Photonic Crystal Fiber-Based Interferometer Sensors

Abstract

A combination of interferometric architectures with photonic crystal fiber techniques is a new configuration in the field of sensing technologies. Since photonic crystal fibers have the extraordinary capability of light guiding and confinement, the photonic crystal fiber-based interferometers offer great potential for the realization of novel sensing applications. In this chapter, principal, fabrication, and typical applications of the photonic crystal fiber-based fiber interferometers are reviewed.

Introduction

The investigations of modal interferometers are booming with the development of photonic crystal fiber (PCF) techniques. The first photonic crystal fiber was fabricated by P. St. J. Russell et al. since early 1996 (Knight et al. 1996). Such fibers are manufactured by the same methods as conventional optical fibers. Before drawing to a small diameter, the photonic crystal fiber preform has to be constructed on the scale of centimeters in size. In the drawing process, the transverse structure is shrinking on the scale of micrometers in size but maintaining the original features. Due to the periodic transverse microstructure and the existence of linear defect, photonic crystal fibers have the capacity of guiding low-loss mode over a very broad spectral range. According to the different light-guiding mechanism (Hansen et al. 2001; Sun and Hu 2010), photonic crystal fibers have two fundamental types, i.e., index-guiding photonic crystal fiber (IG-PCF) and band gap photonic crystal fiber (BG-PCF), which is shown in Fig. 1. The IG-PCF has a solid silica core, which effective refractive index is higher than the micro-structured cladding. Its light-guiding mechanism is the same index-guiding principle as conventional optical fiber; therefore, it is also called multi-hole fibers or micro-structured fibers. However, its light confinement is stronger than conventional optical fiber on account of its periodic transverse micro-structured cladding. The BG-PCF has a core (generally a hollow core) which effective refractive index is lower than the micro-structured cladding. Its light-guiding mechanism is on account of the photonic band gap generated by the hollow core and the micro-structured cladding. Hollow-core photonic crystal fibers have the capability to confine and guide light in wavelengths for which transparent materials are not available since its core is air, not solid materials. An important advantage of photonic crystal fiber is that one can deliberately fill different materials into its micro-holes, which makes it more suitable for sensing applications than conventional optical fibers (Huang et al. 2004). Photonic crystal fibers overcome the limitations of conventional optical fiber optics, which is bringing new possibilities and opportunities to optical fiber sensing technology.

Fig. 1

Fundamental types of the photonic crystal fiber

Traditional optical interferometry technologies include Fabry-Perot interferometer , Mach-Zehnder interferometer, Michelson interferometer, and Sagnac interferometer. Fabry-Perot interferometer is typically formed of a transparent medium with two closely reflecting surfaces. For the fiber Fabry-Perot interferometer (Rao 2006), the reflecting surfaces are usually in the form of fusion splicing point between two different fibers. Each of the two surfaces reflects a beam of light, resulting in dual-beam interference. Mach-Zehnder interferometer is a configuration used to detect the relative phase shift variations between two split light beams derived from the same light source. For the fiber Mach-Zehnder interferometer (Tian et al. 2008a), a 3-dB fiber coupler is needed to split a single light into two light beams, these two light beams transmit through two fiber (i.e., the sensing arm and the reference arm), and then another 3-dB fiber coupler is used to couple the light beams to generate light interference. Michelson interferometer is a configuration used to detect the relative phase shift variations between two reflected light beams derived from splitting a single light source. For the fiber Michelson interferometer (Tian et al. 2008b), a 3-dB fiber coupler is needed to split a single light and couple lights into two different fiber arms. The split light will be reflected back to the coupler by the reflecting mirrors which are on the end face of the two fiber arms. Then the coupler collects the two reflected light beams to generate light interference. Sagnac interferometer is a configuration used to detect the rotation. For the fiber Sagnac interferometer (also called ring interferometer) (Kim and Kang 2004), a single light beam is split into two light beams and coupled into a fiber ring by a 3-dB coupler. The two light beams go through the same path (i.e., the optical fiber ring) but in opposite directions and then transmit back to the fiber coupler. Finally, the coupler collects the two light beams to generate light interference.

The combination of optical fiber with optical interferometers promotes the prosperity of sensing applications. Since the fabrication of photonic crystal fibers was realized, classical and novel interferometric architectures have been implemented with photonic crystal fibers. The fiber interferometers based on photonic crystal fiber exhibit excellent properties for sensing applications. In this chapter, the principal, fabrication, and typical applications of the photonic crystal fiber-based fiber interferometers are exhibited. The fiber interferometer configurations contain refractive index sensor, temperature sensor, strain sensor, pressure sensor, torsion sensor, curvature sensor, magnetic sensor, and their cross-sensing structure.

PCF-Based Fabry-Perot Interferometers

A Fabry-Perot interferometer (FPI) is generally composed of two parallel reflecting surfaces separated by a certain distance (Hercher 1968). The structure of FPI based on PCF can be classified into two categories: one is in-fiber and the other is tip.

Basic Structure of In-Fiber FPI

Principal

The basic schematic of in-fiber FPI on a PCF is given by Fig. 2. The air cavity is formed between the SMF and the PCF, including two reflective surfaces indicated by 1 and 2. Thus, such an air cavity could be used as a sensing element.

Fig. 2

Basic schematic of in-fiber FPI on a PCF

For FPI, the output intensity can be modeled using the two-beam optical interference equation (Yu et al. 2015):

$$ I={I}_1+{I}_2+2\sqrt{I_1{I}_2}\cos \left(\frac{4\pi n\cdot L}{\lambda}\right) $$

(1)

where I₁ and I₂ are the reflective intensities at the two cavity surfaces, L is the cavity length, λ is the operating wavelength, and n is the refractive index in the FPI cavity. For a certain dip, λ_m is in the spectrum under observation; its optical phase difference should be an odd number of π. That is, 4πnL/λ_m = (2 m + 1)π; here m is an integer. The wavelength of the dip is given by:

$$ {\lambda}_m=\frac{4 nL}{2m+1} $$

(2)

The air cavity can be used as a sensing element, while the wavelength shift of a given dip is induced by the variation of the cavity refractive index or the cavity length. The performance of the sensors based on in-fiber FPI can be detected by the wavelength shift of the reflective spectrum.

Fabrication

Several typical ways of fabricating the air cavity between the SMF and the PCF are illustrated as follows:

• 1. The self-enclosed air cavity can be created by splicing the SMF to a PCF with a precise hole micro-machined by a 157-nm laser at the end face of the PCF in Ran et al. (2015). First, a circular hole at the center of the cross section of the PCF is fabricated by using a 157-nm laser micromachining system; its diameter is larger than the core but smaller than the cladding. Then, the air cavity is formed by splicing the PCF with hole to the cleaved SMF. Next, the fiber is cleaved with a short distance from the air cavity, and another cleaved SMF is spliced to it for protecting the PCF.

