Fiber optic grating sensors are very attractive in many areas of application due to some unique advantages such as immunity to electromagnetic interference(EMI) and harsh environments,chemically inert, high sensitivity, rapid response, long lifetime, and what's more, for some measurands such as temperature and strain the sensor response information is wavelength-encoded, thus it provides robustness to noise or power fluctuation and also enables wavelength division multiplexing (WDM) and distributed measurement.In the last two decades extensive studies on fiber optic grating sensors have been performed by researchers all over the world. By now some fiber optic grating sensors have reached commercialization stages for civil health monitoring and oil industries .
In the early years of the research on fiber grating sensors, the attention was mainly attracted by the traditional fabrications such as normal Fiber Bragg gratings (FBG) and Long Period gratings (LPG).But in recent years the tilted Fiber Bragg gratings (TFBG) emerge as the new focus of research owing to its unique sensing characteristics.
Fiber Bragg gratings and tilted Fiber Bragg gratings are both periodic structure inscribed in the core of an optical fiber. Their most simple form can be defined as a periodic modulation of the index of refraction along the fiber core. The FBGs and TFBGs both reflect a narrowband portion of the broadband incident light and transmit most of the rest. The center wavelength of the reflected narrowband light namely which is determined by the periodicity of the gratings and the tilt angle of the grating planes can be described by the Bragg condition :
Whereis the effective index of refraction of the single core mode of the fiber is the periodicity of the grating and Î¸ is the tilt angle of the grating planes as shown in the figure bellow:
Before we move on in this work, we must clarify the definition of the FBG and TFBG mentioned in this paper. We refer a grating to FBG when the tilt angle and TFBG when, both the FBG and TFBG mentioned are inscribed in single mode fiber. The tilted structure was realized by rotating the mask with respect to the fiber axis in the inscription . The tilted grating planes could couple light backward to cladding modes , which distribute at discrete wavelengths below the Bragg wavelength . The cladding mode resonances wavelength are given by a phase-matching condition and can be expressed as follows :
Where and are the effective indices of the core mode and the ith cladding mode at the wavelength respectively, and and are the periodicity and the tilt angle of the TFBG.
A peak can be observed both in the reflection spectrums of FBG and TFBG at the wavelength determined by equation (1), correspondingly a notch will present itself in the transmission spectrums. The contra-propagating cladding mode resonances determined by equation (2) attenuate rapidly and are therefore not observable in the reflection spectrum  but are observed as numerous discrete notches in the transmission spectrum of the TFBG. The reflection and transmission spectrum of TFBG is shown below:
The appearance of the cladding modes changes the sensing characteristics of the TFBG significantly comparing with the FBG. In this paper, we devote to a comparison of the sensing characteristics of FBG and TFBG, show that they occupy different application niches and thus enormously widen the application fields of fiber optic sensor technology.
2. Comparison of the sensing characteristics of FBG and TFBG
2.1 Temperature and Strain
2.1.1 Theoretical Analysis
Temperature Sensitivity of FBG
The effective index of refraction , as well as the periodic spacing between the grating planes , will be affected by temperature changes. As a resultï¼Œthe Bragg grating resonance, namely the centre wavelength of the reflected light from a Bragg grating, which depends on the effective index of refraction of the core and the periodicity of the grating will have a shift. Regardless of the interferences of strain and other perturbations, the Bragg shift due to temperature change is given by the following equation [7, 8]:
As a matter of convenience we use the equation below [7, 8]:
Where is the thermo-optic coefficient for a germanium-doped silica core fiber while represents the thermal expansion coefficient for a silica fiber. According to silica FBG the quantity of is approximately equal to and is approximately equal to . Apparently the thermal-optic effect is the dominant factor of the Bragg shift. The expected sensitivity for a Bragg grating with a center wavelength 1550 nm is approximately 13.7 pm/â„ƒ [7, 8].
