1. Introduction

Optical fiber sensors have attracted a high level of research interest due to its excellent intrinsic properties including compact and lightweight size, immunity to electromagnetic interference, capability of application in harsh environments and multiplexing measurements [1]. One of the most effective and promising sensing schemes is to tune the electromagnetic resonances by integrating thin films on optical fibers [2,3]. Depending on the optical properties of nanocoatings, two electromagnetic resonances can be distinguished, including surface plasmon resonance (SPR) [2] and lossy mode resonance (LMR) [3].

The SPR is the most well-known phenomena for sensing purposes in thin film coated optical fibers [4–6]. The SPR can be excited by p-polarized light in noble metal materials like gold and silver that have small real part of refractive index but with a high imaginary component. Among the configurations for the generation of SPR, the tilted fiber Bragg grating (TFBG) presents promising performance in terms of figure-of-merit, Q-factor, and limit-of-detection [7,8].

The LMR can be generated when the nanocoating has a high real part of refractive index but with a small imaginary component [9,10]. The lossy modes correspond to these modes that are guided in the high index nanocoating. As compared with the SPR, the LMR presents a much higher sensitivity [11]. In addition, the LMR can be generated by both p- and s-polarized lights and multiple LMRs in the same spectrum window become possible [12].

It should be noted that the modes involved in the electromagnetic resonances including the SPR and LMR are these modes that present higher real part of effective refractive index (ERI) than surrounding refractive index (SRI) of external environment [2,3]. The leaky modes that have smaller real part of ERI than the SRI are widely ignored for the generation of resonances in optical fibers. Recently a new kind of resonance, i.e., enhanced leaky mode resonance (eLMR) has been reported in TFBG coated with few-layer graphene [13–15]. It is shown that the eLMR presents several advantages for sensing over the SPR approach in terms of sensitivity, bandwidth, and Q-factor [15], making it interesting and promising in the field of fiber-optic sensors. One of the fundamental issues on the excitation of the eLMR by graphene is the fabrication process, that is, it is difficult to coat desirable few-layer graphene on the optical fiber that has a cylindrical surface.

In this work we propose and investigate theoretically dense comb-like eLMR excited by metallic oxide film coated on TFBG, which has not been reported before this study. Here indium tin oxide (ITO) that is a typical metallic oxide material is considered as the supporting layer. The ITO nanocoating induces a sharper reduction in the imaginary component of ERI of s-polarized leaky modes than that of p-polarized counterpart. Consequently, strong dense comb-like eLMR bands are generated in s-polarized transmission spectrum. Furthermore, the sensing performance of the eLMR is explored. Benefiting from the dense comb-like eLMR in a wide window, an extended detection range is attained from low to high SRI environment with an improved sensing performance, as compared with the bare TFBG. Finally, similarities and differences between the eLMR and other resonances including LMR and SPR are discussed.

2. Theory and sensing principle

2.1 Sensor design

Figure 1 depicts schematically the ITO thin film coated TFBG sensor for which the model consists of four layers including fiber core where the tilted grating is inscribed, fiber cladding, ITO nanocoating, and external environment. A standard commercial Corning SMF-28e+ single mode fiber is considered, with typical parameters: core radius $4.1 \mu m$ and cladding radius $62.5 \mu m$.

 

Fig. 1. Schematic diagram of ITO nanocoating integrated TFBG.

Download Full Size | PDF

The TFBG is assumed to be inscribed through ultraviolet laser irradiation that is a mature technique and hence it is a weakly modulated tilted grating. In this sense, the amplitude of refractive index perturbation $\delta n$ is estimated to be $6.0 \times 10 ^{-4}$. The axial grating period $\Lambda$ is $600 nm$ and grating length $L$ is $20 mm$. The tilted angle $\theta$ with respect to fiber axis is $13 ^{\circ }$, an angle that is slightly larger than that of conventional TFBGs generally having $\theta\;<\;10 ^{\circ }$. The main reason is that the leaky modes correspond to higher order modes having real part of ERI lower than the SRI and therefore a highly tilted grating should be inscribed to excite them effectively [6,14,16].