• 2. The air cavity is an air bubble that can be formed by fusion splicing a PCF and an SMF with a commercialized fusion splicer in Deng et al. (2011). The SMF and the PCF fibers can be pressed together to form a permanent fusion splice joint, while the surface tension overcomes the viscosity of the glass (Chong and Rao 2003). The PCF with big air holes in the cladding is spliced to the SMF, and the surface tension will overcome the viscosity caused by the high temperature during the arc discharge which is high enough to exceed the MPCF softening point. The process not only forms a joint but also collapses the fine voids of MPCF as well (Yablon 2005; Xiao et al. 2005). As a result, a part of air originally inside the voids can be trapped, and the rapidly expanding gases can induce a microbubble.

Applications of In-Fiber FPI on a PCF

In order to perform physical sensing of the ambient medium, an in-fiber FPI on the PCF should change its reflective spectrum in response to the variation of the sample properties.

Refractive Index In-Fiber FPI Sensor

A miniaturized in-fiber FPI sensor for sensing liquid refractive index was demonstrated in Hu et al. (2011). The sensor was fabricated by a short length (less than 1 mm) of PCF spliced to a SMF. The SEM image of the PCF used in this work is shown in Fig. 3a. During the splicing process, an air bubble was formed in the fully collapsed zone as shown in Fig. 3b. The end of the PCF was fused to spherical shape which acted as a reflective mirror of the device. The air bubble diameter was 27.7 μm and the collapsed PCF length was 150.7 μm in Hu et al. (2011).

Fig. 3

(a) SEM image of the PCF cross section, (b) microscopic image of the sensor head

The response of the sensor was investigated with refractive indices of the liquids from 1.33 to 1.4. The corresponding spatial frequency spectrum was shown in Fig. 4. As RI increased, the fringes moved to longer wavelengths monotonically accompanied with decreasing extinction ratios. A strong higher frequency component in addition to the zero-frequency component was observed in the spectrum, which caused the modal interference sensitive to external fluid RI. In addition, although the FP cavity was not modified at different RI liquid, the reflection coefficient at the spherical fiber tip was varying corresponding to the bulk liquid RI values. As a result, the extinction ratio of the interfering spectrum was dependent on the external fluid RI. The linear curve fitting of the fringe dip wavelength shows that the sensitivity of the probe is around 21.4 nm/RIU (refractive index unit) ranging from 1.33 to 1.4 or 18.1 nm/RIU ranging from 1.33 to 1.37 shown in Fig. 5.

Fig. 4

Measured spectrum of the sensor head in calibrating RI liquid

Fig. 5

Calibration curve of the sensor head based on fringe wavelength measurement

High-Temperature Pressure In-Fiber FPI Sensor

A high-temperature strain sensor based on an in-line FPI formed by splicing a multimode photonic crystal fiber (MPCF) to an SMF with a commercialized fusion splicer was demonstrated in Ran et al. (2015). The air microbubble inserted between the two fibers has two smooth glass-air interfaces separated by a distance as two reflective mirrors of the FPI. Three FPI structures including PCF FPI, SMF FPI, and etched PCF FPI are used in high-temperature and high-temperature pressure tests for comparison. The configuration of the FPI on a PCF was given by Fig. 6a. The microscopic images of the fabricated sensors were shown in Fig. 6b, c, respectively, for both etched and non-etched PCF FPIs. The self-enclosed air cavity could be created by splicing the SMF to a PCF with a precise hole micro-machined by a 157-nm laser at the end face of the PCF. A circular hole at the center of the cross section of the PCF by using a 157-nm laser micromachining system was larger than the core but smaller than the cladding. Then, the air cavity was formed by splicing the PCF with hole to the cleaved SMF. The fiber was cleaved with a short distance from the air cavity, and another cleaved SMF was spliced to it for protecting the PCF.

Fig. 6

(a) Schematic diagram of the PCF FPI sensor, (b) photo of the etched PCF FPI, (c) photo of non-etched PCF FPI

The temperature responses of the PCF FPI and etched PCF FPI were measured from 25 to 700 °C successively, while the temperature response of the SMF FPI was measured in the range of 25–400 °C. The temperature coefficients of the SMF FPI, PCF FPI, and etched PCF FPI were measured to be ∼1.9 pm/°C, ∼0.9 pm/°C, and ∼0.45 pm/°C, respectively, as shown in Fig. 7. The pressure responses of the PCF FPI and etched PCF FPI were measured from 0 to 10 Mpa. The pressure and temperature coefficients of the SMF FPI, PCF FPI, and etched PCF FPI were measured as ∼25.3 pm/MPa, ∼39.3 pm/MPa, and ∼54.7 pm/MPa, respectively, as shown in Fig. 8. The sensitivity of the etched PCF FPI in this paper was much higher than that of the SMF and PCF FPI. The pressure responses of the etched PCF FPI at different temperatures were measured in the range of 0–10 Mpa, as shown in Fig. 9. The pressure and temperature coefficients of the etched PCF FPI were 54.7 pm/MPa and 0.45 pm/°C, respectively. The response of the etched PCF FPI shows good linearity and constant sensitivity at different temperatures, even up to 700 °C.

Fig. 7

Temperature responses of the three FPIs

Fig. 8

Pressure responses of the three FPIs

Fig. 9

Pressure responses of the etched PCF FPI at different temperatures

Strain In-Fiber FPI Sensor

A microscopic FPI whose cavity is an air bubble formed by fusion splicing an index-guiding PCF and a SMF was proposed in Villatoro et al. (2009). The cross section of the PCF and the diagram of the interrogation setup are shown in Fig. 10. The in-line FPI was fabricated with an air bubble with two smooth interfaces, and the reflectivity of each glass-air interface is less than 4%. Therefore, higher-order reflections are negligible, and the device can be considered as a two-beam interferometer. The phase of the FPI can change if it is perturbed by environmental variables; consequently, the interferometer can be used for optical sensing. This in-line FPI shows low-temperature sensitivity (less than 1 pm/°C), which is one order of magnitude lower than that of the popular fiber Bragg grating ∼12 pm/°C.

