Sensing and Demodulation of Special Long-Period Fiber Gratings Induced by Scanning CO 2 Laser Pulses

A review of long-period fiber gratings (LPFGs) with special structures induced by scanning CO2 laser pulses in single mode fiber (SMF) is presented in this paper. In the first part, the special structures and fabrication methods of LPFGs are demonstrated in detail. Next, the special LPFG-based sensors are demonstrated, such as refractive index sensor, strain sensor with temperature compensation, and torsion sensor without temperature crosstalking. Finally, several investigation methods including intensity, wavelength shift, and fiber ring laser demodulation are discussed.

Compared with other techniques, employing scanning CO 2 laser pulses to fabricate LPFG is flexible and lowcost.This is because hydrogen loading and other additional process are not required and it is convenient to fabricate LPFGs with special refractive index modulation distribution [1,[3][4][5][6][7][51][52][53][54][55][56][57].It is important for LPFGs to enhance sensing sensitivity and overcome the crossinfluence among measured parameters, such as refractive index, strain, torsion, and temperature.That is why some special LPFGs are proposed in recent years.In this paper a review of CO 2 laser-induced special LPFGs is presented.The principle and fabrication of the special LPFGs including the LPFGs with rotary refractive index modulation, edge distributed refractive index modulation, or periodic grooves are presented in Section 2. The special LPFG-based sensors used for measuring the ambient refractive index, torsion, and strain are listed in Section 3. The investigation methods of the sensors are summarized in Section 4, such as wavelength shift method, intensity and fiber ring laser demodulation method.Conclusion is in Section 5.

Principle and Fabrication of CO 2
Laser-Induced LPFGs 2.1.Normal LPFGs. Figure 1(a) shows the schematic diagram of the setup for fabricating LPFGs using scanning CO 2 laser.The CO 2 laser beam that focuses on the fiber scans across the fiber transversely (X direction) and then advances along the fiber (Y direction) with a step equal to the grating period.The difference between point CO 2 laser method and scanning CO 2 method is the moving objects; that is, only the fiber is movable for the former while only the CO 2 laser beam is movable for the latter.One scanning cycle is completed when the number of grating periods is reached.And the scanning cycle could be repeated as many times as needed.The typical transmission spectrum of an LPFG with a period of 630 μm and grating length of 37.8 mm is shown in Figure 1(b).There is a loss peak in the spectrum since the fundamental core mode is coupled to the copropagating cladding modes which will leak out from the fiber.The wavelength at which the loss peak occurs is determined by the phase match condition β co − β cl = 2π/Λ, where β co and β cl are the propagation constants of the fundamental core mode and cladding mode, respectively, and Λ is the grating period [9].Thus the resonant wavelength of the LPFG could be given by λ res = (n co − n cl )Λ, where λ res is the resonant wavelength, n co and n cl are the effective indices of the fundamental core mode and cladding mode, respectively.It should be noted that the LPFGs fabricated by scanning CO 2 laser method have asymmetric structures [2], which are different from UV-induced LPFGs.Since the silica glass has strong absorption around the wavelength of the CO 2 laser, that is, 10.6 μm, the beam intensity is gradually attenuated along the incident direction, resulting in asymmetric refractive index modulation within the cross section of the fiber.

LPFGs with Special Structures
2.2.1.Edge-Written LPFG.The refractive index modulation distributes both in the core and cladding in the CO 2 laserinduced normal LPFGs.To make sure that the refractive index disturbance occurs only in the cladding region, a kind of edge-written LPFG (E-LPFG) is fabricated by properly controlling the exposure energy and pulse time of the CO 2 laser using the setup shown in Figure 1(a) [1].The refractive index distribution of the cross section of the E-LPFG is shown in Figure 2(a).The micrograph of the E-LPFG is shown in Figure 2(b), with the written depth of the LPFG ∼35 μm.
To verify that the refractive index modulation occurs only in outer cladding of the fiber, the diameter of a fiber is etched by ∼104 μm, which means that the diameter of the fiber is ∼21 μm.The partial micrographs of the original E-LPFG and the etched E-LPFG are shown in Figure 3(a).The transmission spectra are shown in Figure 3(b), indicating that no grating existed when the diameter of the fiber is ∼21 μm; that is, no refractive index modulation occurs in the fiber core.