The ITO thin film with thickness $d$ that is functionalized as the sensing layer is deposited on the surface of fiber cladding. This can be done through several techniques like sol–gel dip-coating [9] and DC sputter process [17,18]. Note that the properties of the metallic oxide nanocoatings deposited by different techniques may differ from each other in a great manner. For the sake of simplicity, the ITO film in this study is assumed to be deposited on TFBG by the DC sputter process, the same method as reported in Ref. [17,18].

The input light polarized in p- or s- states (marked as P or S in Fig. 1) is launched into the fiber core to excite the p- or s-polarized core guided mode that couples with the cladding guided modes, leaky modes, and even the lossy modes in the tilted grating region. The output light is then collected at the other end of the fiber core to generate the resonances including the cladding mode resonance and eLMR in the transmission spectrum. The LMR may also exist if the generation condition is satisfied [3].

The leaky modes are essentially highly lossy in bare optical fibers, due to the large imaginary part of ERI, and hence they cannot propagate through the waveguide. However, they could become ‘guided’, similarly as a surface wave, only when the imaginary part of ERI is reduced [13,14,19]. In this sense, the core guided mode will interact with the ‘guided’ leaky modes within its propagation length to generate the eLMR. This is verified in Section 4.

2.2 Dispersion of materials

The wavelength dependent refractive index $n_{\textrm {cl}}$ of the fiber cladding made of fused silica is estimated using the Sellmeier equation given by [20]:

The optical constants of ITO nanocoating are obtained from the experimental data reported in Ref. [17], though the Drude model has been widely used [9]. By this approach, the results obtained in this work will agree well with the experiments. The external environment corresponds to the analytes with the SRI. When the sensor operates in air, the initial SRI is estimated to be 1.0, while it is 1.315 and could change as the environment becomes liquid solutions.

2.3 Coupled mode theory

There are various models and theories for the analysis of the mode coupling behavior in optical fiber gratings. Here the transmission spectrum of the ITO film integrated TFBG is calculated using the powerful full-vector complex coupled mode theory and the fiber modes are solved using an improved finite-difference complex mode solver combined with a more effective discretization scheme [21–23]. The TFBG with nanocoating is enclosed by a perfectly matched layer combined with a perfectly reflecting boundary to form a closed waveguide model. Following the principle proposed in Ref. [21], we set the key parameters of the perfectly matched layer as thickness of 10$\mu m$ and reflection coefficient of $10^{-12}$ to obtain convergent result including the effective refractive index and field pattern of fiber modes. The whole closed structure is discretized along the radial axis with the grid sizes of $10nm$, $20nm$, $0.1nm$, and $10nm$ in the fiber core, cladding, nanocoating, and external environment, respectively [23]. For the sake of simplicity, the exact formulas that have been detailed in Ref. [21] are omitted in this study. Following the methodology, the transmission spectrum can be also simplified as [24]:

3. Evolution of mode characteristics

3.1 Variation of effective refractive index

The notation used for the fiber modes is defined as: HE$^{co}_{1,1}$ for the core guided mode, HE/EH$_{v,m}$ with $v,m = 1,2,3\cdots$ for the $vm$th HE/EH mode, and TE/TM$_{0,m}$ for the $m$th TE/TM mode. When $v,m = 1$ it represents the first mode in each mode group. The leaky modes have a much larger $m$ that means higher order modes. In this section, for the HE/EH mode group, only these modes that have $v = 1$ are considered since the HE/EH modes present similar characteristics with each other. However, following the methodology in Ref. [21], the fiber modes having $v = 0 \sim 20$ and 10 modes closely satisfying the phase matching condition (PMC) for each $v$ are taken into account to obtain convergent transmission spectrum. In addition, the polarization state of a fiber mode can be easily determined according to the power factor [25,26]. In this sense, the TE/HE modes are the s-polarized modes while the TM/EH modes correspond to the p-polarized counterpart.