Fig. 10

Diagram of the interrogation setup highlighting the zone of the splice. LED light-emitting diode, OSA optical spectrum analyzer, FOC fiber-optic circulator, SMF single-mode fiber, PCF photonic crystal fiber. d is the diameter of the microcavity. The cross section of the PCF and a micrograph of the splice showing the microbubble are also shown

The performance of the in-line FPI as a strain sensor had been investigated. The in-line FPI with 25-μm and 58-μm diameter bubble was subjected to strain ranging from 0 to 5000 με, respectively. The strain sensitivity of the interferometer with the smaller cavity was 0.62 pm/με, while the other one was 2.7 pm/με, as shown in Fig. 11. The sensitivity in the latter case was about 250% higher than that of FBG-based strain sensors (typically 1.2 pm/με) and that of more complex PCF-based strain sensors (Villatoro et al. 2007). As strain sensors based on the in-line FPI reported here exhibited wider dynamic ranges (between four to five times) than those based on hollow-core or PBG fibers (Rao et al. 2007a, b; Shi et al. 2008; Li et al. 2008), meanwhile, the cavities were shorter than those of FPIs built with such fibers (Rao et al. 2007a, b; Shi et al. 2008). These sensors can be important in space-constrained applications with the advantage that temperature compensation may not be required.

Fig. 11

Shift of the interference pattern as a function of strain observed in a 26-μm sample at 1290 ± 40 nm and in a 58-μm sample at 1550 ± 30 nm. The continuous linear lines are fitting to the data. The inset figure shows the shift of one of the interference dips at 0 (solid curve), 2570 (dashed curve), and 4288 με, (dotted curve) of the 26-μm sample

Basic Structure of Fiber-Tip FPI

Principal

The basic schematic of fiber-tip FPI on a PCF is given by Fig. 12. An intrinsic Fabry-Perot interferometer is formed by the end faces of the SMF and the PCF. As the modes excited in the PCF have different effective indices, the phase difference will depend on the length of the PCF and also on the wavelength of the light source (Ding et al. 2015).

Fig. 12

Basic schematic of fiber-tip FPI on a PCF

The reflection can be expressed as:

$$ I={I}_1+{I}_2+2\sqrt{I_1{I}_2}\cos \left(\frac{2\pi \Delta n\cdot L}{\lambda}\right) $$

(3)

In Eq. 3, I₁ and I₂ are the intensities of the interfering modes, Δn is the difference between the effective indices of the interfering modes, L is the length of the PCF, and λ is the wavelength of the light source. Maxima of Eq. 3 appear when 2πΔnL/λ_m = 2mπ; here m is an integer. The wavelength of the dip is given by:

$$ {\lambda}_m=\frac{\Delta nL}{m} $$

(4)

Fabrication

Fiber-tip FPI sensors are generally fabricated by fusion splicing a segment of PCF to an SMF. A section of endlessly single-mode PCF (SPCF) is used in Rao et al. (2008) and Wu et al. (2011), and a short length of a solid-core PCF is used in Du et al. (2014). The PCF was spliced to the SMF and then cleaved down to form the F-P structure. In some cases, another segment of SMF was spliced to the PCF to protect the F-P structure. The fiber-tip FPI can be used as high-temperature sensor, refractive index sensor, or high-pressure sensor.

Applications

High-Temperature Fiber-Tip FPI Sensor

A high-temperature fiber-tip FPI sensor on a PCF was proposed in Ding et al. (2015); the sensor was fabricated by fusion splicing a segment of the endless single-mode photonic crystal fiber (ESM PCF) to an SMF. The operation principle of the sensor is shown in Fig. 13a, and the microscope photograph of the sensor was illustrated in Fig. 13b.

Fig. 13

(a) The operation principle, (b) the cross section of the ESM PCF

The reflected spectrum of the FFPI was interrogated by using a micro-spectrometer. The temperature response of the sensor with a cavity length of 148 μm was experimentally investigated from the room temperature (17 °C) to 1200 °C. A peak wavelength shift with the change of the temperature is shown in Fig. 14. Experimental results show that the peak wavelength resolution of 10 pm and the temperature sensitivity of 10 pm/°C were achieved. The reflected spectrum kept stable even when the temperature exceeded 1200 °C, which is showing that the FFPI-based sensor exhibited a wide temperature measurement range.

Fig. 14

The relationship between the peak wavelength and temperature

Refractive Index and Temperature Fiber-Tip FPI Sensor

The authors of Rao et al. (2008) presented a fiber-tip FPI sensor formed by splicing a section of endlessly single-mode PCF (SPCF) to a SMF for simultaneous measurement of temperature and refractive index. The EPCF was spliced to the SMF and then cleaved down to splice to another SMF. The structure and the photo of the sensor are shown in Fig. 15.

Fig. 15

(a, b) Configuration and photo of the sensor

In the experiment, the sensor was placed in a furnace, and the temperature was increased with a step of 100 °C from 200 to 1000 °C. As shown in Fig. 16, it shows that the cavity length linearly increased with the temperature increasing. The change of the cavity length is 517 nm and the temperature sensitivity is 6.4 nm/°C.

Fig. 16

Relationship between temperature and cavity length

In addition, the sensor was immersed into glycerin in water whose refractive index modified the reflective coefficient at mirror 2. Hence the visibility of the interferometric signal changed with different indices ranging from 1.35 to 1.47. Figure 17 shows the relationship between the fringe visibility of the sensor and refractive index of the glycerin solution. It could be seen that the visibility reached its minimum and maximum at point B of ∼1.4043 and point C of ∼1.4345, respectively.

Fig. 17

Relationship between refractive index and visibility of the sensor

High-Pressure and High-Temperature Fiber-Tip FPI Sensor

The authors of Wu et al. (2011) presented a high-pressure and high-temperature fiber-tip FPI sensor fabricated by a short length of a solid-core PCF spliced to a SMF using the technique reported in Li et al. (2008). Figure 18 shows the schematic diagram and photograph of the sensor. It could be found that the wavelength shift can be changed with varying the refractive index and axial strain.

Fig. 18

(a) Schematic of the FPI sensor head, (b) photograph of the 2.1-mm-long FPI sensor

In Wu et al. (2011), two sensors with cavity lengths of 1 mm and 2.1 mm were investigated of the high-pressure and high-temperature characteristics. The temperature response of the two FPI sensors was investigated till the temperature reached 700 °C, as shown in Fig. 19a. The temperature sensitivities were 13.7 pm/°C and 13.1 pm/°C for the 2.1-mm sensor and 14.0 pm/°C and 13.5 pm/°C for the 1-mm sensor, respectively. The pressure was increased gradually with a step of 4 MPa in the range of 0–40 MPa. Figure 19b shows the optical spectrum experienced a blue shift with the increase of the pressure, and the pressure sensitivities of the two sensors were measured to be −5.57 pm/MPa and −5.77 pm/MPa, respectively.

