**2. Long-period gratings at phase matching turning point**

LPGs consist of some periodic modulation in the optical fibre which causes the core mode to couple with a number of modes in the cladding, at discrete wavelengths (**Figure 1**). The modes will propagate through the fibre with the propagation constants, *<sup>β</sup>co and <sup>β</sup>cl M* (core and *M-*th cladding mode, respectively) and the wavelengths are dependent upon the satisfaction of the phase matching condition, which is described as [16]:

$$
\lambda = \{n\_{co}(\lambda) - n\_{cl}^M(\lambda)\}\Lambda \tag{1}
$$

**119**

*Optical Fibre Long-Period Grating Sensors Operating at and around the Phase Matching…*

Eq. (1) shows the resonant wavelength is dependent on the effective refractive indices of the core and cladding mode of the fibre. This central resonant wavelength and the sensitivity of an LPG is affected by the order of the coupled cladding mode; choosing the grating period, the type [23] and composition of the fibre [19], and

*Illustration of an LPG transmission spectrum with resonance bands at discrete wavelengths.*

Optical fibre LPG structures (a three layer cylindrical waveguide consisting of the core, cladding and ambient surrounding) can be modelled using coupled mode theory [24–26]. This can be used to describe the power transmitted between the modes of the waveguides. Guided modes propagating in a fibre can be treated as linearly polarised (LP), employing the weakly guided approximation [27]; this approximates the difference between the normalised core and cladding refractive

The coupled mode theory equations that are used to describe the LPG can be

*m*

*m*

of the cladding mode along the z-axis, the *z*-axis is along the axis of the optical fibre, *k* is the coupling constant, *m* is the induced-index fringe modulation. The small-detuning factor for the co-propagating modes is defined as:

<sup>2</sup>(*βco <sup>−</sup> <sup>β</sup>cl*

Phase matching curves of resonance wavelength against grating period of an LPG can be generated by calculating the dispersion of the modes of the core and the cladding. These sets of curves are able to predict coupling from the core to the cladding mode, and that for each cladding mode there will be a turning point [28]. Around the turning point, a single mode can be coupled at two different wavelengths simultaneously [11, 28]. **Figure 3** shows an example of phase matching curves for higher order cladding modes in the 600–1150 nm wavelength range. It

*<sup>M</sup> − \_\_\_ 2π*

*<sup>2</sup> kcl−co <sup>M</sup> Acl*

*nco* ≪ 1 (2)

*,* (3)

is the amplitude

*<sup>M</sup> e (−i <sup>2</sup> <sup>δ</sup>cl−co <sup>M</sup> z)*

*<sup>2</sup> kcl−co <sup>M</sup> Aco <sup>e</sup> (+i <sup>2</sup> <sup>δ</sup>cl−co <sup>M</sup> z)* (4)

*M*

*<sup>Λ</sup>* ) (5)

any external perturbations can alter the coupled mode.

index, ∆, to be very small [24, 25, 27]:

simplified to [24]:

**Figure 2.**

*\_\_\_\_*

∑*<sup>v</sup>*

*Δ = n\_\_\_\_\_\_ co <sup>−</sup> ncl*

*dAco*

*δcl−co <sup>M</sup>* ≡ \_1

*dz <sup>=</sup> ikco−co* <sup>+</sup> *<sup>i</sup>*∑*<sup>v</sup> \_\_*

*dz <sup>=</sup> +i \_\_*

Where *Aco* is the amplitude of the core mode along the z-axis, *Acl*

*dAcl M \_\_\_\_*

*DOI: http://dx.doi.org/10.5772/intechopen.81179*

Where λ is the resonant wavelength, *nco* is the effective refractive index of the propagating core mode, *ncl M* is the effective refractive index of the *M-*th cladding mode, and the *Λ* is the period of the LPG.

Light that couples to the fibre cladding modes is lost rapidly through scattering and absorption at the cladding and the surrounding medium interface. This is presented as a transmission spectrum, as shown in **Figure 2**, that contains one or more resonance bands with wavelengths, λn.

**Figure 1.** *Schematic diagram of an LPG.*

*Optical Fibre Long-Period Grating Sensors Operating at and around the Phase Matching… DOI: http://dx.doi.org/10.5772/intechopen.81179*

**Figure 2.** *Illustration of an LPG transmission spectrum with resonance bands at discrete wavelengths.*

Eq. (1) shows the resonant wavelength is dependent on the effective refractive indices of the core and cladding mode of the fibre. This central resonant wavelength and the sensitivity of an LPG is affected by the order of the coupled cladding mode; choosing the grating period, the type [23] and composition of the fibre [19], and any external perturbations can alter the coupled mode.