The evolution of the ERI as a function of the ITO thickness is depicted in Fig. 2 at $\lambda = 1.65 \mu m$ at SRI = 1.315. The imaginary component of ERI is plotted in absolute value. For the sake of simplicity, we mainly focus on the analysis of mode characteristics of the HE/EH modes, but the main conclusion is also applicable for the TE/TM modes.

 

Fig. 2. Evolution of ERI: (a) and (c) real part, (b) and (d) imaginary part. In all cases, solid lines represent the TE/HE modes and dash dotted lines correspond to the TM/EH modes. The SRI is considered to be 1.315 and the numbers represent the value of $m$.

Download Full Size | PDF

As shown in Figs. 2(a) and (c), two kinds of leaky modes exist [14]. One is the guided-like leaky modes that have the curve varying very similarly with the case of cladding guided modes, i.e., the real component of ERI increases with the ITO thickness. The other corresponds to the radiation-like leaky modes that present a stable ERI. Here for the HE/EH mode group, the HE/EH$_{1,45}$ modes correspond to the first two leaky modes that can be clearly identified by the ERI as compared with the SRI. It is important to remark that these two modes are the radiation-like leaky modes in bare TFBG as well as in the TFBG coated with thin ITO film having $d\;<\;\sim 30 nm$, but they then become the guided-like leaky modes as the ITO thickness increases continuously. In the meanwhile, the adjacent higher order modes are the guided-like leaky modes at first and then become the radiation-like counterpart. This mode transition is obviously indicated by the curve variation showing a stable state at $d\;<\;\sim 30 nm$ and a subsequent increase process for the HE/EH$_{1,45}$ modes. The opposite variation is observed for the adjacent HE/EH$_{1,46}$ modes. Therefore, when it comes to the discussion on the leaky modes below, the first guided-like leaky mode is the HE/EH$_{1,46}$ mode at $d\;<\;\sim 30 nm$ and the HE/EH$_{1,45}$ mode for a larger ITO thickness. Other leaky modes are characterized by a more clear variation, that is, the guided-like components behave very similarly with the case of cladding guided modes while the radiation-like counterparts always keep steady.

Here it is also remarkable to highlight that the leaky modes and lossy modes are completely different fiber modes though both of them are highly lossy (indicated by a very large imaginary part of ERI). The leaky modes correspond to higher order modes that have the ERI (real part) smaller than the SRI, whereas the lossy modes present a higher ERI (real part) than that of the core guided mode [3].

Another very important property associated with the leaky modes is that lower order leaky modes could become ‘guided’ as the ITO thickness increases. This is clearly demonstrated in Fig. 2(a) where it is shown that the real part of ERI of the HE/EH$_{1,45}$ leaky modes becomes larger than the SRI when $d\;>\;\sim 70/100 nm$, respectively. This is interesting since it seems that the leaky modes are transited to become the cladding guided modes in the ITO coated TFBG. However, these transited cladding guided modes still present higher loss than that of actual cladding guided modes. This is further verified according to the evolution of imaginary part of ERI, as shown in Figs. 2(b) and (d). A more clear comparison at specific ITO thickness is depicted in Fig. 3 where the highly lossy radiation-like leaky modes are ignored.

 

Fig. 3. Variation of ERI: (a) TE/TM modes and (b) HE/EH modes.

