Abstract

All-optical fiber sensors based on ultracompact fiber inline Mach-Zehnder interferometer (MZI) are fabricated by side-ablating a U-shape microcavity in a single-mode optical fiber with the fiber core partially removed using femtosecond (fs) laser pulses, in which the two light paths are accordingly formed in the remaining D-type fiber core and the U-shape microcavity. Beam propagation method (BPM) analysis is utilized to illustrate the dependences of good transmission spectra on parameters including the ablation depth, ablation length and the refractive index of U-shape micocavity, which gives some guidelines to optimize parameters for fs laser micromachining and predicts RI (refractive index) sensitivities within given RI ranges. The modeling results of ultrahigh RI sensitivities for gases and solutions are −3243.75 ± 0.65nm/RIU (refractive index unit) and −10789.29 ± 18.91nm/RIU, respectively. In RI testing experiments, the sensor exhibits ultrahigh RI sensitivities of −3754.79 ± 44.24nm/RIU with refractive indices ranging from 1.0001143 to 1.0002187 by testing different mixture ratios of N2 and He gases, and −12162.01 ± 173.92nm/RIU with refractive indices ranging from 1.3330 to 1.33801 by testing different concentrations of sucrose solutions, which is essentially in agreement with the modeling results.

© 2011 OSA

1. Introduction

In recent years, all-optical fiber sensors based on MZI have attracted significant research attentions for their unique advantages of high fringe visibility, high RI sensitivity, long temperature sensing range, versatile assemble element, electromagnetic immunity, compact size, and low cost [15]. In situ sensing of refractive index, temperature, pressure and physical, chemical and biological parameters is of great importance in industrial applications, and is advanced realized and improved by novel fiber optics sensors. Fs laser has opened many exciting opportunities in micromachining of transparent materials, because precise materials ablation can be realized with extremely high peak power with minimized heat-affected zones [6]. All-optical fiber sensors based on Fabry-Perot interferometer and MZI have been successfully fabricated in various structures by fs laser pulses [4,7]. That is, more and more complicated structures of fiber sensors would be realized and designed in future that might be of some difficulties in experimental mechanism illustration. Therefore, BPM analysis can be applied and has been used to simulate an MZI as a most unique and versatile tool in fiber optics [1].

What’s more, as for all-optical fiber sensor based on MZI in RI sensing applications, low RI sensitivity values of −26.087nm/RIU and −17.1nm/RIU have been previously reported in recent years [8, 9]. Another sensor has been fabricated by fs laser for RI measurement with high sensitivity of −9370nm/RIU in RI range from 1.31 to 1.335 lately [4]. However, the fringe visibility of the sensor is not large enough and the experimental result of RI sensitivity for gas is still not given yet. In our team work, the fs laser micromachining process of the sensor is demonstrated in details and the MZI structure exhibits some unique advantages although the reduced mechanism is almost the same [2]. The two sides of the U-shape microcavity in the fiber with two gradient slopes like ‘ribs’ fabricated by fs laser pulses are not required strictly orthogonal with the bottom plane and the fringe visibility is pretty large.

This study presents an all-optical fiber sensor based on an ultracompact fiber inline MZI by side-ablating a U-shape microcavity in a single-mode optical fiber with the fiber core partially removed using fs laser pulses. The free spectral range (FSR) and the fringe visibility of the sensor are about 64.5nm and 24dB respectively. Computer modeling of BPM analysis is utilized to simulate the characteristics and applications of the sensor. The simulated RI sensitivities of −3243.75±0.65nm/RIU for gases and −10789.29±18.91nm/RIU for solutions are predicted respectively. As for sensing test experiments, the sensor exhibits ultrahigh RI sensitivities of −3754.79±44.24nm/RIU with refractive indices ranging from 1.0001143 to 1.0002187 by testing different mixture ratios of N2 and He gases, and −12162.01±173.92nm/RIU with refractive indices ranging from 1.3330 to 1.33801 by testing different concentrations of sucrose solutions, which is essentially in agreement with the modeling results.