Edge-Written LPFG with Periodic Grooves.
Based on the method mentioned in Section 2.2.1, an edge-written LPFG with periodic grooves could be fabricated by increasing the laser energy [3].The photograph of the grating structure is shown in Figure 4(a).The transmission spectrum evolution of the LPFG with a grating pitch of 400 μm is shown in Figure 4(b).By increasing the laser energy and enlarging the grating period of the E-LPFG, an ultra-long-period fiber grating with periodic grooves (G-ULPFG) distributed in outer cladding region of the fiber could be fabricated.The micrograph of a G-ULPFG with groove depth of ∼30 μm and grating period of 2 mm is shown in Figure 5(a).
The transmission spectrum of the G-ULPFG is shown in Figure 5(b), indicating that the fundamental core mode couples with the cladding mode LP μk of the Nth diffraction order [4].That means every resonant peak of G-ULPFG has independent sensing sensitivity, which provides one way to realize multiparameters sensing by using one single sensor.

LPFG with Rotary Refractive Index Modulation.
To fabricate an LPFG with rotary refractive index modulation (R-LPFG), two ends of the fiber are fixed at two holders separated by a distance L, and the fiber is twisted by rotating a disc attached to one of the holders by N circles, as shown in Figure 6.A normal twisted LPFG is fabricated in the fiber with a twist period Λ T = L/N.Such an LPFG is referred to as T-LPFG [5].The twist is removed by rotating the disc in opposite direction or releasing the fiber from the holders directly.Hence, there is a rotary refractive index modulation distribution along the fiber and it is referred to as R-LPFG.Unlike the LPFG with a screw-type index modulation, the rotary refractive index modulation of R-LPFG is discrete [52].
A comparison of the transmission spectra of several R-LPFGs and the corresponding T-LPFGs is shown in Figure 7.The gratings have a period of Λ G = 0.57 mm and a length of L G = 28.5 mm (50 periods).When the twist period is larger than ∼60 mm, 2 or 3 scanning cycles are needed to generate a strong T-LPFG.When the twist period is smaller than ∼60 mm, however, only one scanning cycle is sufficient.As shown in Figure 7, the transmission spectrum of the T-LPFG consists of two rejection bands (at ∼1430 and ∼1550 nm) within the wavelength range of the broadband source, which correspond, respectively, to the couplings to two different orders of the cladding modes.The rejection bands of the T-LPFG are insensitive to the twist rate.On the other hand, the transmission spectrum of the R-LPFG is highly sensitive to the twist rate.At a low twist rate (Λ T = 100 mm), the spectrum of the R-LPFG is similar to that of the corresponding T-LPFG, which is expected.At a high twist  rate (Λ T = 37.5 and 30 mm), each of the rejection bands is split into two completely.At a medium twist rate (Λ T = 75, 60, and 50 mm), the split rejection bands overlap.It can be seen that the amount of wavelength splitting increases with the twist rate.The results show that untwisting a T-LPFG produces an R-LPFG whose characteristics depend strongly on the amount of applied twist in the writing of the T-LPFG.