Optical fibre LPG structures (a three layer cylindrical waveguide consisting of the core, cladding and ambient surrounding) can be modelled using coupled mode theory [24–26]. This can be used to describe the power transmitted between the modes of the waveguides. Guided modes propagating in a fibre can be treated as linearly polarised (LP), employing the weakly guided approximation [27]; this approximates the difference between the normalised core and cladding refractive index, ∆, to be very small [24, 25, 27]:

$$
\Delta = \frac{n\_{co} - n\_{cl}}{n\_{co}} \ll \mathbf{1} \tag{2}
$$

The coupled mode theory equations that are used to describe the LPG can be simplified to [24]:

$$\frac{dA\_{co}}{dx} = ik\_{co-co} + i\sum\_{v} \frac{m}{2} \left. k\_{cl-co}^{M} A\_{cl}^{M} \, e^{\left(-i\,\,2\,\delta\_{cl-o}^{M} x\right)}\right. \tag{3}$$

$$\sum\_{\nu} \frac{dA\_{cl}^{M}}{dx} = \, \, \, \text{i} \, \, \frac{m}{2} \, k\_{cl-co}^{M} \, A\_{co} \, e^{\left( \, \, \text{i} \, \, \, \mathcal{B}\_{cl-co}^{M} \, x \right)} \tag{4}$$

Where *Aco* is the amplitude of the core mode along the z-axis, *Acl M* is the amplitude of the cladding mode along the z-axis, the *z*-axis is along the axis of the optical fibre, *k* is the coupling constant, *m* is the induced-index fringe modulation.

The small-detuning factor for the co-propagating modes is defined as:

$$\delta\_{d\text{-}co}^{M} \equiv \frac{1}{2} \left( \beta\_{co} - \beta\_{d}^{M} - \frac{2\pi}{\Lambda} \right) \tag{5}$$

Phase matching curves of resonance wavelength against grating period of an LPG can be generated by calculating the dispersion of the modes of the core and the cladding. These sets of curves are able to predict coupling from the core to the cladding mode, and that for each cladding mode there will be a turning point [28]. Around the turning point, a single mode can be coupled at two different wavelengths simultaneously [11, 28]. **Figure 3** shows an example of phase matching curves for higher order cladding modes in the 600–1150 nm wavelength range. It

*Applications of Optical Fibers for Sensing*

tions outside of the laboratory [2].

propagation constants, *<sup>β</sup>co and <sup>β</sup>cl*

which is described as [16]:

propagating core mode, *ncl*

where PMTP LPGs have been demonstrated.

**2. Long-period gratings at phase matching turning point**

*M*

*λ =* [*nco(λ) − ncl*

*M*

mode, and the *Λ* is the period of the LPG.

more resonance bands with wavelengths, λn.

By appropriately selecting the period of an LPG, it is possible to ensure the core mode will couple to a cladding mode operating at the turn around point (TAP) [11], also known as the phase matching turning point (PMTP), or dispersion turning point (DTP). A feature known as the dual resonance band can also be produced in this region. This type of LPG configuration has become increasingly popular due to its ultra-high sensitivity, a property usually desirable for a sensor. Approaches employed to improve the sensing capability of LPGs have included methods such as tapering [12] and etching [13]; however this can weaken the structure of the fibre and requires more delicate handling or complicated packaging. These sensors have been successfully used for measuring parameters such as temperature [14–16], strain [14–16] and refractive index (RI) [17–20]. The properties of LPGs at PMTP can be tailored further by adding a functional nanoscale coating for chemical and gas sensing [21]. This enables users to adapt the sensor to their own needs and applications. Chemical and bio-chemical based sensors, or those that can be applied to healthcare, are attracting increasing attention as they can have a more direct impact on the wellbeing of people. However, many are still yet to be applied in real situa-

This chapter aims to provide a more comprehensive coverage of LPGs which operate at and around the phase matching turning point, with respect to what can be found in existing literature [22]. The typical characteristics and fabrication considerations will be discussed. This will be followed by the different applications

LPGs consist of some periodic modulation in the optical fibre which causes the core mode to couple with a number of modes in the cladding, at discrete wavelengths (**Figure 1**). The modes will propagate through the fibre with the

wavelengths are dependent upon the satisfaction of the phase matching condition,

Where λ is the resonant wavelength, *nco* is the effective refractive index of the

