Towards the design of a wideband reflective long period grating distributed sensor

In this paper, we computationally investigate the effects of metal coating length and coating coverage on the reflected spectrum of a long period grating (LPG) over a broad bandwidth. Simulation results indicate that coating the tail end of the fiber between the LPG and the end facet of the fiber provides a reflected spectrum that mimics the LPG transmission spectrum shape over a 400 nm bandwidth. Based on single LPG simulation results, we present the design of a distributed LPG structure containing a multiple number (n) of LPGs in reflection mode for the first time. Simulation results for n = 1, 2, and 3 are presented here to demonstrate the concept of a distributed reflective LPG design. It is expected that such a sensor will open a new window for distributed sensing using reflective LPGs.


Introduction
A long period grating (LPG) works on the principle of light coupling between the fundamental core mode and a number of co-propagating cladding modes [1][2][3]. Such coupling results in an LPG transmission spectrum with a number of discrete attenuation bands depending on the phase matching condition for a resonance wavelength l m ( ) given by [1]: where n eff co , is the effective refractive index of the guided core mode, n eff cl m , is the effective refractive index of the m-th order cladding mode and L is the grating period. It can be seen from equation (1) that the resonance wavelengths are dependent on the grating period and the effective refractive indices of the core and the cladding modes.
Since external parameters, such as temperature, pressure, or a secondary medium in close proximity with the cladding can directly influence the effective indices of the cladding modes, the resonance wavelengths also respond to these changes. Thus, LPG sensors have found several potential applications in monitoring temperature, strain, and refractive index [4][5][6][7][8]. However, an LPG is limited in applications in that it can only be used as a transmission sensor, compared to a fiber Bragg grating (FBG) sensor which is convenient as a reflection mode sensor. From a packaging viewpoint, it is preferable to use the same facet for coupling light into and out of the fiber to maximize their applications [9].
To overcome the abovementioned limitation of a conventional LPG design, several LPG designs have recently been reported in literature that can operate in the reflection mode [10][11][12][13][14]. For example, in [11], an LPG based on the Michelson interferometer was investigated to collect light reflected from the end facet of fiber at the input facet. However, interferometric fringes containing reflected spectrum made data interpretation cumbersome. Then in [12], a reflective LPG containing a polymer microtip at the end facet that reflects select cladding modes was proposed. Although this reflective LPG was able to measure the refractive indices of water/ glycerol solution, a complex fabrication process for polymer microtip using photo polymerization was utilized. In [14], a very compact reflective LPG that reflects light without interferometric fringes was reported. In this design, both the fiber end facet and the side of the fiber was coated with silver metal in order to obtain a reflected spectrum that mimicked the transmitted spectrum. The design and operation of the reflective LPG was limited to within a narrow bandwidth around one of the resonance wavelengths, thus limiting the understanding of the use of the sensor across a wide bandwidth, specifically for distributed sensing applications. Additionally, the reflective LPG design used a very short length of end coating which was not optimized to completely mimic the transmission spectrum shape.
In this work, we show that-(1) the coating length, defined as length of the metal coating from the end facet of the fiber, and (2) the coating coverage, defined as the ratio of metal coating length over the LPG to the total length of the LPG, have a significant impact on the reflected spectrum over a wide bandwidth. Using these results, we present an optimized design for reflective distributed LPG structure comprising of n number of LPGs with different periods in a single fiber that entirely mimics the transmission spectrum over a wide bandwidth for the first time.

Geometric structure of a distributed reflective LPG
A schematic diagram of the proposed distributed sensor design comprising of cascaded reflective LPGs is shown in figure 1. The grating period of the n-th LPG is denoted by L . n L c denotes the coating length, L gn is the length of n-th LPG, L end is the length of the tail end of the fiber measured from the end facet to the end of the n-th LPG, d i is the distance between two adjacent LPGs. In this design, we used gold as the metal coating the fiber. Please note that in all of the cases considered in this paper for reflective LPG, the fiber end facet is always coated with metal. We used commercially available FIMMWAVE Photon Design software, a fully-vectorial mode solver, to simulate the reflective LPG design. We considered the fiber parameters of commercially available SMF-28 fiber in our FIMMWAVE models and used the grating strength value of the proposed LPG of´-3 10 4 [15].

Simulation results and discussions
The simulation results and associated discussions are organized in the following way. First, in section 3.1, based on our recent work [16], we discuss the effects of design parameters on the spectrum of a single reflective LPG. Next, in section 3.2, we present the simulation results for a distributed reflective LPG design and present the optimized design of a distributed reflective LPG structure that completely mimics the transmission spectrum shape over a 400 nm wide bandwidth.

Single reflective LPG
The effect of coating length and coating coverage on the reflected spectrum of a single LPG is discussed thoroughly and then the same principle is used to demonstrate the distributed reflected LPGs.