LPFG with Rotary Grooves.
According to the same procedure of R-LPFG fabrication, an LPFG with periodic grooves (G-R-LPFG) rotating along the fiber could be fabricated if the laser power is high enough to carve grooves on the cladding of the fiber [6].The structure of a grating with N rotary grooves over a length of L g = NΛ is shown in Figure 8.The fiber used is a conventional single-mode fiber (Corning, SMF-28).The grating period and the period number are 500 μm and 60, respectively.Figure 9(a) shows the growth of the resonance peak of the T-LPFG during the writing of the grating, where the twist rate used is η = 6 • /mm.The resonance peak shifts towards shorter wavelength as the number of the scanning cycles increases, similar to the case of writing a normal LPFG with highfrequency CO 2 -laser pulses.Figure 9(b) shows the evolution of the G-R-LPFG.After the fiber is untwisted, two original resonance peaks of T-LPFG split into two smaller ones, respectively, and the coupling coefficients are different.For example, the peak at 1569.4 nm splits into two smaller ones at 1557.8 nm and 1593.7 nm, respectively.The amplitudes of the two split peaks are −4.92dB and −8.13 dB.However, the peak at 1403.5 nm splits into two very weak ones.In the experiments, the peak splitting phenomena of the G-R-LPFG were not observed when twist rate η is less than 3.6 • /mm or so.It is a pity that the exact physical mechanism responsible for the observed phenomena is yet to be fully understood.

Sensing Applications of Special LPFGs
3.1.Refractometer.The transmission spectra of the E-LPFGs with different writing depths but same length are shown in Figure 10.It can be seen that the writing efficiency of the E-LPFG with writing depth of ∼35 μm is higher than that of ∼15 μm since complete coupling between the core mode and higher order cladding modes needs a larger refractive index modulation.
To measure the ambient refractive index within the range of 1.33 ∼1. 45at room temperature, the E-LPFG with a writing depth of ∼15 μm and grating period of 500 μm is used.Compared with the conventional LPFG, the E-LPFG has much higher refractive index sensitivity, especially in higher refractive index range, as shown in Figure 11.The resonant wavelength shifts nonlinearly with respect to the refractive index and the wavelength of the E-LPFG shifts ∼24.2 nm for an index range from 1.33 μm to 1.45 μm.
It should be noted that the temperature change will influence the refractive index measurement of E-LPFG.However, the cross effect could be decreased by employing G-ULPFG because there are several resonant peaks with different temperature and refractive index sensitivities due to the different coupling orders.
The refractive index responses of the resonant peaks N1 LP 03 and N2 LP 01 at room temperature are shown in such a G-ULPFG could be used as a refractive index sensor with temperature self-compensation.The principle is that the resonant peak with higher differential order is used to measure refractive index while the resonant peak with a low differential order is used to measure temperature.Also the error of refractive index measurement based on its temperature characteristics should be compensated.

Torsion
Sensor with Temperature Self-Compensation.It has been found that LPFGs fabricated by different methods demonstrate different torsion response.LPFGs induced by UV laser or mechanical pressure cannot be used to sense applied torsion while the LPFGs fabricated by electric-arc discharging, etching or CO 2 laser irradiation can be used to measure the torsion rate and direction simultaneously [36,52,[58][59][60][61].However, the LPFGs induced by CO 2 laser in SMF are also sensitive to temperature change, resulting in errors for torsion measurement [2].To eliminate the cross effect of temperature change, an R-LPFG could be used as a torsion sensor.An LPFG with a period of 570 μm and a length of 28.5 mm is fabricated in a twisted SMF with twist period of 30 mm and then released gradually.The transmission spectra of the T-LPFG and R-LPFG are shown in Figure 14, demonstrating the wavelength splitting phenomena.The wavelength separation between every two regenerated resonant peaks changes with the applied torsion, as shown in Figures 15(a) and 15(b), enabling it to be useful for torsion measurement.
The temperature experiment of a 50-period R-LPFG with grating period of 570 μm and twist period of 50 mm is shown in Figure 16.It can be seen that the temperature sensitivities of two split wavelengths are the same with a value of ∼0.07 nm/ • C and the changes in the amplitudes of two resonant peaks with temperature are small.Hence, the applied torsion could be measured without temperature cross effect by tracing the wavelength separation.