Download Full Size | PDF

Interestingly but importantly, the leaky modes present a large reduction in the imaginary component of ERI as the ITO thickness increases, unlike the situation of cladding guided modes in which the imaginary ERI increases due to the mode transition [27]. It is worth emphasizing that a larger imaginary part of ERI leads to a higher loss. In this sense, the ITO nanocoating greatly decreases the mode loss of leaky modes that are essentially highly lossy in bare optical fibers, which in turn gives rise to that these leaky modes will surely propagate a much longer distance in ITO film coated TFBG as compared with the bare counterpart. This is demonstrated in Fig. 4 that will be discussed below. Another impressive property drawn from Figs. 2(b) and (d) and Fig. 3 is that the HE/TE leaky modes that are s-polarized modes show a larger reduction in the imaginary part of ERI than that of the EH/TM counterparts corresponding to p-polarized modes. This indicates that the p-polarized modes are still highly lossy after integrating the ITO nanocoating. The same goes for the p-/s-polarized radiation-like leaky modes that are ignored in Fig. 3 and Fig. 4. Furthermore, a more close observation shows that the loss of the HE/TE leaky modes is still higher than that of the cladding guided modes though it is greatly reduced by the ITO film. This indicates that the leaky modes having reduced imaginary component of ERI are not those actual cladding guided modes with very small loss though they are transited to have a larger ERI (real part) than the SRI in ITO nanocoating integrated TFBG. However, these leaky modes surely have an increased propagation length.

 

Fig. 4. Evolution of propagation length: (a) TE/TM modes and (b) HE/EH modes. The numbers represent the value of $m$.

Download Full Size | PDF

The propagation length calculated in Fig. 4 is defined as:

3.2 Variation of mode field profile

The intensity $I_{m}$ is considered to illustrate the variation of mode field profile, which is given by:

 

Fig. 5. Evolution of mode field of HE/EH modes: (top) bare case, (middle) $d = 100 nm$, and (bottom) $d = 200 nm$. The insets display the field profile around the fiber core.

Download Full Size | PDF

 

Fig. 6. Evolution of mode field of TE/TM modes: (top) bare case, (middle) $d = 100 nm$, and (bottom) $d = 200 nm$. The insets display the field profile around the fiber core.

Download Full Size | PDF

One of the most impressive property drawn from these two figures is that the ITO nanocoating leads to the intensity equilibrium between s- and p-polarized modes. As for the cladding guided mode in Fig. 5, the intensity variation of the HE/EH modes presents an opposite trend indicated by the increase of $I_{m,\textrm {HE}}$ and decrease of $I_{m,\textrm {EH}}$ when the ITO thickness increases. But the variation ends up with a very similar intensity profile at thickness of $200 nm$.

The guided-like leaky modes have a very similar mode field with the cladding guided modes, showing almost the same intensity and profile. This is because we select the first leaky mode that is closest to the last cladding guided mode. For higher order leaky modes, there is a large field content outside the fiber cladding [14]. During the increase of ITO thickness, the $I_{m,\textrm {HE}}$ increases slightly while a much larger change is observed for the $I_{m,\textrm {EH}}$. As a result, the HE/EH guided-like leaky modes are tuned to have a very similar intensity profile, i.e., being in equilibrium. The same is true for the radiation-like leaky modes as well as the TE/TM modes shown in Fig. 6. The field equilibrium between s- and p-polarized modes seems to lead to the same or very similar interaction with the core guided mode, i.e., giving rise to a approximate equivalent resonance spectrum. However, it is important to emphasize that the coupling strength is determined by two factors (highlighted by Eq. (2)): coupling coefficient and propagation length. Since the p-polarized leaky modes propagate a much shorter length due to its higher loss (see Fig. 4), great difference in the resonance amplitude is expected between s- and p-polarized spectra. More specifically, the s-polarized resonance will be much stronger than the p-polarized counterpart.