Light that couples to the fibre cladding modes is lost rapidly through scattering and absorption at the cladding and the surrounding medium interface. This is presented as a transmission spectrum, as shown in **Figure 2**, that contains one or

(core and *M-*th cladding mode, respectively) and the

is the effective refractive index of the *M-*th cladding

*M(λ)*]*Λ* (1)

**118**

**Figure 1.**

*Schematic diagram of an LPG.*

### **Figure 3.**

*Phase matching curves of the 20–25th cladding modes of an optical fibre with a cut-off wavelength of 670 nm. The relationship between the grating period and wavelength is shown. Reprinted with permission from Ref. [28], OSA.*

can be observed that, at the turning point, the gradient of the curve tends to zero, <sup>∣</sup>*d*/*d*∣→0 (and <sup>∣</sup>*d*/*d*∣→∞). The waveguide dispersion of an LPG, expressed as γ=(*d*/*d*) *Δncore* [29], will tend to infinity. As γ can be used to generalise the sensitivity of an LPG [11] it indicates that the transmission spectrum of an LPG that is fabricated with a period that closely matches a turning point, will have the highest sensitivity to external perturbations [11, 14]. The appearance of turning points will move towards shorter wavelengths when the cladding mode order is increased, as presented in **Figure 3**.

With increasing wavelength, the cladding mode's effective refractive index will decrease more than the effective refractive index of the core mode [15, 30]; this corresponds to the dual bands that become apparent in the LPG transmission spectrum.

**Figure 4** shows how the grating period of an LPG approaching the turning point of the LP021 mode affects the transmission spectrum of the LP020 and LP021 cladding modes. **Figure 4**(**b**) shows the transmission spectrum where the period of the LPG chosen does not cut across the phase matching curve (**Figure 4**(**a**)) of LP021 at the turning point. A single resonant band develops (**Figure 4**(**d**)) followed by a small change in the central wavelength of the LP020 band as the period of the LPG hits the PMTP (**Figure 4**(**c**)). As the LPG crosses the turning point, the single band will split leading to the formation of two resonance bands. A much larger evolution can be seen for the LP021 mode when compared to the LP020 mode due to the much smaller gradient of the phase matching curve.

When an external perturbation is applied to the LPG, the two resonance bands of the mode around the turning point can either move towards or away from each other. This depends on the perturbation and the initial period of the LPG. The two bands respond differently to each other due to a non-symmetrical resonance [14], which may be due to modal dispersion [31]. For a 202.5 μm period LPG with dual resonance bands around the turning point, exposed to different temperatures, each band shows a sensitivity of 2.54 nm/°C (red shifted) and 3.29 nm/°C (blue shifted), respectively [14]. In the circumstance where the two bands shift towards each other, a single broad bandwidth band appears, similar to what is shown in **Figure 4**(**d**). Under the influence of an external measurand, the coupling strength between the core mode and the cladding mode changes, altering only the amplitude of this single band and not the resonant wavelength [15].

**121**

**3. Fabrication**

**Figure 4.**

change in the order of 2 × 10<sup>−</sup><sup>4</sup>

femtosecond laser radiation [42].

*Optical Fibre Long-Period Grating Sensors Operating at and around the Phase Matching…*

LPGs at PMTP can be fabricated using the same methods as those used for conventional LPGs, albeit with higher precision - the effective refractive indices of the optical fibre modes can be altered via photo-induction, or by physical deformation [7]. The refractive index can be altered using a number of different methods. Some of these include local exposure of the fibre to a UV laser [28, 32, 33, 34], CO2 laser [35, 36], femtosecond laser [23, 37] or by electrical arc discharge [30, 38]. PMTPs have been written in conventional single mode and doped fibres [12, 11, 33, 34, 36, 39], and have been theoretically investigated using photonic crystal fibres [23]. The length of an LPG tends to range from 30 to 50 mm and have refractive index changes of around 10–4 [40]. Coelho et al. [41] calculated a refractive index

*Illustration of the phase matching curve ((a), (c), (e)) with their corresponding transmission spectrum ((b), (d), (f)) for cladding modes LP020 and LP021 as coupling approaches and crosses the turning point. Korposh et al., adapted from [31]; originally published under CC BY 3.0 licence. Available from: 10.5772/52935*

and 3 × 10<sup>−</sup><sup>4</sup>

same order of magnitude of refractive index change (4.49 × 10<sup>−</sup><sup>4</sup>

when writing an LPG in a single mode fibre using mid-infrared laser radiation. The