2. Fabrication and characteristics

The fs laser (Spectra-Physics, Inc.) with central wavelength of 800nm, pulse width of 35fs and repetition rate of 1 kHz is utilized for the sensor micromachining. The laser pulse energy is attenuated through a half-wave plate and a polarizer to less than 50 μJ. Then, several neutral density filters are applied to reduce the pulse energy to less than 600 nJ before the objective lens. The attenuated fs laser beam is focused by an objective lens (Olympus MPFLN 20× and NA=0.45) and the focal spot diameter is about 2 μm. The single-mode optical fiber (Corning SMF-28e) is used whose core diameter and cladding diameter are 8.2 μm and 125 μm, respectively. A detection system (Agilent Technologies Inc.) consisting of a tunable laser (81980A) and an optical power meter (81636B) is employed to monitor the transmission spectra by wavelength sweeping.

A fiber is uncoated in a certain length and mounted on a six-axial moving stage with a resolution of 1 μm in x and y directions and 0.5 μm in z direction. Then the laser beam is used to ablate a micro-cavity on the fiber with a relatively scanning speed of 100 μm/s. During the whole fs laser micromachining process, nitrogen gas is used to blow off debris. The transmission spectra of the sensor are timely monitored during the fs laser micromachining process and the tunable laser scans through its wavelength range (1465-1575nm) at the rate of 0.5 nm per step. Figure 1 shows the schematic structure, SEM images and transmission spectrum in atmosphere of the ultracompact fiber inline MZI with the ablation depth of about 60 μm and the ablation length of about 75 μm fabricated by fs laser pulses. As shown in Fig. 1 (d), the FSR and the fringe visibility of the sensor are about 64.5 nm and 24 dB respectively, which indicates a good transmission spectrum for RI sensing applications.

 

Fig. 1 The fabricated MZI structure. (a) Schematic illustration. (b) Side view (a half part). (c) Cross section. (d) Transmission spectrum.

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3. Theory and BPM analysis

3.1MZI theory

The fabricated structure forms an MZI whose two main light transmission paths are 1) the remaining D-type fiber core and 2) the U-shape microcavity. So the interference intensity can be expressed by [1]

I=I1+I2+2I1I2cosϕ.
where I1 and I2 are the intensities along the two light paths and ϕ=2πΔneffL/λ+φ0is the phase difference; Δneff is the difference between effective refractive indices of the D-type fiber core and that of the U-shape microcavity; λ is the wavelength; L is the ablation length; and φ0 is the initial interference phase. The fringe visibility is optimized to maximum when I1 = I2.

According to Eq. (1), the phase difference of two adjacent minimum interference signals is 2π. That is

(2πΔneffL/λm+1+φ0)(2πΔneffL/λm+φ0)=2π.
Where λm and λm + 1 are the wavelengths corresponding to the two adjacent minimum interference signals. Note that m is the mth interference order. Thus, the ablation length can be derived as

L=λmλm+1/(Δneff(λmλm+1)).

It indicates that the free spectral range (FSR = λm-λm + 1) decreases as the ablation length increases. While the effective refractive index of the D-type fiber core and that of the U-shape microcavity in atmosphere are approximately estimated as 1.4682 and 1.0002926 respectively, Δneff (≈0.4679) is obtained. As shown in Fig. 2(d) , the two measured parameters of and are 1533.6nm and 1469.1nm respectively. According to these aforementioned parameters, the calculated L (≈74.6μm) is obtained which is in good agreement with the experimental ablation length of 75μm.

 

Fig. 2 (a) Contour map of the computed fundamental mode. (b) The schematic diagram illustration of MZI in DOL coordinate for BPM analysis.

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3.2 BPM analysis

As for Corning SMF-28e optical fiber, the effective refractive index of the fundamental mode in fiber core is 1.4682@1550nm, so the physical refractive indices of the fiber core and the cladding are calculated to be 1.4712 and 1.4659 respectively [10]. Based on these two parameters, the contour map of the simulated fundamental mode for further verification through the reversed deduction using the simulated mode solver is shown in Fig. 2(a). The effective refractive index is 1.468232@1550nm and the mode field diameter (MFD) is less than 14μm. So BPM analysis is conducted then according to these two parameters. Figure 2(b) shows the schematic diagram illustration of fiber inline MZI with the ablation depth (D) and the ablation length (L) in the two dimensional orthogonal coordinate DOL for BPM analysis. Note that ncavity represents the refractive index of U-shape microcavity.