3.3 Reflection of fiber modes

Figure 7 displays the optical ray picture in bare and ITO coated TFBGs. The reflection at the inner interface of the fiber cladding is calculated based on the multilayer Fresnel reflection theory [15], as shown in the inset in Fig. 7(f). As for the bare TFBG (see Figs. 7(a) and (b)), the total internal reflection appears at $\theta\;>\;65 ^{\circ }$, an angle that actually corresponds to the critical angle, while the reflectivity decreases to near 0 when $\theta$ becomes smaller than $65 ^{\circ }$. This clearly indicates that the light having $\theta\;>\;65 ^{\circ }$ corresponds to the cladding guided modes that can propagate in the fiber cladding while the leaky modes occur at $\theta\;<\;65 ^{\circ }$ and they always radiate out of the fiber cladding into the external environment. Higher reflectivity will enhance the mode coupling and hence a stronger resonance can be attained. In this sense, the cladding mode resonance is much stronger than the leaky mode resonance in bare TFBG. The ITO nanocoating induces an obvious polarization-dependent variation of the light behavior (see Figs. 7(c) and (d)). A specific illustration at $1.65 \mu m$ is depicted in Figs. 7(e) and (f). It can be seen that the reflectivity of p-/s-polarized cladding guided modes firstly decreases with the ITO thickness and then increases again to a value that is a little smaller than 1. The reflectivity reaches its minimum at higher incident angle (near $90 ^{\circ }$) where the lower order modes that are actually ghost modes exist [8,24]. Since the ghost mode resonance is always very weak (at $\lambda\;>\;1.7 \mu m$ in Fig. 8 below), the ITO induces a very small variation of the ghost mode resonance. Furthermore, the reflectivity of s-polarized leaky modes becomes much higher than that of p-polarized counterparts. The increased reflection leads to a stronger interaction with the core guided mode since the s-polarized leaky modes can propagate over much longer distance. Consequently, a stronger s-polarized leaky mode resonance than the p-polarized counterpart will be obtained.

 

Fig. 7. Reflection at internal interface of fiber cladding of (a) and (b) bare TFBG and (c) and (d) 150nm-ITO coated TFBG. Evolution of p- and s-polarized reflection with ITO thickness at $1.65\mu m$ is depicted in (e) and (f) respectively. The inset in (f) shows the reflection model in which $\theta$ represents the incident angle of light.

Download Full Size | PDF

 

Fig. 8. Transmission spectra at different ITO thicknesses.

Download Full Size | PDF

4. Sensing performance of eLMR

4.1 Excitation of dense comb-like eLMR

The spectrum evolution with the ITO thickness is displayed in Fig. 8, which agrees well with the wave picture shown in Fig. 2–Fig. 6 and optical ray picture depicted in Fig. 7. A dense comb-like cladding mode resonance is visible for all polarizations in bare TFBG at SRI = 1.0. When the bare TFBG is immersed into watery environment with SRI = 1.315, more than half of the cladding guided modes (corresponding to higher order modes) are cut off and become the leaky modes, resulting in extremely weak leaky mode resonance for both p- and s-polarizations at shorter wavelength.

The integration of ITO nanocoating induces a large difference in the leaky mode resonance of these two polarizations. As can be observed, a great number of s-polarized leaky mode resonances are greatly enhanced by simply increasing the film thickness, leading to strong dense comb-like eLMR at $d \geqslant 100 nm$. In contrast, a very small change is visible for the p-polarized counterpart as well as the p-/s-polarized cladding mode resonances. The variation of the transmission spectrum induced by the ITO nanocoating is in well agreement with the change of the mode characteristics and confirms the predictions as analyzed above.

It is remarkable to note that the eLMR excited by the ITO nanocoating (representing metallic oxides materials) is similar to the eLMR generated by the few-layer graphene (corresponding to two-dimensional materials) in some respect, that is, only the s-polarized eLMR can be effectively excited [13,14]. However, there are several differences between these two cases. First, the ITO nanocoating permits to generate strong dense comb-like eLMR bands in a wide wavelength range whereas the graphene only enables the excitation of the first a few eLMR bands. Second, there is a small reduction in the cladding mode resonance amplitude for these two polarizations in the ITO case, but the graphene leads to a weak s-polarized cladding mode resonance and induces little influence on the p-polarized counterpart. These differences are apparently determined by the optical properties of the nanocoatings at the wavelength where the TFBG operates: ITO is the material having a high real part of refractive index combined with a very small imaginary component, whereas graphene tuned in dielectric state has high both real and imaginary refractive indices. Furthermore, the eLMR excited by graphene is contributed to the propagation of s-polarized light in the graphene layer [13,14,19]. The conclusion seems to be valid for the eLMR generated by the ITO nanocoating, clearly evidenced by the great reduction in the mode loss and the increased propagation length of the leaky modes. However the difference also exists. The mode characteristics of p-polarized leaky modes are affected by the ITO nanocoating as well, though the influence is much weaker than the s-polarized case. In contrast, the variation of p-polarized leaky modes is ignorable in the case of graphene.