A PMTP can also be tuned after an LPG has been fabricated, by tuning the mode coupling and effective index guiding via the means of tapering [12], UV exposure [43], with a thin film overlay [31, 28], etching [44] and radiation exposure [12].

for the core and cladding, respectively

) is also needed for

*DOI: http://dx.doi.org/10.5772/intechopen.81179*

*Optical Fibre Long-Period Grating Sensors Operating at and around the Phase Matching… DOI: http://dx.doi.org/10.5772/intechopen.81179*

### **Figure 4.**

*Applications of Optical Fibers for Sensing*

can be observed that, at the turning point, the gradient of the curve tends to zero, <sup>∣</sup>*d*/*d*∣→0 (and <sup>∣</sup>*d*/*d*∣→∞). The waveguide dispersion of an LPG, expressed as γ=(*d*/*d*) *Δncore* [29], will tend to infinity. As γ can be used to generalise the sensitivity of an LPG [11] it indicates that the transmission spectrum of an LPG that is fabricated with a period that closely matches a turning point, will have the highest sensitivity to external perturbations [11, 14]. The appearance of turning points will move towards shorter wavelengths when the cladding mode order is increased, as pre-

*Phase matching curves of the 20–25th cladding modes of an optical fibre with a cut-off wavelength of 670 nm. The relationship between the grating period and wavelength is shown. Reprinted with permission from Ref.* 

With increasing wavelength, the cladding mode's effective refractive index will decrease more than the effective refractive index of the core mode [15, 30]; this corresponds to the dual bands that become apparent in the LPG transmission spectrum. **Figure 4** shows how the grating period of an LPG approaching the turning point of the LP021 mode affects the transmission spectrum of the LP020 and LP021 cladding modes. **Figure 4**(**b**) shows the transmission spectrum where the period of the LPG chosen does not cut across the phase matching curve (**Figure 4**(**a**)) of LP021 at the turning point. A single resonant band develops (**Figure 4**(**d**)) followed by a small change in the central wavelength of the LP020 band as the period of the LPG hits the PMTP (**Figure 4**(**c**)). As the LPG crosses the turning point, the single band will split leading to the formation of two resonance bands. A much larger evolution can be seen for the LP021 mode when compared to the LP020 mode due to the much

When an external perturbation is applied to the LPG, the two resonance bands of the mode around the turning point can either move towards or away from each other. This depends on the perturbation and the initial period of the LPG. The two bands respond differently to each other due to a non-symmetrical resonance [14], which may be due to modal dispersion [31]. For a 202.5 μm period LPG with dual resonance bands around the turning point, exposed to different temperatures, each band shows a sensitivity of 2.54 nm/°C (red shifted) and 3.29 nm/°C (blue shifted), respectively [14]. In the circumstance where the two bands shift towards each other, a single broad bandwidth band appears, similar to what is shown in **Figure 4**(**d**). Under the influence of an external measurand, the coupling strength between the core mode and the cladding mode changes, altering only the amplitude of this single

**120**

sented in **Figure 3**.

**Figure 3.**

*[28], OSA.*

smaller gradient of the phase matching curve.

band and not the resonant wavelength [15].

*Illustration of the phase matching curve ((a), (c), (e)) with their corresponding transmission spectrum ((b), (d), (f)) for cladding modes LP020 and LP021 as coupling approaches and crosses the turning point. Korposh et al., adapted from [31]; originally published under CC BY 3.0 licence. Available from: 10.5772/52935*

### **3. Fabrication**

LPGs at PMTP can be fabricated using the same methods as those used for conventional LPGs, albeit with higher precision - the effective refractive indices of the optical fibre modes can be altered via photo-induction, or by physical deformation [7]. The refractive index can be altered using a number of different methods. Some of these include local exposure of the fibre to a UV laser [28, 32, 33, 34], CO2 laser [35, 36], femtosecond laser [23, 37] or by electrical arc discharge [30, 38]. PMTPs have been written in conventional single mode and doped fibres [12, 11, 33, 34, 36, 39], and have been theoretically investigated using photonic crystal fibres [23]. The length of an LPG tends to range from 30 to 50 mm and have refractive index changes of around 10–4 [40]. Coelho et al. [41] calculated a refractive index change in the order of 2 × 10<sup>−</sup><sup>4</sup> and 3 × 10<sup>−</sup><sup>4</sup> for the core and cladding, respectively when writing an LPG in a single mode fibre using mid-infrared laser radiation. The same order of magnitude of refractive index change (4.49 × 10<sup>−</sup><sup>4</sup> ) is also needed for femtosecond laser radiation [42].