Strain Sensor.
The LPFG formed by carving periodic grooves with CO 2 laser has a strain sensitivity of 0.12 nm/με in the range from 0 to 100 με but suffers from temperature interference [3].Although R-LPFGs could be used as strain sensors with temperature self compensation [62], the strain sensitivity of the R-LPFG is only ∼0.0053 nm/με.Like R-LPFGs, wavelength splitting also occurs in G-R-LPFGs when the applied torsion is released, as shown in Figure 17.Moreover the experimental results show that the temperature sensitivities of λ 1 and λ 2 separated by 33.6 nm are 0.072 nm/ • C and 0.0726 nm/ • C, respectively, indicating that it is insensitive to temperature vibration.
The strain responses of λ 1 and λ 2 are shown in Figures 18(a) and 18(b), respectively.Within 700 με the strain sensitivities of λ 1 and λ 2 are −0.05237nm/με and +0.053 nm/με, respectively.The separation between the two wavelengths as a function of strain is shown in Figure 18(c), demonstrating that the strain sensitivity of the G-R-LPFG is 0.1067 nm/με when the strain is less than 700 με.The sensitivity of the G-R-LPFG is much higher than that of R-LPFG (∼20 times).

Demodulation of LPFGs
4.1.Wavelength Shift.Most of the LPFG-based sensors are demodulated by wavelength shift since it is easy to trace the shift with the help of optical spectrum analyzer (OSA).However the OSA is generally very expensive and bulky, increasing the cost and decreasing the flexibility of the measurement system.Moreover, the bandwidth of the LPFG is much broader than that of the FBG, implying that it requires higher resolution OSA to minimize the measurement error.Another inconvenience for demodulating the LPFGs is that the light source and demodulation terminals are separated since LPFGs work in the transmission mode.To overcome the difficulties, the transmission spectrum of the LPFG is inverted by putting a mirror in the cladding region of a fiber end-face to reflect only the cladding modes [63].The end face mirror can be realized through four steps: (a) to fabricate an LPFG, (b) to make a polymetric microtip using photopolymer, (c) to coat the fiber end face with sputtering deposition, (d) to break the microtip under CCD camera.The typical grating structure is shown in Figure 19.However, the inherent broad bandwidth of the LPFG limits the precision of measurements when the measurement is realized by means of wavelength shift.

Intensity Demodulation.
For some LPFGs, the amplitudes of resonant peaks change with the strain, ambient refractive index or other perturbations, leading to that the LPFGs can be demodulated by monitoring the intensity vibrations of resonant peaks.One solution to intensity demodulation proposed by Wang et al. is shown in Figure 19 [7].The light from the broadband light source LED with symmetric spectrum near the resonant wavelength λ 0 of the LPFG is equally divided into two parts by a 3 dB coupler (C 0 ) and then illuminates FBG 1 and FBG 2 with Bragg wavelengths of λ 1 and λ 2 , respectively.λ 1 and λ 2 should be specially selected to satisfy the relation λ 1 + λ 2 ≈ 2λ 0 .The light reflected by FBG 1 and FBG 2 is directed to an LPFG and received by PD 1 and PD 2 , respectively.By subtracting the intensities I 1 and I 2 detected by PD 1 and PD 2 , the intensity fluctuations at λ 1 and λ 2 could be eliminated and  Figure 15: (a) Transmission spectra of R-LPFG with grating period of 570 μm and twist period of 46 mm under different torsion, where "+" and "−" mean that the direction of the applied torsion is the same or opposite to that of the original twist applied to the fiber, respectively.(b) Wavelength separation of resonant peaks with respect to applied torsion [5]. the temperature sensitivity could also be doubled by this method.
Another solution to intensity demodulation is to detect the intensity at a certain wavelength that is slightly larger than the resonant wavelength [64].Therefore only a monochromatic source is needed to illuminate the LPFG and the variation in core power could be measured by a power meter, reducing the cost but increasing the robustness of the system.It is also convenient to realize real-time measurement with this method.However, it has the problem of limiting the measurement range of the LPFG since the transmission spectrum of LPFG is symmetric with respect to the resonant wavelength.