Effects of grating length on the reflected spectrum of LPG
We first studied the effect of the grating length (number of grating periods, N) on the reflected spectrum. For our chosen design parameters ( m L = 390 m and grating strength of´-3 10 4 ), the core mode couples to LP 05 , LP 07 , LP 09 cladding modes. This results in three discrete resonances at 1382 nm, 1406 nm, and 1558 nm, respectively, as shown in figure 2. The higher the order of the coupled cladding mode, higher is the sensitivity of the corresponding resonance wavelength to external parameters since higher order cladding modes are in close proximity to the interface between cladding and surrounding medium.
We increased the value of N from 25 to 65 in steps of 10. It is known from the coupled mode theory that the coupling strength depends on the refractive index contrast and the local variation of mode fields over a specific fiber length [17]. This can be seen from the simulated reflected spectra in figures 2(b)-(f) for N=25-65, that with an increasing N, the resonance dips get narrower and deeper due to an increase in the coupling strength. However, the positions of the resonant dips remain unaltered. A reference transmission spectrum for N=45 is shown in figure 2(a), and it can be seen that the transmission and the reflected spectra for N=45 completely resemble each other in shape. Hence, for our studies throughout the paper, we choose a value of N=45. L 1450 , the reflected spectrum follows the transmission spectrum without any splitting. We hypothesize that the side coating effectively absorbs the coupled cladding modes beyond the critcal length of the coating while it propagates at the cladding/metal interface. Since the coupled cladding modes are absorbed by the metal coating, the LPG reflected spectrum does not show any interferometric fringes. However, a suitable coating length is highly required to absorb all the coupled cladding modes. It can be said that coating length less than L 1450 is not sufficient to absorb all the coupled cladding modes, especially for operating over a wide bandwidth. The threshold value of the coating length beyond which the transmitted and reflected spectra mimic substantially was determined by calculating the correlation coefficient between these two spectra. We determined the coating length by setting a threshold correlation factor of 99.5% over which the reflected spectrum follows the transmitted spectrum completely. Therefore, we choose a value of L c = L 1450 for our design.  4(d)), the reflected spectrum increasingly mimics the transmitted spectrum ( figure 4(a)), where at 100%, the reflected and transmitted spectrum are identical over a 400 nm bandwidth.
In all cases in figure 4, the reflected spectra show reduced intensity but increased resonance depth compared to transmission spectrum.  5 (b)). It can be seen that for 25% coverage (figure 5(c)), the shape of the dip centered around 1558 nm starts to change and continues for 50% coverage ( figure 5(d)) and completely   . This happens because the metal coated directly over the grating influences the cladding modes, which in turn alters the coupling condition. From the single reflective LPG simulations, we conclude that in order for the reflected spectrum to completely mimic the transmission spectrum shape over a large bandwidth, a coating length greater than 1450 L and a coating coverage of 0% are the optimal parameters.    1 the reflected spectrum mimics the transmitted spectrum completely. It can also be observed that dips for the higher order cladding modes are at   Figure 7 shows the effect of coating coverage on the LPG spectrum. It can be seen from figures 7(c)-(f) that similar to the single LPG case, coating coverage leads to splitting or disappearance of dips.

Distributed reflective LPG
We also considered the effect of coating the metal over the length of the fiber between the two LPGs.   shape of the reflected spectrum. For these cases of figures 8(d)-(e), disappearance, and shifting of the dips can be observed, and the reflected spectra do not mimic the transmitted spectrum for any configuration. Thus, it can be concluded that the reflected spectrum follows the transmitted spectrum only when the metal coating is over the coating length = L L c end 1450 L 1 and is absent elsewhere.

Effects of coating coverage and coating length for n=3
Simulation results from the single LPG and the dual cascaded LPGs indicate that = L L c e n d 1450 L 1 provides reflected spectrum that mimics the transmitted spectrum. Following this, a three cascaded reflection mode LPG It can be seen that the reflected spectrum completely mimics the transmitted spectrum when = L L c e n d =1450 L 1 and no metal is coated anywhere else. Thus, we have generated an optimized design solution for a distributed reflective LPG comprising of multiple LPGs. Since the designed triple cascaded LPGs consists of these three grating periods, it is expected that it will couple light at wavelengths of 1558 nm, 1500 nm and 1400 nm. It can be seen from figure 9 that dips for the higher order cladding modes are at wavelengths of 1558 nm, 1500 nm and 1400 nm as expected.

Conclusion
In conclusion, in this paper, the effects of metal coating parameters on the spectrum of reflective LPGs for n=1, 2, and 3 number of gratings in a single fiber have been presented. Coating metal over the grating or over any region between the LPGs either splits or leads to disappearance of some of the dips since it influences the cladding modes directly, and therefore, changes the coupling conditions. On the other hand, coating the tail end after the last LPG alone with metal provides a reflected spectrum that completely mimics the transmitted spectrum. The design methodology presented in this paper can be applied to a distributed sensor design comprising of n number of cascaded LPGs

Acknowledgments
This work was supported in part through the Department of Energy In-Pile Instrumentation program under DOE Idaho Operations Office Contract DE-AC07-05ID14517. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US Government or any agency thereof.