Fig. 19

(a) Wavelength shifts of the two sensors with temperatures increasing, (b) wavelength shift of the two sensors under different hydrostatic pressure

Composite Structure

Dual-Core Photonic Crystal Fiber

The authors of Du et al. (2014) proposed a sensor fabricated by alignment splicing a small section of dual-core photonic crystal fiber (DC-PCF) to a SMF for high-temperature measurement up to 900 °C. Two reflective surfaces of glass-air at splicing region and DC-PCF end face formed the FP cavity with a 72.3-μm-long DC-PCF in Du et al. (2014). The schematic diagram, cross section, and microscope image of the sensor are shown in Fig. 20.

Fig. 20

(a) Schematic diagram of the DC-PCF-based interferometer, (b) cross section of the DC-PCF, (c) microscope image of the sensing head

The sensor was inserted into a tube furnace to monitor the temperature, while the temperature was stepwise increased to 900 °C and then cooled down to the room temperature. Figure 21a, b shows the spectrum under different temperatures in heating and cooling processes. Figure 22 indicates the relationship between the wavelength and the temperature, and sensitivities of the heating/cooling processes are 13.88 pm/°C and 13.92 pm/°C, respectively, which is in well agreement with theoretical result.

Fig. 21

Reflection spectrum of the sensor in (a) heating and (b) cooling processes

Fig. 22

Experimental and simulated wavelength shift as functions of temperature change

Dual Hollow-Core Fibers (HCFs)

The sensor based on dual hollow-core fibers (HCFs) was demonstrated in Lee et al. (2015) for measuring the thermo-optic coefficients (TOCs) of liquids. A tiny segment of the HCF₁ (diameter D = 30 μm) filled with liquid was spliced with another section of HCF₂ (diameter D = 5 μm). The sensor was fabricated by a SMF spliced with two HCFs. Figure 23 shows the microphotograph of the sensor tip for measuring the TOCs of liquids.

Fig. 23

Microphotograph of the MFFPI sensor tip. Here, HCF₁ has a diameter of 30 μm, and HCF₂ has a diameter of 5 μm. The cavity length of the HCF₁ herein is about 33.84 μm

Figure 24 shows the wavelength shift of the liquid-filled sensor with the Cargille liquid, the DI water, and the ethanol in temperature from 20 to 60 °C. It shows that the wavelength is blue shift and the peak intensity is increased with the decreasing RI and the increasing T due to the thermal effect on the RI of the liquids.

Fig. 24

Sensitivity of the wavelength shift in temperature from 20 to 60 °C for (a) the Cargille liquid where n_D = 1.3, (b) the DI water, and (c) the ethanol. Inset figures show corresponding spectra with an increasing T

PCF-Based Mach-Zehnder Interferometers

Single-Core Fiber MZI

Principal

Mach-Zehnder interferometer (MZI) has been commonly used in diverse sensing applications because of its flexible configuration. Early MZI had two independent arms, which are the reference arm and the sensing arm (Lee et al. 2012). An incident light is split into two arms by a fiber coupler and then recombined by another fiber coupler, while the recombined light has the interference component between the two arms. In Fig. 25, it shows the basic schematic of MZI on a PCF and the cross section of a single-core PCF (Sales et al. 2015).

Fig. 25

(a) Basic schematic of MZI on a PCF, (b) cross section of a single-core PCF

The output light intensity can be expressed by:

$$ I={I}_{01}+{I}_{11}+2\sqrt{I_{01}{I}_{11}}\cos \left(\varphi +{\varphi}_0\right) $$

(5)

where I₀₁ and I₁₁ are the intensity of LP₀₁ and LP₁₁ modes, respectively, and φ₀ is an initial phase. φ is the phase difference as a function of the LF-PCF physical length L and can be expressed as:

$$ \varphi =\frac{2\pi \Delta {n}_{\mathrm{eff}}L}{\lambda } $$

(6)

When φ = (2m + 1)π, m = 0, 1, 2…, the minimum wavelength value of output light intensity is located at:

$$ {\lambda}_{\mathrm{dip}}^m=\frac{2{n}_{\mathrm{eff}}L}{2m+1} $$

(7)

where ${\lambda}_{\mathrm{dip}}^m$ is the wavelength with a minimum light intensity in the interference spectrum. When ambient temperature changes, due to the thermo-optic effect, the refractive index of the index-matching oil filled into the micro-holes of PCF significantly changes; therefore, it will inevitably cause the change of n_eff between the two modes.

Fabrication

Single-core photonic crystal fiber-based Mach-Zehnder interferometers are generally fabricated by fusion splicing a segment of PCF between two SMFs. The sensor is consisted of a short piece of single-core photonic crystal fiber and two single-mode fibers. The micro-holes in PCF can be filled by refractive index-matching oil or something else alike to enhance the sensor sensitivity. The PCF-based MZI fiber sensor can be used as temperature sensor or refractive index sensor.

Applications

Temperature MZI Sensor

A compact and ultrasensitive all-fiber temperature sensor was proposed in Geng et al. (2014); the proposed sensor is based on an in-line fully liquid-filled PCF MZI. The interferometer was consisted of a short piece of PCF and two SMFs. The PCF was filled with the refractive index-matching oil. Then both ends of PCF undergone heat treatment by the liquefied petroleum gas flame quickly, and the index-matching oil with around 1-mm length from the end of PCF was gasified. After that, the SMF and PCF were welded manually with accurate control over the micro-displacement in x and y directions. The structure of the sensor is shown in Fig. 26.

Fig. 26

(a) Cross section of PCF, (b) side view of completely filled PCF, (c) transition region of pretreated LF-PCF stub, (d, e) side views of splice point between SMF and LF-PCF

Figure 27 shows the sensor response to temperature. It could be seen from Fig. 27 that the sensitivities of the interference reach −1.83 nm/°C and −1.09 nm/°C for wavelength at 1281 nm and 1199 nm, respectively, and blue shift occurred with the temperature increased.

Fig. 27

Temperature response (a) and spectra shift (b) for the LF-PCF-based MZI with cavity length of L = 7.5 mm

Refractive Index MZI Sensor

An MZI refractive index sensor was presented in Wang et al. (2016); the proposed sensor is composed of a segment of PCF and two segments of SMF. The cross section of PCF is shown in Fig. 28a. The single-core PCF was spliced with SMF at both of ends, and then the splicing points are tapered (Fig. 28b, c).

Fig. 28

Photonic crystal fiber and SMF-PCF splicing and taper

Figure 29 presents the relationship between the wavelength and the refractive index with the lengths of PCF are 2 cm, 3 cm, and 4 cm, respectively. It could be seen that while the length is 4 cm, the refractive index reached a maximum value of 224.2 nm/RIU.

