Abstract

Microfiber gratings with diameters in the subwavelength scale have recently attracted much attention for developments of sensitive sensors; however, a specific structure is usually chosen for sensing one parameter according to the optical response. In this work, a superstructure microfiber grating combined with microfiber Bragg grating and long-period microfiber grating is reported for the first time. The proposed superstructure is formed by ultraviolet laser inscription and femtosecond laser scratching techniques, which simultaneously endows the unique properties of the two individual gratings. The reflection and transmission spectral characteristics differing to conventional counterparts are demonstrated. The responsivities of the two gratings to temperature, strain and refractive index are investigated, providing a possibility for simultaneous multi-parameter sensing.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Microfiber grating devices with diameters of several micrometers have recently attracted enormous research interests due to the compactness and flexibility, large evanescent fields, manageable large dispersion, and compatibility to conventional fibers [15]. The distinct features stimulate various applications in biomedical, chemistry, communication, and sensing fields [6,7]. However, with the size scaling down, the fiber is easily broken during the grating inscription, and the photosensitivity also degrades, making it difficult to form gratings via the ultraviolet light compared to the case in a conventional fiber. Recently, efforts have been made to fabricate Bragg gratings or long-period gratings in microfibers, which show some unique optical properties different from those in conventional fibers. Microfiber Bragg gratings (mFBGs) have been reported using techniques such as ultraviolet laser irradiation [2,3], femtosecond laser writing [8], focused ion beam milling [9,10], and lithography [11]. An mFBG, within which the refractive index (RI) is modulated with a period of several hundred nanometers, can allow power exchange from a propagating mode to the counter-propagating mode, leaving a reflection peak in the spectrum at the resonance wavelength. For example, it was found that a 3 $\mu m$-diameter mFBG has a reflection coefficient of over 97$\%$ via the 193 $nm$-wavelength ultraviolet laser writing technique [12]. On the other hand, microfiber long-period gratings (mLPGs) have been manufactured through the CO$_2$ laser irradiation [13], femtosecond laser inscription [14] or arc discharging technique [15]. Unlike an mFBG, the mLPG has the period from tens to hundreds of micrometers, which enables power exchange from one mode to other co-propagating modes, forming dips at resonance wavelengths in the transmission spectrum. In general, both mFBG and mLPG have higher responses to external refractive index (RI) than conventional fiber structures thanks to their high evanescent field effects, making them to be widely used in the RI-based sensing areas [2,13,16]. However, originated from dissimilar mode coupling phenomena, the sensing characteristics of mFBG and mLPG should be different [4,17].

In this work, a superstructure microfiber grating (SMG) is first proposed and fabricated to our knowledge, which shows characteristics of both the mFBG and mLPG. The reflection and transmission spectra compared with conventional counterparts are discussed. The proposed SMG is characterized by detecting the changes on the temperature, applied strain, and surrounding refractive index. By tracking the resonance shifts in both the transmission and reflection spectra, the SMG leads to a method for multi-parameter detection.

2. Fabrication and spectral characteristics

A microfiber with a diameter of 9.8 $\mu m$ and with a length of 4.5 $mm$ was fabricated by heating and pulling a 9/125-$\mu m$ standard single mode fiber with a butane torch. In order to avoid the degradation and surface contamination during the preservation, the microfiber was post-treated by flame brushing for a few seconds before the Bragg grating inscription.

A microfiber Bragg grating with a period of 538.57 $nm$ was then inscribed using a 193 $nm$ ArF excimer laser (Fig. 1(a)). The phase mask with a corresponding period was placed in front of the microfiber with a distance of $\sim$0.1 $mm$. A cylindrical lens was used to focus the ultraviolet (UV) beam to enhance the energy density that is estimated to be 160 $mJ/cm^2$. The efficiency of the two-photon excitation process is high enough [18,19], so that the mFBG was directly inscribed in the microfiber without the hydrogen loading and other photosensitization process. The resonance wavelength of the mFBG can be expressed by [6]

$$\lambda_{mFBG}=2n_{eff}\Lambda$$

 figure: Fig. 1.

Fig. 1. The schematic (a) and SEM images (b) of the superstructure microfiber grating. The inset shows the SEM image of one notch of the mLPG.

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where $\Lambda$ denotes the grating period, and $n_{eff}$ is the effective refractive index of the fundamental guided mode.

The microfiber long-period grating was then fabricated by a point-by-point scratching process, using a femtosecond (fs) laser with a wavelength and repetition rate of 800 $nm$ and 1 $kHz$ respectively. The laser power determines the depth and width of the notches that form the mLPG. When the power is not high enough, extra irradiations are required to induce coupling between guided modes, while the microfiber is easily broken and lossy when the power is too high. The laser power is thus optimized to be 1.2 $mW$, so that a notch with a depth of $\sim$1 $\mu m$ and with a width of only $\sim$2 $\mu m$ was formed (Fig. 1(b)). The notch is more uniform than the one reported previously [14]. After one notch was formed, the microfiber was moved 200 $\mu m$ along the axial direction in order to obtain another notch via the laser irradiation. Finally, an mLPG with 20 notches was fabricated with a period of 200 $\mu m$. The duty cycle, defined as the ratio between the notch width and the grating period, is as small as 1$\%$. The theoretical resonance wavelength $\lambda _{mLPG}$ of an mLPG can be expressed by [20,21]

$$\lambda_{mLPG} = (n_{eff}-n_{cl,k})\Lambda$$
where $n_{eff}$ and $n_{cl,k}$ are the refractive indices of the fundamental mode and the $k^{th}$-higher-order mode respectively.