Temperature Sensitivity of TFBG
For TFBG, if we consider the wavelength shifts and caused by temperature changes () only, the wavelength shifts and can be given by:
If we do a little math with equation (6) it will turn out to be equation (5) exactly, which demonstrates that the core modes of FBG and TFBG have the same sensitivity to temperature. As a matter of fact ,in equation (7) as discussed in the section above the is neglectable compared to , therefore the wavelength shift of the cladding modes with temperature is expected to be the same as for the core mode, especially for the low order cladding modes. By now the conclusion comes out to be that the FBG and TFBG exhibit the same temperature sensitivity.
Strain Sensitivity of FBG
When only the longitudinal stretch along the fiber () is taken into account, the wavelength shift can be given by equation (8) [7, 8]:
After rearrangement, the equation above turns out to be a more useful one:
Apparently, the applied strain: and this leads to:
For silica fiber, approximately equals to 0.78, thus. Using light source with center wavelength at 1550 nm, this gives [7, 8]. The axial strain sensitivity of FBG is much smaller than the temperature sensitivity, thus the temperature affect must be removed during strain detection.
Strain Sensitivity of TFBG
Taking the tilt angle into account, the sensitivity of the core mode will not change definitely and can be given by equation (10), too. But for the cladding mode, things have changed. The axial strain sensitivity of the ith cladding mode is given by:
For silica, the quantity of is slightly larger than .Considering the fact that ,lower strain sensitivity is expected for cladding modes than Bragg mode, however the difference does not contribute noticeably for lower order cladding modes within 10 nm away from the Bragg mode. Given that the core mode resonance and the cladding mode resonances have the same temperature sensitivities while they exhibit differential strain sensitivity, by comparing the core mode resonance and cladding mode resonances, the effect caused by temperature can be removed and the development of temperature compensated strain sensor become feasible.
2.1.2 Discrimination of Temperature and Strain
Temperature and Strain Discrimination of FBG
It is apparent that any wavelength shift of FBG or TFBG is the combined effect of strain and temperature perturbations in practical applications. Combining equation (4) and equation (8), the total wavelength shift is given by:
However, in sensing applications where only one perturbation is of interest the cross sensitivity to strain and temperature becomes one of the most significant drawbacks of FBG sensors. Therefore, the discrimination of temperature and strain becomes necessary.
In general, there are two ways to discriminate temperature and strain: the first is to compensate the temperature perturbation during strain measurement; the second is to measure temperature and strain simultaneously.
In pure strain measurements, the effect of temperature change on the Bragg wavelength has to be suitablely compensated . It is impossible to differentiate between the effect of changes in strain and temperature on a single measurement of the Bragg wavelength shift. As a result, several schemes based on dual-gratings and other methods are developed to achieve the purpose of temperature compensation in literature as the table below shows:
Schemes of temperature compensation
Two separate FBGs, one for strain measurement and the other for temperature reference[1-7]
The most simple and straightforward technique for temperature compensation. However, interrogation of two fibers is burdensome
Two FBGs with entirely different wavelengths and temperature and strain sensing sensitivities[8,9]
Simultaneously measurement of temperature and strain, but this technique requires two light sources and two interrogation units, thereby increasing the overall cost of the system
Single FBG attached onto or embedded into a negative CET(coefficient of thermal expansion) material to compensate temperature shift[10-16]
Strain measure can be realized using only one FBG. But the sensor structure and material must be designed or calculated delicately
Single FBG written on the splice joint between two fibers and has two resonance peaks[17-19]
The splice joint loss make it difficult to interrogate and the sensor is very fragile
Temperature and Strain Discrimination of TFBG
As mentioned above, the core mode resonance and the cladding mode resonances of TFBG have the similar temperature sensitivities while they exhibit differential strain sensitivity. So by comparing the core mode resonance and cladding mode resonances, the effect caused by temperature can be canceled out easily.