BPM analysis is utilized as depicted in Fig. 3 , the fundamental mode is launched into the simulated structure, and four examples are all with simulated parameter of D = 63.5μm which means that the optical fiber core is ablated about 5.1μm off in radial direction. From the four contour maps of Fig. 3(a), (c), (e) and (g), the monitoring power oscillation is apparently available and exhibits two forms because of two different values of ncavity. The higher ncavity is chosen, the larger oscillation period is obtained. All the FSRs calculated from transmission spectra as shown in Fig. 3(b), (d), (f) and (h) are well matched with the MZI theory mentioned above. What’s more, all transmission spectra are of high fringe visibilities which essentially depend on ablation depth at the condition of constant ablation length. Thirteen different ablation depths of 55.5 58.4, 59.5, 60.5, 61.5 62.5, 63, 63.5, 64, 64.5, 65.5, 66.6 and 69.5μm together with two ablation lengths of 100 and 150μm are simulated in BPM analysis and all transmission spectra are analyzed. The high-quality transmission spectra with fringe visibilities greater than 16dB can be obtained while the optimal ablation depth is around 63.5μm. The best fringe visibility of 35dB and even bigger can be reached, when the tolerance of the ablation depth is smaller than 1μm. The exact fine ablation process of the proposed sensor concerned with fringe visibility variations has been reported by us [2].

 

Fig. 3 Contour maps and transmission spectra of BPM analysis with the simulated parameters. (a) & (b) ncavity=1.0002926 and L=100μm. (c) & (d) ncavity=1.333and L=100μm. (e) & (f) ncavity=1.0002926 and L=150μm. (g) & (h) ncavity=1.333 and L=150μm.

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As for RI sensitivity discussions, two RI ranges are simulated with the ablation depth of 63.5μm and the ablation length of 150μm in BPM analysis for gas and solution respectively. As for gas sensing, six RI data of 1.000132, 1.0002926, 1.000449, 1.000686, 1.000891 and 1.00109 corresponding to six different gases of hydrogen, air, carbon dioxide, sulfur dioxide, methyl ether and acetone vapor respectively are simulated in BPM analysis. The wavelengths of the corresponding interference dips for each gas are obtained and the simulated RI sensitivity for gas is estimated of −3243.75 ± 0.65nm/RIU by least square linear fitting, as is shown in Fig. 4 . As for solution sensing, all the RI data ranging from 1.333 to 1.34 with a step of 0.0005 are simulated with BPM analysis. The wavelengths of the corresponding interference dips for each RI data are obtained and the simulated RI sensitivity is estimated of −10789.29 ± 18.91nm/RIU by least square linear fitting, as shown in Fig. 4.

 

Fig. 4 BPM analysis of RI sensitivity for gases (left part of image) and BPM analysis of RI sensitivity for solutions (right part of image)

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3.3 RI testing experiments

The ablation length of the sensor is about 50μm in the experiments and the RI testing experiments for gases are taken at room temperature. The gases are the mixtures of the pure N2 and He with the mixture ratios (in volume) of 70% N2 and 30% He, 60% N2 and 40% He, 50% N2 and 50% He, 40% N2 and 60% He and 30% N2 and 70% He, respectively. The sensor is put into a small chamber, which is vacuumed before the test of each gas with new mixture ratio. The corresponding transmission spectrum for each test is obtained by wavelength sweeping using the detection system. Five corresponding transmission spectra are obtained, as shown in Fig. 5 . The RI data of the five different mixture ratios can be figured out according to the logical and proportional calculation that each value of N2 RI (1.000297) multiplying its ratio adds the corresponding value of He RI (1.000036) multiplying its ratio, which are 1.0002187, 1.0001926, 1.0001665, 1.0001404 and 1.0001143 respectively. Therefore, the wavelengths of the corresponding interference dips for each gas are obtained and the experimental result of RI sensitivity for gas is estimated of −3754.79 ± 44.24nm/RIU by least square linear fitting, as shown in Fig. 6 .