Fig. 29

Measuring sensitivity of the sensor at different PCF length

Figure 30 shows the relationship between the wavelength and the surrounding refractive index of the sensor at different taper waist diameters. It could be concluded that the sensitivity increases with the decrease of the diameter.

Fig. 30

Relations between wavelength shift and surrounding refractive index of the sensor

Dual Core

Principal

Dual-core photonic crystal fiber-based Mach-Zehnder interferometer sensing principal is the same as single-core PCF-based MZI. The dual core is the two independent arms of the MZI. The output light intensity can also be calculated by Eqs. 5–7. Schematic structure of dual-core PCF is given in Fig. 31 (Sales et al. 2015).

Fig. 31

Cross section of a double-core PCF

Fabrication

A simple dual-core photonic crystal fiber-based Mach-Zehnder interferometer is generally fabricated by fusion splicing a segment of PCF between two SMFs. The sensor consisted of a short piece of dual-core photonic crystal fiber and two single-mode fibers. The two silicon cores of the PCF are used to form Mach-Zehnder interferometer. In order to create a sensitive structure, an air hole is induced by using the femtosecond laser technology (Liu et al. 2012), or refractive index is filled in some micro-holes of the PCF (Hou et al. 2016). The dual-core PCF-based MZI fiber sensor can be used as temperature and strain sensor.

Applications

Temperature and Stain MZI Sensor

A simple dual-core PCF-based MZI by use of femtosecond laser drilling and fiber splicing was demonstrated in Liu et al. (2012). Higher-order mode was excited in one fiber core by introducing a conical air hole at the splice point, which interfered with the fundamental mode in the other fiber core. The schematic structure of the sensor device is shown in Fig. 32. The two black cones were the femtosecond laser-induced air holes, and L was the length of the dual-core PCF. Figure 33 shows the cross-sectional view of the dual-core PCF before and after femtosecond laser drilling and the micrograph of the splice point between the single-mode fiber and PCF with a conical air hole.

Fig. 32

Schematic structure of the sensor device

Fig. 33

Cross-sectional view of the dual-core PCF (a) before and (b) after femtosecond laser drilling. (Red circle indicates the location of the focusing point). (c) Micrograph of the splice point between the single-mode fiber and PCF with a conical air hole

The responds of the strain and temperature are shown in Fig. 34. Figure 34a demonstrates that the transmission peaks of the sensor shift to the shorter wavelength under a constant temperature of 22 °C with the increase of the strain from 0 to 4000 με. The strain sensitivities of the three samples with lengths of 7.5 cm, 9.5 cm, and 18.5 cm are 1.64 pm/με, 1.95 pm/με, and 1.99 pm/με, respectively. It could be observed that the length of the DC-PCF has a significant impact on the strain sensitivity of the device, and the strain sensitivity of a 9.5-cm long DC-PCF around 1540-nm wavelength is higher than that around 1570 nm.

Fig. 34

(a) Strain response of DC-PCF interferometer with different fiber lengths, (b) wavelength variation against temperature

The temperature sensitivity of the sensor with the DC-PCF length of 9.5 cm was investigated from 20 to 200 °C by an increment of 25 °C. As shown in Fig. 34, the peak wavelength is found to shift toward longer wavelength due to the fiber expansion and thermo-optic effect, and the temperature sensitivity is estimated to be 6.8 pm/°C.

Temperature and Strain Sensing

A sensor based on partially filled dual-core photonic crystal fiber (DC-PCF) for measuring temperature and strain was demonstrated in Hou et al. (2016). The DC-PCF was prepared by manual gluing method, and the cladding air holes surrounding one core were selectively filled with RI liquid while, other air holes were unfilled. The DC-PCF had a diameter of 125 μm and five rings of circular air holes with 3-μm diameter and 3.7-μm pitch (Liu et al. 2012) hexagonally arranged in the cross section of the cladding and two solid cores located symmetrically on two sides of the fiber center.

Figure 35a shows the microscopic image of the optical alignment and manual gluing procedure for the partially blocked process. The glue-dispensed fiber tip mounted on the V-groove of a fiber fusion splicer was moved and contacted the cleaved DC-PCF with a big offset. Fig. 35b shows the cross-sectional view of the partially blocked DC-PCF. The cladding air holes surrounding core a were blocked by glue, while air holes surrounding core b were remained.

Fig. 35

(a) Microscopic image to explain the optical alignment and manual gluing procedure for the partially blocked process. The glue-dispensed fiber tip mounted on the V-groove of a fiber fusion splicer was moved and contacted the cleaved DC-PCF with a big offset. (b) The cross-sectional view of the partially blocked DC-PCF. The cladding air holes surrounding core a were blocked by glue, while air holes surrounding core b were remained

The temperature response of the sensor tested in the oven increased gradually from 25 to 35 °C with a step of 1 °C. As shown in Fig. 36a, it shows the transmission spectra of the proposed multicomponent interference sensor at 25 °C and 26 °C. Figure 36b shows the wavelength shifts of dip A and dip B are functions of temperature. The temperature sensitivities are 5.43 nm/°C and 0.012 nm/°C for dip A and dip B, respectively.

Fig. 36

(a) Transmission spectra of the proposed multicomponent interference sensor at 25 °C and 26 °C, with a PCF length of 6.8 cm, inset figure: magnified fringe of dip B in a small spectral range, (b) wavelength shifts of dip A and dip B as a function of temperature

The strain characteristics of the sensor were also investigated under a constant temperature of 25 °C with the applied strain ranging from 0 to 1400 με. Figure 37 shows the strain sensitivities of dips A and B are −1.95 pm/με and −2.08 pm/με, respectively.

Fig. 37

Wavelength shifts of dip A and dip B as a function of strain

The simultaneous measurements of strain and temperature could be achieved by using the standard matrix demodulation method (Chen et al. 2013a); the cross sensitivity of temperature and strain could be calculated as below:

$$ \left[\begin{array}{c}\Delta T\\ {}\Delta \varepsilon \end{array}\right]={\left[\begin{array}{cc}5.43\mathrm {nm}/{}^{{}^{\circ}}C& -1.95\mathrm {pm}/\mu \varepsilon \\ {}0.012\mathrm {nm}/{}^{{}^{\circ}}C& -2.08\mathrm {pm}/\mu \varepsilon \end{array}\right]}^{-1}\left[\begin{array}{c}{\Delta}_{\mathrm {dip}A}\\ {}{\Delta}_{\mathrm {dip}B}\end{array}\right] $$

(8)

In the matrix, ΔT and Δε are the variations of the temperature and strain, and Δλ_dipA and Δλ_dipB are the wavelength shifts of dips A and B.