The figure below shows the comparison of the differential wavelength shifts of a single cladding mode resonance for a 4Â° tilted TFBG at wavelength 1536nm due to strain and temperature perturbations. We can see that the differential wavelength shift increases almost linearly as the strain increases, while the differential wavelength shift due to the temperature changes is within Â± 12 pm in a range of 80 Â°C. The strain sensitivity of the differential wavelength shift is 49 nm/unit strain (0.049pm/Î¼Îµ), while the temperature sensitivity of the same resonance is approximately 0.3pm/Â°C with some degree of randomness.
Bending Sensitivity of FBG
Bending a fiber grating can increase the light power loss due to the core mode coupling to radiation modes, the bending increases the polarization dependent loss as well, because it increases the asymmetry of the gratings written in fiber core and also changes refractive indices of core and cladding layer in the inner and outer of the bended region as a tense-compress effect as the fiber has the different strain and stress in the cross section [Chen]. As the figure below shows, the fiber core of FBG which is very thin and determines the sensing characteristics locates in the neutral layer when the FBG is bended, so the total loss will not be significant unless the bending curvature is large enough. Intrinsically regular FBGs are not sensitive to bending.
Apparently, only one regular FBG can not be used to realize the measurement of bending except that the bending measured is micro-bending which causes significant light power loss. But in the real world applications such as Structure Health Monitoring, the bending radii are usually larger than micro-bending's that is macro-bending whose light power loss is not large enough to be detected easily. To solve this problem a dual-grating method based on differential strain measurement was proposed by several groups [1-8].The basic idea of this method is shown by the following schematic figure:
A pair of identical FBGs is attached symmetrically to the middle point of an elastic beam with a core distance of d. When the beam is bended, the grating above the neutral layer will be tensed while the grating below will be compressed. Supposing that the two gratings suffer the same temperature changes during bending measurement, the two Bragg wavelengths of the FBG pair will move apart with bending but move together in the same direction when surrounding temperature varies, both linearly. So a temperature compensated bending measurement can be realized by comparing the two Bragg shifts of this grating pair. The relation between the bending curvature and the differential wavelength shift is determined by [3-5]:
Where represents the strain sensitivity coefficient of the identical grating pair, represents the bending curvature.
The bending sensitivity of this method is dependent on the strain transfer between the beam and FBGs, on the thermal gradient across the beam, and on precise knowledge of the FBGs locations.Considering that these three factors may lead to errors in measurement, the separation between the two FBGs d is the smaller the better. So an improved method utilizing FBGs in multicore optical fiber was proposed .This new method reduced the size of the whole sensor and the opportunity of suffering external interferences.
The scheme mentioned above can only be used to determine the bending magnitude in only one axis: up and down. In some applications both the magnitude and bending direction are required (so-called vector sensing), such as to monitor the spatial shape of colonoscope [10, 11].One solution is using more FBGs to monitor more axes [9, 12], there are also some solutions utilizing only one grating to monitor the bending magnitude and direction simultaneously[13-16], but this is possible only by using LPGs or other special FBGs whose geometric symmetry is broken and can not be classified as regular FBG any more.
Bending Sensitivity of TFBG
The core mode resonance of the TFBG, whose optical field is confined by the core region, is insensitive to the fiber bending, either. But the cladding mode resonances whose optical field can extend to the outermost cladding layer are very sensitive to the fiber bending, especially for the lower order cladding modes which make up a strong notch (so-called ghost mode) in the transmission spectrum locating right to the left of the Bragg resonance. Furthermore, the core mode could be used as a reference to remove the temperature affect and the light source instabilities. So that a temperature and light source intensity independent fiber bending sensor is possible.
C. Caucheteur et al.  proposed a macro-bending sensor based on a TFBG. They researched the relationship between the area delimited by the upper and lower envelopes of the part of the transmission spectrum corresponding to the cladding modes and the bending curvature and discovered that the normalized area which is defined as the ratio between the area of a perturbed spectrum (i.e. subjected to some bending) and the area of the reference grating (without bending) decreases with increasing bending curvature. The evolution of the normalized area with respect to the bending curvature can be fitted by a second order polynomial. In response to temperature variations, the transmitted spectrum was subjected to a wavelength shift without significant change in amplitude, so the bending sensor is temperature insensitive. The bending sensing accuracies were equal to 0.5 cm-1.
