Fiber Bragg Grating Hydrogen Sensor

In this example, we propose a Multiphysics simulation design workflow for a hydrogen (H₂) sensor based on fiber Bragg grating (FBG). Ansys Mechanical^TM and Ansys Lumerical^TM are used to simulate fiber's mechanical deformation and optical performance due to hydrogen gas absorption. The sensitivity of the sensor, for various design configurations, is also calculated and compared with reference.

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Overview

Understand the simulation workflow and key results

Step 1: Palladium Deformation/Strain calculation.

The figure below depicts the design of the sensor used in Ansys Mechanical^TM, where hydrogen molecules are adsorbed on a Palladium (Pd) thin film. The Pd expansion leads to an axial stretch of fiber’s surface sensor. At this step we calculate analytically the thin film expansion, due to H₂ concentration. More information can be found in the Run and Results section.

In our simulation analysis we considered low H₂ concentrations, up to 5% v/v (x = 0.005), keeping the hydride PdH₂ at α-phase [4]. Pressure and temperature can affect the gas concentration and strain of Pd, however for simplicity purposes we consider room temperature (298 K) and atmospheric pressure (50 mbar) [6].

Step 2: Mechanical Simulation - Calculation Strain/Deformation.

We used the longitudinal elongation of Pd as input to Ansys Mechanical^TM simulation software. The short video below animates the longitudinal expansion (-z and +z direction) of a Pd thin film (blue color) deposited on an optical fiber (red color).

The simulation results include the strain distribution and the directional deformation, of a single period FBG grating. Next, we export both strain and deformation results for various H₂ concentrations and use them as input to Ansys Lumerical^TM for optical performance calculations.

Step 3: Bragg wavelengths shift and spectrum.

Using Lumerical’s scripting we transposed the strain to refractive index variation, exploiting the stress-strain Hook’s law equations [8]. The output length deformation is used as an increase of input length at single Bragg’s period, while the refractive index variation is added at core’s unperturbed refractive index. EME solver is used to calculate the reflection spectrum (\({|S_{11}|}^2\)), and the Bragg wavelength shift, for each H₂ concentration.

Run and Results

Instructions for running the model and discussion of key results

At its simplest form a fiber Bragg grating (FBG) is created by a periodic alteration of core’s refractive index. That creates an optical filter in the fiber, where its short section that consists of a few millimeters can reflect specific wavelengths from a broadband light source. The equation that calculates the Bragg wavelength (λ_Bragg) is quoted at the equation below:

$$\lambda_{Bragg} = 2 * \Lambda * n_{eff}$$

where n _eff is the effective index of the fundamental mode and Λ is the period of the grating.

For hydrogen detection the FBG sensor is normally coated with a thin film of Palladium (Pd). This material is well-known for its high absorption capacity to H₂ , as it can absorb up to 900 times its own volume leading to its lattice expansion [1]. This expansion will cause a stretch at the fiber altering both grating’s length and refractive index of the core [2]. These effects will be detected by a shift in the Bragg wavelength. Thus, the Bragg wavelength shift becomes:

$$\Delta\lambda_{Bragg} = \lambda_{Bragg} * (1 - p_{e} )* \Delta \epsilon$$

where p_e (typically, 0.21) is the effective photo-elastic coefficient of a fused silica fiber [5]. More information can be found at Appendix section at the bottom of the article. The relationship between stoichiometric H₂ concentration and Pd expansion is calculated by an analytical equation. The following equation calculates the strain (ε_l) of a Pd sample:

$$ \epsilon_{l} (x)= 1.61*x-12.25*x^2+44.95*x^3-62.41*x^4+30.93*x^5 $$

where x is the hydrogen stoichiometry [6].

Step 1: Calculate strain and elongation of thin film Pd sample

1. Open and run the script “Pd_deform_input.lsf”

The script will calculate the Pd thin film elongation (Δl) with regards to H₂ stoichiometry concentrations up to x = 0.8, as depicted in the figure below. The thickness and length of Pd were set at 500 nm and 40 μm, respectively.