A PMTP can also be tuned after an LPG has been fabricated, by tuning the mode coupling and effective index guiding via the means of tapering [12], UV exposure [43], with a thin film overlay [31, 28], etching [44] and radiation exposure [12].

### **Figure 5.**

*Transmission spectra of a PMTP LPG with a 34.8 μm cladding diameter and 288.5 μm period, showing a large wavelength shift with a surrounding refractive index change of 0.001. SRI is surrounding refractive index. Reprinted with permission from Ref. [49], OSA.*

The LPG can also been enhanced by reducing the cladding via hydrofluoric (HF) acid [13, 45–47] and plasma [48] etching to tailor the coupling strength of the cladding mode at PMTP. Using this method, Biswas et al. were able to increase the refractive index sensitivity of a hydrogen loaded PMTP LPG with a 165 μm period from 1350 to 1847 nm/RIU [45]. A refractive index sensitivity reported by Villar is 143 × 103 nm/RIU [49]. **Figure 5** shows the resonance band of the LPG splitting into two separate bands with a wavelength separation of approximately 200 nm, with a change of 0.001 RIU. This was theoretically obtained by reducing the diameter of a SMF28 single mode to 34.8 μm whilst operating at a period close to PMTP at 288.5 μm [49].

Plasma etching via ion bombardment and chemical reaction has been used to etch the fibre cladding of an LPG to bring the resonance closer to the turning point. This process assists in the precise post processing of nano-coated fibres in hard and chemically resistant films, for example, diamond-like carbon [50]. Radiation exposure has also been demonstrated to alter the refractive index of B-Ge co-doped fibres, with an equivalent increase in core refractive index of around 1 × 10–5 [12].

### **3.1 Fabrication considerations**

Due to the nature of the LPG, they can be highly sensitive to the surrounding environment. There are stringent demands placed on the fabrication process and the system used in order to fabricate LPGs at PMTP reproducibly. The notable constraints are given by ambient temperature (**Figure 6**), duty cycle [32], power of the irradiation source [35] and amplitude of the index modulation [51]. The difference in the final outcome of LPG spectra where the ambient temperature is not controlled and allowed to fluctuate, and maintained to ±0.5°C are shown in **Figure 6**(**a**) and (**b**), respectively.

A period change of less than 1 μm can also influence transmission spectrum significantly and high resolution control has to be taken into account when deciding on the grating period [32, 35]. UV exposure time may also play a part in the sensitivity of LPGs at turning point; the spectrum of a 168.7 μm period PMTP LPG written in

**123**

**4.1 Filters**

loaded fibre [33, 43].

**Figure 6.**

**4. Applications**

*Optical Fibre Long-Period Grating Sensors Operating at and around the Phase Matching…*

boron co-doped fibre had a greater variation with pressure when fabricated with a longer exposure time [34]. Other factors that can affect the grating include the size of the fibre. By changing the diameter of the cladding, but maintaining the same

*Transmission spectra of a 110.9 μm PMTP LPG. The temperature is (a) not controlled (5 spectra) and (b)* 

Hydrogen loading can induce or increase the photosensitivity in a fibre by increasing the effective refractive index difference between the core and cladding [52]. However, hydrogen will diffuse from the fibre gradually over time, causing the LPG spectrum to drift [52, 53]. Annealing a hydrogen loaded fibre at a temperature above the desired operating temperature can help overcome this problem [54]. This rapid removal of hydrogen will still cause the resonance wavelengths to shift, due to the changing effective indices, but will remain stable and permanent after the annealing process has been completed. This has to be taken into consideration when choosing a period to fabricate an LPG, at or around turning point, using a hydrogen

For an LPG to function at its optimum sensitivity when exposed to an external perturbation, its period should be chosen such that it is able to operate at a turning point. Optical LPGs operating at the turning point provide the potential for low cost sensors with fast response time [21, 55, 56] and can provide a simpler detection

LPGs operating at the PMTP have been used for temperature, strain, refractive index sensing [11, 35] and as filters. PMTP LPGs, when modified with a functional film can be adapted for potential uses as enhanced gas and chemical sensors [28].