Bo Liu et al. studied the transmission light power of the TFBG versus the bending curvature perturbations and found that the core mode resonance is unchanged and the transmission light power of cladding modes varies linearly with bending curvature, while the transmission light power of ghost mode changes by the form of two-order polynomial. Since the cladding modes and core mode possess the same temperature sensitivity, the transmission light power will not affect by temperature.
To research the bending sensitivity of the backward propagating cladding modes Tuan-Guo et al. conceived a method to realize partially recoupling of the cladding modes to core mode based on an offset fusion splice upstream from the TFBG. This method is proved to be merely effective for the low order cladding modes; as a result, the reflection spectrum consists of a slightly weakened Bragg resonance at the longest wavelength and a strong group of resonances at shorter wavelengths, the so-called ghost mode. The total intensity of the recoupling ghost mode strongly varies with the curvature of TFBG while the intensity of the Bragg resonance remains the same which can be used to normalize the sensor's response with regard to power source fluctuations, thus providing the bending sensing mechanism.
Y.X. Jin et al.  invented a new technique to recouple the backward propagating cladding modes back into core mode by inserting a small section of Multi-mode fiber (MMF) by fusion splicing between a TFBG and a Single-mode fiber (SMF). Consequently, the recoupled cladding modes can be observed in the reflection spectrum in spite of the power loss caused by the splicing. They found that the average reflection power of the cladding modes decreases with the increase of bending curvature linearly with a sensitivity about -802.4 nW/m-1, while the reflected power of the Bragg resonance is unchanged. The power of the reflected cladding modes against temperature variation at a definite bending curvature was also studied and it proved that the reflected cladding modes power is not sensitive to temperature, so the bending sensor is temperature independent.
The broken of the circular symmetry of TFBG induced by the tilted grating planes lead to a variation of sensitivity in different bending directions. All of the bending sensing schemes utilizing TFBG mentioned above measure the same type of bending whose bending direction leads to the largest variation (i.e. the largest bending sensitivity) of the tilt angle respect to the grating planes. But if the bending direction is not well known the accurate determination of bending curvature will not be possible. Seungin Baek et al.  classified the bending into three types according to the bending directions respect to the tilted grating planes and investigated the bending sensitivity of different types. Baek et al. proved that the different sensitivity of bending directions may cause confusion in a real world bending curvature measurement; they also proposed a scheme to reduce the direction dependence utilizing a twisted TFBG. The experiment result conformed with their expection.
When time parameter is taken account into the strain measurement, FBGs and TFBGs can be used to detect vibration/dynamic strain. Compared with the traditional vibration sensing techniques, the fiber grating method exhibits a unmatchable advantage due to the small size and light weight of fiber gratings which would not induce obvious variation of the dynamic response of the measured structure and promise a true free vibration detection , even can be used as high-quality photonic sound pickup of some musical instruments .
Vibration sensor based on FBG
The vibration measurement used FBG is based on the detection of the Bragg wavelength shift caused by mechanical dynamic strain or sound pressure applied to the FBG. The Bragg shift caused by dynamic strain is given by:
To realize practical application, the wavelength shift must be transformed to another physical quantity which is easily detectable. The popular choice is to convert the wavelength shift to a light intensity variation via a tilt filter as shown below:
The wavelength of narrowband light from a laser or reflected by FBG is tuned at the linear slope of the tilt filter. Thus, the light power passes or reflected by the tilt filter is in proportion to the applied vibration and carries the information about the dynamic strain/vibration. The power detected by photodetecter can be used to reconstruct the amplitude and frequency of the vibration. There are many demodulation schemes utilizing different kinds of light sources and different constructions of tilt filter.