Fiber Ring Laser Investigation.
The interferometric sensor based on Mach-Zehnder interferometers (MZIs) with two cascaded R-LPFGs could also be used as a multichannel bandpass filter, as shown in Figure 20(a).When the MZI is incorporated into a standard fiber ring cavity, the wavelength with the highest intensity in the transmission spectrum of the MZI will be chosen as the lasing wavelength of the fiber ring laser [8].And the lasing wavelength shifts with the torsions applied to the MZI.For example, the emitting wavelength of the fiber ring laser shifts ∼16 nm in the torsion range of ±100 rad/m, as shown in Figure 20(b) [8].Also, the method could be used to measure refractive index, temperature, and strain.
Compared with the passive LPFG-based sensors, the sensors demodulated by using fiber ring laser can realize more precise measurement since the fiber laser has narrower linewidth and higher side-mode suppression ratio (∼40 dB).It can be found from Figure 20(b) that the laser spectra are similar to that of the FBGs, which means that all the demodulation methods applicable to FBGs can be used to demodulate the LPFG-based interferometric sensors.separated by long distance since LPFG works in the transmission mode.To overcome this difficulty, the transmission spectrum of the LPFG is inverted by making a mirror on the cladding region of a fiber end face to reflect the cladding modes.The reflected cladding modes are coupled back to the core by the same LPFG, resulting in pass bands centered at the resonant wavelengths of the LPFG.However, the inherent broad bandwidth of the LPFG limits the precision of measurements when the measurement is realized by means of wavelength shift.Recently, a remote sensing system based on LPFG and fiber ring laser is presented [65].The stopband in the transmission spectrum of the LPFG is inverted into a pass-band by fusion splicing a piece of HCF to the grating.Then such an inverted LPFG is employed in the master and slave ring laser, in which the grating is used as the wavelength selector and sensor head simultaneously.The temperature experiment shows that such a system can measure the temperature more than 1 km away and the sensitivity is ∼0.02 nm/ • C within the range of 20-150 • C. The remote sensing schematic diagram is shown in Figure 21 [65].The LPFG with band pass characteristics working in the reflective mode is used as sensor and band pass filter simultaneously, which is shown schematically in Figure 22(a).The input light is coupled to the cladding by the into the LPFG, respectively.The central wavelength of the bandpass signal that determines the lasing wavelength of the fiber ring laser is also sensitive to the change in the state of polarization (SOP).The measurement error could be improved if the good symmetric LPFGs were fabricated by multiedge exposure of CO 2 laser, or by rotating the fiber during the exposure process.Besides, the resolution limit of the OSA also contributes to the error.

Conclusion
The paper presents a review of special LPFGs fabricated by scanning CO 2 laser, including edge-written LPFGs, LPFGs/ULPFGs with periodic grooves, LPFGs fabricated in twisted fibers, and LPFG with rotary grooves.As for the refractive index sensor, torsion sensor, or strain sensor, the sensitivities of the special LPFGs are higher than that of the normal LPFGs induced by CO 2 laser.More importantly, some of the special LPFGs could realize temperature selfcompensation, avoiding the cross effect between temperature and other measurands.Compared with the wavelength shift and intensity demodulation methods, fiber ring laser investigation method is more competitive since broadband source and OSA are not required and the methods for FBG demodulation can also be used.The special LPFGs could be widely used in optical sensing fields due to its high sensitivity, temperature self-compensation, and easy demodulation.

Figure 1 :Figure 2 :
Figure 1: (a) Schematic diagram of the setup for fabricating the LPFGs using CO 2 laser [1].(b) Transmission spectrum of the LPFG with grating period of 630 μm and grating length of 37.8 mm [2].

Figure 8 :Figure 9 :Figure 10 :Figure 11 :
Figure 8: Structure of a grating with N rotary grooves over a length of L g = NΛ [6]: (a) refractive modulation along the fiber axis, (b) refractive index distribution across the fiber cross section.