 

Fig. 5 Transmission spectra vary with five different mixture ratios of N2 and He gases, the inset is the magnification of interference dips in circle.

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Fig. 6 Experimental results of RI sensitivity for mixture gases.

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RI testing experiment for solution is also carried out at room temperature. Six different weights of sucrose which are 3g, 3.5g, 4g, 4.5g, 5g, and 5.5g mix with 100ml deionized water respectively to form six different sucrose solutions. The sensor is immersed into the sucrose solution during each test and is cleaned with deionized water and dried before the next test. The corresponding transmission spectra in deionized water and six different sucrose solutions are obtained by wavelength sweeping using the detection system, as shown in Fig. 7 . The ablation length of the sensor is about 140μm. The RI data can be figured out according to the relationship between the refractive indices and the corresponding concentrations of sucrose solutions, which are 1.3330, 1.33381, 1.33466, 1.33551, 1.33635, 1.33719 and 1.33801 respectively [11]. Therefore, each interference dip wavelength corresponding to its RI data is obtained and the experimental result of RI sensitivity for solution is estimated of −12162.01 ± 173.92nm/RIU by least square linear fitting, as shown in Fig. 8 .

 

Fig. 7 Transmission spectra vary with seven different concentrations of sucrose solutions.

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Fig. 8 Experimental results of RI sensitivity for sucrose solutions.

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4. Conclusions

All-optical fiber sensor based on an ultracompact inline MZI fabricated by fs laser is demonstrated in this paper. Beam propagation method analysis is employed to analyze the dependences of transmission spectrum on parameters of the ablation depth, the ablation length and the refractive index of U-shape micocavity, which gives some guidelines to optimize parameters for fs laser micromachining and predicts sensitivity within given RI ranges. The modeling results of RI sensitivities for gas and solution are −3243.75 ± 0.65nm/RIU and −10789.29 ± 18.91nm/RIU respectively. As for sensing test experiments, the sensor exhibits ultrahigh RI sensitivities of −3754.79 ± 44.24nm/RIU with refractive indices ranging from 1.0001143 to 1.0002187 by testing different mixture ratios of N2 and He gases, and −12162.01 ± 173.92nm/RIU with refractive indices ranging from 1.3330 to 1.33801 by testing different concentrations of sucrose solutions, which is in good agreement with the modeling results.

Acknowledgments

This research is supported by the National Natural Science Foundation of China (Grant No. 90923039 and 51025521) and the 111 Project of China (grant B08043).

References and links

1. Y. Jung, S. Lee, B. H. Lee, and K. Oh, “Ultracompact in-line broadband Mach-Zehnder interferometer using a composite leaky hollow-optical-fiber waveguide,” Opt. Lett. 33(24), 2934–2936 (2008). [CrossRef]   [PubMed]  

2. L. Zhao, L. Jiang, S. Wang, H. Xiao, Y. Lu, and H. L. Tsai, “A High-Quality Mach-Zehnder Interferometer Fiber Sensor by Femtosecond Laser One-Step Processing,” Sensors (Basel Switzerland) 11(1), 54–61 (2011). [CrossRef]  

3. Y. Wang, Y. Li, C. Liao, D. N. Wang, M. Yang, and P. Lu, “High-Temperature Sensing Using Miniaturized Fiber In-Line Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 22(1), 39–41 (2010). [CrossRef]  

4. Y. Wang, M. Yang, D. N. Wang, S. Liu, and P. Lu, “Fiber in-line Mach-Zehnder interferometer fabricated by femtosecond laser micromachining for refractive index measurement with high sensitivity,” J. Opt. Soc. Am. B 27(3), 370–374 (2010). [CrossRef]  