Composite Structure

Torsion Sensor with an Yb-Doped PCF Based on a MZI

A torsion sensor based on a MZI using a segment of ytterbium-doped double-cladding PCF between two SMFs by fusion splicing was proposed in Sierra-Hernandez et al. (2015). The layout of the MZI and the picture of the YbDPCF cross section are shown in Fig. 38. The YbDPCF core and claddings are the arms of the MZI (Fig. 38a).

Fig. 38

(a) Layout of the MZI and (b) picture of the YbDPCF cross section

The transmission spectrum is shown in Fig. 39, rotating in clockwise (CW) direction from 0 to 360° in steps of 60°. In order to determinate the responds of the sensor, four peaks at 1025, 1031, 1034, and 1039 nm were selected to observe the wavelength shifts.

Fig. 39

Spectra of MZI for different angular position in steps of 60° from 0 to 360°

The torsion sensitivities of the four peaks are 0.008, 0.006, 0.004, and 0.001 nm/°, respectively. Figure 40b shows the output power of the sensor at 1025, 1031, 1035, and 1039 nm, while they decrease as the applied torsion increase.

Fig. 40

(a) Spectra fringe wavelength shifting as a function of the applied torsion, (b) output power level as a function of the applied torsion

A Hybrid MZI for Refractive Index and Temperature Measurement

A hybrid structured in-line MZI composed of an embedded slender air cavity in a microfiber cascaded to a piece of PCF for simultaneous measurement of refractive index (RI) and temperature was demonstrated in Ni et al. (2016). The PCF was fused with the SMF with a little collapsing of air holes, as shown in Fig. 41a. The schematic diagram and microscopic image of the interferometer are shown in Fig. 41b, c.

Fig. 41

Schematic diagram and microimage of the interferometer

The transmission spectra is examined by the fast Fourier transform (FFT) of the sensor with L₁ = 10.84 μm (46.08 μm after tapering) and L₃ = 14 mm in air at 20 °C which are shown in Fig. 42. Three spatial frequency peaks are clearly found at 0.046, 0.089, and 0.135 nm⁻¹ and designated by Peak1 to Peak3, respectively.

Fig. 42

Spatial frequency spectra of the interferometer before and after tapering

The RI response of the hybrid MZI was investigated with sugar solution of different mass fractions from 5% to 65% with increment of 10% at 20 °C. The RI responses of the PCF-based MZI and air-cavity-based MZI are shown in Fig. 43. It presents the RI sensitivities of the PCF-based and air-cavity-based MZI are 55.22 ± 3.32 nm/RIU and 55.84 ± 4.33 nm/RIU, respectively (λ₁ = 1560.41 nm, λ₂ = 1530.02 nm).

Fig. 43

RI response of the hybrid MZI: (a) PCF-based MZI, (b) air-cavity-based MZI

The temperature responses of the PCF-based and air-cavity-based MZI from 20 to 70 °C with a step of 10 °C are demonstrated in Fig. 44, and the temperature sensitivities are 0.045 ± 0.004 nm/°C and 0.143 ± 0.016 nm/°C, respectively.

Fig. 44

Temperature response of the hybrid MZI: (a) PCF-based MZI, (b) air-cavity-based MZI

Hence, the RI and temperature variations could be independently determined by using a sensitivity matrix as below:

$$ \left[\begin{array}{c}\Delta \mathrm{RI}\\ {}\Delta T\end{array}\right]={\left[\begin{array}{c}\mathrm{55.220.045}\\ {}\mathrm{55.840.143}\end{array}\right]}^{-1}\left[\begin{array}{c}\Delta {\lambda}_1\\ {}\Delta {\lambda}_2\end{array}\right] $$

(9)

where ΔRI and ΔT are the RI and temperature variations, and Δλ₁ and Δλ₂ represent the wavelength shifts of the two fringe dips.

PCF-Based Michelson and Sagnac Interferometers

PCF-Based MI

Principal

Fiber-optic sensors based on Michelson interferometers (MIs) are quite similar to MZIs. The basic concept is the interference between the beams in two arms, but each beam is reflected at the end of each arm in an MI (Yuan et al. 2000; Kashyap and Nayar 1983; O’Mahoney et al. 2009; Zhao and Ansari 2001). In fact, an MI is like a half of an MZI in configuration, and the basic structure is shown in Fig. 45.

Fig. 45

Basic structure of PCF-based MI

The interference mechanism of the proposed configuration is a two-mode (which are denoted as mode 1 and mode 2 with intensities of I_m1 and I_m2, respectively) interference due to the weak interference intensities of the modes. Thus, the intensity of the modal interference fringes can be easily expressed as:

$$ I={I}_{m1}+{I}_{m2}+2\sqrt{I_{m1}{I}_{m2}}\cos \left(\varphi \right) $$

(10)

The optical phase difference between the two modes φ = (2π/λ) ⋅ OPD, where $\mathrm{OPD}=\Delta {n}_{\mathrm{eff}}^m2L$ is the optical path difference. λ is the wavelength, L is the liquid-filled PCF section, and $\Delta {n}_{\mathrm{eff}}^m$ is the difference of effective index of the two modes as $\Delta {n}_{\mathrm{eff}}^m={n}_{\mathrm{eff}}^{m1}-{n}_{\mathrm{eff}}^{m2}$. The ${n}_{\mathrm{eff}}^{m1}$ and ${n}_{\mathrm{eff}}^{m2}$ are effective indices of the mode 1 and mode 2 at a certain temperature (T), respectively.

Fabrication

Photonic crystal fiber -based Michelson interferometer is generally manufactured by fusion splicing a segment of PCF to an SMF. During the fusion splicing process, a collapsed region in the PCF is generated near the splicing point. Therefore the sensor is consisted of a single-mode fiber and a short piece of photonic crystal fiber which contains a collapsed region. In order to enhance sensor sensitivity, the micro-holes of photonic crystal can be filled with liquid. The PCF-based Michelson interferometer fiber sensor can be used as temperature sensor or strain sensor.

Applications

Temperature MI Sensor

An ultra-compact and highly sensitive liquid-filled photonic crystal fiber Michelson interferometer (LF-PCFMI) based on material dispersion engineering was proposed in Hsu et al. (2014). The sensor tip is composed of an SMF splicing with a small section of index-guiding PCF. Figure 46a presents the configuration of proposed LF-PCFMI. Figure 46b, c indicates the micrographs of the PCF tips without and with filled liquid, respectively.

Fig. 46

(a) Configuration of the proposed LF-PCFMI. Photographs of the LF-PCFMI sensor tips with the (b) non-filled and (c) liquid-filled conditions, respectively

Figure 47 shows the interference spectra of the liquid-filled (n_D = 1.45) LF-PCFMI filling length L = 31.3 μm of PCF in a temperature range of 25–30 °C. The experimental results show that wavelength shifts toward shorter wavelength side when ambient T increases. The agreement of the results between theoretical analysis and experimental measurements also demonstrates the effectiveness of the device. The sensitivity of the proposed sensor is ∼5.4 nm/°C, which is much greater than that of the traditional long-period fiber grating (LPFG) (∼0.05 nm/°C) in the air surrounding.

