Cladding mode

An interesting feature of LPGs is that their sensitivity characteristics to a specific parameter depend drastically on the order of the coupled cladding mode and on the type of the fiber in which they are inscribed. This makes possible to discriminate between different types of perturbation that act simultaneously on the grating and offers the flexibility to design devices that are very sensitive or insensitive to a particular measurand5 1. 

When the SRI is equal to the cladding one, the cladding layer becomes an infinitely extended medium and thus supports no discrete cladding modes. In this case, a broadband radiation mode coupling occurs with no distinct attenuation bands8. 

As aforementioned, the spectral characteristics of LPGs are determined by the coupling between the fundamental guided core mode and the co-propagating cladding modes when the core propagating light encounters a periodic perturbation... 

In this chapter, we will numerically analyze the effects of the HRI overlay on the cladding modes distribution with particular attention to its influence on the device sensitivity to the SRI changes and to the overlay refractive index changes. The structure to which we refer is depicted in Fig. 3.2. 

The calculation of the cladding mode effective index can be accomplished by an extension of the model for doubly clad fibers28 or by following the transfer matrix method (TMM) proposed by Anemogiannis et al.26 and successively widely adopted for the analysis of coated LPGs29 30. 

In this section, we will analyze the effects of a nano-sized HRI overlay on the distribution of the cladding modes (transversal fields, effective indices, coupling coefficients) to changes of its thickness and refractive index and to changes of the SRI. 

Fig. 3.3 LP03 and LP0s cladding modes in (a) bare fiber and (b) coated fiber with th 200 nm and th 250 nm thin overlay...

Fig. 3.4 (a) LP03 cladding mode in coated fibers with th LP07 cladding modes in a coated fiber with th 250 nm... 

From these figures it is apparent how the HRI overlay stretches the cladding mode fields toward itself for both modes and both overlay thicknesses. In addition, for the same cladding mode, the field content within the overlay increases as the overlay thickness is increased (see Fig. 3.4a). Finally, for a given overlay thickness, the field content within the overlay of higher order modes is higher compared with low order modes (see Fig. 3.4b)31. 

The same observations are true for the evanescent wave of the modes in the surrounding medium. Moreover, these changes in the field distributions are accompanied by an increase of the effective refractive indices of the cladding modes, as will be clarified later. For this reason and by virtue of (3.1), the resonance wavelengths of the coated LPG are expected to blue-shift in response to an overlay thickness change. 

Fig. 3.5 Effective refractive index of the LP02 LP08 cladding modes vs. the SRI in HRI coated fiber with (a) 150 nm (b) 200 nm (c) 250 nm, and (d) 300 nm thin overlays...

Fig. 3.7 Cladding mode fields in a 200 nm coated LPG, before transition (SRI 1), in transition (SRI 1.40) and after transition (SRI 1.45) (a) LP02 (b) LP03 and (c) LP04...

Fig. 3.8 Effective refractive index sensitivity to overlay RI changes vs. overlay thickness for different cladding modes...

Figure 3.12 shows a comparison between the transmitted spectra of a bare and a 160 nm sPS coated LPG, with regard to the cladding mode LP06-... 

The presence of the HRI coating induces an increase in the effective refractive index of the cladding modes and thus a decrease in the resonance wavelengths. In addition, the spatial shift of the cladding mode field profile toward the HRI overlay promotes a decrease of the overlap integral with the core mode and so of the transmission loss peak. The subsequent evaporation of the solvent molecules from the nano-cavities results in a reduction of its refractive index. This explains the partial... 

Fig. 3.12 Comparison of the attenuation band related to the cladding mode LPo6 for a bare LPG and a 160 nm sPS coated LPG just after the dip coating and after solvent evaporation...

To experimentally prove the phenomenon of the modal transition and its effects on the sensitivity of nano-coated LPGs to SRI changes, the dip coating, as deposition technique, and the sPS, as HRI material, were used. Here the LPG sensitivity (different for each cladding mode) is defined as the gradient of the wavelength shift of the attenuation bands minima with respect to the SRI (d esj/dSRI). 

As a preliminary test, the experimental setup just described was used to characterize the bare LPG. In Fig. 3.15 it is reported that the central wavelength and the transmission loss peak of the attenuation band centred around 1,300 nm (related to the cladding mode LP06) as a function of the SRI. The refractive index sensitivity of the bare LPG was found to be 5.06 nm/RIU (refractive index units) and 3.59 dB/ RIU, around the water refractive index, in terms of wavelength shift and amplitude... 

Fig. 3.18 (a) Wavelength shift of different cladding modes for the LPG coated with a 150 nm sPS overlay versus SRI (b) loss peaks of different cladding modes versus SRI for the coated LPG with the same coating thickness... 

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