5. M. Park, S. Lee, W. Ha, D. K. Kim, W. Shin, I. B. Sohn, and K. Oh, “Ultracompact Intrinsic Micro Air-Cavity Fiber Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 21(15), 1027–1029 (2009). [CrossRef]  

6. L. Jiang and H. L. Tsai, “Plasma modeling for ultrashort pulse laser ablation of dielectrics,” J. Appl. Phys. 100(2), 023116 (2006). [CrossRef]  

7. T. Wei, Y. Han, H. L. Tsai, and H. Xiao, “Miniaturized fiber inline Fabry-Perot interferometer fabricated with a femtosecond laser,” Opt. Lett. 33(6), 536–538 (2008). [CrossRef]   [PubMed]  

8. P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009). [CrossRef]  

9. Z. Tian and S. S. H. Yam, “In-Line Single-Mode Optical Fiber Interferometric Refractive Index Sensors,” J. Lightwave Technol. 27(13), 2296–2306 (2009). [CrossRef]  

10. B. E. Little, J. P. Laine, and H. A. Haus, “Analytic theory of coupling from tapered fibers and half-blocks into microsphere resonators,” J. Lightwave Technol. 17(4), 704–715 (1999). [CrossRef]  

11. http://www.piramoon.com/sucrose.php.

References

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  1. Y. Jung, S. Lee, B. H. Lee, and K. Oh, “Ultracompact in-line broadband Mach-Zehnder interferometer using a composite leaky hollow-optical-fiber waveguide,” Opt. Lett. 33(24), 2934–2936 (2008).
    [Crossref] [PubMed]
  2. L. Zhao, L. Jiang, S. Wang, H. Xiao, Y. Lu, and H. L. Tsai, “A High-Quality Mach-Zehnder Interferometer Fiber Sensor by Femtosecond Laser One-Step Processing,” Sensors (Basel Switzerland) 11(1), 54–61 (2011).
    [Crossref]
  3. Y. Wang, Y. Li, C. Liao, D. N. Wang, M. Yang, and P. Lu, “High-Temperature Sensing Using Miniaturized Fiber In-Line Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 22(1), 39–41 (2010).
    [Crossref]
  4. Y. Wang, M. Yang, D. N. Wang, S. Liu, and P. Lu, “Fiber in-line Mach-Zehnder interferometer fabricated by femtosecond laser micromachining for refractive index measurement with high sensitivity,” J. Opt. Soc. Am. B 27(3), 370–374 (2010).
    [Crossref]
  5. M. Park, S. Lee, W. Ha, D. K. Kim, W. Shin, I. B. Sohn, and K. Oh, “Ultracompact Intrinsic Micro Air-Cavity Fiber Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 21(15), 1027–1029 (2009).
    [Crossref]
  6. L. Jiang and H. L. Tsai, “Plasma modeling for ultrashort pulse laser ablation of dielectrics,” J. Appl. Phys. 100(2), 023116 (2006).
    [Crossref]
  7. T. Wei, Y. Han, H. L. Tsai, and H. Xiao, “Miniaturized fiber inline Fabry-Perot interferometer fabricated with a femtosecond laser,” Opt. Lett. 33(6), 536–538 (2008).
    [Crossref] [PubMed]
  8. P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009).
    [Crossref]
  9. Z. Tian and S. S. H. Yam, “In-Line Single-Mode Optical Fiber Interferometric Refractive Index Sensors,” J. Lightwave Technol. 27(13), 2296–2306 (2009).
    [Crossref]
  10. B. E. Little, J. P. Laine, and H. A. Haus, “Analytic theory of coupling from tapered fibers and half-blocks into microsphere resonators,” J. Lightwave Technol. 17(4), 704–715 (1999).
    [Crossref]
  11. http://www.piramoon.com/sucrose.php .