Step 2: Calculate strain and physical length deformation of fiber

1. Open a workbench project and import the simulation file “mechanical_hydrogen_fbg_sensor.wbpz”.
2. Load and Run the script “mechanical_hydrogen_fbg_sensor.wbpz” to run the simulation.

The calculated elongation from previous step is used as mechanical displacement on both edges of the Pd film (-z and +z direction). In that way the sensor stretches due to the bonding between the thin film coating and fiber’s surface. The figures below depict the strain distribution (left) and deformation (right) of fiber’s cross section. The maximum deformation takes place at the surface of the cladding while the minimum is in the center. In addition, the surface strain tension from the Pd expansion is transferred radially from the surface of the fiber towards its core, where the grating is inscribed causing its deformation.

Both results are exported in a “ .txt ” file for each H ₂ concentration, where they are used in the final step of the workflow to measure the optical performance of the sensor. Sensor’s performance is dominated by grating’s directional deformation, as according to references the pitch elongation (ΔΛ) of a FBG exhibits a larger impact compared to its effective refractive index change (Δn_eff ) [9]. For more details on the run procedure of step 2, please refer to section “ Running Mechanical script ” at the bottom of the article.

Step 3: Calculate reflection response and Bragg wavelength shift

1. Open the simulation file “hydrogen_fbg_sensor.lms”.
2. Open and Run script “hydrogen_fbg_EME.lsf”.

The script calculates the S-parameters of the Bragg grating, concentrating at reflection \({|S_{11}|}^2\). The figure below portrays sensor’s Bragg wavelength for low H₂ concentrations, up to 5% (v/v) . The sensor exhibits a linear behavior, as it is expected for low H₂ concentrations (<5 vol%) [10].

Our analysis included three sensor configurations that consist of diameters Ø 120 μm, Ø 80 μm and Ø 50 μm. The figures below depict the reflectance spectra with regards to H ₂ concentration where a red shift (longer wavelengths) is distinctive when concentration increases. The shift becomes larger for the short Ø design (right spectrum Ø 50 μm: Δλ_Bragg = 180 pm), compared to large Ø design (left spectrum Ø 120 μm: Δλ_Bragg = 12 pm).

The figure below portrays the Bragg wavelength shift versus H₂ concentration % (v/v) , from which we calculate the sensitivity by using the slope of each plot. The decrease of optical fiber sensor’s size causes an increase in sensitivity.

This is also depicted in the following plot that portrays the non-linear dependency of the sensitivity (pm/% v/v) with regards to fiber diameter. Various H ₂ sensitivities (up to 100 pm/% v/v) can be obtained by choosing the appropriate FBG sensor design. An unetched fiber (Ø 120 μm) exhibits a sensitivity of 5 pm/% v/v, while an etched fiber with half diameter size (Ø 50 μm) increases sensor’s sensitivity almost an order of magnitude (50 pm/% v/v).There is a good match comparing our simulation sensitivity analysis with experimental work from literature [9].

Important model settings

Description of important objects and settings used in model.

Running Mechanical script

The video below shows an animation of the steps needed to run the script of Ansys Workbench^TM “mechanical _hydrogen_fbg_sensor.wbpz ”.

The script will run the Static Structural “FBG_Hydrogen_Sensor” model in a loop for various input displacements that correspond to a series of Design Points (DP). The displacements, set at column B (+Z direction) and column C (-Z direction), can be seen in the photo below. The deformation and strain for each DP are calculated and saved in columns D and E.

A python script (Python code 1) saves two both “.txt” format,  for each DP, in separate files. One file contains deformation data while the other one strain data. Both results correspond to fiber’s cross section.

A second python script (Python code 2)  creates a single “Mechanical_strain_deform.txt” file that includes a single value of strain and deformation for every DP. The figure below depicts the script and the destination folder (“C:\”).

Taking the model further

Information and tips for users that want to further customize the model

Protective layers around fiber sensor

In our analysis, the design of the optical fiber consists of a core and cladding only. Normally, optical fiber is equipped with a protective coating and plastic jacket. The picture below shows a typical formation of an optical fiber.

Mechanical simulations in this application example did not include any protective layers due to simplicity purposes. Users can extend this model by adding extra layers, creating a more detailed version of optical fiber. The rest of the workflow, such as force application and data extraction should be kept the same. It is expected a decrease in wavelength shift results, as including extra layers around the fiber will decrease the sensitivity of the sensor.