The transmission and reflection spectra were monitored during the fabrication of the superstructure microfiber grating (Fig. 2). No obvious interference fringes were observed in the transmission spectrum (i.e., there was no significant intermodal coupling) before formation of the mLPG. With only one notch fabricated in the microfiber, the transmission spectrum almost remains the same as that of the pure mFBG, because one notch cannot induce the coupling between co-propagating guided modes (Fig. 2(a)). An obvious dip appears when there are 8 notches in the microfiber, which indicates that the fundamental mode starts coupling to the higher-order mode. In the experiment, 20 notches were fabricated, and the transmission dip becomes deeper after each laser irradiation. No distinct dip corresponding to the resonance of the mFBG is found in the transmission spectrum since the fabricated mFBG is relatively weak in the experiment. Meanwhile, no obvious changes are observed in the reflection spectra, indicating that the structure of the mFBG is preserved during the fabrication process of the mLPG (Fig. 2(b)). The fabricated superstructure microfiber grating thus obtains both of the mFBG and mLPG functionalities.

 figure: Fig. 2.

Fig. 2. The selected transmission (a) and reflection (b) spectra when fabricating the superstructure microfiber grating with different number of notches.

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After fabricating 20 notches using fs laser irradiation, the final transmission and reflection spectra of the superstructure microfiber grating are plotted in Fig. 3, which shows the characteristics of both the mFBG and the mLPG. Experimentally, the resonance peak is $\sim$1549 $nm$ in the reflection spectrum, so the effective RI of the mode is $\sim$1.4381 according to Eq. (1). The resonance dip is measured to be $\sim$1301 $nm$ in the transmission spectrum, indicating that the RI difference of the fundamental mode and the cladding mode is $\sim$0.0065 according to Eq. (2). Note that, in the reflection spectra, no side peaks are observed irrespectively of whether the mLPG is inscribed or not as shown in Fig. 2, different from that in a conventional sampled fiber Bragg grating which has side peaks [22]. This feature of our SMG may be attributed to the small duty cycle (1$\%$) between the structure notch and the period of the mLPG.

 figure: Fig. 3.

Fig. 3. The transmission (blue curve) and refection (black curve) spectra of the superstructure microfiber grating. The inset shows the zoom-in details around the resonance peak in the reflection spectrum.

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3. Sensing properties and discussions

The superstructure microfiber grating is applied for temperature, strain and refractive sensing by simultaneously tracking the resonances in the reflection and transmission spectra. The resonance wavelengths are taken as the value with the highest (lowest) intensity in the reflection (transmission) spectra. The sensitivities obtained from the mFBG and mLPG characteristics are compared.

3.1 Temperature sensing

The superstructure microfiber grating is firstly tested for temperature sensing. A heater is placed close to the SMG to vary the temperature of the microfiber ranging from 28 $^{\circ }$C to 98 $^{\circ }$C. The resonance wavelengths of the mFBG and the mLPG show redshifts when the temperature increases. The sensitivity of the mFBG can be descried by

$$S_{mFBG,T}=\frac{d\lambda_{mFBG}}{d T}=\lambda_{mFBG}(\alpha+\frac{\beta}{n_{eff}}\frac{\partial n_{eff}}{\partial n_{si}})$$
where $d\lambda _{mFBG}$ is the wavelength shift of the reflection peaks, $dT$ denotes the temperature change, $\alpha =(1/L)(dL/dT)$ indicates the thermal expansion coefficient, $\beta =dn_{si}/dT$ denotes the thermo-optic coefficient of the microfiber, $n_{si}$ is the refractive index of the microfiber material, and $L$ is the length of the microfiber device. The sensitivity of the mLPG can be expressed by
$$S_{mLPG,T}=\frac{d\lambda_{mLPG}}{d T}=\lambda_{mLPG}\centerdot\gamma\centerdot(\alpha+\frac{\beta}{\Delta n}\frac{\partial\Delta n}{\partial n_{si}})$$
where $d\lambda _{mLPG}$ is the wavelength shift of the transmission dips, $\gamma$ denotes the waveguide dispersion coefficient defined by $\gamma =(d\lambda _{mLPG}/d\Lambda )/(n_{eff}-n_{cl,k})$, and $\Delta n=n_{eff}-n_{cl,k}$.

The sensitivities are considered to be linear in the tested temperature range. By monitoring the resonance wavelength, the sensitivities of the mFBG and the mLPG are measured to be 8.03 pm/$^{\circ }$C and 10.33 pm/$^{\circ }$C respectively (Fig. 4), which are similar as that of the previous studies [15,23]. The sensitivity of the mLPG is slightly larger than that of the mFBG, and can be further enhanced by optimizing the diameter of the microfiber and the period of the grating [21]. Furthermore, the linewidth of the mLPG resonance is possibly narrowed by decreasing the surface roughness of the notches.

 figure: Fig. 4.

Fig. 4. The resonance wavelength shifts in the transmission (blue squares) and reflection (black circles) spectra when the temperature changes. The red lines show the linear fittings. The insets are selected zoom-in spectra to show the wavelength shifts.