Moreover, it should be mentioned that the simulations are performed by considering an uniform ITO nm-thick overlay which might not be in excellent agreement with the real experiments. In addition, the thermal expansion of ITO overlay should be also taken into account. However, this difference will not change the regular features that show the dense comb-like eLMR band in the transmission spectrum. Many techniques like Sol-gel dip-coating deposition process [9] and magnetron sputtering method [28] can be used to deposit uniform, smooth and precisely controlled nanometer ITO film on optical fiber and the theoretical prediction agrees well with the experimental results. In fact, the influence of non-uniform surface of nanocoatings equivalently corresponds to the situation at which an overlay with complex refractive index is coated on the fiber cladding [29]. The effect of non-uniform surface is equivalent to the increase of the imaginary part of refractive index of ITO, which corresponds to the situation similar with the case of graphene that presents a large imaginary refractive index [13,14]. In this sense, the eLMR can also be attained when the uniformity of ITO nanocoating is considered. In addition, the thermal expansion will affect the ITO thickness. However, it is remarkable to notice that the spectrum shows high tolerance of ITO thickness. As clearly shown in Fig. 2 and Fig. 3, the imaginary part of ERI of leaky modes presents a very smooth and small variation when ITO thickness is increased to 150nm$\sim$200nm. As a consequence, there is a very small variation in the transmission spectrum (see Fig. 8), which demonstrates high tolerance of ITO thickness.

In the following analysis on the sensing performance of the eLMR, a $150 nm$ ITO nanocoating, though it may not be the optimal value, is considered, since the further increase of film thickness leads to a small variation, as shown in Fig. 3 and Fig. 8. In addition, bare TFBG is also considered for comparison.

4.2 Sensing performance of eLMR

The spectrum evolution of the first four leaky mode resonances is depicted in Fig. 9 when the SRI changes from 1.315 to 1.455 with a step of 0.01. The first leaky mode resonance shows the most sensitive response to the SRI, indicated by about 17dB and 22dB reduction in the resonance amplitude for bare TFBG and ITO coated TFBG respectively. As can be observed, the leaky mode resonance in bare TFBG experiences a large variation when the SRI changes in lower index region. This is understandable since the leaky mode resonance is sharply reduced and becomes extremely weak when the leaky modes are transited from the cladding guided modes in bare TFBG. However, it is almost insensitive at SRI > 1.34 since the resonance is too weak to vary with the SRI. As for the ITO coated TFBG, the leaky mode resonance corresponds to the eLMR showing a much stronger amplitude. The variation of the eLMR is clearly characterized by an exponential dependence on the SRI, which corresponds to a regular trend that is beneficial greatly to the measurement.

 

Fig. 9. Evolution of leaky mode resonance: (a) bare TFBG, and (b) ITO nanocoating integrated TFBG.

Download Full Size | PDF

The sensing performance evaluated by a single leaky mode resonance is shown in Fig. 10. The local sensitivity defined as $\partial \textrm {T} / \partial (\textrm {SRI})$ is calculated since the resonance amplitude does not vary linearly with the SRI. It is remarkable to say that the local sensitivity shows an impressive advantage that can reveal accurately the sensing performance of a device at specific SRI.

 

Fig. 10. Sensing performance evaluated by single leaky mode resonance.