2011 (1)

L. Zhao, L. Jiang, S. Wang, H. Xiao, Y. Lu, and H. L. Tsai, “A High-Quality Mach-Zehnder Interferometer Fiber Sensor by Femtosecond Laser One-Step Processing,” Sensors (Basel Switzerland) 11(1), 54–61 (2011).
[Crossref]

2010 (2)

Y. Wang, Y. Li, C. Liao, D. N. Wang, M. Yang, and P. Lu, “High-Temperature Sensing Using Miniaturized Fiber In-Line Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 22(1), 39–41 (2010).
[Crossref]

Y. Wang, M. Yang, D. N. Wang, S. Liu, and P. Lu, “Fiber in-line Mach-Zehnder interferometer fabricated by femtosecond laser micromachining for refractive index measurement with high sensitivity,” J. Opt. Soc. Am. B 27(3), 370–374 (2010).
[Crossref]

2009 (3)

Z. Tian and S. S. H. Yam, “In-Line Single-Mode Optical Fiber Interferometric Refractive Index Sensors,” J. Lightwave Technol. 27(13), 2296–2306 (2009).
[Crossref]

M. Park, S. Lee, W. Ha, D. K. Kim, W. Shin, I. B. Sohn, and K. Oh, “Ultracompact Intrinsic Micro Air-Cavity Fiber Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 21(15), 1027–1029 (2009).
[Crossref]

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009).
[Crossref]

2008 (2)

2006 (1)

L. Jiang and H. L. Tsai, “Plasma modeling for ultrashort pulse laser ablation of dielectrics,” J. Appl. Phys. 100(2), 023116 (2006).
[Crossref]

1999 (1)

Chen, Q.

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009).
[Crossref]

Ha, W.

M. Park, S. Lee, W. Ha, D. K. Kim, W. Shin, I. B. Sohn, and K. Oh, “Ultracompact Intrinsic Micro Air-Cavity Fiber Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 21(15), 1027–1029 (2009).
[Crossref]

Han, Y.

Haus, H. A.

Jiang, L.

L. Zhao, L. Jiang, S. Wang, H. Xiao, Y. Lu, and H. L. Tsai, “A High-Quality Mach-Zehnder Interferometer Fiber Sensor by Femtosecond Laser One-Step Processing,” Sensors (Basel Switzerland) 11(1), 54–61 (2011).
[Crossref]

L. Jiang and H. L. Tsai, “Plasma modeling for ultrashort pulse laser ablation of dielectrics,” J. Appl. Phys. 100(2), 023116 (2006).
[Crossref]

Jung, Y.

Kim, D. K.

M. Park, S. Lee, W. Ha, D. K. Kim, W. Shin, I. B. Sohn, and K. Oh, “Ultracompact Intrinsic Micro Air-Cavity Fiber Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 21(15), 1027–1029 (2009).
[Crossref]

Laine, J. P.

Lee, B. H.

Lee, S.

M. Park, S. Lee, W. Ha, D. K. Kim, W. Shin, I. B. Sohn, and K. Oh, “Ultracompact Intrinsic Micro Air-Cavity Fiber Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 21(15), 1027–1029 (2009).
[Crossref]

Y. Jung, S. Lee, B. H. Lee, and K. Oh, “Ultracompact in-line broadband Mach-Zehnder interferometer using a composite leaky hollow-optical-fiber waveguide,” Opt. Lett. 33(24), 2934–2936 (2008).
[Crossref] [PubMed]

Li, Y.

Y. Wang, Y. Li, C. Liao, D. N. Wang, M. Yang, and P. Lu, “High-Temperature Sensing Using Miniaturized Fiber In-Line Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 22(1), 39–41 (2010).
[Crossref]

Liao, C.

Y. Wang, Y. Li, C. Liao, D. N. Wang, M. Yang, and P. Lu, “High-Temperature Sensing Using Miniaturized Fiber In-Line Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 22(1), 39–41 (2010).
[Crossref]

Little, B. E.

Liu, S.

Lu, P.

Y. Wang, M. Yang, D. N. Wang, S. Liu, and P. Lu, “Fiber in-line Mach-Zehnder interferometer fabricated by femtosecond laser micromachining for refractive index measurement with high sensitivity,” J. Opt. Soc. Am. B 27(3), 370–374 (2010).
[Crossref]

Y. Wang, Y. Li, C. Liao, D. N. Wang, M. Yang, and P. Lu, “High-Temperature Sensing Using Miniaturized Fiber In-Line Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 22(1), 39–41 (2010).
[Crossref]

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009).
[Crossref]

Lu, Y.