Schemes using broadband source
The sensing scheme of W. Jin et al.  is to use a Fabry-Perot filter as the tilt filter. The broadband light goes through a coupler and is partially reflected by the sensing FBG with the vibration encoded wavelength shift. The reflected narrowband light goes back through the coupler and arrives at the Fabry-Perot filter. The central Bragg wavelength of the FBG (i.e. the static operation point) is chosen to be at the linear part of the short wavelength side of the Fabry-Perot filter transmission spectrum. Thus the AC component of the light power goes through Fabry-Perot filter varies in phase with the vibration and linearly with its magnitude. The obvious drawback of this scheme is that nothing has been done to compensate the shift of the static operation point caused by temperature change or to cancel out the fluctuation of source power. Some other schemes [3-9] also confront one or both of the two problems. The problems mentioned above can be easily solved by replacing the Fabry-Perot filter with a matched FBG and adding another photodetecter as reference just as what I. Perez et al.  have done. The schematic is shown below:
The matched FBG and sensing FBG are placed in the same temperature condition so their spectrum will experience the same shift and keep the static operation point rest. When the output power of the light source fluctuates, the detected power of channel 1 and channel 2 fluctuate in step with it so the ratio of channel 1 to channel 2 will not change, thus the effect induced by source fluctuation is removed.
Since the above sensors use incoherent broadband light source, it gives rather low signal-to-noise ratio compared to the sensor with a narrowband laser as an optical source.
Schemes using narrowband source
This kind of interrogation schemes use a FBG with relatively broader transmission spectrum (comparing with the bandwidth of light source) as the tilt filter [11.12].The central wavelength of the narrowband light (i.e. the static operation point) from the source is chosen to be at the center of the linear part of the FBG spectrum curve. Thus the light power pass through or reflected by the FBG can be utilized to reconstruct the measured vibration. The stabilization of operation point and the compensation of light source fluctuation also have to be done to make this method useful.
The static operation point will drift due to the central wavelength shift of both the narrowband source and FBG. To stabilize the operation point, different methods are proposed. N.Takahashi et al.  invented a feedback circuit to control the oscillation wavelength of the DFB (distributed feedback) laser diode. The feedback circuit picks up the DC component of the transmission power goes through FBG and compares it with the reference. If the static operation point varies, the difference will be amplified and control the laser wavelength shift to move the operation point back to its initial position. Another method using feedback control principle is invented by S.Tanaka et al. , in their scheme, the laser employs a semiconductor optical amplifier (SOA) as a gain medium and FBGs as wavelength selection components. The wavelength selection FBGs are bonded to PZTs controlled by the feedback circuit, thus the wavelength of the laser source can be tuned to keep operation point stable by applying strain to the FBGs. In Ref.  S.Tanaka et al. proposed an easy way to realize thermal stabilization of operation point by placing the wavelength selection FBGs and vibration sensing FBGs under the same temperature conditions. The effect of light source fluctuation can be cancelled out by normalizing the detected power just as mentioned in Ref.  and Ref. .
Vibration sensor based on TFBG
Mechanical vibrations or acoustic waves  applying to the TFBG will cause bending along the TFBG and act on the backward cladding-core coupling efficiency so affect the total cladding modes power (especially the ghost mode), while leave the Bragg resonance mode alone. Basically, the cladding modes and core mode power is temperature independent, so using Bragg resonance power as a reference the cladding modes power can be normalized to compensate the source fluctuation. The experiment conducted by T.Guo et al.  monitoring the ghost mode power proved the feasibility of a TFBG vibration sensor and tested a frequency response higher than 2 kHz.
2.4 Refractive Index
Refractive index (RI) is a very important physical quantity since it is a fundamental property of matter. Traditional measurements of RI usually use bulk refractometers which are not suitable for biological or chemical in situ/vivo applications which need to measure very small RI changes in small volumes of fluid . However, RI sensors based on optical fiber provide an alternative due to their compact size and high sensitivity. The refractive index sensing principle of both FBG and TFBG is based on the interaction of the evanescent field and the ambient medium with RI to be measured which will change the grating spectrum. Thus, it is possible to identify RI changes by observing their spectral "fingerprint."