Download Full Size | PDF

The first leaky mode resonance in bare TFBG presents the highest sensitivity at SRI = 1.315, due to the sharp reduction in its amplitude, but the sensitivity of other resonances is decreased rapidly. When the SRI becomes larger than 1.34, the sensitivity is reduced to near zero.

The sensing performance is improved in the ITO nanocoating integrated TFBG. These four eLMRs exhibit a higher sensitivity than the bare counterpart, except for the first eLMR at SRI = 1.315 due to the reason discussed above. The sensing performance of the eLMR could be further improved to offer higher sensitivity by optimizing the grating and nanocoating parameters, similar with the case of graphene excited eLMR [15]. In addition to the sensitivity, the Q-factor that is closely related to the sensing performance shows advantage over the bare counterpart as well. This is understandable since the FWHM of the eLMR excited by the ITO nanocoating is reduced to be much narrower than that of leaky mode resonance in bare TFBG. Furthermore, the eLMR with stronger amplitude can increase greatly the single-to-noise-ratio (SNR) that is an important factor in actual applications.

5. Discussion

This work demonstrates that strong dense comb-like eLMR can be effectively excited by the ITO nanocoating integrated on TFBG. There are several similarities and differences between the eLMR and other resonances like the SPR and LMR generated in optical fibers. Here a brief comparison on generation mechanism and sensing characteristics is carried out.

First, the generation of these three resonances can be contributed to the ‘guidance’ of the corresponding modes through the nanocoating integrated optical fibers. More specifically, the eLMR, LMR and SPR are dependent on the leaky modes guided in optical fiber, lossy modes guided in nanocoating and SPR modes guided in nanocoating (only metal film in general), respectively. The propagation characteristics related closely to the mode loss differ in a great manner for these modes. Generally, the nanocoating leads to the leaky modes having the loss larger than that of SPR modes but smaller than the case of lossy modes.

The different fiber modes that are responsible for the generation of resonances should be the second point. The eLMR involves the leaky modes that are higher order modes with the real part of ERI smaller than the SRI. The SPR corresponds to the resonance of the SPR modes that are also higher order modes having the real part of ERI larger than but close to the SRI. The LMR results from the resonance of lossy modes that are transited from lower order guided modes. Consider this difference, it is possible to excite strong dense comb-like eLMRs in a wide spectral window whereas there is only one SPR and a few LMRs in nanocoating integrated optical fibers.

The polarization properties should be also considered. These three resonances are polarization-dependent but present different properties. The eLMR can be effectively excited by the s-polarized light while the p-polarization shows very little variation. The SPR can only be excited by the p-polarized light whereas the LMR is obtained for both p- and s-polarizations.

Furthermore, the resonances show different sensing performances. The LMR presents the highest sensitivity evaluated by the wavelength shift [11]. The sensitivity of SPR is lower than that of the LMR in some cases but the SPR-based devices have experienced an exponential increase during the last two decades. The eLMR is a new kind of resonance that presents promising sensing characteristics with an improved performance. The eLMR excited in TFBG has the narrowest FWHM among these three resonances, which indicates that the Q-factor can be greatly improved.

6. Conclusion

This work reports a very earlier represent, to the best of our knowledge, that demonstrates numerically the excitation of strong dense comb-like eLMR by the deposition of ITO nanocoating on TFBG. The ITO nanocoating induces the guidance of leaky modes, especially for the s-polarized leaky modes. This is clearly confirmed by two phenomena: a large reduction in mode loss and a greatly increased propagation length. Consequently, strong dense comb-like eLMR in a wide window is attained for the s-polarized leaky modes in ITO coated TFBG. As compared with the bare TFBG, the eLMR presents promising sensing performance with higher sensitivity and extended measurement range. In addition, the eLMR with narrow bandwidth and strong amplitude offers capability of high Q measurement that is superior to the LMR and SPR techniques. Furthermore, in view of that the ITO is a typical metallic oxide, it is expected to further excite the eLMR with other promising characteristics by other metallic oxide materials. This study provides a new opportunity and guidelines to generate the eLMR in optical fibers.