By employing the broadband characteristics, PMTP LPGs can make successful bandpass and rejection filters [57, 58]. A coated PMTP LPG with a π phase shift is simulated to provide tuneable broadband characteristics for rejection filtering applications [58]. By introducing multiple π phase shifts, it is possible to adjust the separation between the dual resonant bands. On the other hand, by partially coating a phase shifted PMTP LPG, bandgaps appear over a narrow wavelength band which

method as some are able to work as intensity-based sensors [15, 17, 55].

could be useful for designing spectral filters [59].

period, the dual resonance bands will also change accordingly [44].

*controlled to ±0.5°C (4 spectra). Reprinted with permission from Ref. [32], OSA.*

*DOI: http://dx.doi.org/10.5772/intechopen.81179*

*Optical Fibre Long-Period Grating Sensors Operating at and around the Phase Matching… DOI: http://dx.doi.org/10.5772/intechopen.81179*

**Figure 6.**

*Applications of Optical Fibers for Sensing*

The LPG can also been enhanced by reducing the cladding via hydrofluoric (HF) acid [13, 45–47] and plasma [48] etching to tailor the coupling strength of the cladding mode at PMTP. Using this method, Biswas et al. were able to increase the refractive index sensitivity of a hydrogen loaded PMTP LPG with a 165 μm period from 1350 to 1847 nm/RIU [45]. A refractive index sensitivity reported by Villar is

*Transmission spectra of a PMTP LPG with a 34.8 μm cladding diameter and 288.5 μm period, showing a large wavelength shift with a surrounding refractive index change of 0.001. SRI is surrounding refractive index.* 

two separate bands with a wavelength separation of approximately 200 nm, with a change of 0.001 RIU. This was theoretically obtained by reducing the diameter of a SMF28 single mode to 34.8 μm whilst operating at a period close to PMTP at

Plasma etching via ion bombardment and chemical reaction has been used to etch the fibre cladding of an LPG to bring the resonance closer to the turning point. This process assists in the precise post processing of nano-coated fibres in hard and chemically resistant films, for example, diamond-like carbon [50]. Radiation exposure has also been demonstrated to alter the refractive index of B-Ge co-doped fibres, with an equivalent increase in core refractive index of around 1 × 10–5 [12].

Due to the nature of the LPG, they can be highly sensitive to the surrounding environment. There are stringent demands placed on the fabrication process and the system used in order to fabricate LPGs at PMTP reproducibly. The notable constraints are given by ambient temperature (**Figure 6**), duty cycle [32], power of the irradiation source [35] and amplitude of the index modulation [51]. The difference in the final outcome of LPG spectra where the ambient temperature is not controlled and allowed to fluctuate, and maintained to ±0.5°C are shown in **Figure 6**(**a**) and (**b**),

A period change of less than 1 μm can also influence transmission spectrum significantly and high resolution control has to be taken into account when deciding on the grating period [32, 35]. UV exposure time may also play a part in the sensitivity of LPGs at turning point; the spectrum of a 168.7 μm period PMTP LPG written in

nm/RIU [49]. **Figure 5** shows the resonance band of the LPG splitting into

**122**

respectively.

143 × 103

**Figure 5.**

288.5 μm [49].

**3.1 Fabrication considerations**

*Reprinted with permission from Ref. [49], OSA.*

*Transmission spectra of a 110.9 μm PMTP LPG. The temperature is (a) not controlled (5 spectra) and (b) controlled to ±0.5°C (4 spectra). Reprinted with permission from Ref. [32], OSA.*

boron co-doped fibre had a greater variation with pressure when fabricated with a longer exposure time [34]. Other factors that can affect the grating include the size of the fibre. By changing the diameter of the cladding, but maintaining the same period, the dual resonance bands will also change accordingly [44].

Hydrogen loading can induce or increase the photosensitivity in a fibre by increasing the effective refractive index difference between the core and cladding [52]. However, hydrogen will diffuse from the fibre gradually over time, causing the LPG spectrum to drift [52, 53]. Annealing a hydrogen loaded fibre at a temperature above the desired operating temperature can help overcome this problem [54]. This rapid removal of hydrogen will still cause the resonance wavelengths to shift, due to the changing effective indices, but will remain stable and permanent after the annealing process has been completed. This has to be taken into consideration when choosing a period to fabricate an LPG, at or around turning point, using a hydrogen loaded fibre [33, 43].
