). [CrossRef] [PubMed]
6.	S. S. Wang, Z. F. Hu, Y. H. Li, and L. M. Tong, “All-fiber Fabry-Perot resonators based on microfiber Sagnac loop mirrors,” Opt. Lett. 34(3), 253–255 (2009). [CrossRef] [PubMed]
7.	T. Wang, X. H. Li, F. F. Liu, W. H. Long, Z. Y. Zhang, L. M. Tong, and Y. K. Su, “Enhanced fast light in microfiber ring resonator with a Sagnac loop reflector,” Opt. Express 18(15), 16156–16161 (2010). [CrossRef] [PubMed]
8.	S. D. Lim, K. J. Park, B. Y. Kim, K. Lee, and S. B. Lee, “An optical microfiber Sagnac interferometer with adjustable transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JWA7.
9.	A. M. Zheltikov, “Birefringence of guided modes in photonic wires: Gaussian-mode analysis,” Opt. Comrnun. 252(1–3), 78–83 (2005). [CrossRef]
10.	J. Li, L. P. Sun, S. Gao, Z. Quan, Y. L. Chang, Y. Ran, L. Jin, and B. O. Guan, “Ultrasensitive refractive-index sensors based on rectangular silica microfibers,” Opt. Lett. 36(18), 3593–3595 (2011). [CrossRef] [PubMed]
11.	M. Bass, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009).
12.	M. Koshiba and Y. Tsuji, “Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol. 18(5), 737–743 (2000). [CrossRef]
13.	D. B. Mortimore, “Fiber loop reflectors,” J. Lightwave Technol. 6(7), 1217–1224 (1988). [CrossRef]
14.	Q. Wu, Y. Ma, J. Yuan, Y. Semenova, P. Wang, C. Yu, and G. Farrell, “Evanescent field coupling between two parallel close contact SMS fiber structures,” Opt. Express 20(3), 3098–3109 (2012). [CrossRef] [PubMed]
15.	T. E. Smith and R. F. Bonner, “Refractive index temperature data for anhydrous ethyl alcohol,” Anal. Chem. 24(3), 517–518 (1952). [CrossRef]
16.	P. Wang, L. Zhang, Z. Y. Yang, F. X. Gu, S. S. Wang, Q. Yang, and L. M. Tong, “Fusion spliced microfiber closed-loop resonators,” IEEE Photon. Technol. Lett. 22(15), 1075–1077 (2010). [CrossRef]

OCIS Codes
(060.2340) Fiber optics and optical communications : Fiber optics components
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(260.1440) Physical optics : Birefringence

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: February 22, 2012
Revised Manuscript: April 10, 2012
Manuscript Accepted: April 12, 2012
Published: April 19, 2012

Citation
Lipeng Sun, Jie Li, Yanzhen Tan, Xiang Shen, Xiaodong Xie, Shuai Gao, and Bai-Ou Guan, "Miniature highly-birefringent microfiber loop with extremely-high refractive index sensitivity," Opt. Express 20, 10180-10185 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-9-10180

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References

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature426(6968), 816–819 (2003). [CrossRef] [PubMed]
Y. Wu, X. Zeng, C. L. Hou, J. Bai, and G. G. Yang, “A tunable all-fiber filter based on microfiber loop resonator,” Appl. Phys. Lett.86, 191112 (2008).
X. S. Jiang, L. M. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang, and D. R. Yang, “Demonstration of optical microfiber knot resonators,” Appl. Phys. Lett.88(22), 223501 (2006). [CrossRef]
F. Xu, P. Horak, and G. Brambilla, “Optical microfiber coil resonator refractometric sensor,” Opt. Express15(12), 7888–7893 (2007). [CrossRef] [PubMed]
M. Sumetsky, “Uniform coil optical resonator and waveguide: transmission spectrum, eigenmodes, and dispersion relation,” Opt. Express13(11), 4331–4340 (2005). [CrossRef] [PubMed]
S. S. Wang, Z. F. Hu, Y. H. Li, and L. M. Tong, “All-fiber Fabry-Perot resonators based on microfiber Sagnac loop mirrors,” Opt. Lett.34(3), 253–255 (2009). [CrossRef] [PubMed]
T. Wang, X. H. Li, F. F. Liu, W. H. Long, Z. Y. Zhang, L. M. Tong, and Y. K. Su, “Enhanced fast light in microfiber ring resonator with a Sagnac loop reflector,” Opt. Express18(15), 16156–16161 (2010). [CrossRef] [PubMed]
S. D. Lim, K. J. Park, B. Y. Kim, K. Lee, and S. B. Lee, “An optical microfiber Sagnac interferometer with adjustable transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JWA7.
A. M. Zheltikov, “Birefringence of guided modes in photonic wires: Gaussian-mode analysis,” Opt. Comrnun.252(1–3), 78–83 (2005). [CrossRef]
J. Li, L. P. Sun, S. Gao, Z. Quan, Y. L. Chang, Y. Ran, L. Jin, and B. O. Guan, “Ultrasensitive refractive-index sensors based on rectangular silica microfibers,” Opt. Lett.36(18), 3593–3595 (2011). [CrossRef] [PubMed]
M. Bass, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009).
M. Koshiba and Y. Tsuji, “Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol.18(5), 737–743 (2000). [CrossRef]
D. B. Mortimore, “Fiber loop reflectors,” J. Lightwave Technol.6(7), 1217–1224 (1988). [CrossRef]
Q. Wu, Y. Ma, J. Yuan, Y. Semenova, P. Wang, C. Yu, and G. Farrell, “Evanescent field coupling between two parallel close contact SMS fiber structures,” Opt. Express20(3), 3098–3109 (2012). [CrossRef] [PubMed]
T. E. Smith and R. F. Bonner, “Refractive index temperature data for anhydrous ethyl alcohol,” Anal. Chem.24(3), 517–518 (1952). [CrossRef]
P. Wang, L. Zhang, Z. Y. Yang, F. X. Gu, S. S. Wang, Q. Yang, and L. M. Tong, “Fusion spliced microfiber closed-loop resonators,” IEEE Photon. Technol. Lett.22(15), 1075–1077 (2010). [CrossRef]

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