2.4.1 Refractive index sensors with FBG
Since the optical field is well confined in the fiber core and the evanescent field attenuates quickly in the cladding, the grating parameters are screened from the influence of the surrounding-medium refractive index (SRI) by the cladding, normal FBGs are intrinsically insensitive to SRI, thus can not be directly used to detect chemical and biological properties. To detect the SRI, some structure modification must be carried out to extend the evanescent field to reach the surrounding medium. It has been theoretically and experimentally proved that modified FBG structures can be implemented as SRI sensors, including thinned, D-shaped, and microstructured uniform FBGs.
A uniform thinned FBG and the surrounding medium as a whole can be modeled by a doubly clad FBG [2-4] in which the outer cladding represents the surrounding medium. Mathematical analysis of this model indicated that the effective refractive index of the fiber core shows a nonlinear behavior versus the SRI for different cladding diameters. According to equation (1), the Bragg resonance will has a wavelength shift due to the SRI changing and this is the basic sensing mechanism of the thinned FBG.
Experiment carried out by W. Liang et al.  used an etch-eroded single FBG with a radius of 3 um to measure the indices of four different surrounding mediums (air, methanol, ethanol, and isopropyl alcohol). As expected, the reflection spectrum exhibited a nonlinear redshift as the SRI increases. By monitoring the wavelength they derived the effective RI of the fiber core , and then calculated the radius of the cladding based on the doubly clad FBG model mentioned above. The calculated result agreed very well with the measured one using SEM. Another experiment conducted by A. N. Chryssis et al.  demonstrated that the sensitivity can be appreciably increased by etching the fiber to diameters as small as 3.4 um and having the surrounding index close to that of the fiber core. A maximum sensitivity of 1394 nm/riu is achieved. A. Iadicicco et al. [7, 8] proved it is possible that an almost full etched cladding sensor can achieve resolutions of ~10-5 and ~10-4 for SRI around 1.45 and 1.333, respectively, if easily available wavelength discriminators with a minimum detectable of 1 pm are used. A. Iadicicco et al. [9, 10] and X. Sang et al.  also took the effect of temperature change into account and both proposed a similar scheme for compensation. The basic idea is to use a single nonuniform thinned FBG, where the cladding layer is partially or completely removed only in a part of the grating region. The Bragg resonance of this kind of nonuniform thinned FBG split into two separate peaks in the reflected spectrum. The first one, corresponding to the thinned region, is sensitive to the local temperature and the SRI changes, while the other one, related to the unetched part, would respond only to thermal changes. Experiments showed that the thinned and the unetched part of the FBG exhibit almost the same thermal sensitivity so temperature independent SRI measurement can be realized by monitoring the wavelength difference of the two resonance peaks.
In Ref.  S. Keren et al. demonstrated a D-shaped FBG distributed refractometer. The sensor is based on a D-shaped fiber Bragg grating with a core located close to the flat surface of the fiber. The wavelength shift caused by SRI changes is interrogated by low-coherence spectral interferometry. The sensor showed abilities to simultaneously measure glucose concentration in several droplets along a single sensor and to interrogate the time-dependent evaporation process of a water droplet. Theoretically, the SRI sensitivity is inversely proportional to the spatial resolution of the sensor. In their experiments when the minimal detectable change in the SRI is 4Ã-10-3 the spatial resolution equals 70 um, and the time resolution can be much shorter than 2 minutes.
A schematic diagram of the microstructured FBG refractometer proposed by A. Iadicicco et al. [13-15] is shown below: a standard grating with a localized defect resulting from the etching of the cladding layer over a limited region.