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3.2 Strain sensing

When applying strains $\varepsilon$ on the superstructure microfiber grating, the sensitivity of the mFBG can be expressd by

$$S_{mFBG,S}=\frac{d\lambda_{mFBG}}{d\varepsilon}=\lambda_{mFBG}(1+\frac{p_e}{n_{eff}}\frac{\partial n_{eff}}{\partial n_{si}})$$
where $d\varepsilon$ denotes the strain difference, and $p_{e}=dn_{si}/d\varepsilon$ is the strain-optic coefficient. The sensitivity of the mLPG induced by the strain can be described by
$$S_{mLPG,S}=\frac{d\lambda_{mLPG}}{d\varepsilon}=\lambda_{mLPG}\centerdot\gamma\centerdot(1+\frac{p_{e}}{\Delta n}\frac{\partial \Delta n}{\partial n_{si}}).$$

The measured resonance wavelength shifts of the mFBG and the mLPG induced by strains are shown in Fig. 5. Strains are generated by pulling the SMG with a translational stage. Different from the temperature sensing, the wavelength shifts of the two resonances show opposite trends. The resonance wavelength of the mFBG exhibits red shift because of the increasing grating period when strains are applied. The resonance wavelength of the mLPG blueshifts because of the negative dispersion coefficient $\gamma$ as shown in Eq. (6). When considering a linear dependence between the resonance shifts and $d\varepsilon$, the sensitivities of the mFBG and the mLPG are calculated to be $\sim 1.2$ $pm/\mu \epsilon$ and $\sim -1.8$ $pm/\mu \epsilon$ respectively. The mLPG acts slightly sensitive when used as a strain sensor.

 figure: Fig. 5.

Fig. 5. The resonance wavelength shifts in the transmission (blue squares) and reflection spectra (black circles) when applying strains on the superstructure. The red lines show the linear fittings. The insets are selected zoom-in spectra to show the wavelength shifts.

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3.3 Refractive index sensing

As for the external refractive index, the sensitivity is mainly determined by the amount of evanescent field extending to the surrounding medium. The sensitivity of the mFBG can be expressed by

$$S_{mFBG,RI}=\frac{d\lambda_{mFBG}}{d RI}=\lambda_{mFBG}\centerdot\frac{1}{n_{eff}}\frac{\partial n_{eff}}{\partial RI}$$
where $dRI$ is the change of the refractive index of the surrounding medium. The sensitivity of the mLPG can be described by
$$S_{mLPG,RI}=\frac{d\lambda_{mLPG}}{d RI}=\lambda_{mLPG}\centerdot\gamma\centerdot\frac{1}{\Delta n}\frac{\partial \Delta n}{\partial RI}.$$

Experimentally, the refractive index surrounding the superstructure microfiber grating is varied by placing the sensor in sucrose solutions with different concentrations. When varying the RI, the resonance wavelength shifts of the transmission and reflection spectra are shown in Fig. 6. When the surrounding RI increases from 1.3324 to 1.3607, the transmission dip (i.e., $\lambda _{mLPG}$) redshifts from 1289.49 nm to 1334.76 nm, and the attenuation depth increases from $-17.1$ dB to $-6.0$ dB as more evanescent field extends to the surroundings. Meanwhile, the reflection peak (i.e., $\lambda _{mFBG}$) redshifts from 1550.54 nm to 1550.64 nm with the peak power remaining aroud $-20$ dB.

 figure: Fig. 6.

Fig. 6. The resonance wavelength shifts in the transmission (blue squares) and reflection (black circles) spectra when the surrounding refractive index changes. The red lines show the linear fittings. The insets are selected zoom-in spectra to show the wavelength shifts.

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Considering a linear dependence between the resonance shifts and the external RI changes, the sensitivities of the mFBG and the mLPG are measured to be 3.61 nm/RIU and 1534.78 nm/RIU respectively, where RIU denotes the refractive index unit. $S_{mLPG,RI}$ is 425.15 times larger than $S_{mFBG,RI}$, which is predictable from the power changes of the corresponding spectra. The reflection peaks without obvious power decreases manifest that a smaller portion of the evanescent field of the mFBG mode extends to the surrounding RIs, thus resulting in a smaller sensitivity.

3.4 Discussions

When the superstructure microfiber grating is employed as an optical sensor, the transmission and reflection spectra can be simultaneously performed as sensing signals. The resonance peak in the reflection spectrum shows the characteristics of the mFBG, while the main resonance dip in the transmission spectrum shows the characteristics of the mLPG. The sensitivities of the mLPG structure on the temperature and the strain changes are different from that of the mFBG structure. Especially, the sensitivity of the mLPG on the RI changes is two orders of magnitude higher than that of the mFBG, making the SMG a much better refractive index sensor compared to a single mFBG. Practically, the simultaneous resonance measurements from the transmission dips and reflection peaks make it possible to discriminate the temperature, strain, and refractive index responses using the proposed SMG [21,24].

4. Conclusion

A superstructure microfiber grating is proposed and fabricated via ultraviolet laser inscription and femtosecond laser scratching techniques, which inherits both the spectral characteristics of the mFBG and mLPG. The sensing performances responding to changes of temperatures, strains and refractive indices are investigated and demonstrated, showing that the SMG can provide a platform for applications that a single mFBG and a single mLPG are capable of. The results suggest a possibility for multi-parameter detection by simultaneously identifying the resonances from the mFBG and mLPG.

Funding

National Natural Science Foundation of China (61575083, 61805103, U1701268); Natural Science Foundation of Guangdong Province (2019A1515012100); Fundamental Research Funds for the Central Universities (21618320).

Acknowledgments

The authors thank Yang Ran for helpful discussions.

Disclosures

The authors declare no conflicts of interest.