Fig. 47

Experimental interference spectra of the proposed LF-PCFMI when T varies

Strain MI Sensor

An in-line fiber quasi-Michelson interferometer (IFQMI) fabricated by splicing a section of polarization-maintaining photonic crystal fiber (PM-PCF) with a lead-in single-mode fiber (SMF) was proposed and experimentally demonstrated in Du et al. (2013). The schematic diagram of the experimental setup and the sensor is shown in Fig. 48. Some cladding modes are excited into the PM-PCF via the mismatch-core splicing interface between PM-PCF and SMF. Besides, two orthogonal polarized modes are formed due to the inherent multi-hole cladding structure of the PM-PCF.

Fig. 48

Schematic diagram of the experimental setup

Figure 49 shows the strain and torsion responds of the sensor with 20-cm long PM-PCF. The strain and torsion sensitivities are −1.3 pm∕με and −19.17 pm∕deg, respectively, as shown in Fig. 50. The proposed sensor with 10-cm-long PM-PCF exhibits a considered temperature sensitivity of 9.9 pm∕°C. The IFQMI has a compact structure and small size, making it a good candidate for multiparameter measurements.

Fig. 49

Interference spectrum response to strain and torsion

Fig. 50

Wavelength shift of the dip near 1565.28 nm versus the strain and torsion

PCF-Based SI

Principal

Figure 51 illustrates the schematic of the PCF sensor-based Sagnac interferometer (SI). The sensor consists of an optical fiber loop, along which two beams are propagating in counter directions with different polarization states. The input light is split into two directions by a 3-dB fiber coupler, and the two counter-propagating beams are combined again at the same coupler.

Fig. 51

Schematic of the PCF sensor based on SI

Fabrication

Photonic crystal fiber-based Sagnac interferometer is generally manufactured by fusion splicing a segment of polarization-maintaining PCF into an SMF Sagnac ring. The sensor consists of a section of PM-PCF, two sections of SMF, and an SMF coupler. Filling liquid into the polarization-maintaining photonic crystal can enhance the sensor sensitivity (Cui et al. 2012). The PCF-based Sagnac interferometer fiber sensor can be used as pressure sensor or temperature sensor.

Applications

Pressure SI Sensor

A novel fiber SI pressure sensor realized by using a PM-PCF as the sensing element had been proposed and demonstrated in Fu et al. (2008). Figure 52 shows the experimental setup of the proposed pressure sensor with the PM-PCF-based SI. The sensor consisted of a section of PM-PCF, two sections of SMF, and an SMF coupler. The PM-PCF was slicing between the two sections of SMF, and the inset image in Fig. 52 shows the scanning electronic micrograph of the MF-PCF.

Fig. 52

Schematic diagram of the proposed pressure sensor constructed with PM-PCF-based SI

Experimental results and simplified theoretical analysis of the pressure sensor have been presented. The sensitivity of the pressure sensor is 3.42 nm/MPa. The proposed pressure sensor exhibits the advantages of high sensitivity, compact size, low-temperature sensitivity, and potentially low cost.

As shown in Fig. 53a, the wavelength shift changed 1.04 nm with the increase of the pressure by 0.3 MPa. Figure 53b shows the wavelength shift of the transmission minimum at 1551.86 nm against pressure with variation up to 0.3 MPa based on one atmospheric pressure, and the sensitivity of the pressure sensor is 3.42 nm/MPa.

Fig. 53

(a) Measured transmission spectra under different pressures, (b) wavelength shift of the transmission minimum at 1551.86 nm against applied pressure with variation up to 0.3 MPa based on one atmospheric pressure

Temperature SI Sensor

An SI-based temperature sensor constructed by a selectively filled polarization-maintaining photonic crystal fiber (PM-PCF) was presented in Cui et al. (2012). Figure 54a shows the schematic diagram of the SI-based temperature sensor. L₁ is the infiltration length, and L is the total length of PM-PCF inside the fiber loop. Figure 54b shows the SEM image of the cross section of the PM-PCF used.

Fig. 54

(a) Schematic diagram of the SI-based temperature sensor, (b) SEM image of the cross section of the PM-PCF

The proposed temperature sensor was fabricated by first blocking the small holes, then immersing the PM-PCF tip in water, and, after a while, splicing it with the 3-dB coupler. The performance of the proposed sensor with a piece of selectively filled PM-PCF of 11.7 cm with the whole length infiltrated was investigated. The transmission spectra under different temperatures are shown in Fig. 55a with the increase in the temperature from 25 to 42 °C. The dip wavelength as a function of temperature is shown in Fig. 55b; the sensitivity of the proposed sensor is 2.58 nm/°C. The dip wavelengths of increasing and decreasing temperatures almost overlap with each other, indicating high stability and repeatability of the proposed sensor.

Fig. 55

(a) Transmission spectra of the sensor under temperatures, (b) dip wavelengths of the spectrum under different temperatures

The sensitivity dependence on the infiltration length ratio was also investigated. Another sample with shorter infiltration length and longer total length was examined using the same configuration. Figure 56a shows the transmission spectra of the sensor of 44-cm total length infiltrated with water at 32 °C and 80 °C. The achieved sensitivity is ∼0.15 nm/°C as shown in Fig. 56b, which agreed with the theoretical analysis that a higher infiltration length ratio provides a higher sensitivity.

Fig. 56

(a) Transmission spectra of the sensor with 44-cm PM-PCF under different temperatures, (b) dip wavelength against temperature curve giving the sensitivity

Novel Interferometric Architectures in PCF and Their Applications

All-Photonic Crystal Fiber Interferometer

A highly sensitive tilt angle sensor based on an all-photonic crystal fiber interferometer (All-PCFI) was proposed and demonstrated in Zhao et al. (2016). Figure 57a shows the schematic diagram of the proposed reflected All-PCFI formed by a PCF with two collapse regions forming an MZI, as shown in Fig. 57b, c.