The introduction of the defect in the middle of the grating strongly changes the reflected spectrum. The stopband of the new device increases due to the diminution of the two lateral unperturbed regions. On the other hand, the interference of the two grating regions on both sides of the defect leads to the formation of a narrow allowed band inside the stopband according to the Fabry-Perot effect. The spectral position of the narrow allowed band inside the stopband is related to the phase delay introduced by the etched region. The phase delay is given by:
Where is the working wavelength, is the difference between the core effective refractive index of the unperturbed and perturbed regions, and is the length of the etched region. Since the effective refractive index of the etched region is subject to SRI changes, a wavelength shift of the narrow allowed band due to changes is expected according to the equation above. Thus, by monitoring the wavelength of the narrow allowed band the SRI measurement can be realized. The wavelength of the narrow allowed band has a nonlinear redshift with the increase of SRI and exhibits an increase in the sensitivity as SRI approaches the silica refractive index in their experiments. In Ref.  A. Iadicicco et al. reported that a shift of 680 pm (1558.97 nm to 1559.65 nm) as the SRI changes from 1.33 to 1.44 was measured by their sensor prototype and the sensitivity varied from 2.5 nm/riu around the water refractive index (SRI=1.33) to 14.6 nm/riu for SRI=1.44. Besides, they also investigated the optical losses introduced by the etched defect . They found that the optical losses induced by the etched region directly related to the structure features and the surrounding refractive index. In particular, the optical losses lead to a diminution only of the power reflected by the unperturbed grating located at the right side of the defect. Thus by monitoring the reflected power within a selected narrow bandwidth the SRI can be detected. Their experiments utilizing narrowband intensity measurement showed resolutions of 4Ã-10-5and 6Ã-10-5 for SRI around 1.41 and 1.38, respectively, for a 10.5 um partially etched FBG, by using detection device able to resolve 0.1% intensity changes.
Another refractometer based on microstructured uniform FBG is proposed by K. Zhou et al. . Their structure design is to use liquid as the core of a waveguide instead of its cladding to enhance the RI sensitivity. A micro-slot across a FBG was engraved by using tightly focused femtosecond laser inscription and chemical etching. Refractive index measurement is realized by filling the micro-slot with the liquid to be inspected and monitoring the reflected spectrum. Numerical analysis and experimental results showed that this kind of refractometer exhibit a high sensitivity up to 945nm/riu in the RI region higher than the fiber core.
2.4.2 Refractive index sensors with TFBG
The appearance of cladding modes in the transmission spectrum provides feasibility to use TFBG as refractometer without any structure modification. Since the cladding modes propagate near the cladding-surrounding medium interface, their effective index depends on the RI of the outer medium. According to equation (2), there must be wavelength shifts to all of the cladding modes when the SRI varies. In addition, the sensitivity of the cladding modes effective index to the SRI increases with mode order since the penetration depth of the evanescent field increases for higher order modes. Therefore, as the SRI increases, the higher order cladding modes are first affected and their resonances show a redshift in wavelength and eventually fade out from the cladding. With the SRI increasing further, more and more cladding modes gradually become affected until only two transmission peaks remain: the ghost mode and core mode . Obviously, the transmitted power must be related to the SRI.
Y. Miao et al.  investigated the relationship between cladding modes wavelength and the SRI using TFBG with thinned cladding. The decrease of cladding results in fewer cladding modes which are more widely separated and easier to be discriminated in the transmitted spectrum. Since core mode and cladding modes suffer almost the same thermal sensitivity, the temperature effect can be easily removed by taking the difference between their wavelengths. Experiments show that the higher order cladding modes are much more sensitive than the lower order ones under the same diameter and the cladding modes in the thin cladding are more sensitive than in the thick one. Generally speaking, higher order cladding modes of thinned TFBG exhibit higher sensitivity. Here, the reported resolution of the refractive index measurement is of the order of 10-4 while the SRI changes between 1.333 and 1.4532.