References

1. L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12(6), 1025–1035 (2004). [CrossRef]  

2. Y. Zhang, B. Lin, S. C. Tjin, H. Zhang, G. Wang, P. Shum, and X. Zhang, “Refractive index sensing based on higher-order mode reflection of a microfiber Bragg grating,” Opt. Express 18(25), 26345–26350 (2010). [CrossRef]  

3. Y. Ran, L. Jin, Y.-N. Tan, L.-P. Sun, J. Li, and B.-O. Guan, “High-efficiency ultraviolet inscription of Bragg gratings in microfibers,” IEEE Photonics J. 4(1), 181–186 (2012). [CrossRef]  

4. J.-L. Kou, M. Ding, J. Feng, Y.-Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors 12(7), 8861–8876 (2012). [CrossRef]  

5. B.-O. Guan, J. Li, L. Jin, and Y. Ran, “Fiber Bragg gratings in optical microfibers,” Opt. Fiber Technol. 19(6), 793–801 (2013). [CrossRef]  

6. C. R. Giles, “Lightwave applications of fiber Bragg gratings,” J. Lightwave Technol. 15(8), 1391–1404 (1997). [CrossRef]  

7. G. Brambilla, “Optical fibre nanowires and microwires: a review,” J. Opt. 12(4), 043001 (2010). [CrossRef]  

8. X. Fang, C. R. Liao, and D. N. Wang, “Femtosecond laser fabricated fiber Bragg grating in microfiber for refractive index sensing,” Opt. Lett. 35(7), 1007–1009 (2010). [CrossRef]  

9. Y. Liu, C. Meng, A. P. Zhang, Y. Xiao, H. Yu, and L. Tong, “Compact microfiber Bragg gratings with high-index contrast,” Opt. Lett. 36(16), 3115–3117 (2011). [CrossRef]  

10. M. Ding, M. N. Zervas, and G. Brambilla, “A compact broadband microfiber Bragg grating,” Opt. Express 19(16), 15621–15626 (2011). [CrossRef]  

11. W. Ding, S. R. Andrews, and S. A. Maier, “Surface corrugation Bragg gratings on optical fiber tapers created via plasma etch postprocessing,” Opt. Lett. 32(17), 2499–2501 (2007). [CrossRef]  

12. Y. Ran, Y.-N. Tan, L.-P. Sun, S. Gao, J. Li, L. Jin, and B.-O. Guan, “193nm excimer laser inscribed Bragg gratings in microfibers for refractive index sensing,” Opt. Express 19(19), 18577–18583 (2011). [CrossRef]  

13. H. Xuan, W. Jin, and M. Zhang, “CO2 laser induced long period gratings in optical microfibers,” Opt. Express 17(24), 21882–21890 (2009). [CrossRef]  

14. H. Xuan, W. Jin, and S. Liu, “Long-period gratings in wavelength-scale microfibers,” Opt. Lett. 35(1), 85–87 (2010). [CrossRef]  

15. P. Fan, L.-P. Sun, Z. Yu, J. Li, C. Wu, and B.-O. Guan, “Higher-order diffraction of long-period microfiber gratings realized by arc discharge method,” Opt. Express 24(22), 25380–25388 (2016). [CrossRef]  

16. W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005). [CrossRef]  

17. S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and application,” Meas. Sci. Technol. 14(5), R49–R61 (2003). [CrossRef]  

18. J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, “Comparison of one-photon and two-photon effects in the photosensitivity of germanium-doped silica optical fibers exposed to intense ArF excimer laser pulses,” Appl. Phys. Lett. 67(24), 3529–3531 (1995). [CrossRef]  

19. J. Albert, M. Fokine, and W. Margulis, “Grating formation in pure silica-core fibers,” Opt. Lett. 27(10), 809–811 (2002). [CrossRef]  

20. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996). [CrossRef]  

21. V. Bhatia, “Applications of long-period gratings to single and multi-parameter sensing,” Opt. Express 4(11), 457–466 (1999). [CrossRef]  

22. X. Fang, X. Y. He, C. R. Liao, M. Yang, D. N. Wang, and Y. Wang, “A new method for sampled fiber Bragg grating fabrication by use of both femtosecond laser and CO2 laser,” Opt. Express 18(3), 2646–2654 (2010). [CrossRef]  

23. J. long Kou, S. jie Qiu, F. Xu, and Y. qing Lu, “Demonstration of a compact temperature sensor based on first-order Bragg grating in a tapered fiber probe,” Opt. Express 19(19), 18452–18457 (2011). [CrossRef]  

24. B.-O. Guan, H.-Y. Tam, X.-M. Tao, and X.-Y. Dong, “Simultaneous strain and temperature measurement using a superstructure fiber Bragg grating,” IEEE Photonics Technol. Lett. 12(6), 675–677 (2000). [CrossRef]  

References

  • View by:

  1. L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12(6), 1025–1035 (2004).
    [Crossref]
  2. Y. Zhang, B. Lin, S. C. Tjin, H. Zhang, G. Wang, P. Shum, and X. Zhang, “Refractive index sensing based on higher-order mode reflection of a microfiber Bragg grating,” Opt. Express 18(25), 26345–26350 (2010).
    [Crossref]
  3. Y. Ran, L. Jin, Y.-N. Tan, L.-P. Sun, J. Li, and B.-O. Guan, “High-efficiency ultraviolet inscription of Bragg gratings in microfibers,” IEEE Photonics J. 4(1), 181–186 (2012).
    [Crossref]
  4. J.-L. Kou, M. Ding, J. Feng, Y.-Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors 12(7), 8861–8876 (2012).
    [Crossref]
  5. B.-O. Guan, J. Li, L. Jin, and Y. Ran, “Fiber Bragg gratings in optical microfibers,” Opt. Fiber Technol. 19(6), 793–801 (2013).
    [Crossref]
  6. C. R. Giles, “Lightwave applications of fiber Bragg gratings,” J. Lightwave Technol. 15(8), 1391–1404 (1997).
    [Crossref]
  7. G. Brambilla, “Optical fibre nanowires and microwires: a review,” J. Opt. 12(4), 043001 (2010).
    [Crossref]
  8. X. Fang, C. R. Liao, and D. N. Wang, “Femtosecond laser fabricated fiber Bragg grating in microfiber for refractive index sensing,” Opt. Lett. 35(7), 1007–1009 (2010).
    [Crossref]
  9. Y. Liu, C. Meng, A. P. Zhang, Y. Xiao, H. Yu, and L. Tong, “Compact microfiber Bragg gratings with high-index contrast,” Opt. Lett. 36(16), 3115–3117 (2011).
    [Crossref]
  10. M. Ding, M. N. Zervas, and G. Brambilla, “A compact broadband microfiber Bragg grating,” Opt. Express 19(16), 15621–15626 (2011).
    [Crossref]
  11. W. Ding, S. R. Andrews, and S. A. Maier, “Surface corrugation Bragg gratings on optical fiber tapers created via plasma etch postprocessing,” Opt. Lett. 32(17), 2499–2501 (2007).
    [Crossref]
  12. Y. Ran, Y.-N. Tan, L.-P. Sun, S. Gao, J. Li, L. Jin, and B.-O. Guan, “193nm excimer laser inscribed Bragg gratings in microfibers for refractive index sensing,” Opt. Express 19(19), 18577–18583 (2011).
    [Crossref]
  13. H. Xuan, W. Jin, and M. Zhang, “CO2 laser induced long period gratings in optical microfibers,” Opt. Express 17(24), 21882–21890 (2009).
    [Crossref]
  14. H. Xuan, W. Jin, and S. Liu, “Long-period gratings in wavelength-scale microfibers,” Opt. Lett. 35(1), 85–87 (2010).
    [Crossref]
  15. P. Fan, L.-P. Sun, Z. Yu, J. Li, C. Wu, and B.-O. Guan, “Higher-order diffraction of long-period microfiber gratings realized by arc discharge method,” Opt. Express 24(22), 25380–25388 (2016).
    [Crossref]
  16. W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
    [Crossref]
  17. S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and application,” Meas. Sci. Technol. 14(5), R49–R61 (2003).
    [Crossref]
  18. J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, “Comparison of one-photon and two-photon effects in the photosensitivity of germanium-doped silica optical fibers exposed to intense ArF excimer laser pulses,” Appl. Phys. Lett. 67(24), 3529–3531 (1995).
    [Crossref]
  19. J. Albert, M. Fokine, and W. Margulis, “Grating formation in pure silica-core fibers,” Opt. Lett. 27(10), 809–811 (2002).
    [Crossref]
  20. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
    [Crossref]
  21. V. Bhatia, “Applications of long-period gratings to single and multi-parameter sensing,” Opt. Express 4(11), 457–466 (1999).
    [Crossref]
  22. X. Fang, X. Y. He, C. R. Liao, M. Yang, D. N. Wang, and Y. Wang, “A new method for sampled fiber Bragg grating fabrication by use of both femtosecond laser and CO2 laser,” Opt. Express 18(3), 2646–2654 (2010).
    [Crossref]
  23. J. long Kou, S. jie Qiu, F. Xu, and Y. qing Lu, “Demonstration of a compact temperature sensor based on first-order Bragg grating in a tapered fiber probe,” Opt. Express 19(19), 18452–18457 (2011).
    [Crossref]
  24. B.-O. Guan, H.-Y. Tam, X.-M. Tao, and X.-Y. Dong, “Simultaneous strain and temperature measurement using a superstructure fiber Bragg grating,” IEEE Photonics Technol. Lett. 12(6), 675–677 (2000).
    [Crossref]

2016 (1)

2013 (1)

B.-O. Guan, J. Li, L. Jin, and Y. Ran, “Fiber Bragg gratings in optical microfibers,” Opt. Fiber Technol. 19(6), 793–801 (2013).
[Crossref]

2012 (2)

Y. Ran, L. Jin, Y.-N. Tan, L.-P. Sun, J. Li, and B.-O. Guan, “High-efficiency ultraviolet inscription of Bragg gratings in microfibers,” IEEE Photonics J. 4(1), 181–186 (2012).
[Crossref]

J.-L. Kou, M. Ding, J. Feng, Y.-Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors 12(7), 8861–8876 (2012).
[Crossref]

2011 (4)

2010 (5)

2009 (1)

2007 (1)

2005 (1)

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

2004 (1)

2003 (1)

S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and application,” Meas. Sci. Technol. 14(5), R49–R61 (2003).
[Crossref]

2002 (1)

2000 (1)

B.-O. Guan, H.-Y. Tam, X.-M. Tao, and X.-Y. Dong, “Simultaneous strain and temperature measurement using a superstructure fiber Bragg grating,” IEEE Photonics Technol. Lett. 12(6), 675–677 (2000).
[Crossref]

1999 (1)

1997 (1)

C. R. Giles, “Lightwave applications of fiber Bragg gratings,” J. Lightwave Technol. 15(8), 1391–1404 (1997).
[Crossref]

1996 (1)

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

1995 (1)

J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, “Comparison of one-photon and two-photon effects in the photosensitivity of germanium-doped silica optical fibers exposed to intense ArF excimer laser pulses,” Appl. Phys. Lett. 67(24), 3529–3531 (1995).
[Crossref]

Albert, J.

