In this experiment we used commercially available Corning SMF28 optical fiber (Corning Incorporated, Corning, NY, USA). A set of LPGs was written with a computer-assisted precision arc-discharge apparatus described in [3]. The discharge current was adjusted to be low enough to heat the fiber locally and not to produce any visible tapers due to the axial tension applied to the fiber. The grating period was set to Λ = 500 µm. The optical transmission of the fiber in the range of λ = 1.160 – 1.660 nm was monitored during the LPG fabrication process in order to obtain the desired spectral attenuation notches. We used an Agilent 83437A broadband light source and an Agilent 86142B optical spectrum analyzer (Agilent Technologies, Inc., Santa Clara, CA, USA) for this purpose.

The Al₂O₃ thin films were deposited on the LPGs and reference oxidized silicon wafers using the Savannah-100 ALD system (Cambridge Nanotech, Waltham, MA, USA). The LPG samples were cleaned in isopropanol, while the Si wafers went through the Radio Corporation of America cleaning procedure [25]. Then the Si wafers were thermally oxidized in order to receive SiO₂ on their surface, which is assumed to be a good reference for fused silica fibers. For the Al₂O₃ deposition processes, water and trimethylaluminum (Al(CH₃)₃, TMA) were used as an oxygen and aluminum precursors, respectively. Between gas pulses the chamber was purged with nitrogen. Thickness of the Al₂O₃ films in the range of 100 up to 250 nm was changed by controlling the number of cycles of the ALD process (900 to 1,800). The temperature during the processes was set to 150 °C.

The properties of the Al₂O₃ films including their thickness (d), refractive index (n), and extinction coefficient (k) were measured on reference wafers by means of Horiba Jobin-Yvon UVISEL spectroscopic ellipsometer SE (Horiba Scientific, Edison New Jersey, NJ, USA) in the range λ = 260 to 2,060 nm. To fit the measurement data to a physical model, a three-layer model (Si wafer/SiO₂/Al₂O₃) was used where a single-layer Forouhi-Bloomer dispersion formula [26] of Al₂O₃ film was applied and fitted with mean-square error χ² < 3. The thickness of the SiO₂ layer was measured before the Al₂O₃ deposition to be 99.7 nm.

Moreover, the thicknesses of the deposited films have been directly controlled on the fibers by cleaving some of the samples and by measuring the thickness at the fiber cross-section using a Hitachi SU-70 Scanning Electron Microscope SEM (Hitachi High-Tech, Tokyo, Japan).

The RI response of the LPGs has been measured for samples immersed in glycerin/water mixtures with n_D from 1.3330 to 1.4722 RIU. The n_D of the liquids was determined using a VEE GEE PDX-95 refractometer (VEE GEE Scientific, Inc., Kirkland, WA, USA) working with an accuracy of ±10⁻⁴ RIU. The LPGs were kept under the same tension and temperature during all the experiments.

The optical simulations were performed using the Optigrating v.4.2 software (Optiwave Systems, Inc., Ottawa, ON, Canada). The software employs LP mode approximation and coupled-mode theory [7,24]. The model of the grating and the fiber is based on fiber datasheet, and grating period is determined during the fabrication process. The model has been adjusted up to experimental data by changes of core and cladding diameter [27]. We assumed dispersion curves of n for each of the Al₂O₃ films and water according to SE analysis and data given by Damion et al. [28], respectively.

Spectral response of the LPGs to n_ext highly depends on optical properties and thickness of the overlays [7]. The variation in properties of the Al₂O₃ films deposited on reference Si samples with the number of deposition cycles is shown in Figure 1.

The results prove that thickness of the films deposited with the ALD method can be determined with a sub-nm precision. According to the measurements, thickness of the film increases linearly with the number of cycles and reaches a deposition rate of 0.125 nm/cycle. Moreover, a slight variation in the optical properties of the films with the number of the cycles can be observed. Since the extinction coefficient k of the films is close to 0, we show here only dispersion of n (Figure 1a). In the infrared spectral range (λ = 1,560 nm) the n decreases with the number of cycles by over 0.012 RIU, especially in the range between 1,000 and 1,600 cycles (Figure 1b). The effect can be related to a modification of internal structure of the film or to a stress in the films induced by the substrate with the increase of their thickness [29]. The phenomenon remains in contradiction with the variations of n for the films deposited with other CVD methods where the increase of the film thickness is typically followed by an increase of n [30]. Since in other vapor-based thin film deposition methods plasma or high temperature modifies the film during the deposition, in case of the ALD more likely the substrate effect induces a decrease of the n with the film thickness. Both variations in thickness and optical properties of the overlay are critical from the point of view of the LPG-based structure performance and they must be taken into account in the sensing device design process [10].

Thickness of the films on reference samples has been compared to the thickness of the overlays obtained on optical fibers when their cross-section was investigated (Figure 2). It can be seen that the film thickness on both cylindrical optical fibers and on flat reference samples is very similar. Since the precision of thickness estimation with the SEM is limited, we can assume a very good agreement between the measurement of films properties on optical fibers and on the reference samples.