Fig. 57

(a) Schematic diagram of All-PCFI (b) the first collapse region of the PCF under the microscope (c) the second collapse region of the PCF under the microscope

The core mode and cladding modes arrived to the second collapse region and silver film, and then the reflected cladding modes would recouple back to the core of the PCF and interfere with the reflected core mode light in the first collapse region. The interference spectrum could be analyzed by using a simple two-mode interference model:

$$ I={I}_{\mathrm{core}}+{I}_{\mathrm{cladding}}+2\sqrt{I_{\mathrm{core}}{I}_{\mathrm{cladding}}}\cos \left(\frac{4\pi \Delta {n}_{\mathrm{eff}}\cdot L}{\lambda}\right) $$

(11)

where I_core and I_cladding are light intensities of the core and cladding modes, and Δn_neff is the effective index difference, $\Delta {n}_{\mathrm{eff}}={n}_{\mathrm{core}}^{\mathrm{neff}}-{n}_{\mathrm{cladding}}^{\mathrm{neff}}$. Therefore, when the Δn_neff is changed, the dip wavelength of the interference spectrum would change.

Figure 58a is the device of the tilt angle measurement experiment formed by cantilever beams and iron ball designed to transform the tilt angle to the strain. The diagram of experiment system is shown in Fig. 58b.

Fig. 58

(a) The tilt angle measuring device, (b) the diagram of experimental system

The sensor was pasted in the cantilever beam to measure the tilt angle adjusted from 0 to 90°. Figure 59a shows that the spectrum is red shift with the increase of the tilt angle. The wavelength shift of the dip at 1557 nm is 3.27 nm, while the tilt angle is increased from 0 to 90°. The characteristic wavelength value is plotted and fitted as shown in Fig. 59b. In the measurement range of 0–45°, the linear measurement sensitivity is 55.67 pm/°.

Fig. 59

(a) Spectra under different tilt angle, (b) fitting curve between wavelengths and tilt angle

SMF Cascaded Tapers with a Hollow-Core PCF-Based Microcavity for Curvature Sensing

A highly sensitive curvature sensor based on cascaded SMF tapers with a microcavity was proposed in Dass et al. (2016). The schematic showing the forward and reverse paths of light traveling in an MZI and microcavity is shown in Fig. 60.

Fig. 60

Schematic showing the forward and reverse paths of light traveling in an MZI + microcavity structure

The proposed sensor setup is a combination of two discrete structures, the in-line MZI and the microcavity. The in-line MZI consists of two dissimilar tapers fabricated using the flame and brush technique separated by a distance. The microcavity was created by splicing a small piece of hollow-core photonic crystal fiber (HCPCF) with one end of an SMF (Dash and Jha 2015).

Figure 61a shows the wavelength shifts of the sensors with a microcavity for different taper-2 diameters of 32 μm, 27 μm, and 18 μm. The dip wavelength shifts slightly toward shorter wavelength, and the wavelength sensitivities of the three MZIs are −0.79, −0.58, and −0.17 nm/m⁻¹, respectively, with the curvature range from 0 to 1 m⁻¹. The wavelength sensitivity is decreased with the decrease of the second taper diameter. It could be observed that the reflected intensity is decreased with the increase of the curvature, as shown in Fig. 61b. The amplitude sensitivities for an MZI with taper-2 diameters of 32 μm, 27 μm, and 18 μm are −9.3, −9.5, and −10.4 dB/m⁻¹, respectively, in the curvature range 0–1 m⁻¹.

Fig. 61

(a) Dip wavelength variation of the sensor with curvature change, (b) intensity variation for all three sensor setups for different curvatures

Magnetic-Fluid-Coated Photonic Crystal Fiber and FBG for Magnetic Field and Temperature Sensing

A sensor composed of a cascaded PCF and fiber Bragg grating (FBG) for simultaneous measurement of magnetic field and temperature was proposed and demonstrated in Chen et al. (2016). Figure 62 shows the schematic diagram of the proposed sensor. An FBG close to the PCF spliced between two sections of SMF was inscribed in the lead-in SMF. Both the FBG and PCF were capsuled in a capillary tube full-filled with MF, and the two ends were sealed by UV glue. The sensor was fabricated with the PCF and the FBG lengths of 15 mm and 10 mm, respectively. The distance between the FBG and the PCF was ∼5 mm. The MF consisted of aqueous Fe₃O₄ nanoparticles solution with a complex RI was filled into the glass capillary tube with an inner diameter of 0.3 mm.

Fig. 62

Schematic diagram of the proposed sensor

Figure 63a, b shows the transmission spectra of the sensor and the magnified view of the spectra around Bragg wavelength under different H. It could see that the transmission spectrum of the sensor is changed with the increase of H caused by the H-related RI and absorption coefficient of the MF, while the Bragg wavelength is remained unchanged (Chen et al. 2013b).

Fig. 63

Transmission spectra of (a) the sensor, (b) around the Bragg wavelength under different H

The temperature response of the sensor exhibits an obvious change with the increase of temperature from 30 to 61.2 °C, which is because the MF is temperature-sensitive (Miao et al. 2011) and the cladding mode of PCF is significantly influenced by the MF. Figure 64 shows value shifts of the FBG and the dip at 1567 nm under different temperature. Fitting results indicate that both them have a good linear relationship with temperature. For the PCF interferometer and FBG, the temperature sensitivities are 0.0149 dB/^°C and 8.8 pm/^°C, respectively.

Fig. 64

Transmission changes at 1567 nm and the shifts of Bragg wavelength under different temperatures

After the above characterization, the demodulation equations can be displayed as follows:

$$ \Delta T=0.0149\Delta {T}_{\mathrm{tem}}+4.324\ast \left[\coth \left(0.0098\Delta H\right)-1/\left(0.0098\Delta H\right)\right] $$

(12)

$$ \Delta {\lambda}_{\mathrm{FBG}}=8.8\Delta {T}_{\mathrm{tem}} $$

(13)

The magnetic field change ΔH and the temperature change ΔT_tem could be simultaneously obtained by monitoring the value shifts, i.e., Δλ_FBG (the FBG) and ΔT (the dip at 1567 nm).

Conclusion

Integration of interferometric architectures with photonic crystal fiber techniques is one of the new trends in the field of novel sensing technologies. The photonic crystal fiber-based interferometers exhibit excellent properties for novel sensors and offer great potential for the realization of sensing applications.

Fabry-Perot interferometer, Mach-Zehnder interferometer, Michelson interferometer, and Sagnac interferometer are traditional optical interferometry technologies. Optical fiber (especially the photonic crystal fiber) is a new technology. The combination of optical fiber with optical interferometers promotes the prosperity of sensing applications. The properties of the sensing applications are greatly enhanced by using photonic crystal fiber. The principal, fabrication, and typical applications of the photonic crystal fiber-based fiber interferometers are exhibited in this chapter. The fiber interferometer configurations contain refractive index sensor, temperature sensor, strain sensor, pressure sensor, torsion sensor, curvature sensor, magnetic sensor, and their composite structure. Due to their extraordinary performance, these sensors show great potential value in the field of sensing applications.