J. Albert, M. Fokine, and W. Margulis, “Grating formation in pure silica-core fibers,” Opt. Lett. 27(10), 809–811 (2002).
[Crossref]

J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, “Comparison of one-photon and two-photon effects in the photosensitivity of germanium-doped silica optical fibers exposed to intense ArF excimer laser pulses,” Appl. Phys. Lett. 67(24), 3529–3531 (1995).
[Crossref]

Andrews, S. R.

Bhatia, V.

V. Bhatia, “Applications of long-period gratings to single and multi-parameter sensing,” Opt. Express 4(11), 457–466 (1999).
[Crossref]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

Bilodeau, F.

J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, “Comparison of one-photon and two-photon effects in the photosensitivity of germanium-doped silica optical fibers exposed to intense ArF excimer laser pulses,” Appl. Phys. Lett. 67(24), 3529–3531 (1995).
[Crossref]

Brambilla, G.

J.-L. Kou, M. Ding, J. Feng, Y.-Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors 12(7), 8861–8876 (2012).
[Crossref]

M. Ding, M. N. Zervas, and G. Brambilla, “A compact broadband microfiber Bragg grating,” Opt. Express 19(16), 15621–15626 (2011).
[Crossref]

G. Brambilla, “Optical fibre nanowires and microwires: a review,” J. Opt. 12(4), 043001 (2010).
[Crossref]

Ding, M.

J.-L. Kou, M. Ding, J. Feng, Y.-Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors 12(7), 8861–8876 (2012).
[Crossref]

M. Ding, M. N. Zervas, and G. Brambilla, “A compact broadband microfiber Bragg grating,” Opt. Express 19(16), 15621–15626 (2011).
[Crossref]

Ding, W.

Dong, X.-Y.

B.-O. Guan, H.-Y. Tam, X.-M. Tao, and X.-Y. Dong, “Simultaneous strain and temperature measurement using a superstructure fiber Bragg grating,” IEEE Photonics Technol. Lett. 12(6), 675–677 (2000).
[Crossref]

Erdogan, T.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

Fan, P.

Fang, X.

Feng, J.

J.-L. Kou, M. Ding, J. Feng, Y.-Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors 12(7), 8861–8876 (2012).
[Crossref]

Fokine, M.

Gao, S.

Giles, C. R.

C. R. Giles, “Lightwave applications of fiber Bragg gratings,” J. Lightwave Technol. 15(8), 1391–1404 (1997).
[Crossref]

Guan, B.-O.

P. Fan, L.-P. Sun, Z. Yu, J. Li, C. Wu, and B.-O. Guan, “Higher-order diffraction of long-period microfiber gratings realized by arc discharge method,” Opt. Express 24(22), 25380–25388 (2016).
[Crossref]

B.-O. Guan, J. Li, L. Jin, and Y. Ran, “Fiber Bragg gratings in optical microfibers,” Opt. Fiber Technol. 19(6), 793–801 (2013).
[Crossref]

Y. Ran, L. Jin, Y.-N. Tan, L.-P. Sun, J. Li, and B.-O. Guan, “High-efficiency ultraviolet inscription of Bragg gratings in microfibers,” IEEE Photonics J. 4(1), 181–186 (2012).
[Crossref]

Y. Ran, Y.-N. Tan, L.-P. Sun, S. Gao, J. Li, L. Jin, and B.-O. Guan, “193nm excimer laser inscribed Bragg gratings in microfibers for refractive index sensing,” Opt. Express 19(19), 18577–18583 (2011).
[Crossref]

B.-O. Guan, H.-Y. Tam, X.-M. Tao, and X.-Y. Dong, “Simultaneous strain and temperature measurement using a superstructure fiber Bragg grating,” IEEE Photonics Technol. Lett. 12(6), 675–677 (2000).
[Crossref]

He, X. Y.

Hill, K. O.

J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, “Comparison of one-photon and two-photon effects in the photosensitivity of germanium-doped silica optical fibers exposed to intense ArF excimer laser pulses,” Appl. Phys. Lett. 67(24), 3529–3531 (1995).
[Crossref]

Huang, Y.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

James, S. W.

S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and application,” Meas. Sci. Technol. 14(5), R49–R61 (2003).
[Crossref]

jie Qiu, S.

Jin, L.

B.-O. Guan, J. Li, L. Jin, and Y. Ran, “Fiber Bragg gratings in optical microfibers,” Opt. Fiber Technol. 19(6), 793–801 (2013).
[Crossref]

Y. Ran, L. Jin, Y.-N. Tan, L.-P. Sun, J. Li, and B.-O. Guan, “High-efficiency ultraviolet inscription of Bragg gratings in microfibers,” IEEE Photonics J. 4(1), 181–186 (2012).
[Crossref]

Y. Ran, Y.-N. Tan, L.-P. Sun, S. Gao, J. Li, L. Jin, and B.-O. Guan, “193nm excimer laser inscribed Bragg gratings in microfibers for refractive index sensing,” Opt. Express 19(19), 18577–18583 (2011).
[Crossref]

Jin, W.

Johnson, D. C.

J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, “Comparison of one-photon and two-photon effects in the photosensitivity of germanium-doped silica optical fibers exposed to intense ArF excimer laser pulses,” Appl. Phys. Lett. 67(24), 3529–3531 (1995).
[Crossref]

Judkins, J. B.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

Kou, J.-L.