Y. Miao et al.  also carried out an experiment to quest the relation between the SRI and the mere transmitted power, including that of the core mode and the cladding modes. The transmission power decreases linearly when the surrounding refractive index changes within the range from 1.3723 to 1.4532, and the resolution of the refractive index is predicted to be 10-4. To remove the effect of temperature and source fluctuation, T. Guo et al.  figured out a scheme for simultaneous measurement of refractive index and temperature based on reference power detection. Broadband light was launched into sensing fiber through a 3-dB coupler, the transmitted and reflected power of the sensing TFBG are monitored by two photodiodes, respectively. Meanwhile, for an effective calibration of power variations caused by the instability of the light source, a referenced photodiode is used for monitoring the launched power into the TFBG. Their experiment showed that the normalized power increases monotonously but nonlinearly with the SRI increase. As a result, the sensitivity is very poor for low values of RI and dramatically increases as the RI approaches the value at which all cladding modes become cut-off. With the power measurement accuracy of the order 10-3 dBm, the proposed TFBG sensor can achieve an RI resolution higher than 10-4 within its linear sensing range from 1.425 to 1.445 and higher than 10-3 over its full sensing range.
By recapturing the cladding modes into backward propagating core mode based on an offset fusion splice upstream from the TFBG, T. Guo et al. [20, 21] realized a refractometer based on monitoring the reflected power of cladding modes. Here, a large offset is used to make sure a strong recoupling of the high order cladding modes. They took the reflected core mode power as a reference to normalize the cladding modes power using different functions. Experiments showed that the sensor will occupy different dynamic measurement ranges using different normalized functions. By choosing a proper dynamic range, this kind of refractometer can achieve a high sensitivity for the relatively low SRI values which is near 1.33. Since the whole reflected spectrum of TFBG shifts globally with temperature, the SRI measurement is temperature independent. C. Caucheteur et al.  proposed another trick to derive the value of SRI from the reflected cladding modes power of a narrow wavelength range. To get a narrowband reflected power signal, the sensing TFBG was followed by a uniform FBG which had a nearly total reflectivity. The Bragg wavelength was chosen to be located at the cladding modes area of the TFBG, thus a reflected power signal modulated by SRI can be detected. Experiments showed that the reflected power from the sensor decreases monotonically but nonlinearly as the SRI increases in a certain range. As the SRI sensitivity varies with the cladding mode order, by choosing FBGs of different Bragg wavelengths the dynamic range of the sensor can be adjusted. As for wavelength ranges matching the middle of the cladding modes spectrum, a good mean SRI sensitivity is obtained in the range between 1.33 and 1.44 with a maximum error of 10-3. Since the sensing TFBG and its following FBG are closely spaced and of the same temperature sensitivity, the refractometer is inherently insensitive to temperature.
C. Caucheteur et al. also carried an experiment to verify the SRI sensitivity of the PDL (Polarization Dependent Loss) of the TFBG . The PDL is caused by the birefringence in TFBG introduced by the lateral inscription process. They reported a SRI resolution of 10-3 and a temperature insensitive response property of this sensing scheme.
Besides the two methods mentioned above by monitoring the wavelength shift and power of cladding modes, there is a third way to measure the SRI by calculating the area delimited by all the cladding modes in transmission spectrum [24-27]. The area varies with changes in the refractive index of the surrounding medium. By monitoring the area variation and relating it to the SRI it is possible to use the TFBG as a refractometer. Experiments showed that the normalized area exhibits nonuniform SRI sensitivity in the range of 1.33-1.47, which is relatively low for the RI values near 1.33. To extend the effective measuring range, in Ref.  C. Caucheteur et al. divide the whole area delimited by all the cladding modes into three parts. By calculating the area respectively, the SRI sensitivity of the three different parts are revealed: the short wavelength part, corresponding to the high order cladding modes, exhibits high sensitivity in the range 1.33-1.38; the medium wavelength part, corresponding to the medium order cladding modes, exhibits high sensitivity in the range 1.38-1.43; the long wavelength part, corresponding to the low order cladding modes, exhibits high sensitivity in the range 1.43-1.47. Therefore, by properly choosing a calculating area, high sensitivity measurement in the whole RI range can be realized, provided that you can estimate the SRI value before measurement.