L. Zhao, L. Jiang, S. Wang, H. Xiao, Y. Lu, and H. L. Tsai, “A High-Quality Mach-Zehnder Interferometer Fiber Sensor by Femtosecond Laser One-Step Processing,” Sensors (Basel Switzerland) 11(1), 54–61 (2011).
[Crossref]

Men, L.

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009).
[Crossref]

Oh, K.

M. Park, S. Lee, W. Ha, D. K. Kim, W. Shin, I. B. Sohn, and K. Oh, “Ultracompact Intrinsic Micro Air-Cavity Fiber Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 21(15), 1027–1029 (2009).
[Crossref]

Y. Jung, S. Lee, B. H. Lee, and K. Oh, “Ultracompact in-line broadband Mach-Zehnder interferometer using a composite leaky hollow-optical-fiber waveguide,” Opt. Lett. 33(24), 2934–2936 (2008).
[Crossref] [PubMed]

Park, M.

M. Park, S. Lee, W. Ha, D. K. Kim, W. Shin, I. B. Sohn, and K. Oh, “Ultracompact Intrinsic Micro Air-Cavity Fiber Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 21(15), 1027–1029 (2009).
[Crossref]

Shin, W.

M. Park, S. Lee, W. Ha, D. K. Kim, W. Shin, I. B. Sohn, and K. Oh, “Ultracompact Intrinsic Micro Air-Cavity Fiber Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 21(15), 1027–1029 (2009).
[Crossref]

Sohn, I. B.

M. Park, S. Lee, W. Ha, D. K. Kim, W. Shin, I. B. Sohn, and K. Oh, “Ultracompact Intrinsic Micro Air-Cavity Fiber Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 21(15), 1027–1029 (2009).
[Crossref]

Sooley, K.

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009).
[Crossref]

Tian, Z.

Tsai, H. L.

L. Zhao, L. Jiang, S. Wang, H. Xiao, Y. Lu, and H. L. Tsai, “A High-Quality Mach-Zehnder Interferometer Fiber Sensor by Femtosecond Laser One-Step Processing,” Sensors (Basel Switzerland) 11(1), 54–61 (2011).
[Crossref]

T. Wei, Y. Han, H. L. Tsai, and H. Xiao, “Miniaturized fiber inline Fabry-Perot interferometer fabricated with a femtosecond laser,” Opt. Lett. 33(6), 536–538 (2008).
[Crossref] [PubMed]

L. Jiang and H. L. Tsai, “Plasma modeling for ultrashort pulse laser ablation of dielectrics,” J. Appl. Phys. 100(2), 023116 (2006).
[Crossref]

Wang, D. N.

Y. Wang, M. Yang, D. N. Wang, S. Liu, and P. Lu, “Fiber in-line Mach-Zehnder interferometer fabricated by femtosecond laser micromachining for refractive index measurement with high sensitivity,” J. Opt. Soc. Am. B 27(3), 370–374 (2010).
[Crossref]

Y. Wang, Y. Li, C. Liao, D. N. Wang, M. Yang, and P. Lu, “High-Temperature Sensing Using Miniaturized Fiber In-Line Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 22(1), 39–41 (2010).
[Crossref]

Wang, S.

L. Zhao, L. Jiang, S. Wang, H. Xiao, Y. Lu, and H. L. Tsai, “A High-Quality Mach-Zehnder Interferometer Fiber Sensor by Femtosecond Laser One-Step Processing,” Sensors (Basel Switzerland) 11(1), 54–61 (2011).
[Crossref]

Wang, Y.

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Y. Wang, M. Yang, D. N. Wang, S. Liu, and P. Lu, “Fiber in-line Mach-Zehnder interferometer fabricated by femtosecond laser micromachining for refractive index measurement with high sensitivity,” J. Opt. Soc. Am. B 27(3), 370–374 (2010).
[Crossref]

Wei, T.

Xiao, H.