J.-L. Kou, M. Ding, J. Feng, Y.-Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors 12(7), 8861–8876 (2012).
[Crossref]

Lee, R. K.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

Lemaire, P. J.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

Li, J.

P. Fan, L.-P. Sun, Z. Yu, J. Li, C. Wu, and B.-O. Guan, “Higher-order diffraction of long-period microfiber gratings realized by arc discharge method,” Opt. Express 24(22), 25380–25388 (2016).
[Crossref]

B.-O. Guan, J. Li, L. Jin, and Y. Ran, “Fiber Bragg gratings in optical microfibers,” Opt. Fiber Technol. 19(6), 793–801 (2013).
[Crossref]

Y. Ran, L. Jin, Y.-N. Tan, L.-P. Sun, J. Li, and B.-O. Guan, “High-efficiency ultraviolet inscription of Bragg gratings in microfibers,” IEEE Photonics J. 4(1), 181–186 (2012).
[Crossref]

Y. Ran, Y.-N. Tan, L.-P. Sun, S. Gao, J. Li, L. Jin, and B.-O. Guan, “193nm excimer laser inscribed Bragg gratings in microfibers for refractive index sensing,” Opt. Express 19(19), 18577–18583 (2011).
[Crossref]

Liang, W.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

Liao, C. R.

Lin, B.

Liu, S.

Liu, Y.

long Kou, J.

Lou, J.

Lu, Y.-Q.

J.-L. Kou, M. Ding, J. Feng, Y.-Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors 12(7), 8861–8876 (2012).
[Crossref]

Maier, S. A.

Malo, B.

J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, “Comparison of one-photon and two-photon effects in the photosensitivity of germanium-doped silica optical fibers exposed to intense ArF excimer laser pulses,” Appl. Phys. Lett. 67(24), 3529–3531 (1995).
[Crossref]

Margulis, W.

Mazur, E.

Meng, C.

qing Lu, Y.

Ran, Y.

B.-O. Guan, J. Li, L. Jin, and Y. Ran, “Fiber Bragg gratings in optical microfibers,” Opt. Fiber Technol. 19(6), 793–801 (2013).
[Crossref]

Y. Ran, L. Jin, Y.-N. Tan, L.-P. Sun, J. Li, and B.-O. Guan, “High-efficiency ultraviolet inscription of Bragg gratings in microfibers,” IEEE Photonics J. 4(1), 181–186 (2012).
[Crossref]

Y. Ran, Y.-N. Tan, L.-P. Sun, S. Gao, J. Li, L. Jin, and B.-O. Guan, “193nm excimer laser inscribed Bragg gratings in microfibers for refractive index sensing,” Opt. Express 19(19), 18577–18583 (2011).
[Crossref]

Shum, P.

Sipe, J. E.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

Sun, L.-P.

Tam, H.-Y.

B.-O. Guan, H.-Y. Tam, X.-M. Tao, and X.-Y. Dong, “Simultaneous strain and temperature measurement using a superstructure fiber Bragg grating,” IEEE Photonics Technol. Lett. 12(6), 675–677 (2000).
[Crossref]

Tan, Y.-N.

Y. Ran, L. Jin, Y.-N. Tan, L.-P. Sun, J. Li, and B.-O. Guan, “High-efficiency ultraviolet inscription of Bragg gratings in microfibers,” IEEE Photonics J. 4(1), 181–186 (2012).
[Crossref]

Y. Ran, Y.-N. Tan, L.-P. Sun, S. Gao, J. Li, L. Jin, and B.-O. Guan, “193nm excimer laser inscribed Bragg gratings in microfibers for refractive index sensing,” Opt. Express 19(19), 18577–18583 (2011).
[Crossref]

Tao, X.-M.

B.-O. Guan, H.-Y. Tam, X.-M. Tao, and X.-Y. Dong, “Simultaneous strain and temperature measurement using a superstructure fiber Bragg grating,” IEEE Photonics Technol. Lett. 12(6), 675–677 (2000).
[Crossref]

Tatam, R. P.

S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and application,” Meas. Sci. Technol. 14(5), R49–R61 (2003).
[Crossref]

Thériault, S.

J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, “Comparison of one-photon and two-photon effects in the photosensitivity of germanium-doped silica optical fibers exposed to intense ArF excimer laser pulses,” Appl. Phys. Lett. 67(24), 3529–3531 (1995).
[Crossref]

Tjin, S. C.

Tong, L.

Vengsarkar, A. M.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

Wang, D. N.

Wang, G.

Wang, Y.

Wu, C.

Xiao, Y.

Xu, F.

J.-L. Kou, M. Ding, J. Feng, Y.-Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors 12(7), 8861–8876 (2012).
[Crossref]

J. long Kou, S. jie Qiu, F. Xu, and Y. qing Lu, “Demonstration of a compact temperature sensor based on first-order Bragg grating in a tapered fiber probe,” Opt. Express 19(19), 18452–18457 (2011).
[Crossref]

Xu, Y.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

Xuan, H.

Yang, M.

Yariv, A.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

Yu, H.

Yu, Z.

Zervas, M. N.

Zhang, A. P.

Zhang, H.

Zhang, M.

Zhang, X.

Zhang, Y.