For deposition of the films on the LPGs, a set of gratings has been selected showing a very similar spectral response (Figure 3a). The gratings have resonances at about 1,200, 1,260, 1,350 and 1,550 nm, coming from coupling of LP₀₂, LP₀₃, LP₀₄, and LP₀₅ cladding modes, respectively. The slightly different spectra of the gratings are caused by a limited repeatability of the fabrication procedure. It has been shown that even a very small tapering of the fiber during the arc-induced fabrication process can have a significant influence on the spectrum of the LPGs [27]. Despite the small differences between the gratings fabricated with the arc-method, LPGs are highly resistant to high-temperature post-processing and that is why they are assumed to be a good platform for the experiment [31]. Based on the measured spectra a numerical model of the LPG has been developed. The fitting procedure involved a slight adjustment of the core's n and diameters of both core and cladding. As a result of the fitting, a very good agreement between measured and simulated spectra has been obtained (Figure 3b).

Based on the numerically modeled influence of the Al₂O₃, an overlay thickness on the effective refractive indices (n_eff) of the modes up to LP₀₁₂ has been calculated at λ = 1,550 nm. We assumed here the value of n of the overlay as for 1,200 cycles-long deposition (n = 1.611 RIU, shown in Figure 1). When n_ext is set to 1 (as for air) and 1.318 RIU (as for water at λ = 1,550 [28]), the transition of the modes, resulting in propagation of the lowest order cladding mode (LP₀₂) in the overlay, takes place above 330 and 230 nm of the Al₂O₃ overlay thickness, respectively (Figure 4). The phenomenon induces a reorganization of all the cladding modes and for higher order modes the transition occurs for the lower overlay thicknesses. Since at the mode transition conditions, the LPGs show the highest sensitivity to variations in the n_ext, the properties of the films must be precisely adjusted for certain range of the n_ext. When the transition is assumed to take place at n_eff reaching half between of each mode when no coating is applied [7], the approximated optimum thickness (d_opt) of the Al₂O₃ overlay for each mode is plotted in Figure 5. Significantly thinner overlays are required when coupling of higher order cladding modes is taken into consideration for sensing purposes. The determination of properties of the overlays with a high precision as offered by the ALD technique is than highly requested.

Results of the measurements and simulations have been compared next. A good agreement between theoretical and experimental data for the resonance LP₀₅, which shows the highest sensitivity, can be seen in Figure 6. In our measurements and simulations we had to take into account the dispersion of n_ext. The value of n_ext in visible range (λ = 598 nm) significantly differs from the one in infrared (λ = 1,550 nm). In case of water, the difference reaches almost 0.015 RIU and cannot be neglected when precise measurements are discussed and compared with the results of simulations. When thickness of the Al₂O₃ overlay increases, the resonances experience a shift towards lower wavelength. An increase in the overlay thickness induces an increase in the effective refractive index of mth cladding modes ( n eff 0 m), and according to the fundamental Equation (1) for the LPGs, where Λ is the period of the grating and n eff 01 is effective refractive index of the propagating core mode, causes a decrease in the resonance wavelength ( λ res m): (1) λ res m = Λ ( n eff 01 − n eff 0 m )

A slight disagreement between the measurements and simulations can be seen for the thicker overlays, i.e., 205 and 226 nm in thickness. The phenomenon may be related to the decrease in n of the Al₂O₃ film with its thickness. When the conditions are close to the mode transition, even a slight disagreement of overlay thickness and n matters. Also a slight disagreement between the simulated and measured LPG spectrum before the deposition may have an effect on the discrepancy. The response of the LPGs to the variations in n_ext has been investigated next. It can be seen in Figure 7 that the Al₂O₃ overlay greatly modifies the response depending on properties of the overlay. Increasing the thickness or n of the coating can shift the maximum RI sensitivity to its lower values, while decreasing the sensitivity to the higher n_ext [8]. We successfully shifted the maximum sensitivity of the LPGs from an n_ext of 1.458 RIU (for a grating with no film) to one in the range between 1 and 1.458 RIU. For samples M19 surrounded by water, the coating is thick enough or has high enough n to induce the mode transition in the n_ext range below the one of water. The range of the highest RI sensitivity can be easily adjusted by a number of overlay deposition cycles. When the overlay thickness reaches 205 nm, the highest sensitivity for the LP₀₅ mode is in the n_ext range close to that of water (Figure 8). The sensitivity in this range is highly requested when label-free bio-sensing applications of the LPGs are considered [32]. For the M18 grating with the overlay thickness of 205 nm, the RI sensitivity, defined as the LP₀₅ mode resonance wavelength shift with n_ext, reaches −1,850 nm/RIU, which is over 20 times higher than for the comparable LPG with no coating (−90 nm/RIU) in the same n_ext range, i.e., 1.3330 to 1.342. Since the RI sensitivity is known to increase with the order of the cladding modes [2], and the ALD method allows for relatively low temperature deposition [14], the sensitivity can be further improved by using the gratings induced with a lower period using a UV-writing method [31].