L. Zhao, L. Jiang, S. Wang, H. Xiao, Y. Lu, and H. L. Tsai, “A High-Quality Mach-Zehnder Interferometer Fiber Sensor by Femtosecond Laser One-Step Processing,” Sensors (Basel Switzerland) 11(1), 54–61 (2011).
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Yang, M.

Y. Wang, M. Yang, D. N. Wang, S. Liu, and P. Lu, “Fiber in-line Mach-Zehnder interferometer fabricated by femtosecond laser micromachining for refractive index measurement with high sensitivity,” J. Opt. Soc. Am. B 27(3), 370–374 (2010).
[Crossref]

Y. Wang, Y. Li, C. Liao, D. N. Wang, M. Yang, and P. Lu, “High-Temperature Sensing Using Miniaturized Fiber In-Line Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 22(1), 39–41 (2010).
[Crossref]

Zhao, L.

L. Zhao, L. Jiang, S. Wang, H. Xiao, Y. Lu, and H. L. Tsai, “A High-Quality Mach-Zehnder Interferometer Fiber Sensor by Femtosecond Laser One-Step Processing,” Sensors (Basel Switzerland) 11(1), 54–61 (2011).
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Appl. Phys. Lett. (1)

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009).
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Y. Wang, Y. Li, C. Liao, D. N. Wang, M. Yang, and P. Lu, “High-Temperature Sensing Using Miniaturized Fiber In-Line Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 22(1), 39–41 (2010).
[Crossref]

M. Park, S. Lee, W. Ha, D. K. Kim, W. Shin, I. B. Sohn, and K. Oh, “Ultracompact Intrinsic Micro Air-Cavity Fiber Mach-Zehnder Interferometer,” IEEE Photon. Technol. Lett. 21(15), 1027–1029 (2009).
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J. Appl. Phys. (1)

L. Jiang and H. L. Tsai, “Plasma modeling for ultrashort pulse laser ablation of dielectrics,” J. Appl. Phys. 100(2), 023116 (2006).
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J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

Sensors (Basel Switzerland) (1)

L. Zhao, L. Jiang, S. Wang, H. Xiao, Y. Lu, and H. L. Tsai, “A High-Quality Mach-Zehnder Interferometer Fiber Sensor by Femtosecond Laser One-Step Processing,” Sensors (Basel Switzerland) 11(1), 54–61 (2011).
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Other (1)

http://www.piramoon.com/sucrose.php .

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Figures (8)

Fig. 1
Fig. 1

The fabricated MZI structure. (a) Schematic illustration. (b) Side view (a half part). (c) Cross section. (d) Transmission spectrum.

Fig. 2
Fig. 2

(a) Contour map of the computed fundamental mode. (b) The schematic diagram illustration of MZI in DOL coordinate for BPM analysis.

Fig. 3
Fig. 3

Contour maps and transmission spectra of BPM analysis with the simulated parameters. (a) & (b) ncavity =1.0002926 and L=100μm. (c) & (d) ncavity =1.333and L=100μm. (e) & (f) ncavity =1.0002926 and L=150μm. (g) & (h) ncavity =1.333 and L=150μm.

Fig. 4
Fig. 4

BPM analysis of RI sensitivity for gases (left part of image) and BPM analysis of RI sensitivity for solutions (right part of image)

Fig. 5
Fig. 5

Transmission spectra vary with five different mixture ratios of N2 and He gases, the inset is the magnification of interference dips in circle.

Fig. 6
Fig. 6

Experimental results of RI sensitivity for mixture gases.

Fig. 7
Fig. 7

Transmission spectra vary with seven different concentrations of sucrose solutions.

Fig. 8
Fig. 8

Experimental results of RI sensitivity for sucrose solutions.

Equations (3)

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

I = I 1 + I 2 + 2 I 1 I 2 cos ϕ .
( 2 π Δ n e f f L / λ m + 1 + φ 0 ) ( 2 π Δ n e f f L / λ m + φ 0 ) = 2 π .
L = λ m λ m + 1 / ( Δ n e f f ( λ m λ m + 1 ) ) .

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