Appl. Phys. Lett. (2)

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[Crossref]

J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, “Comparison of one-photon and two-photon effects in the photosensitivity of germanium-doped silica optical fibers exposed to intense ArF excimer laser pulses,” Appl. Phys. Lett. 67(24), 3529–3531 (1995).
[Crossref]

IEEE Photonics J. (1)

Y. Ran, L. Jin, Y.-N. Tan, L.-P. Sun, J. Li, and B.-O. Guan, “High-efficiency ultraviolet inscription of Bragg gratings in microfibers,” IEEE Photonics J. 4(1), 181–186 (2012).
[Crossref]

IEEE Photonics Technol. Lett. (1)

B.-O. Guan, H.-Y. Tam, X.-M. Tao, and X.-Y. Dong, “Simultaneous strain and temperature measurement using a superstructure fiber Bragg grating,” IEEE Photonics Technol. Lett. 12(6), 675–677 (2000).
[Crossref]

J. Lightwave Technol. (2)

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

C. R. Giles, “Lightwave applications of fiber Bragg gratings,” J. Lightwave Technol. 15(8), 1391–1404 (1997).
[Crossref]

J. Opt. (1)

G. Brambilla, “Optical fibre nanowires and microwires: a review,” J. Opt. 12(4), 043001 (2010).
[Crossref]

Meas. Sci. Technol. (1)

S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and application,” Meas. Sci. Technol. 14(5), R49–R61 (2003).
[Crossref]

Opt. Express (9)

P. Fan, L.-P. Sun, Z. Yu, J. Li, C. Wu, and B.-O. Guan, “Higher-order diffraction of long-period microfiber gratings realized by arc discharge method,” Opt. Express 24(22), 25380–25388 (2016).
[Crossref]

M. Ding, M. N. Zervas, and G. Brambilla, “A compact broadband microfiber Bragg grating,” Opt. Express 19(16), 15621–15626 (2011).
[Crossref]

Y. Ran, Y.-N. Tan, L.-P. Sun, S. Gao, J. Li, L. Jin, and B.-O. Guan, “193nm excimer laser inscribed Bragg gratings in microfibers for refractive index sensing,” Opt. Express 19(19), 18577–18583 (2011).
[Crossref]

H. Xuan, W. Jin, and M. Zhang, “CO2 laser induced long period gratings in optical microfibers,” Opt. Express 17(24), 21882–21890 (2009).
[Crossref]

L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12(6), 1025–1035 (2004).
[Crossref]

Y. Zhang, B. Lin, S. C. Tjin, H. Zhang, G. Wang, P. Shum, and X. Zhang, “Refractive index sensing based on higher-order mode reflection of a microfiber Bragg grating,” Opt. Express 18(25), 26345–26350 (2010).
[Crossref]

V. Bhatia, “Applications of long-period gratings to single and multi-parameter sensing,” Opt. Express 4(11), 457–466 (1999).
[Crossref]

X. Fang, X. Y. He, C. R. Liao, M. Yang, D. N. Wang, and Y. Wang, “A new method for sampled fiber Bragg grating fabrication by use of both femtosecond laser and CO2 laser,” Opt. Express 18(3), 2646–2654 (2010).
[Crossref]

J. long Kou, S. jie Qiu, F. Xu, and Y. qing Lu, “Demonstration of a compact temperature sensor based on first-order Bragg grating in a tapered fiber probe,” Opt. Express 19(19), 18452–18457 (2011).
[Crossref]

Opt. Fiber Technol. (1)

B.-O. Guan, J. Li, L. Jin, and Y. Ran, “Fiber Bragg gratings in optical microfibers,” Opt. Fiber Technol. 19(6), 793–801 (2013).
[Crossref]

Opt. Lett. (5)

Sensors (1)

J.-L. Kou, M. Ding, J. Feng, Y.-Q. Lu, F. Xu, and G. Brambilla, “Microfiber-based Bragg gratings for sensing applications: a review,” Sensors 12(7), 8861–8876 (2012).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. The schematic (a) and SEM images (b) of the superstructure microfiber grating. The inset shows the SEM image of one notch of the mLPG.
Fig. 2.
Fig. 2. The selected transmission (a) and reflection (b) spectra when fabricating the superstructure microfiber grating with different number of notches.
Fig. 3.
Fig. 3. The transmission (blue curve) and refection (black curve) spectra of the superstructure microfiber grating. The inset shows the zoom-in details around the resonance peak in the reflection spectrum.
Fig. 4.
Fig. 4. The resonance wavelength shifts in the transmission (blue squares) and reflection (black circles) spectra when the temperature changes. The red lines show the linear fittings. The insets are selected zoom-in spectra to show the wavelength shifts.
Fig. 5.
Fig. 5. The resonance wavelength shifts in the transmission (blue squares) and reflection spectra (black circles) when applying strains on the superstructure. The red lines show the linear fittings. The insets are selected zoom-in spectra to show the wavelength shifts.
Fig. 6.
Fig. 6. The resonance wavelength shifts in the transmission (blue squares) and reflection (black circles) spectra when the surrounding refractive index changes. The red lines show the linear fittings. The insets are selected zoom-in spectra to show the wavelength shifts.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

λ m F B G = 2 n e f f Λ
λ m L P G = ( n e f f n c l , k ) Λ
S m F B G , T = d λ m F B G d T = λ m F B G ( α + β n e f f n e f f n s i )
S m L P G , T = d λ m L P G d T = λ m L P G γ ( α + β Δ n Δ n n s i )
S m F B G , S = d λ m F B G d ε = λ m F B G ( 1 + p e n e f f n e f f n s i )
S m L P G , S = d λ m L P G d ε = λ m L P G γ ( 1 + p e Δ n Δ n n s i ) .
S m F B G , R I = d λ m F B G d R I = λ m F B G 1 n e f f n e f f R I
S m L P G , R I = d λ m L P G d R I = λ m L P G γ 1 Δ n Δ n R I .

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