Interconnect circuit.

A complete sensor circuit can be built using INTERCONNECT. The user can follow the workflow of Step 3: INTERCONNECT – Photonic circuit simulation to connect the sensor component with other optical elements such as a detector and a source. A basic model should include an Optical Network Analyzer (ONA) used as a source and detector, an Optical Time Variant S-parameter that represents the actual bend sensor and finally a DC source representing a radius controller.

Additional resources

Additional documentation, examples, and training material

Related publications

1. Hirokazu Kobayashi, “Double enhancement of hydrogen storage capacity of Pd nanoparticles by 20 at% replacement with Ir; systematic control of hydrogen storage in Pd–M nanoparticles (M = Ir, Pt, Au)”, Chem Sci. 2018 Jul 7; 9(25): 5536–5540
2. Cynthia Cibaka Ndaya, “Recent Advances in Palladium Nanoparticles-Based Hydrogen Sensors for Leak Detection”, Sensors 2019, 19, 4478.
3. N. Lagakos, R. Mohr, and O. H. El-Bayoumi, "Stress optic coefficient and stress profile in optical fibers," Appl. Opt. 20, 2309-2313 (1981).
4. Paolo Tripodi, “The effect of hydrogen stoichiometry on palladium strain and resistivity”, Physics Letters A 373 (2009) 4301–4306.
5. W. Primak and D. Post, "Photoelastic constants of vitreous silica and its elastic coefficient of refractive index", J. Appl. Phys. 30, 779 –788 (1959).
6. Said SAAD, “Hydrogen Detection with FBG Sensor Technology for Disaster Prevention”, Photonic Sensors (2013) Vol. 3, No. 3: 214–223
7. Coelho, “Fiber optic hydrogen sensor based on an etched Bragg grating coated with palladium”, 2015 Applied Optics, Vol. 54, No. 35.
8. Pauli Kiiveri, Joona Koponen, Juha Harra “Stress-Induced Refractive Index Changes in Laser Fibers and Preforms”, DOI: 10.1109/JPHOT.2019.2943208
9. V. V. S. Ch. Swamy, Saidi Reddy Parne, Sanjjev Afzulpurkar, Shivanand Prabhudesai, “Design and development of pressure sensor based on Fiber Bragg Grating (FBG) for ocean applications”. DOI: 10.1051/epjap/2020200036

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Appendix

Additional background information and theory

FBG Strain equations.

When strain is applied at the FBG, both n _eff and Λ will change leading to a shift in Bragg wavelength given by

$$\frac{\Delta\lambda_{Bragg}}{\lambda_{Bragg}} = (\frac{1}{\Lambda}*\frac{\partial \Lambda}{\partial L}+\frac{1}{n_{eff}}*\frac{\partial n_{eff}}{\partial L})*\Delta\Lambda $$

The term (\(\frac{1}{\Lambda} \frac{\partial \Lambda}{\partial L}\)) symbolizes the strain of the grating period due to the extension of the fiber. We consider a fiber length L, with inscribed FBG in it, and apply stress of ΔL that returns a relative strain ΔL/L . At the same time the same relative strain is applied at the FBG, with a length L _FBG .

$$ p_{e} = \frac{n_{eff}^2}{2} [P_{12} - \mu*(P_{11} + P_{21})] $$

The term (\(\frac{1}{n_{eff}} \frac{\partial n_{eff}}{\partial L}\)) is the photo-elastic coefficient (p_e) and describes the variation of the index of refraction with strain.  When external force is applied to the fiber, the two terms create opposite effects. If the external force stretches (elongates) the material, then the related stress is called tension. Tensile stress decreases the refractive index of the glass, so the induced Δn change is negative.

On the contrary, if the external force is compressive, it increases the refractive index of the glass, so the induced Δn change is positive. From the above we expect the Bragg wavelength to shift to shorter wavelengths for extension and longer wavelengths for compression [10]. However, experimental results proved that the physical length of the period overcomes the change of the refractive index, thus under tensile strength the Bragg wavelength shifts to the red part of the spectrum [9].